diff --git a/.devcontainer/Dockerfile b/.devcontainer/Dockerfile new file mode 100644 index 00000000..2b286811 --- /dev/null +++ b/.devcontainer/Dockerfile @@ -0,0 +1,14 @@ +# [Choice] Node.js version (use -bullseye variants on local arm64/Apple Silicon): 18, 16, 14, 18-bullseye, 16-bullseye, 14-bullseye, 18-buster, 16-buster, 14-buster +ARG VARIANT=16-bullseye +FROM mcr.microsoft.com/vscode/devcontainers/javascript-node:0-${VARIANT} + +# [Optional] Uncomment this section to install additional OS packages. +# RUN apt-get update && export DEBIAN_FRONTEND=noninteractive \ +# && apt-get -y install --no-install-recommends + +# [Optional] Uncomment if you want to install an additional version of node using nvm +# ARG EXTRA_NODE_VERSION=10 +# RUN su node -c "source /usr/local/share/nvm/nvm.sh && nvm install ${EXTRA_NODE_VERSION}" + +# [Optional] Uncomment if you want to install more global node modules +# RUN su node -c "npm install -g " diff --git a/.devcontainer/base.Dockerfile b/.devcontainer/base.Dockerfile new file mode 100644 index 00000000..a3e066fd --- /dev/null +++ b/.devcontainer/base.Dockerfile @@ -0,0 +1,55 @@ +# [Choice] Node.js version (use -bullseye variants on local arm64/Apple Silicon): 18-bullseye, 16-bullseye, 14-bullseye, 18-buster, 16-buster, 14-buster +ARG VARIANT=16-bullseye +FROM node:${VARIANT} + +# [Option] Install zsh +ARG INSTALL_ZSH="true" +# [Option] Upgrade OS packages to their latest versions +ARG UPGRADE_PACKAGES="true" + +# Install needed packages, yarn, nvm and setup non-root user. Use a separate RUN statement to add your own dependencies. +ARG USERNAME=node +ARG USER_UID=1000 +ARG USER_GID=$USER_UID +ARG NPM_GLOBAL=/usr/local/share/npm-global +ENV NVM_DIR=/usr/local/share/nvm +ENV NVM_SYMLINK_CURRENT=true \ + PATH=${NPM_GLOBAL}/bin:${NVM_DIR}/current/bin:${PATH} +COPY library-scripts/*.sh library-scripts/*.env /tmp/library-scripts/ +RUN apt-get update && export DEBIAN_FRONTEND=noninteractive \ + # Remove imagemagick due to https://security-tracker.debian.org/tracker/CVE-2019-10131 + && apt-get purge -y imagemagick imagemagick-6-common \ + # Install common packages, non-root user, update yarn and install nvm + && bash /tmp/library-scripts/common-debian.sh "${INSTALL_ZSH}" "${USERNAME}" "${USER_UID}" "${USER_GID}" "${UPGRADE_PACKAGES}" "true" "true" \ + # Install yarn, nvm + && rm -rf /opt/yarn-* /usr/local/bin/yarn /usr/local/bin/yarnpkg \ + && bash /tmp/library-scripts/node-debian.sh "${NVM_DIR}" "none" "${USERNAME}" \ + # Configure global npm install location, use group to adapt to UID/GID changes + && if ! cat /etc/group | grep -e "^npm:" > /dev/null 2>&1; then groupadd -r npm; fi \ + && usermod -a -G npm ${USERNAME} \ + && umask 0002 \ + && mkdir -p ${NPM_GLOBAL} \ + && touch /usr/local/etc/npmrc \ + && chown ${USERNAME}:npm ${NPM_GLOBAL} /usr/local/etc/npmrc \ + && chmod g+s ${NPM_GLOBAL} \ + && npm config -g set prefix ${NPM_GLOBAL} \ + && sudo -u ${USERNAME} npm config -g set prefix ${NPM_GLOBAL} \ + # Install eslint + && su ${USERNAME} -c "umask 0002 && npm install -g eslint" \ + && npm cache clean --force > /dev/null 2>&1 \ + # Install python-is-python3 on bullseye to prevent node-gyp regressions + && . /etc/os-release \ + && if [ "${VERSION_CODENAME}" = "bullseye" ]; then apt-get -y install --no-install-recommends python-is-python3; fi \ + # Clean up + && apt-get autoremove -y && apt-get clean -y && rm -rf /var/lib/apt/lists/* /root/.gnupg /tmp/library-scripts + +# [Optional] Uncomment this section to install additional OS packages. +# RUN apt-get update && export DEBIAN_FRONTEND=noninteractive \ +# && apt-get -y install --no-install-recommends + +# [Optional] Uncomment if you want to install an additional version of node using nvm +# ARG EXTRA_NODE_VERSION=10 +# RUN su node -c "source /usr/local/share/nvm/nvm.sh && nvm install ${EXTRA_NODE_VERSION}" + +# [Optional] Uncomment if you want to install more global node modules +# RUN su node -c "npm install -g "" \ No newline at end of file diff --git a/.devcontainer/devcontainer.json b/.devcontainer/devcontainer.json new file mode 100644 index 00000000..40d74838 --- /dev/null +++ b/.devcontainer/devcontainer.json @@ -0,0 +1,32 @@ +// For format details, see https://aka.ms/devcontainer.json. For config options, see the README at: +// https://github.com/microsoft/vscode-dev-containers/tree/v0.238.0/containers/javascript-node +{ + "name": "Node.js", + "build": { + "dockerfile": "Dockerfile", + // Update 'VARIANT' to pick a Node version: 18, 16, 14. + // Append -bullseye or -buster to pin to an OS version. + // Use -bullseye variants on local arm64/Apple Silicon. + "args": { "VARIANT": "16-bullseye" } + }, + + // Configure tool-specific properties. + "customizations": { + // Configure properties specific to VS Code. + "vscode": { + // Add the IDs of extensions you want installed when the container is created. + "extensions": [ + "dbaeumer.vscode-eslint" + ] + } + }, + + // Use 'forwardPorts' to make a list of ports inside the container available locally. + // "forwardPorts": [], + + // Use 'postCreateCommand' to run commands after the container is created. + // "postCreateCommand": "yarn install", + + // Comment out to connect as root instead. More info: https://aka.ms/vscode-remote/containers/non-root. + "remoteUser": "node" +} diff --git a/.github/CODEOWNERS b/.github/CODEOWNERS new file mode 100644 index 00000000..c4301b94 --- /dev/null +++ b/.github/CODEOWNERS @@ -0,0 +1 @@ +* @CarletonComputerScienceSociety/core diff --git a/.github/workflows/client.yml b/.github/workflows/app.yml similarity index 50% rename from .github/workflows/client.yml rename to .github/workflows/app.yml index 0744269b..df5b0d03 100644 --- a/.github/workflows/client.yml +++ b/.github/workflows/app.yml @@ -1,21 +1,17 @@ -name: Client +name: App on: [push, pull_request] jobs: - test-client: + test-app: runs-on: ubuntu-latest steps: - uses: actions/checkout@v2 - name: Install modules run: | - cd client - yarn + cd app + npm install - name: Run Prettier run: | - cd client - yarn run check - - name: Run Jest - run: | - cd client - yarn run test + cd app + npm run check diff --git a/.github/workflows/deploy-app.yml b/.github/workflows/deploy-app.yml new file mode 100644 index 00000000..9a8b170b --- /dev/null +++ b/.github/workflows/deploy-app.yml @@ -0,0 +1,36 @@ +name: Deploy App + +on: + push: + branches: + - master # Set a branch to deploy + pull_request: + +jobs: + deploy: + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v2 + with: + submodules: true + fetch-depth: 0 + + # Install dependencies with npm + - name: Install dependencies + run: | + cd app + npm ci + + # Build the project and add .nojekyll file to supress default behaviour + - name: Build + run: | + cd app + npm run build + touch ./dist/.nojekyll + + - name: Deploy + uses: peaceiris/actions-gh-pages@v3 + if: github.ref == 'refs/heads/master' + with: + github_token: ${{ secrets.GITHUB_TOKEN }} + publish_dir: ./app/dist \ No newline at end of file diff --git a/README.md b/README.md index 797d911f..e06ba800 100644 --- a/README.md +++ b/README.md @@ -6,7 +6,7 @@ DiscreteMath.ca is an interactive platform built specifically for content from C
-![API](https://github.com/CarletonComputerScienceSociety/discretemath.ca/actions/workflows/api.yml/badge.svg) ![Client](https://github.com/CarletonComputerScienceSociety/discretemath.ca/actions/workflows/client.yml/badge.svg) ![Dynamic](https://github.com/CarletonComputerScienceSociety/discretemath.ca/actions/workflows/dynamic.yml/badge.svg) +![API](https://github.com/CarletonComputerScienceSociety/discretemath.ca/actions/workflows/api.yml/badge.svg) ![Client](https://github.com/CarletonComputerScienceSociety/discretemath.ca/actions/workflows/app.yml/badge.svg) ![Dynamic](https://github.com/CarletonComputerScienceSociety/discretemath.ca/actions/workflows/dynamic.yml/badge.svg)
@@ -17,6 +17,10 @@ DiscreteMath.ca is an interactive platform built specifically for content from C The user interface, written with Svelte. The user interface makes use of Mathjax and Pseudocode.js to render content provided from API. +## App + +The in-development updated version of the client with improved mathjax handling. + ## API The main service used to serve static data to the client. This is a GraphQL based api written with Ruby on Rails. diff --git a/api/Gemfile.lock b/api/Gemfile.lock index 4467df4a..7499de68 100644 --- a/api/Gemfile.lock +++ b/api/Gemfile.lock @@ -113,11 +113,11 @@ GEM multi_xml (>= 0.5.2) i18n (1.8.10) concurrent-ruby (~> 1.0) - jmespath (1.4.0) + jmespath (1.6.1) listen (3.5.1) rb-fsevent (~> 0.10, >= 0.10.3) rb-inotify (~> 0.9, >= 0.9.10) - loofah (2.9.1) + loofah (2.19.1) crass (~> 1.0.2) nokogiri (>= 1.5.9) mail (2.7.1) @@ -128,13 +128,13 @@ GEM mime-types-data (~> 3.2015) mime-types-data (3.2021.0704) mini_mime (1.1.0) - mini_portile2 (2.5.1) + mini_portile2 (2.8.0) minitest (5.14.4) msgpack (1.4.2) multi_xml (0.6.0) nio4r (2.5.7) - nokogiri (1.11.4) - mini_portile2 (~> 2.5.0) + nokogiri (1.13.10) + mini_portile2 (~> 2.8.0) racc (~> 1.4) parallel (1.20.1) parser (3.0.1.1) @@ -143,8 +143,8 @@ GEM promise.rb (0.7.4) puma (4.3.8) nio4r (~> 2.0) - racc (1.5.2) - rack (2.2.3) + racc (1.6.1) + rack (2.2.4) rack-cors (1.1.1) rack (>= 2.0.0) rack-test (1.1.0) @@ -167,8 +167,8 @@ GEM rails-dom-testing (2.0.3) activesupport (>= 4.2.0) nokogiri (>= 1.6) - rails-html-sanitizer (1.3.0) - loofah (~> 2.3) + rails-html-sanitizer (1.4.4) + loofah (~> 2.19, >= 2.19.1) railties (6.0.3.7) actionpack (= 6.0.3.7) activesupport (= 6.0.3.7) @@ -241,7 +241,7 @@ GEM sprockets (>= 3.0.0) thor (1.1.0) thread_safe (0.3.6) - tzinfo (1.2.9) + tzinfo (1.2.10) thread_safe (~> 0.1) unicode-display_width (2.0.0) websocket-driver (0.7.3) diff --git a/app/.gitignore b/app/.gitignore new file mode 100644 index 00000000..7329a851 --- /dev/null +++ b/app/.gitignore @@ -0,0 +1,20 @@ +# build output +dist/ +.output/ + +# dependencies +node_modules/ + +# logs +npm-debug.log* +yarn-debug.log* +yarn-error.log* +pnpm-debug.log* + + +# environment variables +.env +.env.production + +# macOS-specific files +.DS_Store diff --git a/app/.npmrc b/app/.npmrc new file mode 100644 index 00000000..ef83021a --- /dev/null +++ b/app/.npmrc @@ -0,0 +1,2 @@ +# Expose Astro dependencies for `pnpm` users +shamefully-hoist=true diff --git a/app/.vscode/extensions.json b/app/.vscode/extensions.json new file mode 100644 index 00000000..22a15055 --- /dev/null +++ b/app/.vscode/extensions.json @@ -0,0 +1,4 @@ +{ + "recommendations": ["astro-build.astro-vscode"], + "unwantedRecommendations": [] +} diff --git a/app/.vscode/launch.json b/app/.vscode/launch.json new file mode 100644 index 00000000..d6422097 --- /dev/null +++ b/app/.vscode/launch.json @@ -0,0 +1,11 @@ +{ + "version": "0.2.0", + "configurations": [ + { + "command": "./node_modules/.bin/astro dev", + "name": "Development server", + "request": "launch", + "type": "node-terminal" + } + ] +} diff --git a/app/README.md b/app/README.md new file mode 100644 index 00000000..b0a937d0 --- /dev/null +++ b/app/README.md @@ -0,0 +1,42 @@ +# Welcome to [Astro](https://astro.build) + +[![Open in StackBlitz](https://developer.stackblitz.com/img/open_in_stackblitz.svg)](https://stackblitz.com/github/withastro/astro/tree/latest/examples/starter) + +> 🧑‍🚀 **Seasoned astronaut?** Delete this file. Have fun! + +## 🚀 Project Structure + +Inside of your Astro project, you'll see the following folders and files: + +``` +/ +├── public/ +│ └── favicon.ico +├── src/ +│ ├── components/ +│ │ └── Layout.astro +│ └── pages/ +│ └── index.astro +└── package.json +``` + +Astro looks for `.astro` or `.md` files in the `src/pages/` directory. Each page is exposed as a route based on its file name. + +There's nothing special about `src/components/`, but that's where we like to put any Astro/React/Vue/Svelte/Preact components or layouts. + +Any static assets, like images, can be placed in the `public/` directory. + +## 🧞 Commands + +All commands are run from the root of the project, from a terminal: + +| Command | Action | +| :---------------- | :------------------------------------------- | +| `npm install` | Installs dependencies | +| `npm run dev` | Starts local dev server at `localhost:3000` | +| `npm run build` | Build your production site to `./dist/` | +| `npm run preview` | Preview your build locally, before deploying | + +## 👀 Want to learn more? + +Feel free to check [our documentation](https://docs.astro.build) or jump into our [Discord server](https://astro.build/chat). diff --git a/app/astro.config.mjs b/app/astro.config.mjs new file mode 100644 index 00000000..e0d342c8 --- /dev/null +++ b/app/astro.config.mjs @@ 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{ "a": 0, "k": 0, "ix": 10 }, + "p": { "a": 0, "k": [400, 400, 0], "ix": 2 }, + "a": { "a": 0, "k": [400, 400, 0], "ix": 1 }, + "s": { "a": 0, "k": [100, 100, 100], "ix": 6 } + }, + "ao": 0, + "w": 800, + "h": 800, + "ip": 0, + "op": 151, + "st": 0, + "bm": 0 + }, + { + "ddd": 0, + "ind": 3, + "ty": 0, + "nm": "back", + "refId": "comp_2", + "sr": 1, + "ks": { + "o": { "a": 0, "k": 100, "ix": 11 }, + "r": { "a": 0, "k": 0, "ix": 10 }, + "p": { "a": 0, "k": [400, 400, 0], "ix": 2 }, + "a": { "a": 0, "k": [400, 400, 0], "ix": 1 }, + "s": { "a": 0, "k": [100, 100, 100], "ix": 6 } + }, + "ao": 0, + "w": 800, + "h": 800, + "ip": 0, + "op": 151, + "st": 0, + "bm": 0 + } + ], + "markers": [] +} diff --git a/app/src/README.md b/app/src/README.md new file mode 100644 index 00000000..b6b5f2ff --- /dev/null +++ b/app/src/README.md @@ -0,0 +1,8 @@ +# Directories + +- **apps**: used for creating javascript applications, typically structures with state and logic +- **components**: used for shared reusable components (things used all over the app) +- **data**: used for storing static content (questions, written content, etc) +- **layouts**: used for creating page layouts, this is an astro directory as well +- **pages**: directory used by astro to determine the routing of the app +- **utilities**: used for general purpose utility functions diff --git a/app/src/apps/Desmos/Desmos.svelte b/app/src/apps/Desmos/Desmos.svelte new file mode 100644 index 00000000..5bf27112 --- /dev/null +++ b/app/src/apps/Desmos/Desmos.svelte @@ -0,0 +1,45 @@ + + +
+
+
+ + diff --git a/app/src/apps/Examinations/Lab.svelte b/app/src/apps/Examinations/Lab.svelte new file mode 100644 index 00000000..70aa99fc --- /dev/null +++ b/app/src/apps/Examinations/Lab.svelte @@ -0,0 +1,53 @@ + + +
+ {#if lab.getCurrentQuestion()} + + {:else} + + {/if} +
diff --git a/app/src/apps/Examinations/Test.svelte b/app/src/apps/Examinations/Test.svelte new file mode 100644 index 00000000..83400ec8 --- /dev/null +++ b/app/src/apps/Examinations/Test.svelte @@ -0,0 +1,43 @@ + + +
+
+ {#each test.questions as question, questionIndex} + + {/each} +
diff --git a/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/DesmosAsymtopicAnalysisQuestion.svelte b/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/DesmosAsymtopicAnalysisQuestion.svelte new file mode 100644 index 00000000..bd469db7 --- /dev/null +++ b/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/DesmosAsymtopicAnalysisQuestion.svelte @@ -0,0 +1,38 @@ + + +
{@html question.body}
+ +
+ {#each question.options as option, optionIndex} +
handleOptionClick(question, optionIndex)}> + + {@html option.body} +
+ {/each} +
diff --git a/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/index.js b/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/index.js new file mode 100644 index 00000000..3294a583 --- /dev/null +++ b/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/index.js @@ -0,0 +1 @@ +export { default as DesmosAsymtopicAnalysisQuestion } from "./DesmosAsymtopicAnalysisQuestion.svelte"; diff --git a/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/styles.scss b/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/styles.scss new file mode 100644 index 00000000..132eb9b5 --- /dev/null +++ b/app/src/apps/Examinations/components/DesmosAsymtopicAnalysisQuestion/styles.scss @@ -0,0 +1,7 @@ +.desmos-asymtopic-analysis-question-body { + margin-bottom: 2rem; +} + +.desmos-asymtopic-analysis-question-options { + margin-top: 2rem; +} diff --git a/app/src/apps/Examinations/components/Header/Header.svelte b/app/src/apps/Examinations/components/Header/Header.svelte new file mode 100644 index 00000000..869cc66a --- /dev/null +++ b/app/src/apps/Examinations/components/Header/Header.svelte @@ -0,0 +1,11 @@ + + +
+
{title}
+
{description}
+
diff --git a/app/src/apps/Examinations/components/Header/index.js b/app/src/apps/Examinations/components/Header/index.js new file mode 100644 index 00000000..617ba270 --- /dev/null +++ b/app/src/apps/Examinations/components/Header/index.js @@ -0,0 +1 @@ +export { default as Header } from "./Header.svelte"; diff --git a/app/src/apps/Examinations/components/Header/styles.scss b/app/src/apps/Examinations/components/Header/styles.scss new file mode 100644 index 00000000..e69de29b diff --git a/app/src/apps/Examinations/components/MultipleChoiceOption/MultipleChoiceOption.svelte b/app/src/apps/Examinations/components/MultipleChoiceOption/MultipleChoiceOption.svelte new file mode 100644 index 00000000..48f821c8 --- /dev/null +++ b/app/src/apps/Examinations/components/MultipleChoiceOption/MultipleChoiceOption.svelte @@ -0,0 +1,24 @@ + + +
+
({letter})
+
+ +
+
diff --git a/app/src/apps/Examinations/components/MultipleChoiceOption/index.js b/app/src/apps/Examinations/components/MultipleChoiceOption/index.js new file mode 100644 index 00000000..c7300df3 --- /dev/null +++ b/app/src/apps/Examinations/components/MultipleChoiceOption/index.js @@ -0,0 +1 @@ +export { default as MultipleChoiceOption } from "./MultipleChoiceOption.svelte"; diff --git a/app/src/apps/Examinations/components/MultipleChoiceOption/styles.scss b/app/src/apps/Examinations/components/MultipleChoiceOption/styles.scss new file mode 100644 index 00000000..864b904d --- /dev/null +++ b/app/src/apps/Examinations/components/MultipleChoiceOption/styles.scss @@ -0,0 +1,26 @@ +.multiple-choice-option { + display: flex; + justify-content: left; + align-items: center; + height: 3rem; + border-style: solid; + border-radius: 0.6rem; + border-width: 0.1rem; + border-color: #c0c0c0; + margin: 1rem 0rem; +} + +.multiple-choice-option-selected { + // TODO: styling should be updated so we don't need the important + background-color: rgb(60, 203, 255) !important; +} + +.multiple-choice-option-letter { + margin: 0.5rem; +} + +.multiple-choice-option:hover, +.multiple-choice-option:active { + background: #edfeff; + cursor: pointer; +} diff --git a/app/src/apps/Examinations/components/MultipleChoiceQuestion/MultipleChoiceQuestion.svelte b/app/src/apps/Examinations/components/MultipleChoiceQuestion/MultipleChoiceQuestion.svelte new file mode 100644 index 00000000..1a3744fd --- /dev/null +++ b/app/src/apps/Examinations/components/MultipleChoiceQuestion/MultipleChoiceQuestion.svelte @@ -0,0 +1,45 @@ + + +
+ {#if number} +
{number}. {@html question.body}
+ {:else} +
{@html question.body}
+ {/if} +
+ {#each question.options as option, optionIndex} +
handleOptionClick(question, optionIndex)}> + + {@html option.body} +
+ {/each} +
+
diff --git a/app/src/apps/Examinations/components/MultipleChoiceQuestion/index.js b/app/src/apps/Examinations/components/MultipleChoiceQuestion/index.js new file mode 100644 index 00000000..ae7f23c4 --- /dev/null +++ b/app/src/apps/Examinations/components/MultipleChoiceQuestion/index.js @@ -0,0 +1 @@ +export { default as MultipleChoiceQuestion } from "./MultipleChoiceQuestion.svelte"; diff --git a/app/src/apps/Examinations/components/MultipleChoiceQuestion/styles.scss b/app/src/apps/Examinations/components/MultipleChoiceQuestion/styles.scss new file mode 100644 index 00000000..369c83c8 --- /dev/null +++ b/app/src/apps/Examinations/components/MultipleChoiceQuestion/styles.scss @@ -0,0 +1,11 @@ +.multiple-choice-question { + padding: 1rem; + font-family: Arial; +} + +.test-header { + font-family: Arial; + font-size: 2rem; + text-align: center; + margin: 1rem; +} diff --git a/app/src/apps/Examinations/components/Question/Question.svelte b/app/src/apps/Examinations/components/Question/Question.svelte new file mode 100644 index 00000000..a5952894 --- /dev/null +++ b/app/src/apps/Examinations/components/Question/Question.svelte @@ -0,0 +1,55 @@ + + +{#if question instanceof MultipleChoiceQuestionObject} + +{:else if question instanceof DesmosAsymtopicAnalysisQuestionObject} + +{:else if question instanceof WrittenQuestionObject} + +{/if} + +{#if displayLab && question.labId != null} + Go to the associated Lab! +{/if} diff --git a/app/src/apps/Examinations/components/Question/index.js b/app/src/apps/Examinations/components/Question/index.js new file mode 100644 index 00000000..244d405d --- /dev/null +++ b/app/src/apps/Examinations/components/Question/index.js @@ -0,0 +1 @@ +export { default as Question } from "./Question.svelte"; diff --git a/app/src/apps/Examinations/components/WrittenQuestion/WrittenQuestion.svelte b/app/src/apps/Examinations/components/WrittenQuestion/WrittenQuestion.svelte new file mode 100644 index 00000000..26dc206e --- /dev/null +++ b/app/src/apps/Examinations/components/WrittenQuestion/WrittenQuestion.svelte @@ -0,0 +1,29 @@ + + +
+ {#if number} +
{number}. {@html question.body}
+ {:else} +
{@html question.body}
+ {/if} +
+ handleInputChange(question, e.target.value)} /> +
+ {#if submitted} +
{@html question.answer}
+ {/if} +
diff --git a/app/src/apps/Examinations/components/WrittenQuestion/index.js b/app/src/apps/Examinations/components/WrittenQuestion/index.js new file mode 100644 index 00000000..2157e649 --- /dev/null +++ b/app/src/apps/Examinations/components/WrittenQuestion/index.js @@ -0,0 +1 @@ +export { default as WrittenQuestion } from "./WrittenQuestion.svelte"; diff --git a/app/src/apps/Examinations/components/WrittenQuestion/styles.scss b/app/src/apps/Examinations/components/WrittenQuestion/styles.scss new file mode 100644 index 00000000..e69de29b diff --git a/app/src/apps/Examinations/components/index.js b/app/src/apps/Examinations/components/index.js new file mode 100644 index 00000000..c99b065b --- /dev/null +++ b/app/src/apps/Examinations/components/index.js @@ -0,0 +1,6 @@ +export { DesmosAsymtopicAnalysisQuestion } from "./DesmosAsymtopicAnalysisQuestion"; +export { Header } from "./Header"; +export { MultipleChoiceOption } from "./MultipleChoiceOption"; +export { MultipleChoiceQuestion } from "./MultipleChoiceQuestion"; +export { Question } from "./Question"; +export { WrittenQuestion } from "./WrittenQuestion"; diff --git a/app/src/apps/Examinations/index.js b/app/src/apps/Examinations/index.js new file mode 100644 index 00000000..073d67e6 --- /dev/null +++ b/app/src/apps/Examinations/index.js @@ -0,0 +1,2 @@ +export { default as Lab } from "./Lab.svelte"; +export { default as Test } from "./Test.svelte"; diff --git a/app/src/apps/Examinations/lib/Examination.js b/app/src/apps/Examinations/lib/Examination.js new file mode 100644 index 00000000..3237dfe0 --- /dev/null +++ b/app/src/apps/Examinations/lib/Examination.js @@ -0,0 +1,35 @@ +import { MultipleChoiceQuestion } from "./questions/MultipleChoiceQuestion"; + +class Examination { + title; + author; + submitted = false; + + constructor(title, author) { + this.title = title; + this.author = author; + } + + constructQuestions(questions) { + return questions.map((question) => this.constructQuestion(question)); + } + + constructQuestion(question) { + switch (question.type) { + case "MultipleChoice": + return new MultipleChoiceQuestion( + question.body, + question.options, + question.lab + ); + default: + throw "ERROR: Unsupported question type."; + } + } + + submit() { + this.submitted = true; + } +} + +export { Examination }; diff --git a/app/src/apps/Examinations/lib/Factory.js b/app/src/apps/Examinations/lib/Factory.js new file mode 100644 index 00000000..b0268ece --- /dev/null +++ b/app/src/apps/Examinations/lib/Factory.js @@ -0,0 +1,7 @@ +class Factory { + create() { + return {}; + } +} + +export { Factory as default }; diff --git a/app/src/apps/Examinations/lib/Question.js b/app/src/apps/Examinations/lib/Question.js new file mode 100644 index 00000000..d93eb04d --- /dev/null +++ b/app/src/apps/Examinations/lib/Question.js @@ -0,0 +1,15 @@ +class Question { + body; + labId; + + constructor(body, labId) { + this.body = body; + this.labId = labId; + } + + updateOption(event) { + throw "Not implemented"; + } +} + +export { Question }; diff --git a/app/src/apps/Examinations/lib/examinations/Drill.js b/app/src/apps/Examinations/lib/examinations/Drill.js new file mode 100644 index 00000000..c7bd3ab0 --- /dev/null +++ b/app/src/apps/Examinations/lib/examinations/Drill.js @@ -0,0 +1,16 @@ +class Drill extends Examination { + questions = []; + currentQuestionIndex = -1; + + constructor(title, author, questions) { + super(title, author); + this.questions = questions; + } + + randomizeQuestions(questions) { + questions.sort(() => Math.random() - 0.5); + return questions; + } +} + +export { Drill }; diff --git a/app/src/apps/Examinations/lib/examinations/Lab.js b/app/src/apps/Examinations/lib/examinations/Lab.js new file mode 100644 index 00000000..140347d2 --- /dev/null +++ b/app/src/apps/Examinations/lib/examinations/Lab.js @@ -0,0 +1,55 @@ +import { Examination } from "../Examination"; +import { + DesmosAsymtopicAnalysis, + DesmosAsymtopicAnalysisPolynomial, + HowManyFunctions, + HowManyNonOneToOneFunctions, + HowManyOneToOneFunctions, +} from "../factories"; + +class Lab extends Examination { + // TODO: was a list to avoid "null" issue when question was generated, can be removed? + questions = []; + + constructor(title, author, factories) { + // TODO: do labs need titles and authors ??? + super(title, author); + + this.factories = this.contructFactories(factories); + } + + contructFactories(factories) { + return factories.map((factory) => this.constructFactory(factory)); + } + + constructFactory(name) { + switch (name) { + case "DesmosAsymtopicAnalysis": + return new DesmosAsymtopicAnalysis(); + case "DesmosAsymtopicAnalysisPolynomial": + return new DesmosAsymtopicAnalysisPolynomial(); + case "HowManyFunctions": + return new HowManyFunctions(); + case "HowManyNonOneToOneFunctions": + return new HowManyNonOneToOneFunctions(); + case "HowManyOneToOneFunctions": + return new HowManyOneToOneFunctions(); + default: + throw "ERROR: Unsupported lab name."; + } + } + + generateNewQuestion() { + const factory = + this.factories[Math.floor(Math.random() * this.factories.length)]; + + const question = factory.create(); + this.questions.push(question); + } + + getCurrentQuestion() { + return this.questions[this.questions.length - 1]; + } +} + +export { Lab as default }; diff --git a/app/src/apps/Examinations/lib/examinations/Test.js b/app/src/apps/Examinations/lib/examinations/Test.js new file mode 100644 index 00000000..bef0050d --- /dev/null +++ b/app/src/apps/Examinations/lib/examinations/Test.js @@ -0,0 +1,12 @@ +import { Examination } from "../Examination"; + +class Test extends Examination { + questions = []; + + constructor(title, author, questions) { + super(title, author); + this.questions = this.constructQuestions(questions); + } +} + +export { Test as default }; diff --git a/app/src/apps/Examinations/lib/factories/DesmosAsymtopicAnalysis.js b/app/src/apps/Examinations/lib/factories/DesmosAsymtopicAnalysis.js new file mode 100644 index 00000000..668125a6 --- /dev/null +++ b/app/src/apps/Examinations/lib/factories/DesmosAsymtopicAnalysis.js @@ -0,0 +1,125 @@ +import Factory from "../Factory"; +import { DesmosAsymtopicAnalysisQuestion } from "../questions"; + +const LOGARITHMIC_RANK = 1; +const LINEAR_RANK = 2; +const LINEAR_LOG_RANK = 3; +const QUADRATIC_RANK = 4; + +const PARENT_FUNCTIONS = [ + { + expression: "\\log_{2}x", + rank: LOGARITHMIC_RANK, + }, + { + expression: "\\sqrt{x}", + rank: LINEAR_RANK, + }, + { + expression: "x", + rank: LINEAR_RANK, + }, + { + expression: "x\\log_{2}x", + rank: LINEAR_LOG_RANK, + }, + { + expression: "x^2", + rank: QUADRATIC_RANK, + }, +]; + +class DesmosAsymtopicAnalysis extends Factory { + functionTypeTemplates = [ + { + name: "square root", + generator: this.randomSquareRoot, + display: this.squareRootToDesmosExpression, + rank: LINEAR_RANK, + }, + { + name: "logarithmic", + generator: this.randomLogarithm, + display: this.logarithmToDesmosExpression, + rank: LOGARITHMIC_RANK, + }, + + { + name: "loglinear", + generator: this.randomLogarithm, + display: this.logLinearToDesmosExpression, + rank: LINEAR_LOG_RANK, + }, + ]; + + create() { + const functionTemplate = + this.functionTypeTemplates[ + Math.floor(Math.random() * this.functionTypeTemplates.length) + ]; + + const functionData = functionTemplate.generator(); + const expression = functionTemplate.display(functionData); + const parentFunction = this.generateParentFunction(); + const body = this.generateBody(expression, parentFunction.expression); + + const question = new DesmosAsymtopicAnalysisQuestion( + body, + expression, + functionTemplate.rank, + parentFunction.expression, + parentFunction.rank + ); + return question; + } + + generateBody(expression, runtime) { + return String.raw`Is the following function $${expression}$ in $O(${runtime})$ ?`; + } + + generateParentFunction() { + return PARENT_FUNCTIONS[ + Math.floor(Math.random() * PARENT_FUNCTIONS.length) + ]; + } + + randomSquareRoot() { + let exponent = Math.random() * (1 - 0.01) + 0.01; //[0.01, 1) + let coefficient = Math.floor(Math.random() * 20 + 1); //[1, 20] + let constant = Math.floor(Math.random() * 11); + exponent = exponent.toFixed(5); + return { exponent: exponent, coefficient: coefficient, constant: constant }; + } + + squareRootToDesmosExpression(squareRoot) { + return ( + "y = " + + squareRoot.coefficient.toString() + + "x^{" + + squareRoot.exponent.toString() + + "} + " + + squareRoot.constant.toString() + ); + } + + randomLogarithm() { + let outerCoeff = (Math.floor(Math.random() * (11 - 1 + 1)) + 1).toString(); + let innerCoeff = (Math.floor(Math.random() * (11 - 1 + 1)) + 1).toString(); + + return { outerCoeff: outerCoeff, innerCoeff: innerCoeff }; + } + + logarithmToDesmosExpression(logarithm) { + return ( + "y = " + logarithm.outerCoeff + "\\log_{2}" + logarithm.innerCoeff + "x" + ); + } + + logLinearToDesmosExpression(logarithm) { + return ( + "y = " + logarithm.outerCoeff + "x \\log_{2}" + logarithm.innerCoeff + "x" + ); + } +} + +export { DesmosAsymtopicAnalysis }; diff --git a/app/src/apps/Examinations/lib/factories/DesmosAsymtopicAnalysisPolynomial.js b/app/src/apps/Examinations/lib/factories/DesmosAsymtopicAnalysisPolynomial.js new file mode 100644 index 00000000..8e3c7bde --- /dev/null +++ b/app/src/apps/Examinations/lib/factories/DesmosAsymtopicAnalysisPolynomial.js @@ -0,0 +1,100 @@ +import Factory from "../Factory"; +import { DesmosAsymtopicAnalysisQuestion } from "../questions"; + +const LOGARITHMIC_RANK = 1; +const LINEAR_RANK = 2; +const LINEAR_LOG_RANK = 3; +const QUADRATIC_RANK = 4; + +const PARENT_FUNCTIONS = [ + { + expression: "\\log_{2}x", + rank: LOGARITHMIC_RANK, + }, + { + expression: "\\sqrt{x}", + rank: LINEAR_RANK, + }, + { + expression: "x", + rank: LINEAR_RANK, + }, + { + expression: "x\\log_{2}x", + rank: LINEAR_LOG_RANK, + }, + { + expression: "x^2", + rank: QUADRATIC_RANK, + }, +]; + +class DesmosAsymtopicAnalysisPolynomial extends Factory { + create() { + const [coefficients, degree] = this.generateRandomPolynomial(); + const expression = this.polynomialToDesmosExpression(coefficients); + const expressionRank = this.generateExpressionRank(degree); + const parentFunction = this.generateParentFunction(); + const body = this.generateBody(expression, parentFunction.expression); + + const question = new DesmosAsymtopicAnalysisQuestion( + body, + expression, + expressionRank, + parentFunction.expression, + parentFunction.rank + ); + return question; + } + + generateBody(expression, runtime) { + return String.raw`Is the following function $${expression}$ in $O(${runtime})$ ?`; + } + + generateRandomPolynomial() { + let degree = Math.floor(Math.random() * (3 - 2 + 1)) + 2; // this is not the degree, but the number of coefficients + let coefficients = []; + + for (let i = 0; i < degree; i++) { + coefficients.push(Math.floor(Math.random() * (11 - 1 + 1)) + 1); + } + + return [coefficients, degree - 1]; + } + + generateParentFunction() { + return PARENT_FUNCTIONS[ + Math.floor(Math.random() * PARENT_FUNCTIONS.length) + ]; + } + + polynomialToDesmosExpression(coefficients) { + let expressionChunks = []; + let currentExponent = coefficients.length - 1; + + coefficients.forEach(function (coefficient) { + if (currentExponent == 0) { + expressionChunks.push(coefficient.toString()); + } else if (currentExponent == 1) { + expressionChunks.push(coefficient.toString() + "x"); + } else { + expressionChunks.push( + coefficient.toString() + "x^" + currentExponent.toString() + ); + } + currentExponent--; + }); + + return "y = " + expressionChunks.join(" + "); + } + + generateExpressionRank(x) { + if (x == 1) { + return LINEAR_RANK; + } else if (x == 2) { + return QUADRATIC_RANK; + } + } +} + +export { DesmosAsymtopicAnalysisPolynomial }; diff --git a/app/src/apps/Examinations/lib/factories/HowManyFunctions.js b/app/src/apps/Examinations/lib/factories/HowManyFunctions.js new file mode 100644 index 00000000..7f8265f3 --- /dev/null +++ b/app/src/apps/Examinations/lib/factories/HowManyFunctions.js @@ -0,0 +1,84 @@ +import Factory from "../Factory"; +import { MultipleChoiceQuestion } from "../questions"; + +const MIN_SET_SIZE = 1; +const MAX_SET_SIZE = 25; + +class HowManyFunctions extends Factory { + create() { + const [setASize, setBSize] = this.generateSetSizes(); + const body = this.generateQuestionBody(setASize, setBSize); + const options = this.generateQuestionOptions(setASize, setBSize); + const question = new MultipleChoiceQuestion(body, options); + return question; + } + + getRandomSetSize() { + return ( + Math.floor(Math.random() * (MAX_SET_SIZE - MIN_SET_SIZE + 1)) + + MIN_SET_SIZE + ); + } + + generateQuestionBody(setASize, setBSize) { + return String.raw`Let $A$ be a set of size ${setASize} and let $B$ be a set of size ${setBSize}. How many functions $f : A \rightarrow B$ are there?`; + } + + generateSetSizes() { + let setA = this.getRandomSetSize(); + let setB = this.getRandomSetSize(); + + while (setA === setB) { + setB = this.getRandomSetSize(); + } + + if (setA > setB) { + return [setA, setB]; + } + + return [setB, setA]; + } + + generateQuestionOptions(setASize, setBSize) { + let options = []; + + options.push(this.generateOptionOne(setBSize)); + options.push(this.generateOptionTwo(setASize, setBSize)); + options.push(this.generateOptionThree(setASize, setBSize)); + options.push(this.generateOptionFour(setASize, setBSize)); + + options.sort(() => Math.random() - 0.5); + + return options; + } + + generateOptionOne(setBSize) { + return { + body: String.raw`$ {${setBSize}!} $`, + correct: false, + }; + } + + generateOptionTwo(setASize, setBSize) { + return { + body: String.raw`$\frac{${setASize}!}{${setBSize}!}$`, + correct: false, + }; + } + + generateOptionThree(setASize, setBSize) { + return { + body: String.raw`$ {${setBSize}}^{${setASize}} $`, + correct: true, + }; + } + + generateOptionFour(setASize, setBSize) { + return { + body: String.raw`$ {${setASize}}^{${setBSize}} $`, + correct: false, + }; + } +} + +export { HowManyFunctions }; diff --git a/app/src/apps/Examinations/lib/factories/HowManyNonOneToOneFunctions.js b/app/src/apps/Examinations/lib/factories/HowManyNonOneToOneFunctions.js new file mode 100644 index 00000000..5d53d5f1 --- /dev/null +++ b/app/src/apps/Examinations/lib/factories/HowManyNonOneToOneFunctions.js @@ -0,0 +1,88 @@ +import Factory from "../Factory"; +import { MultipleChoiceQuestion } from "../questions"; + +const MIN_SET_SIZE = 1; +const MAX_SET_SIZE = 25; + +class HowManyNonOneToOneFunctions extends Factory { + create() { + const [setASize, setBSize] = this.generateSetSizes(); + const body = this.generateQuestionBody(setASize, setBSize); + const options = this.generateQuestionOptions(setASize, setBSize); + const question = new MultipleChoiceQuestion(body, options); + return question; + } + + getRandomSetSize() { + return ( + Math.floor(Math.random() * (MAX_SET_SIZE - MIN_SET_SIZE + 1)) + + MIN_SET_SIZE + ); + } + + generateQuestionBody(setASize, setBSize) { + return String.raw`Let $A$ be a set of size ${setASize} and let $B$ be a set of size ${setBSize}. How many functions $f : A \rightarrow B$ are there that are not one-to-one?`; + } + + generateSetSizes() { + let setA = this.getRandomSetSize(); + let setB = this.getRandomSetSize(); + + while (setA === setB) { + setB = this.getRandomSetSize(); + } + + if (setA < setB) { + return [setA, setB]; + } + + return [setB, setA]; + } + + generateQuestionOptions(setASize, setBSize) { + let options = []; + + options.push(this.generateOptionOne(setASize, setBSize)); + options.push(this.generateOptionTwo(setASize, setBSize)); + options.push(this.generateOptionThree(setASize, setBSize)); + options.push(this.generateOptionFour(setASize, setBSize)); + + options.sort(() => Math.random() - 0.5); + + return options; + } + + generateOptionOne(setASize, setBSize) { + const setASizeMinusSetBMinusOne = setBSize - setASize - 1; + return { + body: String.raw`$ {${setBSize}}^{${setASize}} - \frac{${setBSize}!}{${setASizeMinusSetBMinusOne}!} $`, + correct: false, + }; + } + + generateOptionTwo(setASize, setBSize) { + const setASizeMinusSetB = setBSize - setASize; + return { + body: String.raw`$ \frac{${setBSize}!}{${setASizeMinusSetB}!} - {${setBSize}}^{${setASize}} $`, + correct: false, + }; + } + + generateOptionThree(setASize, setBSize) { + const setASizeMinusSetB = setBSize - setASize; + return { + body: String.raw`$ {${setBSize}}^{${setASize}} - \frac{${setBSize}!}{${setASizeMinusSetB}!} $`, + correct: true, + }; + } + + generateOptionFour(setASize, setBSize) { + const setASizeMinusSetB = setBSize - setASize; + return { + body: String.raw`$ {${setASize}}^{${setBSize}} - \frac{${setBSize}!}{${setASizeMinusSetB}!} $`, + correct: false, + }; + } +} + +export { HowManyNonOneToOneFunctions }; diff --git a/app/src/apps/Examinations/lib/factories/HowManyOneToOneFunctions.js b/app/src/apps/Examinations/lib/factories/HowManyOneToOneFunctions.js new file mode 100644 index 00000000..f0f959bb --- /dev/null +++ b/app/src/apps/Examinations/lib/factories/HowManyOneToOneFunctions.js @@ -0,0 +1,84 @@ +import Factory from "../Factory"; +import { MultipleChoiceQuestion } from "../questions"; + +const MIN_SET_SIZE = 1; +const MAX_SET_SIZE = 25; + +class HowManyOneToOneFunctions extends Factory { + create() { + const [setASize, setBSize] = this.generateSetSizes(); + const body = this.generateQuestionBody(setASize, setBSize); + const options = this.generateQuestionOptions(setASize, setBSize); + const question = new MultipleChoiceQuestion(body, options); + return question; + } + + getRandomSetSize() { + return ( + Math.floor(Math.random() * (MAX_SET_SIZE - MIN_SET_SIZE + 1)) + + MIN_SET_SIZE + ); + } + + generateQuestionBody(setASize, setBSize) { + return String.raw`Let $A$ be a set of size ${setASize} and let $B$ be a set of size ${setBSize}. How many one-to-one functions $f : A \rightarrow B$ are there?`; + } + + generateSetSizes() { + let setA = this.getRandomSetSize(); + let setB = this.getRandomSetSize(); + + while (setA === setB) { + setB = this.getRandomSetSize(); + } + + if (setA < setB) { + return [setA, setB]; + } + + return [setB, setA]; + } + + generateQuestionOptions(setASize, setBSize) { + let options = []; + + options.push(this.generateOptionOne(setASize, setBSize)); + options.push(this.generateOptionTwo(setASize, setBSize)); + options.push(this.generateOptionThree(setASize, setBSize)); + options.push(this.generateOptionFour(setASize, setBSize)); + + options.sort(() => Math.random() - 0.5); + + return options; + } + + generateOptionOne(setASize, setBSize) { + return { + body: String.raw`$ {${setASize}}^{${setBSize}} $`, + correct: false, + }; + } + + generateOptionTwo(setASize, setBSize) { + return { + body: String.raw`$\frac{${setBSize}!}{${setASize}!}$`, + correct: false, + }; + } + + generateOptionThree(setASize, setBSize) { + return { + body: String.raw`$\frac{${setBSize}!}{${setBSize - setASize}!}$`, + correct: true, + }; + } + + generateOptionFour(setASize, setBSize) { + return { + body: String.raw`$\frac{${setBSize}!}{${setBSize - setASize + 1}!}$`, + correct: false, + }; + } +} + +export { HowManyOneToOneFunctions }; diff --git a/app/src/apps/Examinations/lib/factories/index.js b/app/src/apps/Examinations/lib/factories/index.js new file mode 100644 index 00000000..febbaacd --- /dev/null +++ b/app/src/apps/Examinations/lib/factories/index.js @@ -0,0 +1,5 @@ +export { DesmosAsymtopicAnalysis } from "./DesmosAsymtopicAnalysis"; +export { DesmosAsymtopicAnalysisPolynomial } from "./DesmosAsymtopicAnalysisPolynomial"; +export { HowManyFunctions } from "./HowManyFunctions"; +export { HowManyOneToOneFunctions } from "./HowManyOneToOneFunctions"; +export { HowManyNonOneToOneFunctions } from "./HowManyNonOneToOneFunctions"; diff --git a/app/src/apps/Examinations/lib/questions/DesmosAsymtopicAnalysisQuestion.js b/app/src/apps/Examinations/lib/questions/DesmosAsymtopicAnalysisQuestion.js new file mode 100644 index 00000000..d653db18 --- /dev/null +++ b/app/src/apps/Examinations/lib/questions/DesmosAsymtopicAnalysisQuestion.js @@ -0,0 +1,72 @@ +import { Question } from "../Question"; + +class DesmosAsymtopicAnalysisQuestion extends Question { + selectedOptionIndex = -1; + + constructor( + body, + expression, + expressionRank, + parentFunction, + parentFunctionRank + ) { + super(body, null); + this.expression = expression; + this.parentFunction = parentFunction; + this.desmosExpressions = this.generateDesmosExpressions( + expression, + parentFunction + ); + + const isTheCorrectAnswerTrue = expressionRank <= parentFunctionRank; + this.options = [ + new DesmosAsymtopicAnalysisOption("True", isTheCorrectAnswerTrue), + new DesmosAsymtopicAnalysisOption("False", !isTheCorrectAnswerTrue), + ]; + } + + updateSelectedOption(index) { + this.selectedOptionIndex = index; + } + + isAnsweredCorrectly() { + return options[this.selectedOptionIndex].correct; + } + + generateDesmosExpressions(expression, parentFunction) { + return [ + { + id: "expression1", + latex: expression, + }, + { + id: "expression2", + latex: parentFunction, + }, + { + id: "expression3", + latex: "c = 1", + }, + { + id: "expression4", + latex: "x = k", + }, + { + id: "expression5", + latex: "k = 1", + }, + ]; + } +} + +class DesmosAsymtopicAnalysisOption { + body; + correct; + + constructor(body, correct) { + this.body = body; + this.correct = correct; + } +} + +export { DesmosAsymtopicAnalysisQuestion }; diff --git a/app/src/apps/Examinations/lib/questions/MultipleChoiceQuestion.js b/app/src/apps/Examinations/lib/questions/MultipleChoiceQuestion.js new file mode 100644 index 00000000..62846827 --- /dev/null +++ b/app/src/apps/Examinations/lib/questions/MultipleChoiceQuestion.js @@ -0,0 +1,37 @@ +import { Question } from "../Question"; + +class MultipleChoiceQuestion extends Question { + selectedOptionIndex = -1; + options = []; + + constructor(body, options, labId) { + super(body, labId); + this.options = this.constructOptions(options); + } + + constructOptions(options) { + return options.map( + (option) => new MultipleChoiceOption(option.body, option.correct) + ); + } + + updateSelectedOption(index) { + this.selectedOptionIndex = index; + } + + isAnsweredCorrectly() { + return options[this.selectedOptionIndex].correct; + } +} + +class MultipleChoiceOption { + body; + correct; + + constructor(body, correct) { + this.body = body; + this.correct = correct; + } +} + +export { MultipleChoiceQuestion }; diff --git a/app/src/apps/Examinations/lib/questions/WrittenQuestion.js b/app/src/apps/Examinations/lib/questions/WrittenQuestion.js new file mode 100644 index 00000000..15151ff8 --- /dev/null +++ b/app/src/apps/Examinations/lib/questions/WrittenQuestion.js @@ -0,0 +1,21 @@ +import { Question } from "../Question"; + +class WrittenQuestion extends Question { + input = ""; + + constructor(body, expression, answer) { + super(body, null); + this.expression = expression; + this.answer = answer; + } + + updateInput(input) { + this.input = input; + } + + isAnsweredCorrectly() { + return this.input === this.answer; + } +} + +export { WrittenQuestion }; diff --git a/app/src/apps/Examinations/lib/questions/index.js b/app/src/apps/Examinations/lib/questions/index.js new file mode 100644 index 00000000..e4a856f0 --- /dev/null +++ b/app/src/apps/Examinations/lib/questions/index.js @@ -0,0 +1,3 @@ +export { DesmosAsymtopicAnalysisQuestion } from "./DesmosAsymtopicAnalysisQuestion"; +export { MultipleChoiceQuestion } from "./MultipleChoiceQuestion"; +export { WrittenQuestion } from "./WrittenQuestion"; diff --git a/app/src/apps/Examinations/lib/readme.md b/app/src/apps/Examinations/lib/readme.md new file mode 100644 index 00000000..ce6380bd --- /dev/null +++ b/app/src/apps/Examinations/lib/readme.md @@ -0,0 +1,9 @@ +### Classes + +- **Examinations**: Examination is the "generalized" semantic for an entity that has one or many questions + - Test: A test is an examination with a specific number of questions + - Drill: A drill is an examination that loops over a set of questions + - Lab: A lab is an examination that allows the user to practice a specific type of question (invokes a factory) +- **Questions**: A question class stores the neccesary state of a question. + - MultipleChoiceQuestion: A question with multiple options to select from +- **Factories**: Factories are used to create new questions. (Will be used for dynamic questions) diff --git a/app/src/apps/Examinations/styles.scss b/app/src/apps/Examinations/styles.scss new file mode 100644 index 00000000..9162d3f9 --- /dev/null +++ b/app/src/apps/Examinations/styles.scss @@ -0,0 +1,4 @@ +.test-application .lab-application { + font-family: "Assistant", sans-serif; + width: 100%; +} diff --git a/app/src/apps/Graphs/Graph.svelte b/app/src/apps/Graphs/Graph.svelte new file mode 100644 index 00000000..5aac4e38 --- /dev/null +++ b/app/src/apps/Graphs/Graph.svelte @@ -0,0 +1,284 @@ + + +
diff --git a/app/src/apps/Graphs/index.js b/app/src/apps/Graphs/index.js new file mode 100644 index 00000000..e69de29b diff --git a/app/src/apps/Graphs/lib/Edge.js b/app/src/apps/Graphs/lib/Edge.js new file mode 100644 index 00000000..3b5d83b2 --- /dev/null +++ b/app/src/apps/Graphs/lib/Edge.js @@ -0,0 +1,3 @@ +class Edge {} + +export { Edge as default }; diff --git a/app/src/apps/Graphs/lib/Graph.js b/app/src/apps/Graphs/lib/Graph.js new file mode 100644 index 00000000..321aa393 --- /dev/null +++ b/app/src/apps/Graphs/lib/Graph.js @@ -0,0 +1,3 @@ +class Graph {} + +export { Graph as default }; diff --git a/app/src/apps/Graphs/lib/Vertex.js b/app/src/apps/Graphs/lib/Vertex.js new file mode 100644 index 00000000..da09744b --- /dev/null +++ b/app/src/apps/Graphs/lib/Vertex.js @@ -0,0 +1,3 @@ +class Vertex {} + +export { Vertex as default }; diff --git a/app/src/apps/Graphs/lib/index.js b/app/src/apps/Graphs/lib/index.js new file mode 100644 index 00000000..e69de29b diff --git a/app/src/apps/Graphs/styles.scss b/app/src/apps/Graphs/styles.scss new file mode 100644 index 00000000..ff951e3d --- /dev/null +++ b/app/src/apps/Graphs/styles.scss @@ -0,0 +1,35 @@ +.graph-builder { + svg { + cursor: crosshair; + display: block; + margin: auto; + border: 1px solid #bbb; + } + + .edge { + stroke: #888; + stroke-width: 2px; + stroke-linecap: round; + stroke-linejoin: round; + cursor: default; + } + + .edge:hover, + .dragLine { + stroke: #333; + stroke-width: 3px; + } + + .vertex { + cursor: pointer; + } + + .vertex:hover { + stroke: #333; + opacity: 0.8; + } + + .dragLine.hidden { + stroke-width: 0; + } +} diff --git a/app/src/apps/Guides/Guide.astro b/app/src/apps/Guides/Guide.astro new file mode 100644 index 00000000..1cd937ae --- /dev/null +++ b/app/src/apps/Guides/Guide.astro @@ -0,0 +1,12 @@ +--- +const { Content, frontmatter } = Astro.props.mdx; +--- + +
+

{frontmatter.title}

+

Authored by: {frontmatter.author}

+

Last updated on: {frontmatter.last_updated}

+
+
+ +
diff --git a/app/src/apps/Test/lib/Question.js b/app/src/apps/Test/lib/Question.js new file mode 100644 index 00000000..e69de29b diff --git a/app/src/apps/index.js b/app/src/apps/index.js new file mode 100644 index 00000000..fa0de074 --- /dev/null +++ b/app/src/apps/index.js @@ -0,0 +1 @@ +export { Lab, Test } from "./Examinations"; diff --git a/app/src/components/Button/Button.svelte b/app/src/components/Button/Button.svelte new file mode 100644 index 00000000..489a516a --- /dev/null +++ b/app/src/components/Button/Button.svelte @@ -0,0 +1,15 @@ + + + diff --git a/app/src/components/Button/index.js b/app/src/components/Button/index.js new file mode 100644 index 00000000..fdeef532 --- /dev/null +++ b/app/src/components/Button/index.js @@ -0,0 +1 @@ +export { default as Button } from "./Button.svelte"; diff --git a/app/src/components/Button/styles.scss b/app/src/components/Button/styles.scss new file mode 100644 index 00000000..0987dc8c --- /dev/null +++ b/app/src/components/Button/styles.scss @@ -0,0 +1,18 @@ +button { + border-radius: 0.3rem; + border-width: 0px; + min-width: 6rem; + background-color: #ffab40; + color: white; + font-weight: bold; + font-size: 16px; + text-transform: uppercase; + transition: all 0.15s; + cursor: pointer; + .button_label { + padding: 0.75rem 1.5rem; + } +} +button:hover { + background-color: #d68110; +} diff --git a/app/src/components/ContentCard/ContentCard.svelte b/app/src/components/ContentCard/ContentCard.svelte new file mode 100644 index 00000000..a60c9601 --- /dev/null +++ b/app/src/components/ContentCard/ContentCard.svelte @@ -0,0 +1,16 @@ + + +
+
+ {tag} +
+
{title}
+ +
diff --git a/app/src/components/ContentCard/index.js b/app/src/components/ContentCard/index.js new file mode 100644 index 00000000..206e19ee --- /dev/null +++ b/app/src/components/ContentCard/index.js @@ -0,0 +1 @@ +export { default as ContentCard } from "./ContentCard.svelte"; diff --git a/app/src/components/ContentCard/styles.scss b/app/src/components/ContentCard/styles.scss new file mode 100644 index 00000000..f706d20b --- /dev/null +++ b/app/src/components/ContentCard/styles.scss @@ -0,0 +1,66 @@ +.content-card { + padding: 1rem; + width: 15rem; + height: 125px; + box-shadow: 0 0px 4px 0 rgba(0, 0, 0, 0.02), 0 6px 20px 0 rgba(0, 0, 0, 0.02); + transition: all 0.15s; + overflow: hidden; + font-family: "Assistant", sans-serif; +} + +.content-card:hover { + box-shadow: 0 0px 4px 0 rgba(0, 0, 0, 0.05), 0 6px 20px 0 rgba(0, 0, 0, 0.05); + opacity: 1; +} + +.content-card-tag { + transition: all 0.15s; + background: #ffab0443; + margin-bottom: 1rem; + background: #ffab04; + color: white; + font-weight: bold; + font-size: 0.7rem; + border-radius: 0.2rem; + padding: 0.25rem 0.7rem; + width: fit-content; + opacity: 0.8; +} + +.content-card-title { + font-weight: bold; + font-size: 1rem; + margin-bottom: 10px; + min-height: 60px; + width: 100%; + opacity: 0.55; + transition: all 0.15s; +} + +.content-card-info { + margin-bottom: 5px; + color: #6c717a; + font-size: 0.9rem; + opacity: 0.55; + transition: all 0.15s; +} + +.content-card-info-spacing { + margin-left: 0.25rem; +} + +.content-card:hover { + .content-card-info { + opacity: 1; + } + + .content-card-title { + opacity: 1; + } + + .content-card-tag { + background: #ffab04; + color: white; + opacity: 1; + } +} diff --git a/app/src/components/CourseNavbar/CourseNavbar.svelte b/app/src/components/CourseNavbar/CourseNavbar.svelte new file mode 100644 index 00000000..fa4e5dc7 --- /dev/null +++ b/app/src/components/CourseNavbar/CourseNavbar.svelte @@ -0,0 +1,5 @@ + + +
diff --git a/app/src/components/CourseNavbar/index.js b/app/src/components/CourseNavbar/index.js new file mode 100644 index 00000000..838228db --- /dev/null +++ b/app/src/components/CourseNavbar/index.js @@ -0,0 +1 @@ +export { default as CourseNavbar } from "./CourseNavbar.svelte"; diff --git a/app/src/components/CourseNavbar/styles.scss b/app/src/components/CourseNavbar/styles.scss new file mode 100644 index 00000000..3eb81ed9 --- /dev/null +++ b/app/src/components/CourseNavbar/styles.scss @@ -0,0 +1,8 @@ +.course-navbar { + display: flex; + height: 100vh; + width: 4rem; + background-color: var(--color-main); + position: sticky; + top: 0; +} diff --git a/app/src/components/LoadingAnimation/LoadingAnimation.svelte b/app/src/components/LoadingAnimation/LoadingAnimation.svelte new file mode 100644 index 00000000..c54cd7a4 --- /dev/null +++ b/app/src/components/LoadingAnimation/LoadingAnimation.svelte @@ -0,0 +1,15 @@ + + +
+
+
+
+
+
+
+
+
+
+
diff --git a/app/src/components/LoadingAnimation/index.js b/app/src/components/LoadingAnimation/index.js new file mode 100644 index 00000000..000598b0 --- /dev/null +++ b/app/src/components/LoadingAnimation/index.js @@ -0,0 +1 @@ +export { default as LoadingAnimation } from "./LoadingAnimation.svelte"; diff --git a/app/src/components/LoadingAnimation/styles.scss b/app/src/components/LoadingAnimation/styles.scss new file mode 100644 index 00000000..0e099b03 --- /dev/null +++ b/app/src/components/LoadingAnimation/styles.scss @@ -0,0 +1,94 @@ +.ball-grid-beat > div { + -webkit-animation-fill-mode: both; + -webkit-animation-iteration-count: infinite; + height: 15px; + border-radius: 100%; + display: inline-block; + background-color: rgb(255, 171, 64); + margin: 2px; +} +@-webkit-keyframes ball-grid-beat { + 50% { + opacity: 0.7; + } + 100% { + opacity: 1; + } +} +@keyframes ball-grid-beat { + 50% { + opacity: 0.7; + } + 100% { + opacity: 1; + } +} +.ball-grid-beat { + width: 57px; + margin-top: 250px; + margin-left: 500px; +} +.ball-grid-beat > div:nth-child(1) { + -webkit-animation-delay: 0.15s; + animation-delay: 0.15s; + -webkit-animation-duration: 1.45s; + animation-duration: 1.45s; +} +.ball-grid-beat > div:nth-child(2) { + -webkit-animation-delay: -20ms; + animation-delay: -20ms; + -webkit-animation-duration: 0.97s; + animation-duration: 0.97s; +} +.ball-grid-beat > div:nth-child(3) { + -webkit-animation-delay: 0.66s; + animation-delay: 0.66s; + -webkit-animation-duration: 1.23s; + animation-duration: 1.23s; +} +.ball-grid-beat > div:nth-child(4) { + -webkit-animation-delay: 0.64s; + animation-delay: 0.64s; + -webkit-animation-duration: 1.24s; + animation-duration: 1.24s; +} +.ball-grid-beat > div:nth-child(5) { + -webkit-animation-delay: -0.19s; + animation-delay: -0.19s; + -webkit-animation-duration: 1.13s; + animation-duration: 1.13s; +} +.ball-grid-beat > div:nth-child(6) { + -webkit-animation-delay: 0.69s; + animation-delay: 0.69s; + -webkit-animation-duration: 1.42s; + animation-duration: 1.42s; +} +.ball-grid-beat > div:nth-child(7) { + -webkit-animation-delay: 0.58s; + animation-delay: 0.58s; + -webkit-animation-duration: 1.14s; + animation-duration: 1.14s; +} +.ball-grid-beat > div:nth-child(8) { + -webkit-animation-delay: 0.21s; + animation-delay: 0.21s; + -webkit-animation-duration: 1.17s; + animation-duration: 1.17s; +} +.ball-grid-beat > div:nth-child(9) { + -webkit-animation-delay: -0.18s; + animation-delay: -0.18s; + -webkit-animation-duration: 0.65s; + animation-duration: 0.65s; +} +.ball-grid-beat > div { + width: 15px; + animation-fill-mode: both; + float: right; + -webkit-animation-name: ball-grid-beat; + animation-name: ball-grid-beat; + animation-iteration-count: infinite; + -webkit-animation-delay: 0; + animation-delay: 0; +} diff --git a/app/src/components/index.js b/app/src/components/index.js new file mode 100644 index 00000000..48b1ed7e --- /dev/null +++ b/app/src/components/index.js @@ -0,0 +1,4 @@ +export { Button } from "./Button"; +export { ContentCard } from "./ContentCard"; +export { CourseNavbar } from "./CourseNavbar"; +export { LoadingAnimation } from "./LoadingAnimation"; diff --git a/app/src/data/README.md b/app/src/data/README.md new file mode 100644 index 00000000..e7189b64 --- /dev/null +++ b/app/src/data/README.md @@ -0,0 +1,7 @@ +# Data + +- **guides**: used for static guides, probably written in markdown +- **labs**: used for labs, they store a list of question factories that can appear in that lab +- **lectures**: used for lectures and their timestamps +- **questions**: used for storing simple questions +- **tests**: used for storing tests which are collections of questions found in the questions directory diff --git a/app/src/data/Repository.js b/app/src/data/Repository.js new file mode 100644 index 00000000..0cb92159 --- /dev/null +++ b/app/src/data/Repository.js @@ -0,0 +1,132 @@ +import { parseXmlToJson } from "../utilities/xml"; + +class Repository { + fetchCourse = (courseCode) => { + let courseJson = this.#loadCourse(courseCode); + let tests = this.#loadCourseContent(courseCode, "tests"); + let labs = this.#loadCourseContent(courseCode, "labs"); + + // TODO: this is kinda hacky, but it works for now + courseJson.tests = tests; + courseJson.labs = labs; + + return courseJson; + }; + + // TODO: update this method to take a course code and test id + fetchTest = (testFilePath) => { + // load the test from the data folder + let testJson = this.#loadTest(testFilePath); + + // load all the questions listed on the test + let testJsonQuestions = this.#loadTestQuestions(testJson.questions); + + // TODO: fix this, its kinda dirty + // replace the questions array with the questions loaded from the data folder + testJson.questions = testJsonQuestions; + + return testJson; + }; + + // TODO: update this method to take a course code and lab id + fetchLab = (labFilePath) => { + return this.#loadLab(labFilePath); + }; + + // private ------------------------------------------------------------ + + #loadCourseContent = (courseCode, resource) => { + let resources = []; + try { + fs.readdirSync(`./src/data/${resource}/${courseCode}`).forEach(function ( + file + ) { + let data = fs.readFileSync( + `./src/data/${resource}/${courseCode}/${file}` + ); + resources.push(JSON.parse(data.toString())); + }); + return resources; + } catch (err) { + console.log(err); + } + }; + + // loads json test data + #loadTest = (testFilePath) => { + // TODO: throw error if the file does not exist + let data = fs.readFileSync(`./src/data/tests/${testFilePath}.json`); + return JSON.parse(data.toString()); + }; + + // loads xml questions and converts them to json + #loadTestQuestions = (questionFileNames) => { + let questions = []; + + for (const file of questionFileNames) { + // TODO: throw error if the file does not exist + const xmlQuestion = parseXmlToJson(`questions/${file}`); + const jsonQuestion = this.#transformXmlQuestionToJson(xmlQuestion); + + questions.push(jsonQuestion); + } + + return questions; + }; + + // convert an xml question to json + #transformXmlQuestionToJson = (xmlQuestion) => { + if (xmlQuestion["multiple-choice"] !== undefined) { + return { + body: xmlQuestion["multiple-choice"].question, + type: "MultipleChoice", + lab: null, + factory: null, + options: xmlQuestion["multiple-choice"].answer.map((xmlOption) => + this.#transformXmlOptionToJson(xmlOption) + ), + }; + } + + const questionData = xmlQuestion.question["$"]; + + switch (questionData.type) { + case "MultipleChoice": + return { + body: xmlQuestion.question._, + type: questionData.type, + lab: questionData.lab || null, + factory: questionData.factory, + options: xmlQuestion.question.option.map((xmlOption) => + this.#transformXmlOptionToJson(xmlOption) + ), + }; + default: + throw "ERROR: Unsupported question type."; + } + }; + + // convert an xml option from a MultipleChoice question to json + #transformXmlOptionToJson = (xmlOption) => { + return { + body: xmlOption._, + correct: xmlOption["$"].correct === "true", + }; + }; + + // loads json lab data + #loadLab = (labsFilePath) => { + // TODO: throw error if the file does not exist + let data = fs.readFileSync(`./src/data/labs/${labsFilePath}.json`); + return JSON.parse(data.toString()); + }; + + // loads json course data + #loadCourse = (courseFilePath) => { + // TODO: throw error if the file does not exist + let data = fs.readFileSync(`./src/data/courses/${courseFilePath}.json`); + return JSON.parse(data.toString()); + }; +} + +export { Repository }; diff --git a/app/src/data/courses/comp1805.json b/app/src/data/courses/comp1805.json new file mode 100644 index 00000000..e6f9bfec --- /dev/null +++ b/app/src/data/courses/comp1805.json @@ -0,0 +1,6 @@ +{ + "id": "comp1805", + "title": "Discrete Structures I", + "code": "COMP 1805", + "description": "Introduction to discrete mathematics and discrete structures. Topics include: propositional logic, predicate calculus, set theory, complexity of algorithms, mathematical reasoning and proof techniques, recurrences, induction, finite automata and graph theory. Material is illustrated through examples from computing." +} diff --git a/app/src/data/courses/comp2804.json b/app/src/data/courses/comp2804.json new file mode 100644 index 00000000..7a447a41 --- /dev/null +++ b/app/src/data/courses/comp2804.json @@ -0,0 +1,6 @@ +{ + "id": "comp2804", + "title": "Discrete Structures II", + "code": "COMP 2804", + "description": "A second course in discrete mathematics and discrete structures. Topics include: counting, sequences and sums, discrete probability, basic statistics, recurrence relations, randomized algorithms. Material is illustrated through examples from computing." +} diff --git a/app/src/data/guides/comp2804/test.md b/app/src/data/guides/comp2804/test.md new file mode 100644 index 00000000..3bafbed3 --- /dev/null +++ b/app/src/data/guides/comp2804/test.md @@ -0,0 +1,315 @@ +--- +title: "Test Guide" +last_updated: 2022-06-01T00:00:00Z +draft: false +author: "Test Author" +--- + +# Markdown: Syntax + +- [Overview](#overview) + - [Philosophy](#philosophy) + - [Inline HTML](#html) + - [Automatic Escaping for Special Characters](#autoescape) +- [Block Elements](#block) + - [Paragraphs and Line Breaks](#p) + - [Headers](#header) + - [Blockquotes](#blockquote) + - [Lists](#list) + - [Code Blocks](#precode) + - [Horizontal Rules](#hr) +- [Span Elements](#span) + - [Links](#link) + - [Emphasis](#em) + - [Code](#code) + - [Images](#img) +- [Miscellaneous](#misc) + - [Backslash Escapes](#backslash) + - [Automatic Links](#autolink) + +**Note:** This document is itself written using Markdown; you +can [see the source for it by adding '.text' to the URL](/projects/markdown/syntax.text). + +--- + +## Overview + +### Philosophy + +Markdown is intended to be as easy-to-read and easy-to-write as is feasible. + +Readability, however, is emphasized above all else. A Markdown-formatted +document should be publishable as-is, as plain text, without looking +like it's been marked up with tags or formatting instructions. While +Markdown's syntax has been influenced by several existing text-to-HTML +filters -- including [Setext](http://docutils.sourceforge.net/mirror/setext.html), [atx](http://www.aaronsw.com/2002/atx/), [Textile](http://textism.com/tools/textile/), [reStructuredText](http://docutils.sourceforge.net/rst.html), +[Grutatext](http://www.triptico.com/software/grutatxt.html), and [EtText](http://ettext.taint.org/doc/) -- the single biggest source of +inspiration for Markdown's syntax is the format of plain text email. + +## Block Elements + +### Paragraphs and Line Breaks + +A paragraph is simply one or more consecutive lines of text, separated +by one or more blank lines. (A blank line is any line that looks like a +blank line -- a line containing nothing but spaces or tabs is considered +blank.) Normal paragraphs should not be indented with spaces or tabs. + +The implication of the "one or more consecutive lines of text" rule is +that Markdown supports "hard-wrapped" text paragraphs. This differs +significantly from most other text-to-HTML formatters (including Movable +Type's "Convert Line Breaks" option) which translate every line break +character in a paragraph into a `
` tag. + +When you _do_ want to insert a `
` break tag using Markdown, you +end a line with two or more spaces, then type return. + +### Headers + +Markdown supports two styles of headers, [Setext] [1] and [atx] [2]. + +Optionally, you may "close" atx-style headers. This is purely +cosmetic -- you can use this if you think it looks better. The +closing hashes don't even need to match the number of hashes +used to open the header. (The number of opening hashes +determines the header level.) + +### Blockquotes + +Markdown uses email-style `>` characters for blockquoting. If you're +familiar with quoting passages of text in an email message, then you +know how to create a blockquote in Markdown. It looks best if you hard +wrap the text and put a `>` before every line: + +> This is a blockquote with two paragraphs. Lorem ipsum dolor sit amet, +> consectetuer adipiscing elit. Aliquam hendrerit mi posuere lectus. +> Vestibulum enim wisi, viverra nec, fringilla in, laoreet vitae, risus. +> +> Donec sit amet nisl. Aliquam semper ipsum sit amet velit. Suspendisse +> id sem consectetuer libero luctus adipiscing. + +Markdown allows you to be lazy and only put the `>` before the first +line of a hard-wrapped paragraph: + +> This is a blockquote with two paragraphs. Lorem ipsum dolor sit amet, +> consectetuer adipiscing elit. Aliquam hendrerit mi posuere lectus. +> Vestibulum enim wisi, viverra nec, fringilla in, laoreet vitae, risus. + +> Donec sit amet nisl. Aliquam semper ipsum sit amet velit. Suspendisse +> id sem consectetuer libero luctus adipiscing. + +Blockquotes can be nested (i.e. a blockquote-in-a-blockquote) by +adding additional levels of `>`: + +> This is the first level of quoting. +> +> > This is nested blockquote. +> +> Back to the first level. + +Blockquotes can contain other Markdown elements, including headers, lists, +and code blocks: + +> ## This is a header. +> +> 1. This is the first list item. +> 2. This is the second list item. +> +> Here's some example code: +> +> return shell_exec("echo $input | $markdown_script"); + +Any decent text editor should make email-style quoting easy. For +example, with BBEdit, you can make a selection and choose Increase +Quote Level from the Text menu. + +### Lists + +Markdown supports ordered (numbered) and unordered (bulleted) lists. + +Unordered lists use asterisks, pluses, and hyphens -- interchangably +-- as list markers: + +- Red +- Green +- Blue + +is equivalent to: + +- Red +- Green +- Blue + +and: + +- Red +- Green +- Blue + +Ordered lists use numbers followed by periods: + +1. Bird +2. McHale +3. Parish + +It's important to note that the actual numbers you use to mark the +list have no effect on the HTML output Markdown produces. The HTML +Markdown produces from the above list is: + +If you instead wrote the list in Markdown like this: + +1. Bird +1. McHale +1. Parish + +or even: + +3. Bird +1. McHale +1. Parish + +you'd get the exact same HTML output. The point is, if you want to, +you can use ordinal numbers in your ordered Markdown lists, so that +the numbers in your source match the numbers in your published HTML. +But if you want to be lazy, you don't have to. + +To make lists look nice, you can wrap items with hanging indents: + +- Lorem ipsum dolor sit amet, consectetuer adipiscing elit. + Aliquam hendrerit mi posuere lectus. Vestibulum enim wisi, + viverra nec, fringilla in, laoreet vitae, risus. +- Donec sit amet nisl. Aliquam semper ipsum sit amet velit. + Suspendisse id sem consectetuer libero luctus adipiscing. + +But if you want to be lazy, you don't have to: + +- Lorem ipsum dolor sit amet, consectetuer adipiscing elit. + Aliquam hendrerit mi posuere lectus. Vestibulum enim wisi, + viverra nec, fringilla in, laoreet vitae, risus. +- Donec sit amet nisl. Aliquam semper ipsum sit amet velit. + Suspendisse id sem consectetuer libero luctus adipiscing. + +List items may consist of multiple paragraphs. Each subsequent +paragraph in a list item must be indented by either 4 spaces +or one tab: + +1. This is a list item with two paragraphs. Lorem ipsum dolor + sit amet, consectetuer adipiscing elit. Aliquam hendrerit + mi posuere lectus. + + Vestibulum enim wisi, viverra nec, fringilla in, laoreet + vitae, risus. Donec sit amet nisl. Aliquam semper ipsum + sit amet velit. + +2. Suspendisse id sem consectetuer libero luctus adipiscing. + +It looks nice if you indent every line of the subsequent +paragraphs, but here again, Markdown will allow you to be +lazy: + +- This is a list item with two paragraphs. + + This is the second paragraph in the list item. You're + + only required to indent the first line. Lorem ipsum dolor + sit amet, consectetuer adipiscing elit. + +- Another item in the same list. + +To put a blockquote within a list item, the blockquote's `>` +delimiters need to be indented: + +- A list item with a blockquote: + + > This is a blockquote + > inside a list item. + +To put a code block within a list item, the code block needs +to be indented _twice_ -- 8 spaces or two tabs: + +- A list item with a code block: + + + +### Code Blocks + +Pre-formatted code blocks are used for writing about programming or +markup source code. Rather than forming normal paragraphs, the lines +of a code block are interpreted literally. Markdown wraps a code block +in both `
` and `` tags.
+
+To produce a code block in Markdown, simply indent every line of the
+block by at least 4 spaces or 1 tab.
+
+This is a normal paragraph:
+
+    This is a code block.
+
+Here is an example of AppleScript:
+
+    tell application "Foo"
+        beep
+    end tell
+
+A code block continues until it reaches a line that is not indented
+(or the end of the article).
+
+Within a code block, ampersands (`&`) and angle brackets (`<` and `>`)
+are automatically converted into HTML entities. This makes it very
+easy to include example HTML source code using Markdown -- just paste
+it and indent it, and Markdown will handle the hassle of encoding the
+ampersands and angle brackets. For example, this:
+
+    

+        © 2004 Foo Corporation
+    

+
+Regular Markdown syntax is not processed within code blocks. E.g.,
+asterisks are just literal asterisks within a code block. This means
+it's also easy to use Markdown to write about Markdown's own syntax.
+
+```
+tell application "Foo"
+    beep
+end tell
+```
+
+## Span Elements
+
+### Links
+
+Markdown supports two style of links: _inline_ and _reference_.
+
+In both styles, the link text is delimited by [square brackets].
+
+To create an inline link, use a set of regular parentheses immediately
+after the link text's closing square bracket. Inside the parentheses,
+put the URL where you want the link to point, along with an _optional_
+title for the link, surrounded in quotes. For example:
+
+This is [an example](http://example.com/) inline link.
+
+[This link](http://example.net/) has no title attribute.
+
+### Emphasis
+
+Markdown treats asterisks (`*`) and underscores (`_`) as indicators of
+emphasis. Text wrapped with one `*` or `_` will be wrapped with an
+HTML `` tag; double `*`'s or `_`'s will be wrapped with an HTML
+`` tag. E.g., this input:
+
+_single asterisks_
+
+_single underscores_
+
+**double asterisks**
+
+**double underscores**
+
+### Code
+
+To indicate a span of code, wrap it with backtick quotes (`` ` ``).
+Unlike a pre-formatted code block, a code span indicates code within a
+normal paragraph. For example:
+
+Use the `printf()` function.
diff --git a/app/src/data/index.js b/app/src/data/index.js
new file mode 100644
index 00000000..5db35990
--- /dev/null
+++ b/app/src/data/index.js
@@ -0,0 +1 @@
+export { Repository } from "./Repository";
diff --git a/app/src/data/labs/comp1805/asymtopic-analysis.json b/app/src/data/labs/comp1805/asymtopic-analysis.json
new file mode 100644
index 00000000..8c291981
--- /dev/null
+++ b/app/src/data/labs/comp1805/asymtopic-analysis.json
@@ -0,0 +1,5 @@
+{
+  "id": "asymtopic-analysis",
+  "title": "Practice Asymtopic Analysis",
+  "factories": ["DesmosAsymtopicAnalysis", "DesmosAsymtopicAnalysisPolynomial"]
+}
diff --git a/app/src/data/labs/comp2804/how-many-functions.json b/app/src/data/labs/comp2804/how-many-functions.json
new file mode 100644
index 00000000..117f5552
--- /dev/null
+++ b/app/src/data/labs/comp2804/how-many-functions.json
@@ -0,0 +1,9 @@
+{
+  "id": "how-many-functions",
+  "title": "Practice 'How Many Functions' Problems",
+  "factories": [
+    "HowManyFunctions",
+    "HowManyNonOneToOneFunctions",
+    "HowManyOneToOneFunctions"
+  ]
+}
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f01.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f01.xml
new file mode 100644
index 00000000..c24859b4
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f01.xml
@@ -0,0 +1,12 @@
+
+
+
+    
+    
+    
+    
+    
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f02.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f02.xml
new file mode 100644
index 00000000..022ac0f1
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f02.xml
@@ -0,0 +1,12 @@
+
+
+
+    
+    
+    
+    
+    
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f03.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f03.xml
new file mode 100644
index 00000000..29558980
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f03.xml
@@ -0,0 +1,12 @@
+
+
+
+    not one-to-one?
+    ]]>
+    
+    
+    
+    
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f04.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f04.xml
new file mode 100644
index 00000000..17479ac0
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f04.xml
@@ -0,0 +1,12 @@
+
+
+
+	identical blocks of wood.
+		How many ways are there to arrange these books and blocks in a straight line?
+	]]>
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f05.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f05.xml
new file mode 100644
index 00000000..ffc61639
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f05.xml
@@ -0,0 +1,12 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f06.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f06.xml
new file mode 100644
index 00000000..7ebe5d35
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f06.xml
@@ -0,0 +1,11 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f07.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f07.xml
new file mode 100644
index 00000000..d8ca4a9a
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f07.xml
@@ -0,0 +1,12 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f08.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f08.xml
new file mode 100644
index 00000000..be1fd94c
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f08.xml
@@ -0,0 +1,12 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f09.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f09.xml
new file mode 100644
index 00000000..cb6c05a9
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f09.xml
@@ -0,0 +1,12 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f10.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f10.xml
new file mode 100644
index 00000000..c49ff9af
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f10.xml
@@ -0,0 +1,12 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f11.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f11.xml
new file mode 100644
index 00000000..2c80e3c9
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f11.xml
@@ -0,0 +1,11 @@
+
+
+
+	
+	
+	
+	
+	
+
diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f12.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f12.xml
new file mode 100644
index 00000000..19b70929
--- /dev/null
+++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f12.xml
@@ -0,0 +1,27 @@
+
+
+
+	
+			$\newcommand{\Fib}{{\rm F \scriptsize IB}}$
+
+ + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

+ $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
+ $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
+ $\mathbf{then}\ f = n$
+ $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
+ $\mathbf{endif};$
+ $\mathbf{return}\ f$
+

+ + When running $\Fib(7)$, how many calls are there to $\Fib(3)$? + ]]> + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f13.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f13.xml new file mode 100644 index 00000000..b2cdf1cd --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f13.xml @@ -0,0 +1,26 @@ + + + + + + Consider again the recursive algorithm $\Fib$, which takes as input an integer $n \geq 0$: + +

+ $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
+ $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
+ $\mathbf{then}\ f = n$
+ $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
+ $\mathbf{endif};$
+ $\mathbf{return}\ f$
+

+ + For $n \geq 3$, run algorithm $\Fib(n)$ and let $a_n$ be the number of times that $\Fib(1)$ is called.
+ Which of the following is true? + ]]> + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f14.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f14.xml new file mode 100644 index 00000000..8d0686c4 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f14.xml @@ -0,0 +1,26 @@ + + + + + + + $f(0)$ + $\;=\;$ + $7,$ + + + $f(n + 1)$ + $\;=\;$ + $f(n) + 6n + 1\; \ \text{for all}$ $\text{integers}\ n \geq 0.$ + + + + Which of the following is true? + ]]> + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f15.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f15.xml new file mode 100644 index 00000000..ac91dcf0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f15.xml @@ -0,0 +1,12 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f16.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f16.xml new file mode 100644 index 00000000..bfa06da6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f16.xml @@ -0,0 +1,12 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f17.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f17.xml new file mode 100644 index 00000000..5bfcc192 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f17.xml @@ -0,0 +1,14 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f18.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f18.xml new file mode 100644 index 00000000..aedf4177 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f18.xml @@ -0,0 +1,16 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f19.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f19.xml new file mode 100644 index 00000000..0f422c94 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f19.xml @@ -0,0 +1,17 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f20.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f20.xml new file mode 100644 index 00000000..d1a88eef --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f20.xml @@ -0,0 +1,18 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f21.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f21.xml new file mode 100644 index 00000000..11d55e0c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f21.xml @@ -0,0 +1,14 @@ + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f22.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f22.xml new file mode 100644 index 00000000..4f77fcb1 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f22.xml @@ -0,0 +1,14 @@ + + + + + + + \ No newline at end of file diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f23.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f23.xml new file mode 100644 index 00000000..5510d58d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f23.xml @@ -0,0 +1,15 @@ + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f24.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f24.xml new file mode 100644 index 00000000..5f09bc7d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f24.xml @@ -0,0 +1,12 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f25.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f25.xml new file mode 100644 index 00000000..138a2033 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f25.xml @@ -0,0 +1,10 @@ + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f26.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f26.xml new file mode 100644 index 00000000..f0a60133 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f26.xml @@ -0,0 +1,12 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f27.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f27.xml new file mode 100644 index 00000000..b640d576 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f27.xml @@ -0,0 +1,14 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f28.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f28.xml new file mode 100644 index 00000000..b10c368f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f28.xml @@ -0,0 +1,13 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f29.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f29.xml new file mode 100644 index 00000000..81b92acc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f29.xml @@ -0,0 +1,16 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f30.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f30.xml new file mode 100644 index 00000000..e1184dd8 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f30.xml @@ -0,0 +1,12 @@ + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f31.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f31.xml new file mode 100644 index 00000000..73a010f7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f31.xml @@ -0,0 +1,21 @@ + + + + + + Assume that the vertex set of $K_n$ is $\{1,2,3,\dots,n\}$. Let $K'$ be the subgraph of $K_n$ + induced by the vertices $1,2, \dots,k$ (i.e., an edge $(i,j)$ of $K_n$ is in $K'$ if and only if + both $i$ and $j$ are at most $k$). Let $A$ be the event + [defs] + A = "all edges of $K'$ have the same color." + [/defs] + What is $\Pr(A)$? + ]]> + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f32.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f32.xml new file mode 100644 index 00000000..ae23c5d9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f32.xml @@ -0,0 +1,13 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/f13f33.xml b/app/src/data/questions/comp2804/exam-fall-2013/f13f33.xml new file mode 100644 index 00000000..eb53ad87 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/f13f33.xml @@ -0,0 +1,8 @@ + + + + + + diff --git a/app/src/data/questions/comp2804/exam-fall-2013/test.xml b/app/src/data/questions/comp2804/exam-fall-2013/test.xml new file mode 100644 index 00000000..ca5e8970 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2013/test.xml @@ -0,0 +1,413 @@ + + + + + + + + + + + + + + + + not one-to-one? + ]]> + + + + + + + identical blocks of wood. + How many ways are there to arrange these books and blocks in a straight line? + ]]> + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ +
+ + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

+ $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
+ $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
+ $\mathbf{then}\ f = n$
+ $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
+ $\mathbf{endif};$
+ $\mathbf{return}\ f$
+

+ + When running $\Fib(7)$, how many calls are there to $\Fib(3)$? + ]]> + + + + + + + + + Consider again the recursive algorithm $\Fib$, which takes as input an integer $n \geq 0$: + +

+ $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
+ $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
+ $\mathbf{then}\ f = n$
+ $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
+ $\mathbf{endif};$
+ $\mathbf{return}\ f$
+

+ + For $n \geq 3$, run algorithm $\Fib(n)$ and let $a_n$ be the number of times that $\Fib(1)$ is called.
+ Which of the following is true? + ]]> + + + + + + + + + + + + + + + + + $f(0)$ + $\;=\;$ + $7,$ + + + $f(n + 1)$ + $\;=\;$ + $f(n) + 6n + 1\; \ \text{for all}$ $\text{integers}\ n \geq 0.$ + + + + Which of the following is true? + ]]> + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Assume that the vertex set of $K_n$ is $\{1,2,3,\dots,n\}$. Let $K'$ be the subgraph of $K_n$ + induced by the vertices $1,2, \dots,k$ (i.e., an edge $(i,j)$ of $K_n$ is in $K'$ if and only if + both $i$ and $j$ are at most $k$). Let $A$ be the event + [defs] + A = "all edges of $K'$ have the same color." + [/defs] + What is $\Pr(A)$? + ]]> + + + + + + + + + + + + +How do you fe + + \ No newline at end of file diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f01.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f01.xml new file mode 100644 index 00000000..4bc50e7e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f01.xml @@ -0,0 +1,12 @@ + + + + A password must contain exactly one odd digit. How many passwords are there? + ]]> + + $13 \cdot 5^{12}$ + $13 \cdot 5^{13}$ + $13 \cdot 9^{12}$ + $13 \cdot 5 \cdot 9^{12}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f02.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f02.xml new file mode 100644 index 00000000..96f03605 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f02.xml @@ -0,0 +1,13 @@ + + + + A password must contain at least one odd digit and at most two even digits. How many passwords are + there? + ]]> + + $5^{12} + 13 \cdot 5^{12} + {13 \choose 2}5^{12}$ + $5^{13} + 13 \cdot 9^{12} + {13 \choose 2}9^{12}$ + $5^{13} + 13 \cdot 5^{13} + {13 \choose 2}5^{13}$ + $5 \cdot 9^{12} + 13 \cdot 5 \cdot 9^{12} + {13 \choose 2}5 \cdot 9^{12}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f03.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f03.xml new file mode 100644 index 00000000..a6f8dbc7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f03.xml @@ -0,0 +1,14 @@ + + + + + $(-2)^{45}$ + $4^{45}$ + $(-8)^{45}$ + $10^{45}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f04.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f04.xml new file mode 100644 index 00000000..b34652b7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f04.xml @@ -0,0 +1,11 @@ + + + + + $2^{10} + 2^{11}$ + $3 \cdot 2^{10} - 2^{8}$ + $2^{13} - (2^{10} + 2^{11})$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f05.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f05.xml new file mode 100644 index 00000000..7fc4efe2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f05.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2}\ \mathrm{for}\ n \geq 3.$ + $S_n = S_{n-1} + S_{n-3}\ \mathrm{for}\ n \geq 3.$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}\ \mathrm{for}\ n \geq 3.$ + $S_n = 2 \cdot S_{n-1}\ \mathrm{for}\ n \geq 3.$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f06.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f06.xml new file mode 100644 index 00000000..4080934a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f06.xml @@ -0,0 +1,23 @@ + + + +
  • + 40 like 8:30am classes, +
    • +
  • + 30 like the course COMP 2804, +
    • +
  • + 50 do not like 8:30am classes and do not like the course COMP 2804. +
    • + + How many students in this group like 8:30am classes and like the course COMP 2804? + ]]> +     + 10 + 20 + 30 + 40 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f07.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f07.xml new file mode 100644 index 00000000..b8353a12 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f07.xml @@ -0,0 +1,13 @@ + + + + + $7!{m \choose 7} + 7!{n \choose 7}$ + $m!{m \choose 7} + n!{n \choose 7}$ + $7!{m + n \choose 7}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f08.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f08.xml new file mode 100644 index 00000000..ca69cbd1 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f08.xml @@ -0,0 +1,11 @@ + + + + + $10!$ + $\frac{10!}{2!3!5!}$ + ${10 \choose 3}{10 \choose 2}{10 \choose 5}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f09.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f09.xml new file mode 100644 index 00000000..3c5e8138 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f09.xml @@ -0,0 +1,12 @@ + + + + + ${13 \choose 2}$ + ${14 \choose 2}$ + ${15 \choose 2}$ + ${16 \choose 2}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f10.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f10.xml new file mode 100644 index 00000000..7f2bb29a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f10.xml @@ -0,0 +1,24 @@ + + + + + + $f(0) = $ + $-17,$ + + + $f(n) = $ + $f(n - 1) + 8n - 2\; \ \text{for all}$ $\text{integers}\ n \geq 1.$ + + + + Which of the following is true? + ]]> + + for all $n \geq 0$: $f(n) = 3n^{2} - n - 17$ + for all $n \geq 0$: $f(n) = 3n^{2} + n - 17$ + for all $n \geq 0$: $f(n) = 4n^{2} - 2n - 17$ + for all $n \geq 0$: $f(n) = 4n^{2} + 2n - 17$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f11.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f11.xml new file mode 100644 index 00000000..de7cf924 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f11.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ +
    + + Consider the recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + If we run algorithm $\Fib(20)$, how many calls are there to $\Fib(16)$? + ]]> + + 4 + 5 + 6 + 7 + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f12.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f12.xml new file mode 100644 index 00000000..68224de0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f12.xml @@ -0,0 +1,12 @@ + + + + + $\frac{{5 \choose 2} + {4 \choose 2} + {6 \choose 2}}{{15 \choose 2}}$ + $\frac{{15 \choose 2}}{{5 \choose 2} + {4 \choose 2} + {6 \choose 2}}$ + $\frac{{5 \choose 2}{4 \choose 2}{6 \choose 2}}{{15 \choose 2}}$ + $\frac{{15 \choose 2}}{{5 \choose 2}{4 \choose 2}{6 \choose 2}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f13.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f13.xml new file mode 100644 index 00000000..bdf100cd --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f13.xml @@ -0,0 +1,12 @@ + + + + + $\frac{1}{364 \cdot 365}$ + $\frac{1}{365^2}$ + $\frac{365}{364^{2}}$ + $\frac{1}{365^{3}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f14.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f14.xml new file mode 100644 index 00000000..f8c2f394 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f14.xml @@ -0,0 +1,13 @@ + + + + + $1 - (1/2)^{7}$ + $\sum_{k=0}^{7} (1/2)^{k}$ + $\sum_{k=0}^{7} (1/2)^{k+1}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f15.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f15.xml new file mode 100644 index 00000000..9378cdea --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f15.xml @@ -0,0 +1,17 @@ + + + + + $\frac{{4 \choose 2}}{{5 \choose 2} + {4 \choose 2}}$ + $\frac{{5 \choose 2} + {4 \choose 2}}{{4 \choose 2}}$ + $\frac{{4 \choose 2}}{{9 \choose 2}}$ + $\frac{{4 \choose 2}}{{5 \choose 2}{4 \choose 2}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f16.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f16.xml new file mode 100644 index 00000000..78bdc0a0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f16.xml @@ -0,0 +1,16 @@ + + + + + 3/10 + 1/3 + 1/2 + 2/3 + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f17.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f17.xml new file mode 100644 index 00000000..be64a0f4 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f17.xml @@ -0,0 +1,18 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f18.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f18.xml new file mode 100644 index 00000000..2b910a44 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f18.xml @@ -0,0 +1,18 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f19.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f19.xml new file mode 100644 index 00000000..b0fd3107 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f19.xml @@ -0,0 +1,20 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f20.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f20.xml new file mode 100644 index 00000000..b6c80a7e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f20.xml @@ -0,0 +1,13 @@ + + + + + $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{1}{4} \cdot \frac{1}{3} + \frac{3}{4} \cdot \frac{1}{4}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f21.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f21.xml new file mode 100644 index 00000000..bc6a0fc0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f21.xml @@ -0,0 +1,14 @@ + + + + + 2 + 1 + 1/4 + 1/2 + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f22.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f22.xml new file mode 100644 index 00000000..dcb9061d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f22.xml @@ -0,0 +1,18 @@ + + + + + 2/5 + 2 + 5/2 + 5 + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f23.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f23.xml new file mode 100644 index 00000000..c152c5ba --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f23.xml @@ -0,0 +1,37 @@ + + + + $\newcommand{\ThreeHeadsOrThreeTails}{{\rm T {\scriptsize HREE} H {\scriptsize EADS} O {\scriptsize R} T {\scriptsize HREE} T {\scriptsize AILS}}}$ +
    + + Consider the following recursive algorithm $\ThreeHeadsOrThreeTails$, which takes as input a positive integer $k$: + +
    + $\mathbf{Algorithm}$ $\ThreeHeadsOrThreeTails(k)\mathrm{:}$
    + + + + + + + +
    $//$ + $\text{all coin flips made}$ $\text{are mutually independent}$ +
    + $\text{flip a fair coin three times};$
    + $\mathbf{if}\ \text{the result is \(HHH\) or \(TTT\)}$
    + $\mathbf{then}\ \mathrm{return}\ k$
    + $\mathbf{else}\ \ThreeHeadsOrThreeTails(k + 1)$
    + $\mathbf{endif}$ +
    + + You run algorithm $\ThreeHeadsOrThreeTails(1)$, i.e., with $k = 1$. Define the random variable $X$ to be the value of the output + of this algorithm. What is the expected value of $X$? + ]]> + + 2 + 3 + 4 + 5 + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f24.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f24.xml new file mode 100644 index 00000000..7b1c6f10 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f24.xml @@ -0,0 +1,15 @@ + + + + + $-n/2$ + $n/2$ + $-n$ + $n$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2014/f14f25.xml b/app/src/data/questions/comp2804/exam-fall-2014/f14f25.xml new file mode 100644 index 00000000..d6789cfe --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2014/f14f25.xml @@ -0,0 +1,7 @@ + + Who invented the Fibonacci numbers? + Justin Bieber + Britney Spears + Fibonacci + Carl Friedrich Gauss + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f01.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f01.xml new file mode 100644 index 00000000..b3e9617b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f01.xml @@ -0,0 +1,13 @@ + + + + + ${20 \choose 3}$ + ${15 \choose 3}$ + ${15 \choose 3} + 15 \cdot {5 \choose 2}$ + ${15 \choose 3} + {15 \choose 2} \cdot 5 + 15 \cdot {5 \choose 2}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f02.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f02.xml new file mode 100644 index 00000000..78ec8b0e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f02.xml @@ -0,0 +1,14 @@ + + + + + ${19 \choose 6}$ + ${19 \choose 7}$ + ${20 \choose 6}$ + ${20}\choose{7}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f03.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f03.xml new file mode 100644 index 00000000..71638a4f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f03.xml @@ -0,0 +1,12 @@ + + + + + $2^{17} - 2^{15}$ + $2^{17} - 2^{16}$ + $2^{18} - 2^{16}$ + $2^{18} - 2^{17}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f04.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f04.xml new file mode 100644 index 00000000..a721dce3 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f04.xml @@ -0,0 +1,11 @@ + + + + + ${20 \choose 5} \cdot 3^{15} \cdot 5^5$ + $- {20 \choose 5} \cdot 3^{15} \cdot 5^5$ + ${20 \choose 5} \cdot 5^{15} \cdot 3^5$ + $- {20 \choose 5} \cdot 5^{15} \cdot 3^5$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f05.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f05.xml new file mode 100644 index 00000000..1780940c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f05.xml @@ -0,0 +1,23 @@ + + + +
  • + 10 are blond, +
    • +
  • + 20 have green eyes, +
    • +
  • + 9 are not blond and do not have green eyes. +
    • + + How many people in this group are blond and have green eyes? + ]]> +     + 8 + 9 + 10 + 11 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f06.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f06.xml new file mode 100644 index 00000000..536c7931 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f06.xml @@ -0,0 +1,12 @@ + + + + + $S_n = n \cdot 2^{n-1}$ + $S_n = n \cdot 3^{n-1}$ + $S_n = 3^{n} - n$ + $S_n = 3^{n} - 2^{n}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f07.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f07.xml new file mode 100644 index 00000000..11a49afc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f07.xml @@ -0,0 +1,12 @@ + + + + + $S_n = 2 \cdot S_{n-1} + 3^{n-1}$ + $S_n = 2 \cdot S_{n-1} + 2 \cdot S_{n-2}$ + $S_n = 3 \cdot S_{n-1}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f08.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f08.xml new file mode 100644 index 00000000..b4b6c317 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f08.xml @@ -0,0 +1,24 @@ + + + + + + $f(0) = $ + $7,$ + + + $f(n) = $ + $2 \cdot f(n - 1) + 1\; \ \text{for all}$ $\text{integers}\ n \geq 1.$ + + + + Which of the following is true? + ]]> + + $f(n) = 8n + 7$ + $f(n) = 4n^{2} + 4n + 7$ + $f(n) = 2^{n+3} - 1$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f09.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f09.xml new file mode 100644 index 00000000..e8ed5645 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f09.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ +
    + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + If we run algorithm $\Fib(18)$, how many calls are there to $\Fib(14)$? + ]]> + + 4 + 5 + 6 + 7 + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f10.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f10.xml new file mode 100644 index 00000000..67019f89 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f10.xml @@ -0,0 +1,11 @@ + + + + + $2 \cdot (n-1) \cdot 2^{n-2}$ + $2 \cdot n \cdot 2^{n-1}$ + $2^n - 4$ + $2^n - 2$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f11.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f11.xml new file mode 100644 index 00000000..bd73e2aa --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f11.xml @@ -0,0 +1,15 @@ + + + + + ${79 \choose 4}$ + ${79 \choose 5}$ + ${80 \choose 4}$ + ${80 \choose 5}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f12.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f12.xml new file mode 100644 index 00000000..d33fc4da --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f12.xml @@ -0,0 +1,15 @@ + + + + + $\frac{{5 \choose 2}}{{12 \choose 3}}$ + $\frac{5 \cdot {7 \choose 2}}{{12 \choose 3}}$ + $\frac{{5 \choose 2} \cdot 7}{{12 \choose 3}}$ + $\frac{{7 \choose 2}}{{12 \choose 3}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f13.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f13.xml new file mode 100644 index 00000000..80a5c9ab --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f13.xml @@ -0,0 +1,15 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f14.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f14.xml new file mode 100644 index 00000000..e4afd9c2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f14.xml @@ -0,0 +1,17 @@ + + + + + $n \cdot (1/365) \cdot (364/365)^{n-1}$ + $365 \cdot n \cdot (364/365)^{n-1}$ + $1 - (1/365)^{n}$ + $1 - (364/365)^{n}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f15.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f15.xml new file mode 100644 index 00000000..4d545f44 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f15.xml @@ -0,0 +1,31 @@ + + + +
  • + The course COMP 9999 runs over a period of one year, starting on January 1 and ending on December + 31. There is one lecture every day; thus, the total number of lectures is 365. +
    • +
  • + Dania and Nick take this course. Dania's birthday is on November 19. Nick's birthday is on December + 3. +
    • +
  • + Professor G. Ruesome teaches the course. Professor Ruesome decides to have 20 quizzes during the + year. For this, he chooses a uniformly random subset of 20 days; the quizzes will be on the 20 + chosen days. (It is possible that there is a quiz on January 1.) +
    • + + + Determine $\Pr(A)$, where $A$ is the event + [defs] + A = "There is a quiz on Dania's birthday and there is a quiz on Nick's birthday". + [/defs] + ]]> +     + $1 - \left. {363 \choose 20} \middle/ {365 \choose 20} \right.$ + $\left. {363 \choose 18} \middle/ {365 \choose 20} \right.$ + $\left. {365 \choose 18} \middle/ {365 \choose 20} \right.$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f16.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f16.xml new file mode 100644 index 00000000..e13e1467 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f16.xml @@ -0,0 +1,32 @@ + + + +
  • + The course COMP 9999 runs over a period of one year, starting on January 1 and ending on December + 31. There is one lecture every day; thus, the total number of lectures is 365. +
    • +
  • + Dania and Nick take this course. Dania's birthday is on November 19. Nick's birthday is on December + 3. +
    • +
  • + Professor G. Ruesome teaches the course. Professor Ruesome decides to have 20 quizzes during the + year. For this, he chooses a uniformly random subset of 20 days; the quizzes will be on the 20 + chosen days. (It is possible that there is a quiz on January 1.) +
    • + + + Determine the conditional probability $\Pr(B|C)$, where $B$ and $C$ are the events + [defs] + B = "there is a quiz on Nick's birthday", + C = "there are exactly 5 quizzes in December". + [/defs] + ]]> +     + 4/31 + 5/31 + 4/32 + 5/32 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f17.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f17.xml new file mode 100644 index 00000000..491a50e3 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f17.xml @@ -0,0 +1,26 @@ + + + +
  • + The course COMP 9999 runs over a period of one year, starting on January 1 and ending on December + 31. There is one lecture every day; thus, the total number of lectures is 365. +
    • +
  • + At the beginning of each of the 365 lectures, Nick flips a fair and independent coin twice. + If the coin comes up heads twice, then Nick eats 3 bananas during the lecture; otherwise, + Nick eats 5 bananas during the lecture. +
    • + + + Let $X$ be the total number of bananas that Nick eats during the 365 lectures of the course COMP + 9999. What is the expected value $\mathbb{E}(X)$ of $X$?
    + (n.b., you may find it useful to apply Linearity of Expectation) + ]]> +     + $\frac{9 \cdot 365}{2}$ + $\frac{7 \cdot 365}{2}$ + $\frac{5 \cdot 365}{2}$ + $4 \cdot 365$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f18.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f18.xml new file mode 100644 index 00000000..f3e3a6e0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f18.xml @@ -0,0 +1,19 @@ + + + + Let $X$ be the number of students who give their gift to themselves. What is the expected value + $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use an indicator random variable for each student. +

    + ]]> +     + $1$ + $2$ + $1 + 1/n$ + $2 + 1/n$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f19.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f19.xml new file mode 100644 index 00000000..5695abc1 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f19.xml @@ -0,0 +1,19 @@ + + + + For each $i = 1,2,\dots,n$, let $v_i$ be the value (in dollars) of the gift that student $S_i$ + buys. Let $Y$ be the value of the gift that student $S_1$ receives, and let $Z$ be the value of the + gift that student $S_2$ receives. What is $\mathbb{E}(2 \cdot Y - Z)$? +

    + ]]> +     + $2v_1 - v_2$ + $\sum_{i=3}^{n} v_i/n$ + $\sum_{i=1}^{n} v_i/n$ + $2 \sum_{i=2}^{n} v_i/n - (v_1/n + \sum_{i=3}^{n} v_i/n)$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f20.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f20.xml new file mode 100644 index 00000000..f8330fdc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f20.xml @@ -0,0 +1,19 @@ + + + + + What is the expected value $\mathbb{E}(X)$ of $X$? + ]]> + + 3/8 + 8/3 + 8 + 12 + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f21.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f21.xml new file mode 100644 index 00000000..fc9c103b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f21.xml @@ -0,0 +1,20 @@ + + + + + What is the expected value $\mathbb{E}(X)$ of $X$?
    + Hint: Use indicator random variables. + ]]> +     + $2n/27$ + $2(n-2)/27$ + $(n-2)/8$ + $n/8$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f22.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f22.xml new file mode 100644 index 00000000..6425598b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f22.xml @@ -0,0 +1,22 @@ + + + + + Let $X$ be the size of the set $T'$. + What is the expected value $\mathbb{E}(X)$ of $X$?
    + Hint: Use indicator random variables. + ]]> +     + $n/9$ + $m/9$ + $4n/9$ + $4m/9$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f23.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f23.xml new file mode 100644 index 00000000..9bac8de7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f23.xml @@ -0,0 +1,12 @@ + + + + + 1 + 3/2 + 2 + 5/2 + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f24.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f24.xml new file mode 100644 index 00000000..ce225164 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f24.xml @@ -0,0 +1,38 @@ + + + + $\newcommand{\Heads}{{\rm H \scriptsize EADS}}$ +
    + + Consider a coin that comes up heads with probability 1/3 and, thus, tails with probability 2/3. + Consider the following recursive algorithm $\Heads$, which takes as input a positive integer $k$: + +
    + $\mathbf{Algorithm}\ \Heads(k)\mathrm{:}$
    + + + + + + + +
    $//$ + $\text{all coin flips made}$ $\text{are mutually independent}$ +
    + $\text{flip the coin};$
    + $\mathbf{if}\ \text{the coin came up heads}$
    + $\mathbf{then}\ \mathrm{return}\ k + 1$
    + $\mathbf{else}\ \Heads(k + 1)$
    + $\mathbf{endif}$ +
    + + You run algorithm $\Heads(1)$, i.e., with $k = 1$. Define the random variable $X$ to be the value of + the output of this algorithm. Let $m \geq 1$ be an integer. What is $\Pr(X = m + 1)$? + ]]> + + $2^{m-1}/3^{m}$ + $(2/3)^{m}$ + $2^{m}/3^{m+1}$ + $(2/3)^{m+1}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2015/f15f25.xml b/app/src/data/questions/comp2804/exam-fall-2015/f15f25.xml new file mode 100644 index 00000000..d92a6220 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2015/f15f25.xml @@ -0,0 +1,9 @@ + + + Who discovered Newton's Binomial Theorem? + + Professor Binomial. + Justin Bieber. + Isaac Newton. + Professor G. Ruesome (the guy teaching COMP 9999). + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f01.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f01.xml new file mode 100644 index 00000000..2b153042 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f01.xml @@ -0,0 +1,12 @@ + + + + + $7^9$ + $9^7$ + $7!$ + $9!$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f02.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f02.xml new file mode 100644 index 00000000..02e46142 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f02.xml @@ -0,0 +1,12 @@ + + + + + $\frac{7!}{2}$ + $\frac{7!}{3}$ + $\frac{9!}{2}$ + $\frac{9!}{3}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f03.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f03.xml new file mode 100644 index 00000000..de6a6637 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f03.xml @@ -0,0 +1,11 @@ + + + + + $2^{55} - 2^{48}$ + $2^{51} + 2^{52}$ + $2^{51} + 2^{52} - 2^{48}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f04.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f04.xml new file mode 100644 index 00000000..e2e51ce7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f04.xml @@ -0,0 +1,11 @@ + + + + + The number of bitstrings of length $n$ that have at least two 1's. + The number of bitstrings of length $n$ that have at most two 1's. + The number of subsets of a set of size $n$ that have size at least two. + The number of subsets of a set of size $n$ that have size at least three. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f05.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f05.xml new file mode 100644 index 00000000..1bd5e5c4 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f05.xml @@ -0,0 +1,23 @@ + + + +
  • + 25 drink cider, +
    • +
  • + 50 drink beer, +
    • +
  • + 33 do not drink cider and do not drink beer. +
    • + + How many people in this group drink both cider and beer? + ]]> +     + 8 + 9 + 10 + 11 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f06.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f06.xml new file mode 100644 index 00000000..443a686a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f06.xml @@ -0,0 +1,13 @@ + + + + + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ + $S_n = S_{n-1} + 2 \cdot S_{n-2}$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-3}$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-2}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f07.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f07.xml new file mode 100644 index 00000000..e8fa1ec8 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f07.xml @@ -0,0 +1,13 @@ + + + + + $S_n = {n \choose 2}$ + $S_n = {n \choose 2} - n - 1$ + $S_n = {n \choose 2} - n$ + $S_n = {n \choose 2} - n + 1$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f08.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f08.xml new file mode 100644 index 00000000..fa76de8c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f08.xml @@ -0,0 +1,16 @@ + + + + + $f(n) = \frac{5}{n!}$ + $f(n) = \frac{5^{n}}{n!}$ + $f(n) = \frac{5^{n}}{(n+1)!}$ + $f(n) = \frac{5^{n+1}}{n!}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f09.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f09.xml new file mode 100644 index 00000000..0c05a838 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f09.xml @@ -0,0 +1,30 @@ + + + + $\newcommand{\Hello}{{\rm H {\scriptsize ELLO}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ +
    + + Consider the recursive algorithm $\Hello$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Hello(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \text{print ``hello''}$
    + $\mathbf{else}\ \mathbf{if}\ n\ \mathrm{is}\ \mathrm{even}$
    + $\elsesp \mathbf{then}\ \Hello(n / 2)$
    + $\elsesp \mathbf{else}\ \Hello(n - 1);$
    + $\elsesp \elsesp \Hello(n - 2)$
    + $\elsesp \mathbf{endif};$
    + $\mathbf{endif}$ +

    + + If we run algorithm $\Hello(7)$, how many times is the word "hello" printed? + ]]> + + 4 + 5 + 6 + 7 + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f10.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f10.xml new file mode 100644 index 00000000..e06f4c11 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f10.xml @@ -0,0 +1,13 @@ + + + + + $S_n = 5 \cdot 4^{n-1}$ + $S_n = 5 \cdot 4^{n-2}$ + $S_n = 5^{n} - 5(n-1) \cdot 4^{n-2}$ + $S_n = 5^{n} - 5(n-1) \cdot 4^{n-1}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f11.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f11.xml new file mode 100644 index 00000000..d6452817 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f11.xml @@ -0,0 +1,16 @@ + + + $x_5 \geq 0$ are integers? + ]]> + + ${33 \choose 4}$ + ${33 \choose 5}$ + ${32 \choose 4}$ + ${32 \choose 5}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f12.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f12.xml new file mode 100644 index 00000000..759a82c2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f12.xml @@ -0,0 +1,17 @@ + + + + + 1/3 + 1/4 + 1/5 + 1/6 + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f13.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f13.xml new file mode 100644 index 00000000..5f6a5b6a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f13.xml @@ -0,0 +1,16 @@ + + + + + $\frac{{12 \choose 4}+{8 \choose 3}}{20 \choose 7}$ + $\frac{{12 \choose 4}{8 \choose 3}}{20 \choose 7}$ + $\frac{{20 \choose 3}{17 \choose 4}}{20 \choose 7}$ + $\frac{{20 \choose 4}{16 \choose 3}}{20 \choose 7}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f14.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f14.xml new file mode 100644 index 00000000..9041d246 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f14.xml @@ -0,0 +1,17 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f15.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f15.xml new file mode 100644 index 00000000..5a29de62 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f15.xml @@ -0,0 +1,16 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f16.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f16.xml new file mode 100644 index 00000000..89712421 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f16.xml @@ -0,0 +1,17 @@ + + + + + ${n \choose 2} \cdot \left( \frac{1}{365} \right)^2 \cdot \left( \frac{364}{365} \right)^{n-2}$ + $1 - {n \choose 2} \cdot \left( \frac{1}{365} \right)^2 \cdot \left( \frac{364}{365} \right)^{n-2}$ + $1 - \left( \frac{364}{365} \right)^n - n \cdot \frac{1}{365} \cdot \left( \frac{364}{365} \right)^{n-1}$ + ${\sum_{k=2}^{n}} {n \choose k} \cdot \left( \frac{1}{365} \right)^k$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f17.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f17.xml new file mode 100644 index 00000000..f4644b82 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f17.xml @@ -0,0 +1,15 @@ + + + + + $1 - \frac{{98}\choose{15}}{{100}\choose{17}}$ + $1 - \frac{{100 \choose 2} \cdot {98 \choose 15}}{100 \choose 17}$ + $\frac{2 \cdot {99 \choose 16}}{100 \choose 17}$ + $\frac{2 \cdot {99 \choose 16} - {98 \choose 15}}{100 \choose 17}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f18.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f18.xml new file mode 100644 index 00000000..7606eadc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f18.xml @@ -0,0 +1,15 @@ + + + + + 1/2 + 1/3 + 1/4 + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f19.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f19.xml new file mode 100644 index 00000000..bb9ef31c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f19.xml @@ -0,0 +1,19 @@ + + + + + What is the expected value $\mathbb{E}(X)$ of $X$?
    + Hint: Use indicator random variables. + ]]> +     + $\frac{n-1}{4}$ + $\frac{n}{4}$ + $\frac{n-1}{2}$ + $\frac{n}{2}$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f20.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f20.xml new file mode 100644 index 00000000..69b9555e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f20.xml @@ -0,0 +1,19 @@ + + + + + Define the random variable $X$ to be the number of unordered pairs $\{P_i,P_j\}$ of people that have + the same birthday.
    + + What is the expected value $\mathbb{E}(X)$ of $X$?
    + Hint: Use indicator random variables. + ]]> +     + $\frac{1}{365} \cdot {n \choose 2}$ + $\left( \frac{1}{365} \right)^2 \cdot {n \choose 2}$ + $\frac{1}{365} \cdot n^2$ + $\left( \frac{1}{365} \right)^2 \cdot n^2$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f21.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f21.xml new file mode 100644 index 00000000..8d3ea6c6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f21.xml @@ -0,0 +1,14 @@ + + + + + What is the expected value $\mathbb{E}(X)$ of $X$? + ]]> + + 7/2 + 32/7 + 17/7 + 7/17 + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f22.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f22.xml new file mode 100644 index 00000000..bd04621b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f22.xml @@ -0,0 +1,19 @@ + + + + + The random variables $X$ and $Y$ are independent. + The random variables $X$ and $Y$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f23.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f23.xml new file mode 100644 index 00000000..eff64287 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f23.xml @@ -0,0 +1,28 @@ + + + + + The random variables $X$ and $Y$ are independent. + The random variables $X$ and $Y$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f24.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f24.xml new file mode 100644 index 00000000..aed29a19 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f24.xml @@ -0,0 +1,15 @@ + + + + + What is the expected value $\mathbb{E}(X)$ of $X$? + ]]> + + 2 + 3 + 4 + 5 + diff --git a/app/src/data/questions/comp2804/exam-fall-2016/f16f25.xml b/app/src/data/questions/comp2804/exam-fall-2016/f16f25.xml new file mode 100644 index 00000000..883b2797 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2016/f16f25.xml @@ -0,0 +1,11 @@ + + + + + Beer + Cider + Hot chocolate + Poutine + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f01.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f01.xml new file mode 100644 index 00000000..aab53076 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f01.xml @@ -0,0 +1,21 @@ + + + +
  • + the leftmost 10 bottles are all beer bottles, and +
    • +
  • + the rightmost 10 bottles are all cider bottles. +
    • + + How many such arrangements are there? (The order of the bottles matters.) + ]]> +     + ${20 \choose 10} \cdot {30 \choose 10} \cdot 30!$ + ${20 \choose 10} \cdot 10! \cdot {30 \choose 10} \cdot 10! \cdot 30!$ + ${20 \choose 10} \cdot 10! \cdot {30 \choose 10} \cdot 10!$ + $50!$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f02.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f02.xml new file mode 100644 index 00000000..e17f6121 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f02.xml @@ -0,0 +1,17 @@ + + + awesome if $a_2 = 2 \cdot a_1$.
    + + For example, if $n = 6$, then the permutation $3,6,4,1,5,2$ is awesome, whereas the permutation + $3,5,4,1,6,2$ is not awesome.
    + + How many awesome permutations of the set $\{1,2,\dots,n\}$ are there? + ]]> +     + $n \cdot (n-1)!$ + $n \cdot (n-2)!$ + ${\frac{n}{2}} \cdot (n-1)!$ + ${\frac{n}{2}} \cdot (n-2)!$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f03.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f03.xml new file mode 100644 index 00000000..a82386c5 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f03.xml @@ -0,0 +1,24 @@ + + + cool if +
      +
    • + it contains exactly 8 many $a$'s +
      • +
    + or +
      +
    • + it contains exactly 7 many $b$'s. +
      • +
    + How many cool strings are there? + ]]> +     + ${{40 \choose 8} \cdot 2^{32} + {40 \choose 7} \cdot 2^{33}}$ + ${{40 \choose 8} \cdot 2^{32} + {40 \choose 7} \cdot 2^{33} - {40 \choose 15} \cdot {15 \choose 8} \cdot 2^{25}}$ + ${{40 \choose 8} \cdot 2^{32} + {40 \choose 7} \cdot 2^{33} - {40 \choose 15} \cdot {15 \choose 8}}$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f04.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f04.xml new file mode 100644 index 00000000..5a6d5bb7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f04.xml @@ -0,0 +1,12 @@ + + + + + ${40 \choose 3}$ + $3^{40} - 1 - 40 \cdot 3^{39} - {40 \choose 2} \cdot 3^{38}$ + $3^{40} - 2^{40} - 40 \cdot 2^{39} - {40 \choose 2} \cdot 2^{38}$ + $3^{40} - 2^{40} - 40 \cdot 2^{39} - {40 \choose 2} \cdot 2^{38}\ -$ $ {40 \choose 3} \cdot 2^{37}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f05.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f05.xml new file mode 100644 index 00000000..a4abc7c2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f05.xml @@ -0,0 +1,15 @@ + + + + + The number of subsets having size 3 of a set consisting of $n$ positive numbers and $m$ negative numbers. + The number of subsets having size at most 3 of a set consisting of $n$ positive numbers and $m$ negative numbers. + The number of subsets having size 2 or 3 of a set consisting of $n$ positive numbers and $m$ negative numbers. + The number of subsets having size 2 and 3 of a set consisting of $n$ positive numbers and $m$ negative numbers. + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f06.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f06.xml new file mode 100644 index 00000000..fa305668 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f06.xml @@ -0,0 +1,23 @@ + + + +
  • + 13 students like Donald Trump, +
    • +
  • + 25 students like Justin Bieber, and +
    • +
  • + 8 students like Donald Trump and like Justin Bieber. +
    • + + How many students do not like Donald Trump and do not like Justin Bieber? + ]]> +     + 69 + 70 + 71 + 72 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f07.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f07.xml new file mode 100644 index 00000000..55b719c9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f07.xml @@ -0,0 +1,14 @@ + + + + BOOKKEEPER +

    + ]]> +     + $2! \cdot 2! \cdot 3!$ + ${10 \choose 2} \cdot {8 \choose 2} \cdot {6 \choose 3} \cdot 3 \cdot 2$ + ${10 \choose 2} \cdot {8 \choose 2} \cdot {6 \choose 3} \cdot {3 \choose 2}$ + ${10 \choose 2} \cdot {8 \choose 2} \cdot {5 \choose 3} \cdot 3 \cdot 2$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f08.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f08.xml new file mode 100644 index 00000000..0830cff5 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f08.xml @@ -0,0 +1,18 @@ + + + + + For any integer $n \geq 1$, let $E_n$ be the number of such strings of length $n$ that contain an even + number of $c$'s, and let $O_n$ be the number of such strings of length $n$ that contain an odd + number of $c$'s. (Remember that 0 is an even number.)
    + + Which of the following is true for any integer $n \geq 2$? + ]]> +     + $E_n = 2 \cdot E_{n-1} + O_{n-1}$ + $E_n = 2 \cdot E_{n-1} + E_{n-1}$ + $E_n = 2 \cdot O_{n-1} + O_{n-1}$ + $E_n = 2 \cdot O_{n-1} + E_{n-1}$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f09.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f09.xml new file mode 100644 index 00000000..cf9bd12b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f09.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-2}$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-3}$ + $S_n = S_{n-1} + S_{n-2} + 1$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f10.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f10.xml new file mode 100644 index 00000000..9eb38703 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f10.xml @@ -0,0 +1,30 @@ + + + + $\newcommand{\IFeelLikeSinging}{{\rm IF {\scriptsize EEL} L {\scriptsize IKE} S {\scriptsize INGING}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ +
    + + Consider the recursive algorithm $\IFeelLikeSinging$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \IFeelLikeSinging(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \mathrm{sing}\ {\it O\ Canada}$
    + $\mathbf{else}\ \mathbf{if}\ n\ \text{is odd}$
    + $\elsesp \mathbf{then}\ \IFeelLikeSinging(n + 1)$
    + $\elsesp \mathbf{else}\ \IFeelLikeSinging(\frac{n}{2});$
    + $\elsesp \elsesp \IFeelLikeSinging(\frac{n}{2} - 1)$
    + $\elsesp \mathbf{endif};$
    + $\mathbf{endif}$ +

    + + If you run algorithm $\IFeelLikeSinging(9)$, how many times do you sing O Canada? + ]]> + + 6 + 7 + 8 + 9 + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f11.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f11.xml new file mode 100644 index 00000000..9b185bd6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f11.xml @@ -0,0 +1,21 @@ + + + + + Assume that you answer each question uniformly at random, where the choices for different questions are + independent of each other.
    + + What is the probability that you have exactly 17 correct answers? + ]]> +     + ${25 \choose 17} \cdot \left( 1 \middle/ 4 \right)^{17}$ + ${25 \choose 17} \cdot \left( 3 \middle/ 4 \right)^{17}$ + + ${25 \choose 17} \cdot \left( 1 \middle/ 4 \right)^{17} \cdot \left( 3 \middle/ 4 \right)^8$ + + + ${25 \choose 17} \cdot \left( 1 \middle/ 4 \right)^8 \cdot \left( 3 \middle/ 4 \right)^{17}$ + +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f12.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f12.xml new file mode 100644 index 00000000..bfb8a064 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f12.xml @@ -0,0 +1,19 @@ + + + palindrome if + $$ + b_1b_2{\dots}b_{n-1}b_n = b_nb_{n-1}{\dots}b_2b_1, + $$ + i.e., reading the string from left to right gives the same result as reading the string from right + to left.
    + + Let $n \geq 2$ be an even integer. You are given a uniformly random bitstring of length $n$. What is + the probability that this bitstring is a palindrome? + ]]> +     + $(1/2)^{n}$ + $(1/2)^{n/2}$ + $(1/2)^{2n}$ + $1/2$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f13.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f13.xml new file mode 100644 index 00000000..626aa388 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f13.xml @@ -0,0 +1,16 @@ + + + + + 3/16 + 4/16 + 5/16 + 6/16 + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f14.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f14.xml new file mode 100644 index 00000000..e1e5c7d6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f14.xml @@ -0,0 +1,19 @@ + + + + + Consider the string + $$ + a_1 + b_1,a_2 + b_2,\dots,a_n + b_n. + $$ + What is the probability that each element in this string is non-zero? + ]]> + + $1 - (1/4)^{n}$ + $1 - (3/4)^{n}$ + $(1/4)^{n}$ + $(3/4)^{n}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f15.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f15.xml new file mode 100644 index 00000000..a07ab805 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f15.xml @@ -0,0 +1,15 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f16.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f16.xml new file mode 100644 index 00000000..b4456ce3 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f16.xml @@ -0,0 +1,17 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f17.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f17.xml new file mode 100644 index 00000000..30a47175 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f17.xml @@ -0,0 +1,15 @@ + + + + + $1 - (1/2)^{7}$ + $(1/2)^{7}$ + $1 - \frac{{50 \choose 7}}{{100 \choose 7}}$ + $\frac{{50 \choose 7}}{{100 \choose 7}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f18.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f18.xml new file mode 100644 index 00000000..38f195ef --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f18.xml @@ -0,0 +1,42 @@ + + + + + + + + + + + + + + + + + + + + + + + + +
    $X = \bigg\{$$1\ $if the red coin flip resulted in heads$,$
    $0\ $if the red coin flip resulted in tails$,$
    $Y = \bigg\{$$1\ $if the blue coin flip resulted in heads$,$
    $0\ $if the blue coin flip resulted in tails$,$
    + + and + [defs] + Z = $\max(X,Y).$ + [/defs] + What is the expected value $\mathbb{E}(Z)$ of the random variable $Z$? + ]]> +     + 1/4 + 1/2 + 3/4 + 1 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f19.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f19.xml new file mode 100644 index 00000000..3e27f13a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f19.xml @@ -0,0 +1,17 @@ + + + + + Define the random variable $X$ to be the number of indices $i$ with $1 \leq i < n$ for which $b_i \neq b_{i+1}$.
    + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]> +     + $\frac{n-1}{2}$ + $\frac{n}{2}$ + $\frac{n+1}{2}$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f20.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f20.xml new file mode 100644 index 00000000..25b953af --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f20.xml @@ -0,0 +1,17 @@ + + + + + ${\sum_{k=1}^{100}} k \cdot \frac{k^{2}}{100^{2}}$ + ${\sum_{k=1}^{100}} k \cdot \frac{k(k-1)}{100^{2}}$ + ${\sum_{k=1}^{100}} k \cdot \frac{2k}{100^{2}}$ + ${\sum_{k=1}^{100}} k \cdot \left( \frac{1+2(k-1)}{100^{2}} \right)$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f21.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f21.xml new file mode 100644 index 00000000..edfab514 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f21.xml @@ -0,0 +1,20 @@ + + + + + The random variables $X$ and $Y$ are independent. + The random variables $X$ and $Y$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f22.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f22.xml new file mode 100644 index 00000000..da7942e1 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f22.xml @@ -0,0 +1,48 @@ + + + + $\newcommand{\WhoGoesFirst}{{\rm W {\scriptsize HO} G {\scriptsize OES} F {\scriptsize IRST}}} + \newcommand{\thensp}{\phantom{\mathbf{then}\ }}$ +
    + + Alexa and May want to play the game of Monopoly. They use the following recursive algorithm + to decide who goes first: + +
    + $\mathbf{Algorithm}\ \WhoGoesFirst(k)\mathrm{:}$
    + + + + + + + +
    $//$ + $k \geq 1,$ $\text{the die is fair},$ $\text{and all rolls are independent}$ +
    + $\text{Alexa rolls the die, let \(a\) be the result};$
    + $\text{May rolls the die, let \(m\) be the result};$
    + $\mathbf{if}\ a > m$
    + $\mathbf{then}\ \mathrm{print}\ {\tt Alexa\ goes\ first};$
    + $\thensp \mathrm{return}\ k$
    + $\mathbf{endif};$
    + $\mathbf{if}\ a < m$
    + $\mathbf{then}\ \mathrm{print}\ {\tt May\ goes\ first};$
    + $\thensp \mathrm{return}\ k$
    + $\mathbf{endif};$
    + $\mathbf{if}\ a = m$
    + $\mathbf{then}\ \WhoGoesFirst(k + 1)$
    + $\mathbf{endif}$ +
    + + The ladies run algorithm $\WhoGoesFirst(1)$, i.e., with $k = 1$. Define the random variable $X$ to + be the value of the output of this algorithm.
    + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? + ]]> + + 3/2 + 5/4 + 5/6 + 6/5 + diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f23.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f23.xml new file mode 100644 index 00000000..0d776fc0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f23.xml @@ -0,0 +1,14 @@ + + + + For any random variable $X$, $\mathbb{E}\left(1 \middle/ X \right) = 1 / \mathbb{E}(X)$. +

    + ]]> +     + The statement is true. + The statement is false. + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f24.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f24.xml new file mode 100644 index 00000000..0faf30e2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f24.xml @@ -0,0 +1,44 @@ + + + + The Carleton Computer Science Society (CCSS) is having their annual Christmas Holiday Season Party, which + is attended by $n$ students. + + + + + + + + + + + + + +
    (a) + $k$ of these $n$ students are politically correct and, thus, refuse to say Merry Christmas. + Instead, they say Happy Holidays. +
    (b) + $n - k$ of these $n$ students do not care about political correctness and, thus, they say + Merry Christmas. +
    + + Consider a uniformly random permutation of these $n$ students. The positions in this permutation are numbered + as $1,2,...,n$.
    + + Define the following random variable $X$: + [defs] + X = the number of positions $i$ with $1 \leq i \leq \left. n \middle/ 2 \right.$ such that both students at positions $i$ and $2i$ are politically correct. + [/defs] + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]> +     + $n \cdot \frac{k(k - 1)}{n(n - 1)}$ + $n \cdot \frac{(k - 1)(k - 2)}{n(n - 1)}$ + $\frac{n}{2} \cdot \frac{k(k - 1)}{n(n - 1)}$ + $\frac{n}{2} \cdot \frac{(k - 1)(k - 2)}{n(n - 1)}$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2017/f17f25.xml b/app/src/data/questions/comp2804/exam-fall-2017/f17f25.xml new file mode 100644 index 00000000..d8bd1037 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2017/f17f25.xml @@ -0,0 +1,6 @@ + + + How do you feel about writing an exam on Friday evening? + + I would rather sit in the pub and have a beer. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f01.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f01.xml new file mode 100644 index 00000000..72a0fcca --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f01.xml @@ -0,0 +1,12 @@ + + + + + $70 \cdot 2^{69}$ + $70 \cdot 3^{69}$ + $70 \cdot 2^{70}$ + $70 \cdot 3^{70}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f02.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f02.xml new file mode 100644 index 00000000..643cb34a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f02.xml @@ -0,0 +1,12 @@ + + + and exactly 30 letters $b$? + ]]> + + ${70 \choose 12} + {58 \choose 30}$ + ${70 \choose 12} \cdot {58 \choose 30}$ + ${70 \choose 12} \cdot {58 \choose 30} \cdot 2^{28}$ + ${70 \choose 12} \cdot {58 \choose 30} \cdot 3^{28}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f03.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f03.xml new file mode 100644 index 00000000..c7625bb6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f03.xml @@ -0,0 +1,12 @@ + + + or exactly 30 letters $b$? + ]]> + + ${70 \choose 12} + {70 \choose 30} - {58 \choose 30}$ + ${70 \choose 12} \cdot 2^{58} + {70 \choose 30} \cdot 2^{40}$ + ${70 \choose 12} \cdot 2^{58} + {70 \choose 30} \cdot 2^{40} - {70 \choose 12} \cdot {58 \choose 30}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f04.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f04.xml new file mode 100644 index 00000000..a2ea5fa3 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f04.xml @@ -0,0 +1,12 @@ + + + + + $3^{70} - 2^{70} - 70 \cdot 2^{69}$ + $3^{70} - 2^{70} - 70 \cdot 2^{69} - {70 \choose 2} \cdot 2^{68}$ + $\sum_{k=4}^{70} {70 \choose k} \cdot 2^{k}$ + $\sum_{k=4}^{70} {70 \choose k} \cdot 2^{70-k}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f05.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f05.xml new file mode 100644 index 00000000..85f2b9a9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f05.xml @@ -0,0 +1,14 @@ + + + + + The number of subsets of $S$ that are non-empty. + The number of subsets of $S$ that contain at least two elements. + The number of bitstrings of length $n$ that contain at least one 0. + The number of bitstrings of length $n$ that contain at least three 0's. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f06.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f06.xml new file mode 100644 index 00000000..5d4a231d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f06.xml @@ -0,0 +1,11 @@ + + + + + ${55 \choose 20} \cdot 5^{35} \cdot 3^{20}$ + $- {55 \choose 20} \cdot 5^{35} \cdot 3^{20}$ + ${55 \choose 35} \cdot 5^{20} \cdot 3^{35}$ + $- {55 \choose 35} \cdot 5^{20} \cdot 3^{35}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f07.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f07.xml new file mode 100644 index 00000000..336f0ad7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f07.xml @@ -0,0 +1,17 @@ + + + + SUCCESS +

    + is called awesome, if the string contains the substring UE or EU. + Thus, both SCUESCS and SCSEUCS are awesome, whereas SUCCESS is not awesome. + What is the number of awesome strings? + ]]> +     + 30 + 60 + 90 + 120 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f08.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f08.xml new file mode 100644 index 00000000..0a0959d0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f08.xml @@ -0,0 +1,17 @@ + + + + + $S_n = S_{n-2} + S_{n-4}$ + $S_n = 2 \cdot S_{n-2} + S_{n-4}$ + $S_n = S_{n-2} + 4 \cdot S_{n-4}$ + $S_n = 2 \cdot S_{n-2} + 4 \cdot S_{n-4}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f09.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f09.xml new file mode 100644 index 00000000..e146ba52 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f09.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2} + 1$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-2}$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f10.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f10.xml new file mode 100644 index 00000000..2638ff06 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f10.xml @@ -0,0 +1,18 @@ + + + + + $T(n) = \frac{5}{2} \cdot 3^{n} - 1$ + $T(n) = \frac{3}{2} \cdot 3^{n} - \frac{1}{2}$ + $T(n) = \frac{5}{2} \cdot 3^{n} - \frac{1}{2}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f11.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f11.xml new file mode 100644 index 00000000..cf01ce24 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f11.xml @@ -0,0 +1,12 @@ + + + + + 2/3 + 1/2 + 1/3 + 1/4 + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f12.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f12.xml new file mode 100644 index 00000000..207dfc4f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f12.xml @@ -0,0 +1,15 @@ + + + suit and a rank. + There are four suits (spades ♠, hearts ♡, clubs ♣, and diamonds ♢), + and 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King).
    + Assume you get a uniformly random hand consisting of 5 cards. What is the probability that the 5 + cards in this hand are all of the same suit? + ]]> +     + $\left. {13 \choose 5} \middle/ {52 \choose 5} \right.$ + $\left. {52 \choose 5} \middle/ {13 \choose 5} \right.$ + $4 \cdot \left. {13 \choose 5} \middle/ {52 \choose 5} \right.$ + $4 \cdot \left. {52 \choose 5} \middle/ {13 \choose 5} \right.$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f13.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f13.xml new file mode 100644 index 00000000..39c7ce64 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f13.xml @@ -0,0 +1,18 @@ + + + + + 2/7 + 1/7 + 2/11 + 1/11 + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f14.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f14.xml new file mode 100644 index 00000000..4591cc23 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f14.xml @@ -0,0 +1,20 @@ + + + + You are given two bitstrings $a_1,a_2,\dots,a_n$ and $b_1,b_2,\dots,b_n$ of length $n$. In both + bitstrings, each bit is 0 with probability 1/2, and 1 with probability 1/2 (independent of all + other bits).
    + Consider the bitstring + $$ + a_1 \cdot b_1,a_2 \cdot b_2,\dots,a_n \cdot b_n + $$ + where $a_i \cdot b_i$ is the result of multiplying the two bits $a_i$ and $b_i$. What is the probability that this + bitstring contains exactly $k$ many 1's? + ]]> +     + ${n \choose k} \cdot \left. 3^{n - k} \middle/ 4^n \right.$ + ${n \choose k} \cdot \left. 4^{n - k} \middle/ 3^n \right.$ + ${n \choose k} \cdot \left. 4^{n - k} \middle/ 3^k \right.$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f15.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f15.xml new file mode 100644 index 00000000..01e60019 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f15.xml @@ -0,0 +1,17 @@ + + + a_2$", + B = "$a_4 > a_3$". + [/defs] + Which of the following is correct? + ]]> + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f16.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f16.xml new file mode 100644 index 00000000..9d4dd721 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f16.xml @@ -0,0 +1,16 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f17.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f17.xml new file mode 100644 index 00000000..38f4fb99 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f17.xml @@ -0,0 +1,12 @@ + + + + + 5/6 + 2/3 + 3/4 + 1/3 + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f18.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f18.xml new file mode 100644 index 00000000..e24001c9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f18.xml @@ -0,0 +1,19 @@ + + + + + 9/13 + 13/9 + 8/9 + 9/8 + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f19.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f19.xml new file mode 100644 index 00000000..a0ed5c5c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f19.xml @@ -0,0 +1,17 @@ + + + + Define the random variable $X$ to be the number of indices $i$ with $1 \leq i < n$ + for which $c_i = c_{i+1}$.
    + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]> +     + $\left. n \middle/ 25 \right.$ + $\left. (n - 1) \middle/ 25 \right.$ + $\left. n \middle/ 5 \right.$ + $\left. (n - 1) \middle/ 5 \right.$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f20.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f20.xml new file mode 100644 index 00000000..f1f3f0d4 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f20.xml @@ -0,0 +1,17 @@ + + + + + $\frac{2 {{n}\choose{2}} + n}{{{n+2}\choose{3}}}$ + $\frac{2 {{n}\choose{2}} + n + 1}{{{n+2}\choose{3}}}$ + $\frac{2 {{n}\choose{2}} + 2n}{{{n+2}\choose{3}}}$ + $\frac{2 {{n}\choose{2}} + n - 1}{{{n+2}\choose{3}}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f21.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f21.xml new file mode 100644 index 00000000..ae7aba26 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f21.xml @@ -0,0 +1,29 @@ + + + + + + $\Pr(X = 0)$ + + $= \Pr(X = 1) = \Pr(Y = 0)$ + $= \Pr(Y = 1) = 1/2.$ + + + + + + Define the random variable + $$ + Z = (X + Y)\ \mathrm{mod}\ 2. + $$ + Which of the following is correct? + ]]> + + The random variables $X$ and $Z$ are independent. + The random variables $X$ and $Z$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f22.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f22.xml new file mode 100644 index 00000000..9769789e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f22.xml @@ -0,0 +1,55 @@ + + + + $\newcommand{\TriIsHungry}{{\rm T {\scriptsize RI} I {\scriptsize S} H {\scriptsize UNGRY}}}$ +
    + + Zoltan's Noodle House is a popular restaurant in downtown Ottawa. When you order the surprise dish, + you get Mi Quang with probability 1/4, Bun Cha Ca with probability 1/3, and + Banh Xeo with probability 5/12.
    + Tri enjoys going to this restaurant, because the food reminds him of his mommy's food back home in Da Nang.
    + Tri runs the following recursive algorithm: + + +
    + $\mathbf{Algorithm}\ \TriIsHungry\mathrm{:}$
    + + + + + + + +
    $//$ + $\text{the results of all}$ $\text{orders are independent}$ +
    + $\text{Tri orders the surprise dish;}$
    + $\mathbf{if}\ \mathrm{Tri}\ \mathrm{gets}\ \mathit{Mi}\ \mathit{Quang}$
    + $\mathbf{then}\ \text{Tri eats the dish;}$
    + $\qquad\ \ \TriIsHungry$
    + $\mathbf{else}\ \mathbf{if}\ \mathrm{Tri}\ \mathrm{gets}\ \mathit{Bun}\ \mathit{Cha}\ \mathit{Ca}$
    + $\qquad\, \mathbf{then}\ \text{Tri eats the dish;}$
    + $\qquad \qquad\ \ \, \TriIsHungry$
    + $\qquad\, \mathbf{else}\ \text{Tri eats the dish;}$
    + + + + + + + +
    $\hspace{4.05em}$$\text{Tri pays the bill}$ $\text{and goes home}$
    + $\qquad\, \mathbf{endif}$
    + $\mathbf{endif}$
    +
    + + Define the random variable $X$ to be the number of dishes that Tri eats when running algorithm $\TriIsHungry$.
    + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? + ]]> + + 5/12 + 12/5 + 5/7 + 7/5 + diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f23.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f23.xml new file mode 100644 index 00000000..9166ede4 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f23.xml @@ -0,0 +1,25 @@ + + + + + Jim is one of the students and answers the 25 questions, by choosing a uniformly random answer for + each question; the choices are independent of each other.
    + + Define the random variable + [defs] + X = the number of marks that Jim recevies. + [/defs] + For what value of $z$ is the expected value $\mathbb{E}(X)$ equal to 0?
    + + Hint: Use the Linearity of Expectation. + ]]> +     + $z = 1/4$ + $z = 1/3$ + $z = 1/2$ + $z = 3/4$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f24.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f24.xml new file mode 100644 index 00000000..5f48fcb9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f24.xml @@ -0,0 +1,23 @@ + + + + + At the end of the exam, the proctor places the backpacks in a uniformly random order $b_1,b_2,\dots,b_n$, + and, for each $i = 1, 2, ..., n$, gives backpack $b_i$ to student $S_i$.
    + + Define the following random variable $X$: + [defs] + X = the number of students who get their own backpack. + [/defs] + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]> +     + 1 + 2 + $\left. (n + 1) \middle/ n \right.$ + $\left. (n - 1) \middle/ n \right.$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2018/f18f25.xml b/app/src/data/questions/comp2804/exam-fall-2018/f18f25.xml new file mode 100644 index 00000000..ff04a7f8 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2018/f18f25.xml @@ -0,0 +1,11 @@ + + + + + Professor Identity + Donald Trump + Alexandre-Théophile Vandermonde + Justin Bieber + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f01.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f01.xml new file mode 100644 index 00000000..98333659 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f01.xml @@ -0,0 +1,10 @@ + + + How many such strings have exactly 5 letters $c$? + ]]> + ${85 \choose 5} \cdot 3^{80}$ + ${85 \choose 5} \cdot 3^{85}$ + ${85 \choose 5} \cdot 4^{80}$ + ${85 \choose 5} \cdot 4^{85}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f02.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f02.xml new file mode 100644 index 00000000..00465258 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f02.xml @@ -0,0 +1,10 @@ + + + How many such strings have exactly 15 letters $a$ and exactly 30 letters $d$? + ]]> + ${85 \choose 15} \cdot {70 \choose 30} \cdot 2^{40}$ + ${85 \choose 15} \cdot {70 \choose 30} \cdot 3^{40}$ + ${85 \choose 15} \cdot {70 \choose 30} \cdot 4^{40}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f03.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f03.xml new file mode 100644 index 00000000..84e3db5d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f03.xml @@ -0,0 +1,12 @@ + + + How many such strings have exactly 15 letters $a$ or exactly 30 letters $d$? + ]]> + ${85 \choose 15} \cdot 3^{70} + {85 \choose 30} \cdot 3^{55}$ + + ${85 \choose 15} \cdot 3^{70} + {85 \choose 30} \cdot 3^{55} - {85 \choose 15} \cdot {70 \choose 30} \cdot 2^{40}$ + + ${85 \choose 15} \cdot 4^{70} + {85 \choose 30} \cdot 4^{55}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f04.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f04.xml new file mode 100644 index 00000000..e723fd58 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f04.xml @@ -0,0 +1,13 @@ + + + Consider subsets of these 70 bottles, that contain exactly 12 beer bottles (and any number of cider bottles) + or exactly 12 cider bottles (and any number of beer bottles). How many such subsets are there? + ]]> + ${20 \choose 12} + {50 \choose 12}$ + ${20 \choose 12} + {50 \choose 12} - {20 \choose 12} \cdot {50 \choose 12}$ + ${20 \choose 12} \cdot 2^{50} + {50 \choose 12} \cdot 2^{20}$ + + ${20 \choose 12} \cdot 2^{50} + {50 \choose 12} \cdot 2^{20} - {20 \choose 12} \cdot {50 \choose 12}$ + + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f05.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f05.xml new file mode 100644 index 00000000..9bede1e5 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f05.xml @@ -0,0 +1,13 @@ + + + Consider subsets of these 70 bottles, that contain at least 3 beer bottles (and any number of cider bottles). + How many such subsets are there? + ]]> + $2^{70} - 2^{50} - 20 - {20 \choose 2}$ + + $2^{70} - 2^{50} - 20 \cdot 2^{50} - {20 \choose 2} \cdot 2^{50}$ + + $2^{70} - 2^{50} - 20 \cdot 2^{50}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f06.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f06.xml new file mode 100644 index 00000000..670f6f9c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f06.xml @@ -0,0 +1,15 @@ + + + Let $m \geq 2$ and $n \geq 2$ be integers. What does + $$ + {m \choose 2} + {n \choose 2} + m \cdot n + $$ + count? + + The number of ways to choose a subset from a set consisting of $m + n$ elements. + The number of ways to choose an ordered pair of 2 elements from a set consisting of $m + n$ elements. + + The number of ways to choose a 2-element subset from a set consisting of $m + n$ elements. + + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f07.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f07.xml new file mode 100644 index 00000000..3ce098d8 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f07.xml @@ -0,0 +1,12 @@ + + + Nick eats lots of bananas. During a period of 7 days, Nick eats a total of 25 bananas. A banana schedule + is a sequence of 7 numbers, whose sum is equal to 25, and whose numbers indicate the number of bananas + that Nick eats on each day. Three examples of such schedules are (3,2,7,4,1,3,5), (2,3,7,4,1,3,5), and + (3,0,9,4,1,0,8). How many banana schedules are there? + + ${31 \choose 6}$ + ${31 \choose 7}$ + ${32 \choose 6}$ + ${32 \choose 7}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f08.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f08.xml new file mode 100644 index 00000000..9fea4814 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f08.xml @@ -0,0 +1,11 @@ + + awesome, if + the string does not contain the substring OO. Thus, GEOROB is awesome, whereas GREOOB is not awesome. + What is the number of awesome strings? + ]]> + $6 \cdot {5 \choose 2} \cdot 3 \cdot 2$ + $(6 \cdot {5 \choose 2} \cdot 3 \cdot 2) - 5!$ + $6! - 5!$ + $(6 \cdot {5 \choose 2} \cdot 3) - 5!$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f09.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f09.xml new file mode 100644 index 00000000..37d66145 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f09.xml @@ -0,0 +1,11 @@ + + + $S_n = S_{n - 1} + S_{n - 2} + S_{n - 3}$ + $S_n = S_{n - 1} + S_{n - 2} + 2^{n - 2}$ + $S_n = S_{n - 1} + S_{n - 2} + 2^{n - 3}$ + $S_n = S_{n - 1} + S_{n - 2} + 1$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f10.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f10.xml new file mode 100644 index 00000000..1fdc799e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f10.xml @@ -0,0 +1,26 @@ + + + $\newcommand{\IFeelLikeSinging}{{\rm IF {\scriptsize EEL} L {\scriptsize IKE} S {\scriptsize INGING}}}$ +
    + + Consider the recursive algorithm $\IFeelLikeSinging$, which takes as input an integer $n \geq 0$: + +

    + $\IFeelLikeSinging(n):$
    + $\quad \mathbf{if}\ n = 0\ \mathrm{or}\ n = 1\ \mathbf{then}$
    + $\quad \quad \text{sing O Canada}$
    + $\quad \mathbf{else}\ \mathbf{if}\ n\ \text{is odd}\ \mathbf{then}$
    + $\quad \quad \IFeelLikeSinging(n + 1)$
    + $\quad \mathbf{else}$
    + $\quad \quad \IFeelLikeSinging(\frac{n}{2})$
    + $\quad \quad \IFeelLikeSinging(\frac{n}{2} - 1)$
    +

    + + If you run algorithm $\IFeelLikeSinging(9)$, how many times do you sing O Canada? + ]]> + 6 + 7 + 8 + 9 + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f11.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f11.xml new file mode 100644 index 00000000..3c48d30f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f11.xml @@ -0,0 +1,16 @@ + + + Assume you write a multiple-choice exam that has 25 questions. For each question, four options are given + to you, and exactly one of these options is the correct answer. Assume that you answer each question + uniformly at random, where the choices for different questions are independent of each other. What is the + probability that you have exactly 17 correct answers? + + ${25 \choose 17} \cdot \left( 1 \middle/ 4 \right)^{17}$ + ${25 \choose 17} \cdot \left( 3 \middle/ 4 \right)^{17}$ + + ${25 \choose 17} \cdot \left( 1 \middle/ 4 \right)^{17} \cdot \left( 3 \middle/ 4 \right)^8$ + + + ${25 \choose 17} \cdot \left( 1 \middle/ 4 \right)^8 \cdot \left( 3 \middle/ 4 \right)^{17}$ + + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f12.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f12.xml new file mode 100644 index 00000000..ba36ef52 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f12.xml @@ -0,0 +1,15 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f13.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f13.xml new file mode 100644 index 00000000..d2081ed7 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f13.xml @@ -0,0 +1,19 @@ + + + When Nika writes the exam, what is the expected number of questions that appear on the exam and that + Nika has practiced on? +

    + + (n.b., depending on your background, it may be helpful to observe that this can be modelled using the hypergeometric + distribution) + ]]>     + 2 + 5 + 10 + 20 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f14.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f14.xml new file mode 100644 index 00000000..1e4d0f5d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f14.xml @@ -0,0 +1,10 @@ + + + Continuing from the previous question, what is the probability that Nika has not practiced on any of the + actual exam questions? + + 0 + $\left. {225 \choose 50} \middle/ {250 \choose 50} \right.$ + $\left. {225 \choose 25} \middle/ {250 \choose 50} \right.$ + $\left. {225 \choose 25} \middle/ {225 \choose 50} \right.$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f15.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f15.xml new file mode 100644 index 00000000..3c8e0980 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f15.xml @@ -0,0 +1,16 @@ + + + $\frac{{4 \choose 2}}{{5 \choose 2} + {4 \choose 2}}$ + $\frac{{5 \choose 2} + {4 \choose 2}}{{4 \choose 2}}$ + $\frac{{4 \choose 2}}{{9 \choose 2}}$ + $\frac{{4 \choose 2}}{{5 \choose 2} \cdot {4 \choose 2}}$ + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f16.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f16.xml new file mode 100644 index 00000000..67e50890 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f16.xml @@ -0,0 +1,16 @@ + + + 3/10 + 1/3 + 1/2 + 2/3 + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f17.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f17.xml new file mode 100644 index 00000000..7165fd5a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f17.xml @@ -0,0 +1,15 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f18.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f18.xml new file mode 100644 index 00000000..d2aad426 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f18.xml @@ -0,0 +1,15 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f19.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f19.xml new file mode 100644 index 00000000..b851a637 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f19.xml @@ -0,0 +1,17 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f20.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f20.xml new file mode 100644 index 00000000..39052993 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f20.xml @@ -0,0 +1,12 @@ + + + 2 + 1 + 1/4 + 1/2 + diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f21.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f21.xml new file mode 100644 index 00000000..cff9248e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f21.xml @@ -0,0 +1,18 @@ + + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? +

    + + Hint: Use indicator random variables. + ]]>     + $\frac{2}{3} \cdot n$ + $\frac{2}{3} \cdot (n - 1)$ + $\frac{4}{9} \cdot n$ + $\frac{4}{9} \cdot (n - 1)$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f22.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f22.xml new file mode 100644 index 00000000..14584456 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f22.xml @@ -0,0 +1,21 @@ + + + Experiment: Roll each die once and take the sum of the two rolls. You repeat this experiment until + the sum of the two rolls is equal to 7. Consider the random variable +

    + + [defs] + X = the number of times you do the experiment. + [/defs] + + (This value $X$ includes the experiment in which the sum is 7 for the first time.)
    + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? + ]]>     + 6 + 5 + 4 + 3 +     diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f23.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f23.xml new file mode 100644 index 00000000..a1ac8a97 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f23.xml @@ -0,0 +1,12 @@ + + + For any random variable $X$, $\mathbb{E}\left(1 \middle/ X \right) = 1 / \mathbb{E}(X)$. +

    + ]]>     + The statement is true. + The statement is false. + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f24.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f24.xml new file mode 100644 index 00000000..34b6e471 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f24.xml @@ -0,0 +1,46 @@ + + Christmas Holiday Season Party, which + is attended by $n$ students. + + + + + + + + + + + + + +
    (i) + $k$ of these $n$ students are politically correct and, thus, refuse to say Merry Christmas. + Instead, they say Happy Holidays. +
    (ii) + $n - k$ of these $n$ students do not care about political correctness and, thus, they say + Merry Christmas. +
    + + Consider a uniformly random permutation of these $n$ students. The positions in this permutation are numbered + as $1,2,...,n$. + +

    + Define the random variable $X$ as the number of positions $i$ with $1 \leq i \leq \left. n \middle/2 \right.$ + such that both students at positions $i$ and $2i$ are politically correct. +

    + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? + +

    + Hint: Use indicator random variables. +

    + ]]>     + $n \cdot \frac{k(k - 1)}{n(n - 1)}$ + $n \cdot \frac{(k - 1)(k - 2)}{n(n - 1)}$ + $\frac{n}{2} \cdot \frac{k(k - 1)}{n(n - 1)}$ + $\frac{n}{2} \cdot \frac{(k - 1)(k - 2)}{n(n - 1)}$ +     diff --git a/app/src/data/questions/comp2804/exam-fall-2019/f19f25.xml b/app/src/data/questions/comp2804/exam-fall-2019/f19f25.xml new file mode 100644 index 00000000..66df427a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-fall-2019/f19f25.xml @@ -0,0 +1,10 @@ + + + How do you feel about writing an exam on Friday evening? + + I would rather sit in the pub and have a beer. + I would rather sit in the pub and have a beer. + I would rather sit in the pub and have a beer. + I would rather sit in the pub and have a beer. + I would rather sit in the pub and have a beer. + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f01.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f01.xml new file mode 100644 index 00000000..237c5365 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f01.xml @@ -0,0 +1,13 @@ + + + a, e, i, o, or u). + How many passwords are there? + ]]> + + $5 \cdot 21^{27}$ + $28 \cdot 5 \cdot 21^{27}$ + $28 \cdot 5 \cdot 27^{21}$ + $28 \cdot 5 \cdot 26^{27}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f02.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f02.xml new file mode 100644 index 00000000..305b3e0a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f02.xml @@ -0,0 +1,14 @@ + + + + + ${10 \choose 1}26^9 + {10 \choose 2}26^8 + {10 \choose 3}26^7$ + $10 \cdot 26^9 + 10^2 \cdot 26^8 + 10^3 \cdot 26^7$ + + ${10 \choose 1} \cdot 10 \cdot 26^9 + {10 \choose 2} \cdot 10^2 \cdot 26^8\ +$ $ {10 \choose 3} \cdot 10^3 \cdot 26^7$ + + none of the above + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f03.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f03.xml new file mode 100644 index 00000000..97b8842d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f03.xml @@ -0,0 +1,14 @@ + + + + + $(-2)^{45}$ + $4^{45}$ + $(-8)^{45}$ + $10^{45}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f04.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f04.xml new file mode 100644 index 00000000..4248d008 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f04.xml @@ -0,0 +1,13 @@ + + + + + $7 \cdot 6!$ + $2 \cdot 7 \cdot 6!$ + $8 \cdot 6!$ + $2 \cdot 8 \cdot 6!$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f05.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f05.xml new file mode 100644 index 00000000..7567dc28 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f05.xml @@ -0,0 +1,13 @@ + + + + + $S_{n+1} = S_n + S_{n-1}\ \mathrm{for}\ n \geq 2.$ + $S_{n+1} = 2 \cdot S_n + S_{n-1}\ \mathrm{for}\ n \geq 2.$ + $S_{n+1} = S_n + 2 \cdot S_{n-1}\ \mathrm{for}\ n \geq 2.$ + $S_{n+1} = 2 \cdot S_n + 2 \cdot S_{n-1}\ \mathrm{for}\ n \geq 2.$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f06.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f06.xml new file mode 100644 index 00000000..1da6fd40 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f06.xml @@ -0,0 +1,23 @@ + + + +
  • + 30 weigh at least 150 pounds, +
    • +
  • + 60 are at least 6 feet tall, +
    • +
  • + 70 weigh less than 150 pounds and are less than 6 feet tall. +
    • + + How many people weigh at least 150 pounds and are at least 6 feet tall? + ]]> +     + 10 + 20 + 30 + 40 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f07.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f07.xml new file mode 100644 index 00000000..a0bc0ee8 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f07.xml @@ -0,0 +1,13 @@ + + + + + 64 + 74 + 84 + 94 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f08.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f08.xml new file mode 100644 index 00000000..c30601f2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f08.xml @@ -0,0 +1,15 @@ + + + + + $\frac{n!}{k(n-k)!}$ + $\frac{n!}{k!(n-k)!}$ + $\frac{n!}{(n-k)!}$ + $\frac{2 \cdot n!}{(n-k)!}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f09.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f09.xml new file mode 100644 index 00000000..88271ee2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f09.xml @@ -0,0 +1,12 @@ + + + + + ${780 \choose 3}$ + ${780 \choose 4}$ + ${781 \choose 3}$ + ${781 \choose 4}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f10.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f10.xml new file mode 100644 index 00000000..7b0f0a5d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f10.xml @@ -0,0 +1,26 @@ + + + + + + $f(0)$ + $\;=\;$ + $3,$ + + + $f(n + 1)$ + $\;=\;$ + $f(n) + 10n + 2\; \ \text{for all}$ $\text{integers}\ n \geq 0.$ + + + + Which of the following is true? + ]]> + + for all $n \geq 0$: $f(n) = 5n^{2} - 3n + 2$ + for all $n \geq 0$: $f(n) = 5n^{2} - 3n + 3$ + for all $n \geq 0$: $f(n) = 5n^{2} + 3n + 3$ + for all $n \geq 0$: $f(n) = 5n^{2} - 2n + 3$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f11.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f11.xml new file mode 100644 index 00000000..18421c17 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f11.xml @@ -0,0 +1,30 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ +
    + + The Fibonacci numbers are defined as follows: $f_0 = 0$, $f_1 = 1$, and $f_n = f_{n-1} + f_{n-2}$ for + $n \geq 2$.
    + + Consider the recursive algorithm $\Fib$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + For $n \geq 5$, run algorithm $\Fib(n)$ and let $a_n$ be the number of times that $\Fib(4)$ is called.
    + Which of the following is true? + ]]> + + for all $n \geq 5$, $a_n = f_n$ + for all $n \geq 5$, $a_n = f_{n-1}$ + for all $n \geq 5$, $a_n = f_{n-2}$ + for all $n \geq 5$, $a_n = f_{n-3}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f12.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f12.xml new file mode 100644 index 00000000..3d95ae0a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f12.xml @@ -0,0 +1,12 @@ + + + + + 4/16 + 4/32 + 5/16 + 5/32 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f13.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f13.xml new file mode 100644 index 00000000..008ee8f9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f13.xml @@ -0,0 +1,12 @@ + + + + + $\frac{1}{100}$ + $\frac{1}{100 \cdot 99}$ + $\frac{1}{100 \cdot 100}$ + $\frac{1}{{100 \choose 2}}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f14.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f14.xml new file mode 100644 index 00000000..ecd3322e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f14.xml @@ -0,0 +1,13 @@ + + + + + 4/8 + 5/8 + 6/8 + 7/8 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f15.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f15.xml new file mode 100644 index 00000000..d8f8c3e0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f15.xml @@ -0,0 +1,16 @@ + + + + + 1/2 + 1/4 + 1/8 + 1/9 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f16.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f16.xml new file mode 100644 index 00000000..a186337c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f16.xml @@ -0,0 +1,18 @@ + + + + + 1/3 + 1/2 + 2/3 + none of the above + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f17.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f17.xml new file mode 100644 index 00000000..ce14074f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f17.xml @@ -0,0 +1,12 @@ + + + + + 1/5 + 2/5 + 3/5 + 4/5 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f18.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f18.xml new file mode 100644 index 00000000..59c42744 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f18.xml @@ -0,0 +1,13 @@ + + + + + $1 - \frac{12!}{12^{4} \cdot 7!}$ + $1 - \frac{11!}{12^{4} \cdot 7!}$ + $1 - \frac{11!}{12^{4} \cdot 6!}$ + $1 - \frac{11!}{12^{4} \cdot 8!}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f19.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f19.xml new file mode 100644 index 00000000..6764d249 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f19.xml @@ -0,0 +1,13 @@ + + + + + $\frac{1}{3}$ + $\frac{1}{4}$ + $\frac{1}{4} \cdot \frac{1}{3} + \frac{3}{4} \cdot \frac{1}{4}$ + none of the above + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f20.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f20.xml new file mode 100644 index 00000000..28865f75 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f20.xml @@ -0,0 +1,14 @@ + + + + + 3 + 2 + 5/2 + 3/2 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f21.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f21.xml new file mode 100644 index 00000000..4158cb5c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f21.xml @@ -0,0 +1,19 @@ + + + + + Yes + No + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f22.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f22.xml new file mode 100644 index 00000000..af3ac037 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f22.xml @@ -0,0 +1,18 @@ + + + + + 27/4 + 28/4 + 29/4 + 30/4 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f23.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f23.xml new file mode 100644 index 00000000..e6f5cf95 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f23.xml @@ -0,0 +1,13 @@ + + + + + 4 + 5 + 6 + 7 + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f24.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f24.xml new file mode 100644 index 00000000..8365f4cf --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f24.xml @@ -0,0 +1,15 @@ + + + + + $n/2$ + $n/4$ + $n/8$ + $0$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2014/w14f25.xml b/app/src/data/questions/comp2804/exam-winter-2014/w14f25.xml new file mode 100644 index 00000000..b9c4d8cd --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2014/w14f25.xml @@ -0,0 +1,15 @@ + + + + + Justin Bieber + Fibonacci + Carl Friedrich Gauss + Simon Pratt + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f01.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f01.xml new file mode 100644 index 00000000..103c29d5 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f01.xml @@ -0,0 +1,12 @@ + + + + + ${20 \choose 7}$ + ${5\choose 3} + {15 \choose 4}$ + ${5 \choose 3}{15 \choose 4}$ + ${5 \choose 4}{15 \choose 3}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f02.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f02.xml new file mode 100644 index 00000000..c5d6b998 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f02.xml @@ -0,0 +1,15 @@ + + + + + + ${5 \choose 5}{15 \choose 2} + {5 \choose 2}{15 \choose 5} + {5 \choose 1}{15 \choose 6} + {5 \choose 0}{15 \choose 7}$ + + ${5 \choose 5}{15 \choose 2} + {5 \choose 2}{15 \choose 5} - {5 \choose 5}{15 \choose 5}$ + ${20 \choose 7} - {5 \choose 4}{15 \choose 4}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f03.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f03.xml new file mode 100644 index 00000000..f3835277 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f03.xml @@ -0,0 +1,11 @@ + + + + + $2^{73} + 2^{73}$ + $2^{74} - 2^{69}$ + $2^{77} - 2^{69}$ + $2^{77} - 2^{73} - 2^{73}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f04.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f04.xml new file mode 100644 index 00000000..35a47dd1 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f04.xml @@ -0,0 +1,11 @@ + + + + + ${15 \choose 11} \cdot 2^4 \cdot 7^{11}$ + $- {15 \choose 11} \cdot 2^4 \cdot 7^{11}$ + ${15 \choose 11} \cdot 2^{11} \cdot 7^4$ + $- {15 \choose 11} \cdot 2^{11} \cdot 7^4$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f05.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f05.xml new file mode 100644 index 00000000..6ef089f9 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f05.xml @@ -0,0 +1,23 @@ + + + +
  • + 6 are blond, +
    • +
  • + 7 have green eyes, +
    • +
  • + 11 are not blond and do not have green eyes. +
    • + + How many people in this group are blond and have green eyes? + ]]> +     + 3 + 4 + 5 + 6 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f06.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f06.xml new file mode 100644 index 00000000..dcfccace --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f06.xml @@ -0,0 +1,18 @@ + + + + + Because both sides count the number of pairs $(A,B)$ of subsets of the $n$ people, such that $|A| = 2$, $|B| = 5$, and $A \subseteq B$. + Because both sides count the number of pairs $(A,B)$ of subsets of the $n$ people, such that $|A| = 5$, $|B| = 2$, and $A \subseteq B$. + Because both sides count the number of ways to choose 2 committees in a group of $n$ people, one committee has 5 members, the other committee has 2 members, and a person can be on both committees. + + no person can be on both committees. + ]]> + + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f07.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f07.xml new file mode 100644 index 00000000..44d1da8c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f07.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2}$ + $S_n = 2 \cdot S_{n-1} + S_{n-2}$ + $S_n = S_{n-1} + (3^{n-1} - S_{n-1})$ + $S_n = 2 \cdot S_{n-1} + (3^{n-1} - S_{n-1})$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f08.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f08.xml new file mode 100644 index 00000000..24289148 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f08.xml @@ -0,0 +1,16 @@ + + + + + For all $n \geq 0$: $f(n) = 2n^2 + 7$ + For all $n \geq 0$: $f(n) = 3n^2 + 7$ + For all $n \geq 0$: $f(n) = 4n^2 + 7$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f09.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f09.xml new file mode 100644 index 00000000..c411bf35 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f09.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + + Consider the recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + If we run algorithm $\Fib(77)$, how many calls are there to $\Fib(73)$? + ]]> +     + 3 + 4 + 5 + 6 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f10.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f10.xml new file mode 100644 index 00000000..fd8da1ea --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f10.xml @@ -0,0 +1,23 @@ + + + +
  • + $(1,6) \in S$. +
    • +
  • + If $(a,b) \in S$ then $(a+3, b+4) \in S$. +
    • +
  • + If $(a,b) \in S$ then $(a+5, b+2) \in S$. +
    • + + Which of the following is true? + ]]> +     + For every element $(a,b)$ in $S$, $a + b$ is divisible by 7. + For every element $(a,b)$ in $S$, $a + b$ is not divisible by 7. + $S = \{(a,b) : a > 0$ and $b > 0$ are integers and $a + b$ is divisible by 7$\}$. + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f11.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f11.xml new file mode 100644 index 00000000..9c9a9c75 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f11.xml @@ -0,0 +1,12 @@ + + + + + ${102 \choose 3}$ + ${102 \choose 4}$ + ${103 \choose 3}$ + ${103 \choose 4}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f12.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f12.xml new file mode 100644 index 00000000..237810d0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f12.xml @@ -0,0 +1,12 @@ + + + + + 5/15 + 6/15 + 7/15 + 8/15 + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f13.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f13.xml new file mode 100644 index 00000000..8f70765a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f13.xml @@ -0,0 +1,18 @@ + + + + + + $\Pr\bigl(A \cup (\overline{B} \cap \overline{C})\bigr) = $ + $\Pr(A) + \Pr(B)\ - $ $\Pr(C).$ + + + + ]]> + + True + False + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f14.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f14.xml new file mode 100644 index 00000000..a6f514c6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f14.xml @@ -0,0 +1,13 @@ + + + + + $\left. {30 \choose 1} \middle/ {100 \choose 20} \right.$ + $\left. {30 \choose 1}{70 \choose 19} \middle/ {100 \choose 20} \right.$ + $1 - \left. {70 \choose 20} \middle/ {100 \choose 20} \right.$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f15.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f15.xml new file mode 100644 index 00000000..f0ce5637 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f15.xml @@ -0,0 +1,13 @@ + + + + + $\frac{1}{{100 \choose 20}} \sum_{k=0}^{20} \left({70 \choose k} + {30 \choose 20 - k}\right)$ + $\frac{1}{{100 \choose 20}} \sum_{k=0}^{20} {70 \choose k}{30 \choose 20 - k}$ + $\frac{1}{{100 \choose 20}} \sum_{k=0}^{10} \left({70 \choose 2k} + {30 \choose 20 - 2k}\right)$ + $\frac{1}{{100 \choose 20}} \sum_{k=0}^{10} {70 \choose 2k}{30 \choose 20 - 2k}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f16.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f16.xml new file mode 100644 index 00000000..68cd9145 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f16.xml @@ -0,0 +1,13 @@ + + + + + ${77 \choose 15}(1/3)^{15}(2/3)^{62}$ + ${77 \choose 15}((1/3)^{15} + (2/3)^{62})$ + ${77 \choose 15}(1/3)^{62}(2/3)^{15}$ + ${77 \choose 15}((1/3)^{62} + (2/3)^{15})$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f17.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f17.xml new file mode 100644 index 00000000..1af5f9bc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f17.xml @@ -0,0 +1,16 @@ + + + + + $\left. {5 \choose 2} \middle/ 2^3 \right.$ + $\left. {5 \choose 2} \middle/ 2^4 \right.$ + $\left. {5 \choose 2} \middle/ 2^5 \right.$ + $\left. 2^5 \middle/ {5 \choose 2} \right.$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f18.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f18.xml new file mode 100644 index 00000000..94466448 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f18.xml @@ -0,0 +1,18 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f19.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f19.xml new file mode 100644 index 00000000..f1cae8cf --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f19.xml @@ -0,0 +1,13 @@ + + + + + $n/2$ + $n$ + $3n/2$ + $2n$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f20.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f20.xml new file mode 100644 index 00000000..ca434366 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f20.xml @@ -0,0 +1,15 @@ + + + + + $m/2$ + $m/4$ + $m/8$ + $m/16$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f21.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f21.xml new file mode 100644 index 00000000..3a46b32f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f21.xml @@ -0,0 +1,20 @@ + + + + + The random variables $X$ and $Y$ are independent. + The random variables $X$ and $Y$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f22.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f22.xml new file mode 100644 index 00000000..cb3acef4 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f22.xml @@ -0,0 +1,20 @@ + + + + + $\mathbb{E}(L) = 50$ and $\mathbb{E}(\max(L,S)) = 50$. + $\mathbb{E}(L) = 100$ and $\mathbb{E}(\max(L,S)) = 100$. + $\mathbb{E}(L) = 50$ and $\mathbb{E}(\max(L,S)) = 100$. + $\mathbb{E}(L) = 100$ and $\mathbb{E}(\max(L,S)) = 50$. + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f23.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f23.xml new file mode 100644 index 00000000..31a70880 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f23.xml @@ -0,0 +1,38 @@ + + + + $\newcommand{\TwoTails}{{\rm T {\scriptsize WO} T {\scriptsize AILS}}}$ + + + Consider the following recursive algorithm $\TwoTails$, which takes as input a positive integer $k$: + +
    + $\mathbf{Algorithm}\ \TwoTails(k)\mathrm{:}$
    + + + + + + + +
    $//$ + $\text{all coin flips made are mutually}$ $\text{independent}$ +
    + $\text{flip a fair coin twice};$
    + $\mathbf{if}\ \text{the coin came up heads exactly twice}$
    + $\mathbf{then}\ \mathrm{return}\ 2^k$
    + $\mathbf{else}\ \TwoTails(k + 1)$
    + $\mathbf{endif}$
    +
    + + You run algorithm $\TwoTails(1)$, i.e., with $k = 1$. Define the random variable $X$ to be the value of the + output of this algorithm. + Let $k \geq 1$ be an integer. What is $\Pr(X = 2^k)$? + ]]> +     + $(1/4)^{k} \cdot 3/4$ + $(1/4)^{k-1} \cdot 3/4$ + $(3/4)^{k} \cdot 1/4$ + $(3/4)^{k-1} \cdot 1/4$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f24.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f24.xml new file mode 100644 index 00000000..e0ccfe5b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f24.xml @@ -0,0 +1,13 @@ + + + + + 36 + 30 + 20 + 12 + diff --git a/app/src/data/questions/comp2804/exam-winter-2015/w15f25.xml b/app/src/data/questions/comp2804/exam-winter-2015/w15f25.xml new file mode 100644 index 00000000..d32cabb0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2015/w15f25.xml @@ -0,0 +1,15 @@ + + Who is Lindsay Bangs? + A world-renowned rapper. + + The Hamburglar. + ]]> + + President of the Carleton Computer Science Society. + + Leo's Early Breakfast IPA. + ]]> + + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f01.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f01.xml new file mode 100644 index 00000000..1b224fdc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f01.xml @@ -0,0 +1,20 @@ + + + +
  • + $a_1,a_3,a_5,a_7,a_9$ are all odd and +
    • +
  • + $a_2,a_4,a_6,a_8,a_{10}$ are all even. +
    • + + How many such permutations are there? + ]]> +     + $10!$ + $5^5 \cdot 5^5$ + $(5!)^2$ + $2 \cdot (5!)^2$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f02.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f02.xml new file mode 100644 index 00000000..a1d9992c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f02.xml @@ -0,0 +1,12 @@ + + + + + $\frac{n!}{2}$ + $n!$ + $2{n \choose 2} \cdot (n-2)!$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f03.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f03.xml new file mode 100644 index 00000000..efd10353 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f03.xml @@ -0,0 +1,24 @@ + + + +
  • + exactly 5 beer bottles and zero or more cider bottles, +
    • + + or +
      +
    • + exactly 5 cider bottles and zero or more beer bottles. +
      • +
    + How many such subsets are there? + ]]> +     + ${17 \choose 5} \cdot 2^{28} + 2^{17} \cdot {28 \choose 5}$ + ${17 \choose 5} \cdot 2^{28} + 2^{17} \cdot {28 \choose 5} - {17 \choose 5} \cdot {28 \choose 5}$ + $2^{45} - {17 \choose 5} - {28 \choose 5}$ + $2^{45} - {17 \choose 5} \cdot {28 \choose 5}$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f04.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f04.xml new file mode 100644 index 00000000..f1797acc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f04.xml @@ -0,0 +1,13 @@ + + + + + $2^{n-1}$ + $2^{n-2}$ + $2^{(n-1)/2}$ + $2^{(n+1)/2}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f05.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f05.xml new file mode 100644 index 00000000..f058dd4c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f05.xml @@ -0,0 +1,11 @@ + + + + + The number of bitstrings of length $n$ in which the first bit is 0 or the last bit is 1. + The number of bitstrings of length $n$ in which the first bit is 0 and the last bit is 1. + The number of bitstrings of length $n$ in which the first bit is equal to the last bit. + The number of bitstrings of length $n$ in which the first bit is not equal to the last bit. + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f06.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f06.xml new file mode 100644 index 00000000..f0dc99e1 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f06.xml @@ -0,0 +1,23 @@ + + + +
  • + 63 students like beer, +
    • +
  • + 71 students like cider, and +
    • +
  • + 25 students do not like beer and do not like cider. +
    • + + How many students like beer and cider? + ]]> +     + 57 + 58 + 59 + 60 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f07.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f07.xml new file mode 100644 index 00000000..cfd0109d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f07.xml @@ -0,0 +1,24 @@ + + + + + For any even integer $n$, let $S_n$ be the number of bitstrings of length $n$ that have both of the + following two properties: +
      +
    • + There is a 0 at every even position. +
      • +
    • + The entire bitstring does not contain the substring 101. +
      • +
    + Which of the following is true for all even integers $n \geq 6$? + ]]> +     + $S_n = S_{n/2} + S_{(n/2)-3}$ + $S_n = S_{n-1} + S_{n-3}$ + $S_n = S_{n-2} + S_{n-3}$ + $S_n = S_{n-2} + S_{n-4}$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f08.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f08.xml new file mode 100644 index 00000000..edc3ebbc --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f08.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2} + 2^{n-2}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-4}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f09.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f09.xml new file mode 100644 index 00000000..00a5430a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f09.xml @@ -0,0 +1,32 @@ + + + + $\newcommand{\Hello}{{\rm H {\scriptsize ELLO}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }} + \newcommand{\thensp}{\phantom{\mathbf{then}\ }}$ + + + Consider the recursive algorithm $\Hello$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Hello(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \text{print ``hello''}$
    + $\mathbf{else}\ \mathbf{if}\ n\ \mathrm{is}\ \mathrm{even}$
    + $\elsesp \mathbf{then}\ \Hello(\frac{n}{2});$
    + $\elsesp \thensp \Hello(\frac{n}{2} - 1)$
    + $\elsesp \mathbf{else}\ \Hello(n - 1);$
    + $\elsesp \elsesp \Hello(n - 2)$
    + $\elsesp \mathbf{endif};$
    + $\mathbf{endif}$ +

    + + If we run algorithm $\Hello(7)$, how many times is the word "hello" printed? + ]]> +     + 9 + 10 + 11 + 12 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f10.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f10.xml new file mode 100644 index 00000000..f35240ce --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f10.xml @@ -0,0 +1,16 @@ + + + + + $1 - (21/26)^{14}$ + $1 - (26/21)^{14}$ + $5 \cdot (5/26) \cdot (21/26)^{13}$ + $14 \cdot (5/26) \cdot (21/26)^{13}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f11.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f11.xml new file mode 100644 index 00000000..d5353f48 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f11.xml @@ -0,0 +1,13 @@ + + + + + $11 \cdot {6 \choose 2} \cdot 10!$ + $11 \cdot 6 \cdot 5 \cdot 10!$ + $12 \cdot 6 \cdot 5 \cdot 10!$ + $13 \cdot 6 \cdot 5 \cdot 10!$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f12.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f12.xml new file mode 100644 index 00000000..7da2d186 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f12.xml @@ -0,0 +1,17 @@ + + + + + 4/8 + 5/8 + 4/9 + 5/9 + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f13.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f13.xml new file mode 100644 index 00000000..06599cf0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f13.xml @@ -0,0 +1,16 @@ + + + + + 1/3 + 2/3 + 2/5 + 1/4 + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f14.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f14.xml new file mode 100644 index 00000000..62201d34 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f14.xml @@ -0,0 +1,16 @@ + + + a_1$". + [/defs] + Which of the following is true? + ]]> + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f15.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f15.xml new file mode 100644 index 00000000..07e9c81e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f15.xml @@ -0,0 +1,17 @@ + + + + + ${\frac{1}{n}} - {\frac{1}{n(n-1)}}$ + ${\frac{2}{n}} - {\frac{1}{n(n-1)}}$ + ${\frac{2}{n}} - {\frac{1}{n^{2}}}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f16.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f16.xml new file mode 100644 index 00000000..21d4f2e3 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f16.xml @@ -0,0 +1,19 @@ + + + 0. + \end{align} + $$ + Which of the following is true? + ]]> + + $\Pr(A) < 1/2$ + $\Pr(A) > 1/2$ + $\Pr(A) < 1$ + $\Pr(A) > 0$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f17.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f17.xml new file mode 100644 index 00000000..ec6c7703 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f17.xml @@ -0,0 +1,15 @@ + + + + + 1/3 + 2/3 + 1/5 + 1/6 + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f18.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f18.xml new file mode 100644 index 00000000..67c68335 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f18.xml @@ -0,0 +1,18 @@ + + + + + 5/18 + 1/6 + 1/4 + 1/3 + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f19.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f19.xml new file mode 100644 index 00000000..755beacd --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f19.xml @@ -0,0 +1,19 @@ + + + + + Define the random variable $X$ to be the number of unordered triples $\{P_i,P_j,P_k\}$ of people + (i.e., subsets consisting of three people) that have the same birthday.
    + + What is the expected value $\mathbb{E}(X)$ of $X$?
    + Hint: Use indicator random variables. + ]]> +     + ${\frac{1}{365^2}} \cdot {n \choose 3}$ + ${\frac{1}{365^3}} \cdot {n \choose 3}$ + ${\frac{1}{365^2}} \cdot n^3$ + ${\frac{1}{365^3}} \cdot n^3$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f20.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f20.xml new file mode 100644 index 00000000..a474e7da --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f20.xml @@ -0,0 +1,14 @@ + + + + + What is the expected value $\mathbb{E}(X)$ of $X$? + ]]> + + 80 + 100 + 120 + 140 + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f21.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f21.xml new file mode 100644 index 00000000..e4e844aa --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f21.xml @@ -0,0 +1,20 @@ + + + + + The random variables $X$ and $Y$ are independent. + The random variables $X$ and $Y$ are not independent. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f22.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f22.xml new file mode 100644 index 00000000..30f6675c --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f22.xml @@ -0,0 +1,38 @@ + + + + $\newcommand{\TwoTails}{{\rm T {\scriptsize WO} T {\scriptsize AILS}}}$ + + + Consider the following recursive algorithm $\TwoTails$, which takes as input a positive integer $k$: + +
    + $\mathbf{Algorithm}\ \TwoTails(k)\mathrm{:}$
    + + + + + + + +
    $//$ + $\text{all coin flips made are mutually}$ $\text{independent}$ +
    + $\text{flip a fair coin twice};$
    + $\mathbf{if}\ \text{the coin came up heads exactly twice}$
    + $\mathbf{then}\ \mathrm{return}\ 2^k$
    + $\mathbf{else}\ \TwoTails(k + 1)$
    + $\mathbf{endif}$
    +
    + + You run algorithm $\TwoTails(1)$, i.e., with $k = 1$. Define the random variable $X$ to be the value of the + output of this algorithm.
    + Let $m \geq 1$ be an integer. What is $\Pr(X = 2^m)$? + ]]> +     + $(1/4)^{m} \cdot 3/4$ + $(1/4)^{m-1} \cdot 3/4$ + $(3/4)^{m} \cdot 1/4$ + $(3/4)^{m-1} \cdot 1/4$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f23.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f23.xml new file mode 100644 index 00000000..2c88d0c6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f23.xml @@ -0,0 +1,14 @@ + + + + For any two random variables $X$ and $Y$, + $\mathbb{E}(X \cdot Y) = \mathbb{E}(X) \cdot \mathbb{E}(Y)$. +

    + ]]> +     + The statement is true. + The statement is false. + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f24.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f24.xml new file mode 100644 index 00000000..3d882b35 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f24.xml @@ -0,0 +1,22 @@ + + + + + Elisa orders 7 ciders, one cider at a time. Let $(D_1,D_2,\dots,D_7)$ be the sequence of drinks + that Tan serves. Define the following random variable $X$: + [defs] + X = the number of indices $i$ such that $D_i$ is a cider and $D_{i+1}$ is not a cider. + [/defs] + What is the expected value $\mathbb{E}(X)$ of $X$? + ]]> + + 44/144 + 55/144 + 66/144 + 77/144 + diff --git a/app/src/data/questions/comp2804/exam-winter-2017/w17f25.xml b/app/src/data/questions/comp2804/exam-winter-2017/w17f25.xml new file mode 100644 index 00000000..480fc2d6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2017/w17f25.xml @@ -0,0 +1,4 @@ + + How do you feel about writing an exam on Sunday afternoon? + I hate it! + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f01.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f01.xml new file mode 100644 index 00000000..8434375f --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f01.xml @@ -0,0 +1,13 @@ + + + + + ${20 \choose 12} \cdot {38 \choose 18}$ + ${20 \choose 12} \cdot {50 \choose 18}$ + ${50 \choose 12} \cdot {20 \choose 18}$ + ${70 \choose 30} \cdot {20 \choose 12}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f02.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f02.xml new file mode 100644 index 00000000..5ddbbc89 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f02.xml @@ -0,0 +1,14 @@ + + + + + ${20 \choose 12} + {50 \choose 12}$ + ${20 \choose 12} + {50 \choose 12} - {20 \choose 12} \cdot {50 \choose 12}$ + ${20 \choose 12} \cdot 2^{50} + {50 \choose 12} \cdot 2^{20}$ + ${20 \choose 12} \cdot 2^{50} + {50 \choose 12} \cdot 2^{20} - {20 \choose 12} \cdot {50 \choose 12}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f03.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f03.xml new file mode 100644 index 00000000..6a5e4d6d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f03.xml @@ -0,0 +1,13 @@ + + + + + $2^{70} - 2^{50} - 20 - {20 \choose 2}$ + $2^{70} - 2^{50} - 20 \cdot 2^{50} - {20 \choose 2} \cdot 2^{50}$ + $2^{70} - 2^{50} - 20 \cdot 2^{50}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f04.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f04.xml new file mode 100644 index 00000000..61b4e4af --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f04.xml @@ -0,0 +1,12 @@ + + + + + $2 \cdot {40 \choose 5} \cdot 3^{35} - {40 \choose 5} \cdot {35 \choose 5} \cdot 2^{30}$ + $2 \cdot {40 \choose 5} \cdot 3^{35}$ + ${40 \choose 5} + {35 \choose 5} - {40 \choose 5} \cdot {35 \choose 5}$ + $2 \cdot {40 \choose 5} - {40 \choose 5} \cdot {35 \choose 5}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f05.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f05.xml new file mode 100644 index 00000000..5d138168 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f05.xml @@ -0,0 +1,15 @@ + + + + + The number of ways to choose a subset from a set consisting of $m + n$ elements. + The number of ways to choose an ordered pair of 2 elements from a set consisting of $m + n$ elements. + The number of ways to choose a 2-element subset from a set consisting of $m + n$ elements. + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f06.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f06.xml new file mode 100644 index 00000000..ecf6995b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f06.xml @@ -0,0 +1,14 @@ + + + + + ${31 \choose 6}$ + ${31 \choose 7}$ + ${32 \choose 6}$ + ${32 \choose 7}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f07.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f07.xml new file mode 100644 index 00000000..1a64422a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f07.xml @@ -0,0 +1,17 @@ + + + + BOOGER +

    + is called awesome, if the string does not contain the substring OO. + Thus, GEOROB is awesome, whereas GREOOB is not awesome. + What is the number of awesome strings? + ]]> +     + $6 \cdot {5 \choose 2} \cdot 3 \cdot 2$ + $(6 \cdot {5 \choose 2} \cdot 3 \cdot 2) - 5!$ + $6! - 5!$ + $(6 \cdot {5 \choose 2} \cdot 3) - 5!$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f08.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f08.xml new file mode 100644 index 00000000..56d9e86b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f08.xml @@ -0,0 +1,15 @@ + + + valid, if it does not contain $aa$, it does not contain $bb$, + it does not contain $cc$, and it does not contain $dd$.
    + + For any integer $n \geq 2$, what is the number of valid strings of length $n$? + ]]> +     + $4^{n} - 4(n-1)$ + $4^{n} - 4n$ + $4 \cdot 3^{n}$ + $4 \cdot 3^{n-1}$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f09.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f09.xml new file mode 100644 index 00000000..e146ba52 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f09.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2} + 1$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-2}$ + $S_n = S_{n-1} + S_{n-2} + 2^{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f10.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f10.xml new file mode 100644 index 00000000..b22563bd --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f10.xml @@ -0,0 +1,48 @@ + + + + $\newcommand{\SundayEveningExam}{{\rm S {\scriptsize UNDAY} E {\scriptsize VENING} E {\scriptsize XAM}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the recursive algorithm $\SundayEveningExam$, which takes as input an integer $n \geq 1$: + +
    + $\mathbf{Algorithm}\ \SundayEveningExam(n)\mathrm{:}$
    + $\mathbf{if}\ n = 1$
    + + + + + + + +
    + $\mathbf{then}\ \mathrm{print}\ \text{``}$ + $\text{I don't like Sunday}$ $\text{evening exams''}$
    + $\mathbf{else}\ \mathbf{for}\ i = 1\ \mathbf{to}\ n$
    + + + + + + + +
    + $\elsesp \mathbf{do}\ \mathrm{print}\ \text{``}$ + $\text{I don't like Sunday}$ $\text{evening exams''}$
    + $\elsesp \mathbf{endfor};$
    + $\elsesp \SundayEveningExam(n - 1)$
    + $\mathbf{endif}$ +
    + + Let $P(n)$ be the number of times the line "I don't like Sunday evening exams" is printed when running + algorithm $\SundayEveningExam(n)$. Which of the following is true for all $n \geq 1$? + ]]> +     + $P(n) = 1 + \frac{n(n-1)}{2}$ + $P(n) = \frac{n(n-1)}{2}$ + $P(n) = \frac{n(n+1)}{2}$ + $P(n) = 1 + \frac{n(n+1)}{2}$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f11.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f11.xml new file mode 100644 index 00000000..f3cc2f1d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f11.xml @@ -0,0 +1,12 @@ + + + + + ${18 \choose 3} \cdot \left(5 \middle/ 6 \right)^{18}$ + $18 \cdot \left. 5^{15} \middle/ 6^{18} \right.$ + ${18 \choose 3} \cdot \left. 5^{15} \middle/ 6^{18} \right.$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f12.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f12.xml new file mode 100644 index 00000000..ee2cec45 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f12.xml @@ -0,0 +1,20 @@ + + + palindrome, if + $$ + s_1s_2{\dots}s_{n-1}s_n = s_ns_{n-1}{\dots}s_2s_1, + $$ + i.e., reading the string from left to right gives the + same result as reading the string from right to left.
    + + Let $n \geq 3$ be an odd integer. You are given a string of length $n$, in which each character is a + uniformly random element of $\{a,b,c\}$. The characters are independent of each other. What is the + probability that this string is a palindrome? + ]]> +     + $(1/3)^{(n+1)/2}$ + $(1/3)^{(n-1)/2}$ + $(1/2)^{(n+1)/2}$ + $(1/2)^{(n-1)/2}$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f13.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f13.xml new file mode 100644 index 00000000..0950b6aa --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f13.xml @@ -0,0 +1,16 @@ + + + + + 12/16 + 13/16 + 14/16 + 15/16 + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f14.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f14.xml new file mode 100644 index 00000000..c8527378 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f14.xml @@ -0,0 +1,19 @@ + + + + + Consider the string + $$ + a_1-b_1,a_2-b_2,\dots,a_{77}-b_{77}. + $$ + What is the probability that each element in this string is non-zero? + ]]> + + $(3/8)^{77}$ + $(4/8)^{77}$ + $(5/8)^{77}$ + $(6/8)^{77}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f15.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f15.xml new file mode 100644 index 00000000..d1a127ee --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f15.xml @@ -0,0 +1,16 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f16.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f16.xml new file mode 100644 index 00000000..8ca755b2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f16.xml @@ -0,0 +1,16 @@ + + + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f17.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f17.xml new file mode 100644 index 00000000..9cb1f17a --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f17.xml @@ -0,0 +1,16 @@ + + + + + $\frac{2(2n-1)}{n-1}$ + $\frac{n-1}{4n}$ + $\frac{n-1}{2(2n-1)}$ + $\frac{n}{2(2n-1)}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f18.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f18.xml new file mode 100644 index 00000000..5b3bf191 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f18.xml @@ -0,0 +1,42 @@ + + + + + + + + + + + + + + + + + + + + + + + + +
    $X = \bigg\{$$1\ $if the red coin flip resulted in heads$,$
    $0\ $if the red coin flip resulted in tails$,$
    $Y = \bigg\{$$1\ $if the blue coin flip resulted in heads$,$
    $0\ $if the blue coin flip resulted in tails$,$
    + + and + [defs] + Z = $\min(X,Y).$ + [/defs] + What is the expected value $\mathbb{E}(Z)$ of the random variable $Z$? + ]]> +     + 1/4 + 1/2 + 3/4 + 1 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f19.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f19.xml new file mode 100644 index 00000000..a9826872 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f19.xml @@ -0,0 +1,18 @@ + + + + + Define the random variable $X$ to be the number of indices $i$ with $1 \leq i < n$ for which $b_i + \cdot b_{i+1} = 0$.
    + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]> +     + $n/4$ + $(n-1)/4$ + $3n/4$ + $3(n-1)/4$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f20.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f20.xml new file mode 100644 index 00000000..a8e26cee --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f20.xml @@ -0,0 +1,17 @@ + + + + + 1 + $\frac{n+2}{n+1}$ + $\frac{n+1}{n}$ + $\frac{n+3}{n+1}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f21.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f21.xml new file mode 100644 index 00000000..c69def89 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f21.xml @@ -0,0 +1,25 @@ + + + + + + $\Pr(X = 0)$ + + $= \Pr(X = 1) = \Pr(Y = 0)$ + $= \Pr(Y = 1) = 1/2.$ + + + + + + Define the random variable $Z = X \cdot Y$. Which of the following is correct? + ]]> + + The random variables $X$ and $Z$ are independent. + The random variables $X$ and $Z$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f22.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f22.xml new file mode 100644 index 00000000..6bac896d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f22.xml @@ -0,0 +1,48 @@ + + + + $\newcommand{\WhoGoesFirst}{{\rm W {\scriptsize HO} G {\scriptsize OES} F {\scriptsize IRST}}} + \newcommand{\thensp}{\phantom{\mathbf{then}\ }}$ + + + Alexa and Shelly want to play the game of Monopoly. They use the following recursive algorithm + to decide who goes first: + +
    + $\mathbf{Algorithm}\ \WhoGoesFirst(k)\mathrm{:}$
    + + + + + + + +
    $//$ + $k \geq 1,$ $\text{the die is fair},$ $\text{and all rolls are independent}$ +
    + $\text{Alexa rolls the die, let \(a\) be the result};$
    + $\text{Shelly rolls the die, let \(s\) be the result};$
    + $\mathbf{if}\ a > s$
    + $\mathbf{then}\ \mathrm{print}\ {\tt Alexa\ goes\ first};$
    + $\thensp \mathrm{return}\ k$
    + $\mathbf{endif};$
    + $\mathbf{if}\ a < s$
    + $\mathbf{then}\ \mathrm{print}\ {\tt Shelly\ goes\ first};$
    + $\thensp \mathrm{return}\ k$
    + $\mathbf{endif};$
    + $\mathbf{if}\ a = s$
    + $\mathbf{then}\ \WhoGoesFirst(k + 1)$
    + $\mathbf{endif}$ +
    + + The ladies run algorithm $\WhoGoesFirst(1)$, i.e., with $k = 1$. Define the random variable $X$ to + be the value of the output of this algorithm.
    + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? + ]]> +     + 3/2 + 5/4 + 5/6 + 6/5 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f23.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f23.xml new file mode 100644 index 00000000..3804449b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f23.xml @@ -0,0 +1,17 @@ + + + + + The statement is true. + The statement is false. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f24.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f24.xml new file mode 100644 index 00000000..b64b8b37 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f24.xml @@ -0,0 +1,21 @@ + + + + Define the following random variable $X$: + [defs] + X = the number of students who get exactly 2 ciders. + [/defs] + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]> +     + $2^{4} \cdot 3^{2} \cdot \left. 5^{2} \middle/ 3^{8} \right.$ + $2^{4} \cdot 3^{2} \cdot \left. 2^{5} \middle/ 8^{3} \right.$ + $2^{4} \cdot 3^{2} \left. \cdot 5^{2} \middle/ 8^{3} \right.$ + $3^{2} \cdot \left. 5^{2} \middle/ 8^{3} \right.$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2018/w18f25.xml b/app/src/data/questions/comp2804/exam-winter-2018/w18f25.xml new file mode 100644 index 00000000..d8134dc0 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2018/w18f25.xml @@ -0,0 +1,4 @@ + + Are you happy that this is the last question? + Yes. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f01.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f01.xml new file mode 100644 index 00000000..3aeb8662 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f01.xml @@ -0,0 +1,10 @@ + + + ${85 \choose 5} \cdot 3^{80}$ + ${85 \choose 5} \cdot 3^{85}$ + ${85 \choose 5} \cdot 4^{80}$ + ${85 \choose 5} \cdot 4^{85}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f02.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f02.xml new file mode 100644 index 00000000..55e1c157 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f02.xml @@ -0,0 +1,10 @@ + + + ${85 \choose 15} \cdot {70 \choose 30} \cdot 2^{40}$ + ${85 \choose 15} \cdot {70 \choose 30} \cdot 3^{40}$ + ${85 \choose 15} \cdot {70 \choose 30} \cdot 4^{40}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f03.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f03.xml new file mode 100644 index 00000000..7ab01009 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f03.xml @@ -0,0 +1,10 @@ + + + ${55 \choose 10} - {30 \choose 10} - {30 \choose 9}$ + ${55 \choose 10} - {30 \choose 10} - 25 \cdot {29 \choose 9}$ + ${55 \choose 10} - {30 \choose 10} - 25 \cdot {30 \choose 9}$ + ${55 \choose 10} - {30 \choose 10} - 25 \cdot {30 \choose 10}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f04.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f04.xml new file mode 100644 index 00000000..75c7aec8 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f04.xml @@ -0,0 +1,12 @@ + + awesome, if $x$ is even or $y$ is even. + What is the number of awesome elements in $S$? + ]]> + 104 + 105 + 106 + 107 + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f05.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f05.xml new file mode 100644 index 00000000..623bd7ec --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f05.xml @@ -0,0 +1,18 @@ + + + Let $m \geq 2$ and $n \geq 2$ be integers. Why does the identity + $$ + {m + n \choose 2} = {m \choose 2} + {n \choose 2} + mn + $$ + hold? + + + Because both sides count the number of ways $m$ men and $n$ women can be arranged on a line, + such that no two men are standing next to each other. + + Because both sides count the number of ordered pairs in a set of size $m + n$. + + Because both sides count the number of 2-element subsets of a set of size $m + n$. + + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f06.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f06.xml new file mode 100644 index 00000000..06ba83be --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f06.xml @@ -0,0 +1,9 @@ + + + ${55 \choose 20} \cdot 5^{35} \cdot 3^{20}$ + $-{55 \choose 20} \cdot 5^{35} \cdot 3^{20}$ + ${55 \choose 35} \cdot 5^{20} \cdot 3^{35}$ + $-{55 \choose 35} \cdot 5^{20} \cdot 3^{35}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f07.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f07.xml new file mode 100644 index 00000000..287b7041 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f07.xml @@ -0,0 +1,20 @@ + + POOPERSCOOPER

    + is called cool, if each occurrence of E has the letter R to its left or + right, and each occurrence of R has the letter E to its left or right. Thus, both +

    POOPERSCOOPER

    + and +

    OPRECSOOOERPP

    + are cool, whereas +

    EPOOPRSCOOPER

    + is not cool. What is the number of cool strings? + ]]>     + ${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1}$ + ${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1} \cdot 2$ + ${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1} \cdot 3$ + + ${11 \choose 3} \cdot {8 \choose 4} \cdot {4 \choose 2} \cdot {2 \choose 1} \cdot {1 \choose 1} \cdot 4$ + +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f08.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f08.xml new file mode 100644 index 00000000..1059ea69 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f08.xml @@ -0,0 +1,13 @@ + + free, if it does not contain two 0's next to each other. + In class, we have seen that for any $m \geq 1$, the number of 00-free bitstrings of length $m$ + is equal to the $(m + 2)$-th Fibonacci number $f_{m+2}$.
    + What is the number of 00-free bitstrings of length 20 that have 1 at position 11 and 0 at + position 20? (The positions are numbered $1,2,...,20$.) + ]]>     + $f_{10} \cdot f_{12}$ + $f_9 \cdot f_{12}$ + $f_8 \cdot f_{11}$ + $f_7 \cdot f_{10}$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f09.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f09.xml new file mode 100644 index 00000000..2be5c9b6 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f09.xml @@ -0,0 +1,11 @@ + + + $S_n = 1 + S_{n - 1}$ + $S_n = 1 + S_{n - 2}$ + $S_n = S_{n - 1} + S_{n - 3}$ + $S_n = S_{n - 2} + S_{n - 3}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f10.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f10.xml new file mode 100644 index 00000000..6f8a645b --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f10.xml @@ -0,0 +1,16 @@ + + + $f(n) = \frac{5}{2} \cdot 3^n - 1$ + $f(n) = \frac{3}{2} \cdot 3^n - \frac{1}{2}$ + $f(n) = \frac{5}{2} \cdot 3^n - \frac{1}{2}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f11.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f11.xml new file mode 100644 index 00000000..f91fa4bb --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f11.xml @@ -0,0 +1,11 @@ + + + You flip a fair coin 6 times; the flips are independent of each other. + What is the probability that in these 6 coin flips, the coin comes up heads exactly + 3 times? + + 3/16 + 4/16 + 5/16 + 6/16 + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f12.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f12.xml new file mode 100644 index 00000000..8836d561 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f12.xml @@ -0,0 +1,13 @@ + + suit and a rank. + There are four suits (spades ♠, hearts ♡, clubs ♣, and diamonds ♢), and 13 ranks + (Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, and King).
    + Assume you get a uniformly random hand consisting of 5 cards. What is the probability + that the 5 cards in this hand consist of 3 Aces and 2 Queens? + ]]>     + $\left. 24 \middle/ {52 \choose 5} \right.$ + $\left. 25 \middle/ {52 \choose 5} \right.$ + $\left. 26 \middle/ {52 \choose 5} \right.$ + $\left. 27 \middle/ {52 \choose 5} \right.$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f13.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f13.xml new file mode 100644 index 00000000..6c5d773d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f13.xml @@ -0,0 +1,16 @@ + + + 17/57 + 18/57 + 19/57 + 20/57 + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f14.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f14.xml new file mode 100644 index 00000000..470799ef --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f14.xml @@ -0,0 +1,17 @@ + + + You are given two bitstrings $a_1,a_2,...,a_n$ and $b_1,b_2,...,b_n$, both of length $n$. + In both bitstrings, each bit is 0 with probability 1/2, and 1 with probability 1/2 + (independent of all other bits).
    + For each $i$ with $1 \leq i \leq n$, let $c_i = a_i - b_i$. Consider the set + $$ + P = \{i : 1 \leq i \leq n \text{ and } c_i \geq 0\}. + $$ + What is the probability that the size of the set $P$ is equal to $k$? + ]]>     + ${n \choose k} \cdot (3/4)^{n - k} \cdot (1/4)^k$ + ${n \choose k} \cdot (3/4)^k \cdot (1/4)^{n - k}$ + ${n \choose k} \cdot (3/4)^k \cdot (1/2)^k$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f15.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f15.xml new file mode 100644 index 00000000..bec46e75 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f15.xml @@ -0,0 +1,17 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f16.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f16.xml new file mode 100644 index 00000000..98a1cd8e --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f16.xml @@ -0,0 +1,17 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f17.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f17.xml new file mode 100644 index 00000000..a9414c08 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f17.xml @@ -0,0 +1,17 @@ + + + The events $A$ and $B$ are independent. + The events $A$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f18.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f18.xml new file mode 100644 index 00000000..0ce3ba83 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f18.xml @@ -0,0 +1,11 @@ + + + 3/4 + 2/3 + 1/2 + 1/3 + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f19.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f19.xml new file mode 100644 index 00000000..cec56320 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f19.xml @@ -0,0 +1,33 @@ + + + Step 1: Choose a uniformly random number from + the red box, and denote it by $x$.
    + Step 2: +
      +
    • + If $x = 0$ or $x = 2$, + then choose a uniformly random number from the green box, and denote it by $y$. +
      • +
    • + Otherwise (i.e., if $x = 1$), + choose a uniformly random number from the blue box, and denote it by $y$. +
      • +
    + Consider the random variables + + [defs] + X = the number $x$ you choose in Step 1, + Y = the number $y$ you choose in Step 2, + Z = $\max(X,Y).$ + [/defs] + + What is the expected value $\mathbb{E}(Z)$ of the random variable $Z$? + ]]>     + 1 + 3/2 + 2 + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f20.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f20.xml new file mode 100644 index 00000000..850e83a2 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f20.xml @@ -0,0 +1,14 @@ + + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]>     + $\frac{2}{3} \cdot n$ + $\frac{2}{3} \cdot (n - 1)$ + $\frac{4}{9} \cdot n$ + $\frac{4}{9} \cdot (n - 1)$ +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f21.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f21.xml new file mode 100644 index 00000000..11ff4f36 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f21.xml @@ -0,0 +1,17 @@ + + + $\frac{n}{n + 2} + \frac{2n + 6}{(n + 1)(n + 2)}$ + $\frac{n}{n + 2} + \frac{2n + 2}{(n + 1)(n + 2)}$ + $\frac{n}{n + 2} + \frac{4n + 6}{(n + 1)(n + 2)}$ + $\frac{n}{n + 2} + \frac{4n + 2}{(n + 1)(n + 2)}$ + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f22.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f22.xml new file mode 100644 index 00000000..1f055969 --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f22.xml @@ -0,0 +1,21 @@ + + + The random variables $G$ and $B$ are independent. + The random variables $G$ and $B$ are not independent. + None of the above. + All of the above. + diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f23.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f23.xml new file mode 100644 index 00000000..ae3f1f3d --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f23.xml @@ -0,0 +1,19 @@ + + Experiment: Roll each die once and take the sum of the two rolls.

    + You repeat this experiment until the sum of the two rolls is equal to 7.
    + Consider the random variable + + [defs] + X = the number of times you do the experiment. + [/defs] + + (This value $X$ includes the experiment in which the sum is 7 for the first time.)
    + What is the expected value $\mathbb{E}(X)$ of the random variable $X$? + ]]>     + 6 + 5 + 4 + 3 +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f24.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f24.xml new file mode 100644 index 00000000..791391ad --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f24.xml @@ -0,0 +1,27 @@ + + + Consider $n$ students $S_1,S_2,...,S_n$ who hand in an assignment for COMP 2804. This assignment has 2 questions. + For $i = 1,2,...,n$ let $A_i$ be the assignment handed in by student $S_i$.
    + Alexa and Zoltan are TAs for the course. Alexa is supposed to mark the first question, whereas Zoltan + is supposed to mark the second question. Since both TAs are lazy, they use the following scheme + (all random choices are mutually independent):
    + For $i = 1,2,...,n$, +
      +
    • Alexa marks the first question of assignment $A_i$ with probability $p,$
      • +
    • Zoltan marks the second question of assignment $A_i$ with probability $q.$
      • +
    + Consider the random variable + + [defs] + X = the number of assignments that are marked by both Alexa and Zoltan. + [/defs] + + What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
    + Hint: Use indicator random variables. + ]]>     + $(p + q) \cdot n$ + $\frac{n}{p \cdot q}$ + $p \cdot q \cdot n$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/exam-winter-2019/w19f25.xml b/app/src/data/questions/comp2804/exam-winter-2019/w19f25.xml new file mode 100644 index 00000000..a71893fb --- /dev/null +++ b/app/src/data/questions/comp2804/exam-winter-2019/w19f25.xml @@ -0,0 +1,11 @@ + + + Who discovered the Fibonacci numbers? + + Donald Trump + + The Italian mathematician Fibonacci, also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano + + Alexandre-Théophile Vandermonde + Keith Richards (the guitarist of the greatest rock band in the universe) + diff --git a/app/src/data/questions/comp2804/midterm-fall-2013/f13m01.xml b/app/src/data/questions/comp2804/midterm-fall-2013/f13m01.xml new file mode 100644 index 00000000..5076bcf2 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2013/f13m01.xml @@ -0,0 +1,12 @@ + + + + + + + + + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m01.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m01.xml new file mode 100644 index 00000000..cc74191a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m01.xml @@ -0,0 +1,12 @@ + + + + + ${n \choose 2} \cdot 2^{n-2}$ + $n \cdot 2^{n-1}$ + $2^{n} - 1 - n$ + $2^{n} - n$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m02.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m02.xml new file mode 100644 index 00000000..50db1f9c --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m02.xml @@ -0,0 +1,11 @@ + + + + + $2^{91}$ + $2^{95} + 2^{95}$ + $2^{96} - 2^{91}$ + $2^{99} - 2^{96}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m03.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m03.xml new file mode 100644 index 00000000..8ff10b58 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m03.xml @@ -0,0 +1,12 @@ + + + + + $17! + 17!$ + $2(17! + 17!)$ + $(17!)^2$ + $2(17!)^2$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m04.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m04.xml new file mode 100644 index 00000000..9b757822 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m04.xml @@ -0,0 +1,25 @@ + + + +
  • + all boys stand next to each other, +
    • +
  • + all girls stand next to each other, +
    • +
  • + all dogs stand next to each other, +
    • +
  • + none of the boys are standing next to any of the girls. +
    • + + ]]> +     + $12! + 17! + 25!$ + $2(12! + 17! + 25!)$ + $(12!)(17!)(25!)$ + $2(12!)(17!)(25!)$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m05.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m05.xml new file mode 100644 index 00000000..de11e9e0 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m05.xml @@ -0,0 +1,10 @@ + + + + + True + False + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m06.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m06.xml new file mode 100644 index 00000000..516fbf4b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m06.xml @@ -0,0 +1,12 @@ + + + + + At least two of these $n$ points are at distance at most $1$. + At least two of these $n$ points are at distance at most $\left. 1 \middle/ \sqrt{2} \right.$. + At least two of these $n$ points are at distance at most $\sqrt{2}$. + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m07.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m07.xml new file mode 100644 index 00000000..b2af2669 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m07.xml @@ -0,0 +1,11 @@ + + + + + $-{100 \choose 80} 5^{20}3^{80}$ + ${100 \choose 80} 5^{20}3^{80}$ + ${100 \choose 80} 5^{80}3^{20}$ + ${80 \choose 100} 5^{20}3^{80}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m08.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m08.xml new file mode 100644 index 00000000..a0f1bfdc --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m08.xml @@ -0,0 +1,12 @@ + + + + + ${30 \choose 3}$ + ${30 \choose 4}$ + ${31 \choose 3}$ + ${31 \choose 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m09.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m09.xml new file mode 100644 index 00000000..c2f6e282 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m09.xml @@ -0,0 +1,27 @@ + + + valid, if in each step, it either goes one unit to the right or one unit upwards.
    + In the example below, you see a valid path for the case when $m = 5$ and $n = 3$. + + + + How many valid paths are there? + ]]> +     + ${m + n \choose n - 1}$ + ${m + n \choose n}$ + $2^{m + n}$ + $2^m + 2^n$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m10.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m10.xml new file mode 100644 index 00000000..116cc109 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m10.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = 2n^{2} - 5n + 7$ + $f(n) = 2n^{2} - 5n + 8$ + $f(n) = 3n^{2} - 5n + 8$ + $f(n) = 4n^{2} - 5n + 8$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m11.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m11.xml new file mode 100644 index 00000000..33581606 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m11.xml @@ -0,0 +1,12 @@ + + + + + $B_n = B_{n-1} + B_{n-2} + B_{n-3}$ + $B_n = B_{n-1} + B_{n-2} + B_{n-3} + B_{n-4}$ + $B_n = 2^{n} - 2^{n-4}$ + $B_n = 2^{n} - (n-3) \cdot 2^{n-4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m12.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m12.xml new file mode 100644 index 00000000..236fef2f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m12.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + When running $\Fib(9)$, how many calls are there to $\Fib(4)$? + ]]> +     + 6 + 7 + 8 + 9 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m13.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m13.xml new file mode 100644 index 00000000..00a48f13 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m13.xml @@ -0,0 +1,33 @@ + + + + $\newcommand{\Silly}{{\rm S \scriptsize ILLY}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the following recursive algorithm $\Silly$, which takes as input an integer $n \geq 1$ which is a power of 2: + +

    + $\mathbf{Algorithm}\ \Silly(n)\mathrm{:}$
    + $\mathbf{if}\ n = 1$
    + $\mathbf{then}\ \text{drink one pint of beer}$
    + $\mathbf{else}\ \mathbf{if}\ n = 2$
    + $\elsesp \mathbf{then}\ \text{fart once}$
    + $\elsesp \mathbf{else}\ \text{fart once};$
    + $\elsesp \elsesp \Silly(n / 2);$
    + $\elsesp \elsesp \text{fart once}$
    + $\elsesp \mathbf{endif}$
    + $\mathbf{endif}$ +

    + + For $n$ a power of 2, let $F(n)$ be the number of times you fart when running algorithm $\Silly(n)$. + Which of the following is true?
    + (n.b., $\log$ denotes the base-2 logarithm) + ]]> +     + $F(n) = \log n\ \mathrm{for}\ n \geq 1.$ + $F(n) = 2 \log n\ \mathrm{for}\ n \geq 1.$ + $F(n) = (2 \log n) - 1\ \mathrm{for}\ n \geq 1.$ + $F(n) = (2 \log n) - 1\ \mathrm{for}\ n \geq 2.$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m14.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m14.xml new file mode 100644 index 00000000..ec2c0b23 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m14.xml @@ -0,0 +1,12 @@ + + + + + 1/4 + 1/2 + 3/4 + 1 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m15.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m15.xml new file mode 100644 index 00000000..d4658b4e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m15.xml @@ -0,0 +1,18 @@ + + + + + $\Pr(A) = \Pr(B)$ + $\Pr(A) < \Pr(B)$ + $\Pr(A) > \Pr(B)$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m16.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m16.xml new file mode 100644 index 00000000..38c39218 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m16.xml @@ -0,0 +1,12 @@ + + + + + $\frac{10!}{10^{10}}$ + $\frac{10^{10}}{10!}$ + $1 - \frac{10 \cdot (9/10)^{10}}{10^{10}}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2014/f14m17.xml b/app/src/data/questions/comp2804/midterm-fall-2014/f14m17.xml new file mode 100644 index 00000000..65ea8110 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2014/f14m17.xml @@ -0,0 +1,13 @@ + + + + + $\frac{100}{4^{100}}$ + $\frac{3^{99}}{4^{100}}$ + $\frac{100 + 3^{99}}{4^{100}}$ + $\frac{100 \cdot 3^{99}}{4^{100}}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m01.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m01.xml new file mode 100644 index 00000000..c7c13a7d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m01.xml @@ -0,0 +1,15 @@ + + + + + $n{n \choose 2}{n \choose 5}$ + $(n-2){n\choose 2}{n-2 \choose 5}$ + $(n-5){n \choose 2}{n-1 \choose 5}$ + $(n-7){n \choose 2}{n-2 \choose 5}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m02.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m02.xml new file mode 100644 index 00000000..fbf44223 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m02.xml @@ -0,0 +1,12 @@ + + + + + $2^{25} - 2^{22}$ + $2^{25} - 2^{24} + 2^{23}$ + $2^{22}$ + $2^{23}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m03.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m03.xml new file mode 100644 index 00000000..52f9cf9c --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m03.xml @@ -0,0 +1,12 @@ + + + + + $5 \cdot 6 \cdot 7 \cdot 8 \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13$ + $6 \cdot 7 \cdot 8 \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13$ + $7 \cdot 8 \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13$ + $8 \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m04.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m04.xml new file mode 100644 index 00000000..d69f490a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m04.xml @@ -0,0 +1,12 @@ + + + + + $S_n = 2^{n-2}$ + $S_n = 2^{n-1}$ + $S_n = 2^{n} - 2^{n-2}$ + $S_n = 2^{n} - 2^{n-1} + 2^{n-2}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m05.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m05.xml new file mode 100644 index 00000000..b8b653d1 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m05.xml @@ -0,0 +1,12 @@ + + + + + $3^{96} + 3^{96}$ + $3^{99} - 2 \cdot 3^{96}$ + $2 \cdot 3^{96} - 3^{93}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m06.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m06.xml new file mode 100644 index 00000000..ff59120b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m06.xml @@ -0,0 +1,15 @@ + + + + + The number of non-empty subsets of a set of size $m$. + The number of subsets of a set of size $m$. + The number of bitstrings of length $m$ having exactly $k$ many 1s. + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m07.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m07.xml new file mode 100644 index 00000000..78674a6e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m07.xml @@ -0,0 +1,17 @@ + + + + $\newcommand{\ShortLastName}{{\rm S {\scriptsize HORT} L {\scriptsize AST} N {\scriptsize AME}}}$ + + + In the city of $\ShortLastName$, every person has a last name consisting of two characters, the first one being + an uppercase letter and the second one being a lowercase letter. What is the minimum number of people + needed so that we can guarantee that at least 4 of them have the same last name? + ]]> + + $3 \cdot 26^{2}$ + $4 \cdot 26^{2}$ + $3 \cdot 26^{2} + 1$ + $4 \cdot 26^{2} + 1$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m08.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m08.xml new file mode 100644 index 00000000..9dacc0c0 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m08.xml @@ -0,0 +1,11 @@ + + + + + ${88 \choose 7} \cdot 3^{81} \cdot 17^7$ + $- {88 \choose 7} \cdot 3^{81} \cdot 17^7$ + ${88 \choose 7} \cdot 3^7 \cdot 17^{81}$ + $- {88 \choose 7} \cdot 3^7 \cdot 17^{81}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m09.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m09.xml new file mode 100644 index 00000000..69ca408c --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m09.xml @@ -0,0 +1,12 @@ + + + + + ${58 \choose 3}$ + ${58 \choose 4}$ + ${59 \choose 3}$ + ${59 \choose 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m10.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m10.xml new file mode 100644 index 00000000..21051dc9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m10.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = 4n^2 - 2n + 7$ + $f(n) = 4n^2 - n + 7$ + $f(n) = 5n^2 - 2n + 7$ + $f(n) = 5n^2 - n + 7$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m11.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m11.xml new file mode 100644 index 00000000..26e812c2 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m11.xml @@ -0,0 +1,12 @@ + + + + + $S_n = S_{n-1} + S_{n-2} + S_{n-3} + S_{n-4}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3} + S_{n-4}\ +$ $ 2^{n-4}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m12.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m12.xml new file mode 100644 index 00000000..36013787 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m12.xml @@ -0,0 +1,35 @@ + + + +
  • + the order in which the 1s and 2s occur in the sum matters, and +
    • +
  • + it is not allowed to have two consecutive 2s. +
    • + + For example, if $n = 7$, then both + $$ + 7 = 1 + 2 + 1 + 2 + 1 + $$ + and + $$ + 7 = 2 + 1 + 1 + 2 + 1 + $$ + are allowed, whereas + $$ + 7 = 1 + 2 + 2 + 1 + 1 + $$ + is not allowed.
    + + Which of the following is true? + ]]> +     + $S_n = S_{n-1} + S_{n-2}$ + $S_n = S_{n-1} + S_{n-3}$ + $S_n = S_{n-2} + S_{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m13.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m13.xml new file mode 100644 index 00000000..56caa3ef --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m13.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + When running $\Fib(55)$, how many calls are there to $\Fib(50)$? + ]]> +     + 6 + 7 + 8 + 9 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m14.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m14.xml new file mode 100644 index 00000000..db4a18b9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m14.xml @@ -0,0 +1,53 @@ + + + + $\newcommand{\JustinBieber}{{\rm J {\scriptsize USTIN} B {\scriptsize IEBER}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the following recursive algorithm $\JustinBieber$, which takes as input an integer $n \geq 1$, + which is a power of 2: + +
    + $\mathbf{Algorithm}\ \JustinBieber(n)\mathrm{:}$
    + $\mathbf{if}\ n = 1$
    + $\mathbf{then}\ \text{order chicken wings}$
    + $\mathbf{else}\ \mathbf{if}\ n = 2$ + + + + + + + +
    $\elsesp \mathbf{then}$ + $\text{drink one pint of}$ $\text{India Pale Ale}$ +
    + + + + + + + +
    + $\elsesp \mathbf{else}\ \mathrm{print}\ \text{``}$ + + $\text{I don't like}$ $\text{Justin Bieber''};$ +
    + $\elsesp \elsesp \JustinBieber(n / 2)$
    + $\elsesp \mathbf{endif}$
    + $\mathbf{endif}$ +
    + + For $n$ a power of 2, let $B(n)$ be the number of times you print "I don't like Justin Bieber" when + running algorithm $\JustinBieber(n)$. Which of the following is true?
    + (n.b., $\log$ denotes the base-2 logarithm) + ]]> +     + $B(n) = \log n - 1\ \text{for all}\ n \geq 2.$ + $B(n) = \log n - 1\ \text{for all}\ n \geq 1.$ + $B(n) = \log n\ \text{for all}\ n \geq 2.$ + $B(n) = n - 2\ \text{for all}\ n \geq 2.$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m15.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m15.xml new file mode 100644 index 00000000..37d9376e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m15.xml @@ -0,0 +1,15 @@ + + + + + $\frac{2^5 + 2}{2^7}$ + $1/2$ + $1/3$ + $1/4$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m16.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m16.xml new file mode 100644 index 00000000..dce84e8f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m16.xml @@ -0,0 +1,19 @@ + + + + + $\Pr(A) = \Pr(B)$ + $\Pr(A) < \Pr(B)$ + $\Pr(A) > \Pr(B)$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2015/f15m17.xml b/app/src/data/questions/comp2804/midterm-fall-2015/f15m17.xml new file mode 100644 index 00000000..f1f4dec3 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2015/f15m17.xml @@ -0,0 +1,17 @@ + + + + + 7/15 + 15/7 + 3/7 + 7/3 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m01.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m01.xml new file mode 100644 index 00000000..4e6b5654 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m01.xml @@ -0,0 +1,15 @@ + + + + + ${f + m \choose 4}$ + $f \cdot {f + m - 1 \choose 3}$ + $f \cdot {f + m \choose 3}$ + $(f - 1) \cdot {f + m \choose 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m02.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m02.xml new file mode 100644 index 00000000..d9879574 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m02.xml @@ -0,0 +1,12 @@ + + + and do not contain 2? + ]]> + + ${n - 1 \choose k - 1}$ + ${n - 1 \choose k}$ + ${n - 2 \choose k - 2}$ + ${n - 2 \choose k}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m03.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m03.xml new file mode 100644 index 00000000..05571924 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m03.xml @@ -0,0 +1,12 @@ + + + or do not contain 2? + ]]> + + ${n - 1 \choose k} + {n - 1 \choose k}$ + ${n - 2 \choose k}$ + ${n \choose k} - {n - 2 \choose k - 2}$ + ${n \choose k} - {n - 1 \choose k - 1} - {n - 1 \choose k - 1}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m04.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m04.xml new file mode 100644 index 00000000..f9f20b95 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m04.xml @@ -0,0 +1,12 @@ + + + + + $B_n = 2 \cdot 2^{n - 3}$ + $B_n = 6 \cdot 2^{n - 3}$ + $B_n = 2^n - 2$ + $B_n = 2^n - 6$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m05.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m05.xml new file mode 100644 index 00000000..0c855c14 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m05.xml @@ -0,0 +1,12 @@ + + + + + 17 + 18 + 19 + 20 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m06.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m06.xml new file mode 100644 index 00000000..866d1b9f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m06.xml @@ -0,0 +1,12 @@ + + + + + $4^{n - 2} + 4^{n - 3} - 4^{n - 5}$ + $4^{n - 2} + 4^{n - 3}$ + $4^n - 4^{n - 5}$ + $4^n - 4^{n - 2} - 4^{n - 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m07.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m07.xml new file mode 100644 index 00000000..18a72f34 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m07.xml @@ -0,0 +1,25 @@ + + + What does + $$ + {w \choose 3} \cdot {m \choose 2} + {w \choose 4} \cdot m + {w \choose 5} + $$ + count? + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at most 3 women can be chosen. + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at most 3 men can be chosen. + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at least 3 women must be chosen. + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at least 3 men must be chosen. + + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m08.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m08.xml new file mode 100644 index 00000000..3f04f2a5 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m08.xml @@ -0,0 +1,13 @@ + + + + + $n - 1$ + $n$ + $n + 1$ + $n + 2$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m09.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m09.xml new file mode 100644 index 00000000..f623ae77 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m09.xml @@ -0,0 +1,11 @@ + + + + + $- {50 \choose 24} \cdot 5^{26} \cdot 7^{24}$ + $- {50 \choose 26} \cdot 5^{24} \cdot 7^{26}$ + ${50 \choose 24} \cdot 5^{26} \cdot 7^{24}$ + ${50 \choose 26} \cdot 5^{24} \cdot 7^{26}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m10.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m10.xml new file mode 100644 index 00000000..93a4fed7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m10.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = 7 \cdot \frac{n!}{3^n}$ + $f(n) = 7^n \cdot \frac{n!}{3^n}$ + $f(n) = 7 \cdot \frac{(n + 1)!}{3^n}$ + $f(n) = 7^n \cdot \frac{(n + 1)!}{3^n}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m11.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m11.xml new file mode 100644 index 00000000..82fa1abb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m11.xml @@ -0,0 +1,13 @@ + + + + + $B_n = B_{n - 1} + B_{n - 2}$ + $B_n = B_{n - 1} + B_{n - 3}$ + $B_n = B_{n - 2} + B_{n - 3}$ + $B_n = B_{n - 2} + B_{n - 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m12.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m12.xml new file mode 100644 index 00000000..08974e67 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m12.xml @@ -0,0 +1,28 @@ + + + + + + $11$ + + $= 3 + 4 + 4 = 4 + 3 + 4$ + $= 4 + 4 + 3.$ + + + + + + Which of the following is true for any $n \geq 5$? + ]]> + + $S_n = 2 \cdot S_{n - 1}$ + $S_n = S_{n - 1} + S_{n - 2}$ + $S_n = S_{n - 2} + S_{n - 3}$ + $S_n = S_{n - 3} + S_{n - 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m13.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m13.xml new file mode 100644 index 00000000..38e9221a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m13.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + When running $\Fib(12)$, how many calls are there to $\Fib(8)$? + ]]> +     + 4 + 5 + 6 + 7 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m14.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m14.xml new file mode 100644 index 00000000..d5ea4d54 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m14.xml @@ -0,0 +1,31 @@ + + + + $\newcommand{\ElisaDrinksCider}{{\rm E {\scriptsize LISA} D {\scriptsize RINKS} C {\scriptsize IDER}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the following recursive algorithm $\ElisaDrinksCider$, which takes as input an integer + $n \geq 1$, which is a power of 2: + +

    + $\mathbf{Algorithm}\ \ElisaDrinksCider(n)\mathrm{:}$
    + $\mathbf{if}\ n = 1$
    + $\mathbf{then}\ \text{order Fibonachos}$
    + $\mathbf{else}\ \ElisaDrinksCider(n / 2);$
    + $\elsesp \text{drink \(n\) bottles of cider};$
    + $\elsesp \ElisaDrinksCider(n / 2)$
    + $\mathbf{endif}$ +

    + + For $n$ a power of 2, let $C(n)$ be the total number of bottles of cider that you drink when running algorithm + $\ElisaDrinksCider(n)$. Which of the following is true for any $n \geq 1$ that is a power of 2?
    + (n.b., $\log$ denotes the base-2 logarithm) + ]]> +     + $C(n) = n \log n - 1$ + $C(n) = n \log n + 1$ + $C(n) = n \log n$ + $C(n) = 2n \log n$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m15.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m15.xml new file mode 100644 index 00000000..2fa3e89d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m15.xml @@ -0,0 +1,16 @@ + + + + + 1/4 + 1/3 + 1/2 + 1 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m16.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m16.xml new file mode 100644 index 00000000..b7ca9ccb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m16.xml @@ -0,0 +1,20 @@ + + + + + ${4 \choose 2} \cdot \frac{1}{365}$ + + ${4 \choose 2} \cdot \frac{1}{365} + {4 \choose 3} \cdot \frac{1}{365^2} + {4 \choose 4} \cdot \frac{1}{365^3}$ + + $1 - \frac{361 \cdot 362 \cdot 363 \cdot 364}{365^4}$ + $1 - \frac{362 \cdot 363 \cdot 364}{365^3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2016/f16m17.xml b/app/src/data/questions/comp2804/midterm-fall-2016/f16m17.xml new file mode 100644 index 00000000..94774750 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2016/f16m17.xml @@ -0,0 +1,18 @@ + + + Hearthstone, you are given a deck of 18 distinct cards. One of the cards is the Raven Idol. + You choose a uniformly random hand of 3 cards. Define the event + + [defs] + A = $\text{``}$the hand of 3 cards contains the Raven Idol$\,\text{''}.$ + [/defs] + + What is $\Pr(A)$? + ]]> + + 3/17 + 3/18 + 3/19 + 4/19 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m01.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m01.xml new file mode 100644 index 00000000..d8074714 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m01.xml @@ -0,0 +1,12 @@ + + + + + ${n/2 \choose 4} \cdot {n/2 \choose 3}$ + ${n \choose 4} \cdot {n \choose 3}$ + ${n/2 \choose 4} + {n/2 \choose 3}$ + ${n \choose 4} + {n \choose 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m02.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m02.xml new file mode 100644 index 00000000..9879809d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m02.xml @@ -0,0 +1,26 @@ + + + +
  • + $s$ students who are dressed up as Superman, +
    • +
  • + $t$ students who are dressed up as Donald Trump, +
    • +
  • + $k$ students who are dressed up as Kim Jong Un. +
    • + + These $s+t+k$ students are arranged on a line, such that all Supermen are standing next to each + other, all Trumps are standing next to each other, all Kims are standing next to each other, and no + Trump is standing next to any Kim. How many such arrangements are there? + ]]> +     + $\left. (s+t+k)! \middle/ (s! \cdot t! \cdot k!) \right.$ + $\left. (s+t+k)! \middle/ (2 \cdot s! \cdot t! \cdot k!) \right.$ + $s! \cdot t! \cdot k!$ + $2 \cdot s! \cdot t! \cdot k!$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m03.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m03.xml new file mode 100644 index 00000000..186d74a0 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m03.xml @@ -0,0 +1,16 @@ + + + + + $(7n)^{n}$ + $n^{7n}$ + $n^{n}$ + $7^{n}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m04.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m04.xml new file mode 100644 index 00000000..167a9c88 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m04.xml @@ -0,0 +1,14 @@ + + + + + ${n \choose 5} + {n \choose 3} \cdot {m \choose 2} + n \cdot {m \choose 4}$ + ${m \choose 5} + {m \choose 3} \cdot {n \choose 2} + m \cdot {n \choose 4}$ + ${m+n \choose 5} - {n \choose 5}$ + ${m \choose 5} \cdot {n \choose 5}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m05.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m05.xml new file mode 100644 index 00000000..269d43a7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m05.xml @@ -0,0 +1,12 @@ + + + + + $(n/2) \cdot 2^{n/2}$ + $2^{n/2} + 2^{n/2}$ + $2^{n} - 2^{n/2}$ + $2^{n} + 2^{n/2}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m06.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m06.xml new file mode 100644 index 00000000..91c7aee6 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m06.xml @@ -0,0 +1,12 @@ + + + + + $4^{n-3} + 4^{n-4}$ + $4^{n-3} + 4^{n-4} - 4^{n-7}$ + $2 \cdot 4^{n-3} - 4^{n-7}$ + $2 \cdot 4^{n-4} - 4^{n-7}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m07.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m07.xml new file mode 100644 index 00000000..e5396e04 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m07.xml @@ -0,0 +1,15 @@ + + + + + The number of strings of length $n$, where each character is $a$ or $b$, that contain at least one $a$. + The number of strings of length $n$, where each character is $a$ or $b$, that contain at least 2 many $a$'s. + The number of strings of length $n$, where each character is $a$, $b$, or $c$, that contain at least one $a$. + The number of strings of length $n$, where each character is $a$, $b$, or $c$, that contain at least 2 many $a$'s. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m08.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m08.xml new file mode 100644 index 00000000..82306d7b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m08.xml @@ -0,0 +1,13 @@ + + + + + 4 + 5 + 6 + 7 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m09.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m09.xml new file mode 100644 index 00000000..24a4d334 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m09.xml @@ -0,0 +1,11 @@ + + + + + ${100 \choose 80} \cdot 7^{20} \cdot 13^{80}$ + $- {100 \choose 80} \cdot 7^{20} \cdot 13^{80}$ + ${100 \choose 20} \cdot 7^{80} \cdot 13^{20}$ + $- {100 \choose 20} \cdot 7^{80} \cdot 13^{20}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m10.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m10.xml new file mode 100644 index 00000000..9f2df3d2 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m10.xml @@ -0,0 +1,12 @@ + + + free if it does not contain 01. + Let $n \geq 2$ be an integer. How many 01-free bitstrings of length $n$ are there? + ]]> + + $n-1$ + $n$ + $n+1$ + $n+2$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m11.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m11.xml new file mode 100644 index 00000000..291e9da1 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m11.xml @@ -0,0 +1,16 @@ + + + free if it does not contain two 0's next to each other. + In class, we have seen that for any $m \geq 1$, the number of 00-free + bitstrings of length $m$ is equal to the $(m + 2)$-th Fibonacci number $f_{m+2}$.
    + + What is the number of 00-free bitstrings of length 20 that have 0 at position 7? + (The positions are numbered $1,2,\dots,20$.) + ]]> +     + $f_{7} \cdot f_{15}$ + $f_{8} \cdot f_{14}$ + $f_{8} \cdot f_{15}$ + $f_{7} \cdot f_{14}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m12.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m12.xml new file mode 100644 index 00000000..ae58c3c0 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m12.xml @@ -0,0 +1,38 @@ + + + + + + $f(m, 0)$ + $= m\ \;$ + $\mathrm{if}\ m \geq 0,$ + + + $f(m, n)$ + $= 1 + f(m, n - 1)\ \;$ + $\mathrm{if}\ m \geq 0$ $\mathrm{and}\ n \geq 1,$ + + + $g(0)$ + $= 1,$ + + + $g(n)$ + $= 5 \cdot g(n - 1)\ \;$ + $\mathrm{if}\ n \geq 1.$ + + + + + For any integer $n \geq 0$, what is $f(g(n), g(n))$? + ]]> + + $2 \cdot 5^{n}$ + $2 \cdot 5^{n-1}$ + $(5^{n})^{2}$ + $(5^{n-1})^{2}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m13.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m13.xml new file mode 100644 index 00000000..14fb77bb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m13.xml @@ -0,0 +1,14 @@ + + + ccc-free + if it does not contain ccc.
    + + For any integer $n \geq 4$, let $B_n$ be the number of ccc-free strings of length $n$. Which of the following is true? + ]]> +     + $B_n = B_{n-1} + B_{n-2} + B_{n-3}$ + $B_n = 2 \cdot B_{n-1} + 2 \cdot B_{n-2} + 2 \cdot B_{n-3}$ + $B_n = 2 \cdot B_{n-1} + 2 \cdot B_{n-2} + B_{n-3}$ + $B_n = B_{n-1} + B_{n-2} + 2 \cdot B_{n-3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m14.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m14.xml new file mode 100644 index 00000000..c6cd52d4 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m14.xml @@ -0,0 +1,35 @@ + + + + + A brick is a horizontal or vertical board consisting of 2 square cells; see the bottom part of the figure + above. A tiling of the board $B_n$ is a placement of bricks on the board such that +
      +
    • the bricks exactly cover $B_n$ and
      • +
    • no two bricks overlap.
      • +
    + The figure below shows a tiling of $B_{13}$. + + + + Let $T_n$ be the number of different tilings of the board $B_n$. Which of the following is true for any $n \geq 3$? + ]]> +     + $T_n = T_{n + 1} + T_{n + 2}$ + $T_n = T_{n - 1} + T_{n - 2}$ + $T_n = 2 \cdot T_{n - 1} + T_{n - 2}$ + $T_n = T_{n - 1} + 2 \cdot T_{n - 2}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m15.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m15.xml new file mode 100644 index 00000000..3968cc1a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m15.xml @@ -0,0 +1,28 @@ + + + + $\newcommand{\Hello}{{\rm H {\scriptsize ELLO}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the recursive algorithm $\Hello$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Hello(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \text{print ``hello''}$
    + $\mathbf{else}\ \Hello(n - 1);$
    + $\elsesp \text{print ``hello''};$
    + $\elsesp \Hello(n - 2)$
    + $\mathbf{endif}$ +

    + + If you run algorithm $\Hello(5)$, how many times is the word "hello" printed? + ]]> +     + 13 + 14 + 15 + 16 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m16.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m16.xml new file mode 100644 index 00000000..4b755133 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m16.xml @@ -0,0 +1,16 @@ + + + + + $\frac{{19 \choose 6} + {19 \choose 6}}{{20 \choose 7}}$ + $\frac{2 \cdot {20 \choose 6} - {20 \choose 5}}{{20 \choose 7}}$ + $\frac{2 \cdot {19 \choose 7} - {18 \choose 7}}{{20 \choose 7}}$ + $\frac{2 \cdot {19 \choose 6} - {18 \choose 5}}{{20 \choose 7}}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2017/f17m17.xml b/app/src/data/questions/comp2804/midterm-fall-2017/f17m17.xml new file mode 100644 index 00000000..5f653ad9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2017/f17m17.xml @@ -0,0 +1,22 @@ + + + + + Let $m \geq 7$ and $n \geq 7$ be integers. There are $m$ houses whose owners hand out candy and + there are $n$ houses whose owners do not hand out candy.
    + + The ladies choose a uniformly random subset of 7 houses and visit these 7 houses. Define the event + [defs] + A = "the ladies throw rotten eggs at exactly 2 of the 7 chosen houses". + [/defs] + What is $\Pr(A)$? + ]]> +     + $\frac{{m \choose 5} + {n \choose 2}}{{m+n \choose 7}}$ + $\frac{{m \choose 5} \cdot {n \choose 2}}{{m+n \choose 7}}$ + $\frac{{7 \choose 2}}{{m \choose 5} \cdot {n \choose 2}}$ + $\frac{{7 \choose 2}}{{m+n \choose 7}}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m01.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m01.xml new file mode 100644 index 00000000..677cfce9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m01.xml @@ -0,0 +1,13 @@ + + + + + $2^n$ + $3^n$ + $4^n$ + $5^n$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m02.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m02.xml new file mode 100644 index 00000000..48d78487 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m02.xml @@ -0,0 +1,20 @@ + + + +
  • + the bit at each even position is 0, or +
    • +
  • + the bitstring starts with 1010? +
    • + + ]]> +     + 54 + 56 + 58 + 60 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m03.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m03.xml new file mode 100644 index 00000000..eb895664 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m03.xml @@ -0,0 +1,12 @@ + + + + + $52^{15} - 26^{15} - 15 \cdot 26^{14}$ + $52^{15} - 26^{15} - 15 \cdot 26^{15}$ + $52^{15} - 15 \cdot 26^{15}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m04.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m04.xml new file mode 100644 index 00000000..5392dc35 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m04.xml @@ -0,0 +1,16 @@ + + + + In how many ways can Elisa place these orders of cider, such that exactly 4 of her friends get a + cider of type $C_3$? + ]]> + + ${7 \choose 4} \cdot 7^3$ + ${7 \choose 4} \cdot 8^3$ + ${7 \choose 4} \cdot 7^4$ + ${7 \choose 4} \cdot 8^4$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m05.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m05.xml new file mode 100644 index 00000000..5b1f19de --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m05.xml @@ -0,0 +1,16 @@ + + + + + ${22 \choose 5}$ + ${22 \choose 4}$ + ${21 \choose 5}$ + ${21 \choose 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m06.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m06.xml new file mode 100644 index 00000000..84952642 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m06.xml @@ -0,0 +1,12 @@ + + + + What is the minimum size of this subset $S$, such that there must be at least two elements in $S$ whose sum is equal to 51? + ]]> + + 25 + 26 + 27 + 28 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m07.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m07.xml new file mode 100644 index 00000000..373819b9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m07.xml @@ -0,0 +1,13 @@ + + + + How many such subsets have the property that $x_3 = 7$? + ]]> + + ${6 \choose 2} \cdot {10 \choose 2}$ + ${6 \choose 2} \cdot {9 \choose 2}$ + ${7 \choose 2} \cdot {10 \choose 2}$ + ${7 \choose 2} \cdot {9 \choose 2}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m08.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m08.xml new file mode 100644 index 00000000..c234af29 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m08.xml @@ -0,0 +1,17 @@ + + + + + Consider subsets $X$ of $\mathcal{B} \cup \mathcal{C}$, such that $X$ consists of exactly 5 beer + bottles and all cider bottles in $X$ have an even index.
    + + How many such subsets $X$ are there? + ]]> +     + ${12 \choose 5} \cdot 2^6$ + ${13 \choose 5} \cdot 2^5$ + ${13 \choose 5} \cdot 2^6$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m09.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m09.xml new file mode 100644 index 00000000..4c349692 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m09.xml @@ -0,0 +1,16 @@ + + + palindrome, if $$s_1s_2...s_{n-1}s_n = s_ns_{n-1}...s_2s_1,$$ + i.e., reading the string from left to right gives the same string as when reading from right to left.
    + + For any integer $n \geq 1$, let $P_n$ be the number of bitstrings of length $n$ that are palindromes.
    + + Which of the following is true for any integer $n \geq 3$? + ]]> +     + $P_n = 2 + P_{n-2}$ + $P_n = 2 \cdot P_{n/2}$ + $P_n = 2 \cdot P_{n-1}$ + $P_n = 2 \cdot P_{n-2}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m10.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m10.xml new file mode 100644 index 00000000..f17e8d26 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m10.xml @@ -0,0 +1,19 @@ + + + + + For any integer $k$ with $0 \leq k \leq n$, consider subsets $X$ of $\mathcal{B} \cup \mathcal{C}$, + such that $X$ consists of exactly $k$ bottles and no two bottles in $X$ have the same index. (For + example, if $B_n \in X$, then $C_n \notin X$.)
    + + Let $F(n,k)$ be the number of such subsets X.
    + Which of the following is true for all integers $n \geq 2$ and $k$ with $1 \leq k \leq n - 1$? + ]]> +     + $F(n,k) = F(n-1,k)\ +$ $ F(n-1,k-1)$ + $F(n,k) = F(n-1,k)\ +$ $ 2 \cdot F(n-1,k-1)$ + $F(n,k) = F(n,k-1)\ +$ $ F(n-1,k-1)$ + $F(n,k) = F(n,k-1)\ +$ $ 2 \cdot F(n-1,k-1)$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m11.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m11.xml new file mode 100644 index 00000000..8872d37f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m11.xml @@ -0,0 +1,16 @@ + + + free, if it does not contain two 0's next to each other. + In class, we have seen that for any $m \geq 1$, + the number of 00-free bitstrings of length $m$ is equal to the $(m+2)$-th Fibonacci number $f_{m+2}$.
    + + What is the number of 00-free bitstrings of length 55 that have 0 at position 9, and 1 at position 40? + (The positions are numbered $1,2,\dots,55$.) + ]]> +     + $f_7 \cdot f_{29} \cdot f_{15}$ + $f_8 \cdot f_{30} \cdot f_{16}$ + $f_9 \cdot f_{31} \cdot f_{17}$ + $f_{10} \cdot f_{32} \cdot f_{18}$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m12.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m12.xml new file mode 100644 index 00000000..422e38e9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m12.xml @@ -0,0 +1,21 @@ + + + + + $3 + 5 \cdot 2^{n}$ + $5 + 3 \cdot 2^{n}$ + $2^{3 + 5n}$ + $2^{5 + 3n}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m13.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m13.xml new file mode 100644 index 00000000..82ff6b78 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m13.xml @@ -0,0 +1,15 @@ + + + -free, if it does not contain two $q$'s next to each other. + For any integer $n \geq 1$, let $Q_n$ be the number of $qq$-free strings of length $n$.
    + + Which of the following is true for any integer $n \geq 3$? + ]]> +     + $Q(n) = 26 \cdot Q(n-1) + 26 \cdot Q(n-2)$ + $Q(n) = 25 \cdot Q(n-1) + 25 \cdot Q(n-2)$ + $Q(n) = 26 \cdot Q(n-1) + 25 \cdot Q(n-2)$ + $Q(n) = 25 \cdot Q(n-1) + 26 \cdot Q(n-2)$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m14.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m14.xml new file mode 100644 index 00000000..aaf25f2b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m14.xml @@ -0,0 +1,33 @@ + + + + $\newcommand{\Fart}{{\rm F {\scriptsize ART}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }} + \newcommand{\thensp}{\phantom{\mathbf{then}\ }}$ + + + Consider the recursive algorithm $\Fart$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fart(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \text{eat one can of beans}$
    + $\mathbf{else}\ \mathbf{if}\ n\ \mathrm{is}\ \mathrm{even}$
    + $\elsesp \mathbf{then}\ \text{fart once};$
    + $\elsesp \thensp \Fart \left( n \middle/ 2 \right)$
    + $\elsesp \mathbf{else}\ \Fart(n + 1);$
    + $\elsesp \elsesp \text{fart once};$
    + $\elsesp \elsesp \Fart(n - 1)$
    + $\elsesp \mathbf{endif};$
    + $\mathbf{endif}$ +

    + + If you run algorithm $\Fart(9)$, how many times do you fart? + ]]> +     + 11 + 12 + 13 + 14 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m15.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m15.xml new file mode 100644 index 00000000..e47b28ab --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m15.xml @@ -0,0 +1,29 @@ + + + +
  • + one student is dressed up as Donald Trump, +
    • +
  • + one student is dressed up as Kim Jong Un, +
    • +
  • + the remaining 57 students are dressed up as Kim Kardashian. +
    • + + These students are arranged, uniformly at random, on a line. +
    + Define the event, + [defs] + A = "Donald Trump is standing next to Kim Jong Un". + [/defs] + What is $\Pr(A)$? + ]]> +     + 1/58 + 2/58 + 1/59 + 2/59 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m16.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m16.xml new file mode 100644 index 00000000..33bbf22b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m16.xml @@ -0,0 +1,18 @@ + + + + + Define the event + [defs] + A = "Alexa, Tri, and Zoltan have different birthdays". + [/defs] + What is $\text{Pr}(A)$? + ]]> + + $\frac{365^2}{363 \cdot 364}$ + $\frac{363^3}{362 \cdot 363 \cdot 364}$ + $\frac{363 \cdot 364}{365^2}$ + $\frac{362 \cdot 363 \cdot 364}{365^3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2018/f18m17.xml b/app/src/data/questions/comp2804/midterm-fall-2018/f18m17.xml new file mode 100644 index 00000000..444d39eb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2018/f18m17.xml @@ -0,0 +1,18 @@ + + + + + Define the event + [defs] + A = "you answer exactly 7 questions correctly". + [/defs] + What $\Pr(A)$? + ]]> + + $\frac{{17 \choose 7} \cdot 3^{10}}{4^{17}}$ + $\frac{{17 \choose 7} \cdot 2^{10}}{4^{17}}$ + $\frac{{17 \choose 7}}{4^{17}}$ + $\frac{4^{17}}{{17 \choose 7}}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m01.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m01.xml new file mode 100644 index 00000000..7031cbd4 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m01.xml @@ -0,0 +1,13 @@ + + + ${f + m \choose 3}$ + $f \cdot {f + m - 1 \choose 3}$ + $f \cdot {f + m \choose 3}$ + $(f - 1) \cdot {f + m \choose 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m02.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m02.xml new file mode 100644 index 00000000..f9addcde --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m02.xml @@ -0,0 +1,10 @@ + + and do not contain 2? + ]]> + ${n - 1 \choose k - 1}$ + ${n - 1 \choose k}$ + ${n - 2 \choose k - 2}$ + ${n - 2 \choose k}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m03.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m03.xml new file mode 100644 index 00000000..873a746d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m03.xml @@ -0,0 +1,10 @@ + + or do not contain 2? + ]]> + ${n - 1 \choose k} + {n - 1 \choose k}$ + ${n - 2 \choose k}$ + ${n \choose k} - {n - 2 \choose k - 2}$ + ${n \choose k} - {n - 1 \choose k - 1} - {n - 1 \choose k - 1}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m04.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m04.xml new file mode 100644 index 00000000..ecb78afb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m04.xml @@ -0,0 +1,10 @@ + + + $B_n = 2 \cdot 2^{n - 3}$ + $B_n = 6 \cdot 2^{n - 3}$ + $B_n = 2^n - 2$ + $B_n = 2^n - 6$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m05.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m05.xml new file mode 100644 index 00000000..18377f1a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m05.xml @@ -0,0 +1,10 @@ + + + 17 + 18 + 19 + 20 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m06.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m06.xml new file mode 100644 index 00000000..801080e7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m06.xml @@ -0,0 +1,10 @@ + + + $4^{n - 2} + 4^{n - 3} - 4^{n - 5}$ + $4^{n - 2} + 4^{n - 3}$ + $4^n - 4^{n - 5}$ + $4^n - 4^{n - 2} - 4^{n - 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m07.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m07.xml new file mode 100644 index 00000000..18a72f34 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m07.xml @@ -0,0 +1,25 @@ + + + What does + $$ + {w \choose 3} \cdot {m \choose 2} + {w \choose 4} \cdot m + {w \choose 5} + $$ + count? + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at most 3 women can be chosen. + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at most 3 men can be chosen. + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at least 3 women must be chosen. + + + The number of ways to choose 5 people out of a group consisting of $w$ women and $m$ men, + where at least 3 men must be chosen. + + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m08.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m08.xml new file mode 100644 index 00000000..e8634d05 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m08.xml @@ -0,0 +1,11 @@ + + + $n - 1$ + $n$ + $n + 1$ + $n + 2$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m09.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m09.xml new file mode 100644 index 00000000..855e005b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m09.xml @@ -0,0 +1,9 @@ + + + $- {50 \choose 24} \cdot 5^{26} \cdot 7^{24}$ + $- {50 \choose 26} \cdot 5^{24} \cdot 7^{26}$ + ${50 \choose 24} \cdot 5^{26} \cdot 7^{24}$ + ${50 \choose 26} \cdot 5^{24} \cdot 7^{26}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m10.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m10.xml new file mode 100644 index 00000000..3d09cc24 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m10.xml @@ -0,0 +1,16 @@ + + + $f(n) = 7 \cdot \frac{n!}{3^n}$ + $f(n) = 7^n \cdot \frac{n!}{3^n}$ + $f(n) = 7 \cdot \frac{(n + 1)!}{3^n}$ + $f(n) = 7^n \cdot \frac{(n + 1)!}{3^n}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m11.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m11.xml new file mode 100644 index 00000000..e3ea3e87 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m11.xml @@ -0,0 +1,11 @@ + + + $B_n = B_{n - 1} + B_{n - 2}$ + $B_n = B_{n - 1} + B_{n - 3}$ + $B_n = B_{n - 2} + B_{n - 3}$ + $B_n = B_{n - 2} + B_{n - 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m12.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m12.xml new file mode 100644 index 00000000..d8ce881a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m12.xml @@ -0,0 +1,26 @@ + + + + + $11$ + + $= 3 + 4 + 4 = 4 + 3 + 4$ + $= 4 + 4 + 3.$ + + + + + + Which of the following is true for any $n \geq 5$? + ]]> + $S_n = 2 \cdot S_{n - 1}$ + $S_n = S_{n - 1} + S_{n - 2}$ + $S_n = S_{n - 2} + S_{n - 3}$ + $S_n = S_{n - 3} + S_{n - 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m13.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m13.xml new file mode 100644 index 00000000..cb6e3504 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m13.xml @@ -0,0 +1,23 @@ + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\Fib(n):$
    + $\quad \mathbf{if}\ n = 0\ \mathrm{or}\ n = 1\ \mathbf{then}$
    + $\quad \quad f = n$
    + $\quad \mathbf{else}$
    + $\quad \quad f = \Fib(n - 1) + \Fib(n - 2)$
    + $\quad \mathbf{return}\ f$ +

    + + When running $\Fib(12)$, how many calls are there to $\Fib(8)$? + ]]>     + 4 + 5 + 6 + 7 +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m14.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m14.xml new file mode 100644 index 00000000..8413f79b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m14.xml @@ -0,0 +1,28 @@ + + + $\newcommand{\ElisaDrinksCider}{{\rm E {\scriptsize LISA} D {\scriptsize RINKS} C {\scriptsize IDER}}}$ + + + Consider the following recursive algorithm $\ElisaDrinksCider$, which takes as input an integer + $n \geq 1$, which is a power of 2: + +

    + $\ElisaDrinksCider(n):$
    + $\quad \mathbf{if}\ n = 1\ \mathbf{then}$
    + $\quad \quad \text{then order Fibonachos}$
    + $\quad \mathbf{else}$
    + $\quad \quad \ElisaDrinksCider\left(n \middle/ 2 \right)$
    + $\quad \quad \mathrm{drink}\ n\ \text{bottles of cider}$
    + $\quad \quad \ElisaDrinksCider\left(n \middle/ 2 \right)$ +

    + + For $n$ a power of 2, let $C(n)$ be the total number of bottles of cider that you drink when running algorithm + $\ElisaDrinksCider(n)$. Which of the following is true for any $n \geq 1$ that is a power of 2?
    + (n.b., $\log$ denotes the base-2 logarithm) + ]]>     + $C(n) = n \log n - 1$ + $C(n) = n \log n + 1$ + $C(n) = n \log n$ + $C(n) = 2n \log n$ +     diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m15.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m15.xml new file mode 100644 index 00000000..4734ec9d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m15.xml @@ -0,0 +1,14 @@ + + + 1/4 + 1/3 + 1/2 + 1 + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m16.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m16.xml new file mode 100644 index 00000000..eb177623 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m16.xml @@ -0,0 +1,18 @@ + + + ${4 \choose 2} \cdot \frac{1}{365}$ + + ${4 \choose 2} \cdot \frac{1}{365} + {4 \choose 3} \cdot \frac{1}{365^2} + {4 \choose 4} \cdot \frac{1}{365^3}$ + + $1 - \frac{361 \cdot 362 \cdot 363 \cdot 364}{365^4}$ + $1 - \frac{362 \cdot 363 \cdot 364}{365^3}$ + diff --git a/app/src/data/questions/comp2804/midterm-fall-2019/f19m17.xml b/app/src/data/questions/comp2804/midterm-fall-2019/f19m17.xml new file mode 100644 index 00000000..06c198a7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-fall-2019/f19m17.xml @@ -0,0 +1,16 @@ + + Raven Idol. + You choose a uniformly random hand of 3 cards. Define the event + + [defs] + A = "the hand of 3 cards contains the Raven Idol". + [/defs] + + What is $\Pr(A)$? + ]]> + 3/17 + 3/18 + 4/19 + $1 - (17/18)^3$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m01.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m01.xml new file mode 100644 index 00000000..0b766122 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m01.xml @@ -0,0 +1,15 @@ + + + + + ${m + n + k \choose 7} - (m + n + k)$ + ${m + n + k \choose 7} - {m \choose 2} - {n \choose 2} - {k \choose 2}$ + + ${m \choose 3}{n \choose 2}{k \choose 2} + {m \choose 2}{n \choose 3}{k \choose 2} + {m \choose 2}{n \choose 2}{k \choose 3}$ + + ${m \choose 2}{n \choose 2}{k \choose 2}(m + n + k)$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m02.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m02.xml new file mode 100644 index 00000000..5c787ee9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m02.xml @@ -0,0 +1,12 @@ + + + + + $\frac{24!}{9!15!}$ + ${24 \choose 9}(9!)(15!)$ + $(9!)(15!)$ + $2(9!)(15!)$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m03.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m03.xml new file mode 100644 index 00000000..55f1294c --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m03.xml @@ -0,0 +1,12 @@ + + + and $y$, but do not contain $z$? + ]]> + + $2^{33}$ + $2^{34}$ + $2^{35}$ + $2^{37} - 2^{35} - 2^{36}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m04.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m04.xml new file mode 100644 index 00000000..e6baff36 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m04.xml @@ -0,0 +1,12 @@ + + + or $y$, but do not contain $z$? + ]]> + + $2^{36} - 2^{34}$ + $2^{36} - 2^{35}$ + $2^{37} - 2^{34}$ + $2^{37} - 2^{35}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m05.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m05.xml new file mode 100644 index 00000000..923a9dec --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m05.xml @@ -0,0 +1,12 @@ + + + + + $10^{12} + 10^{13} - 9^{12} - 9^{13}$ + $12^{10} + 13^{10} - 12^{9} - 13^{9}$ + $10^{12} + 10^{13} - 7^{12} - 7^{13}$ + $12^{10} + 13^{10} - 12^{7} - 13^{7}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m06.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m06.xml new file mode 100644 index 00000000..1c5d4362 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m06.xml @@ -0,0 +1,14 @@ + + + + + $2^k - 1 < {n \choose 7}$ + $2^k - 1 \geq {n \choose 7}$ + $2^k - 1 < \left. 2^n \middle/ {n \choose n-7} \right.$ + $2^k - 1 \geq \left. 2^n \middle/ {n \choose n-7} \right.$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m07.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m07.xml new file mode 100644 index 00000000..fb8824fb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m07.xml @@ -0,0 +1,11 @@ + + + + + ${25 \choose 16} 7^{16}21^{9}$ + ${16 \choose 25} 7^{9}21^{16}$ + ${25 \choose 16} 7^{25}3^{16}$ + none of the above + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m08.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m08.xml new file mode 100644 index 00000000..7dd154c5 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m08.xml @@ -0,0 +1,12 @@ + + + + + ${19 \choose 16}$ + ${19 \choose 17}$ + ${20 \choose 16}$ + ${20 \choose 17}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m09.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m09.xml new file mode 100644 index 00000000..cab38630 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m09.xml @@ -0,0 +1,14 @@ + + + + POOPERSCOOPER +

    + ]]> +     + $13!$ + ${13 \choose 4}{9 \choose 2}{7 \choose 2}{5 \choose 3}$ + ${13 \choose 4}{9 \choose 3}{6 \choose 2}{4 \choose 2}$ + ${13 \choose 1}{12 \choose 4}{8 \choose 2}{6 \choose 1}{5 \choose 2}{3 \choose 3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m10.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m10.xml new file mode 100644 index 00000000..664f1085 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m10.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = 3n^{2} - 5n + 2$ + $f(n) = 3n^{2} + 5n + 2$ + $f(n) = 2n^{2} - 5n + 2$ + $f(n) = 2n^{2} + 5n + 2$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m11.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m11.xml new file mode 100644 index 00000000..d0d16ba0 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m11.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + When running $\Fib(7)$, how many calls are there to $\Fib(3)$? + ]]> +     + 4 + 5 + 6 + 7 +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m12.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m12.xml new file mode 100644 index 00000000..e9e765d7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m12.xml @@ -0,0 +1,26 @@ + + + + + Consider again the recursive algorithm $\Fib$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + For $n \geq 3$, run algorithm $\Fib(n)$ and let $a_n$ be the number of times that $\Fib(2)$ is called.
    + Which of the following is true? + ]]> +     + For $n \geq 3$, $a_n = f_{n - 1}$ + For $n \geq 3$, $a_n = f_n$ + For $n \geq 3$, $a_n = f_{n + 1}$ + For $n \geq 3$, $a_n = -1 + f_n$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m13.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m13.xml new file mode 100644 index 00000000..c7825785 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m13.xml @@ -0,0 +1,12 @@ + + + + + $B_n = B_{n-1} + B_{n-2} + 2^{n-3}$ + $B_n = B_{n-1} + B_{n-2} + 2^{n-3} - B_{n-3}$ + $B_n = B_{n-1} + B_{n-2} + B_{n-3}$ + $B_n = B_{n-1} + B_{n-2} + B_{n-3} + 2^{n-4}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m14.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m14.xml new file mode 100644 index 00000000..9d2c95c2 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m14.xml @@ -0,0 +1,12 @@ + + + + + $1 - \left. {48 \choose 7} \middle/ {52 \choose 9} \right.$ + $\left. \bigl\{ {4 \choose 2} + {48 \choose 7} \bigr\} \middle/ {52 \choose 9} \right.$ + $\left. {52 \choose 9} \middle/ \bigl\{ {4 \choose 2}{48 \choose 7} \bigr\} \right.$ + $\left. {4 \choose 2}{48 \choose 7} \middle/ {52 \choose 9} \right.$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m15.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m15.xml new file mode 100644 index 00000000..5f617a87 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m15.xml @@ -0,0 +1,12 @@ + + + + + $1 - (1/2)^{25} - 25(1/2)^{25}$ + $1 + (1/2)^{25} - 25(1/2)^{25}$ + $\sum_{k=2}^{25} {{25}\choose{k}}(1/2)^{k}$ + none of the above + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m16.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m16.xml new file mode 100644 index 00000000..bcded6f7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m16.xml @@ -0,0 +1,12 @@ + + + + + $1 - \frac{365^2}{364 \cdot 363}$ + $1 - \frac{364 \cdot 363}{365^2}$ + $1 - \left. {3 \choose 2} \middle/ 365^3 \right.$ + $1 - \left. \bigl\{ {3\choose 2} + {3 \choose 3} \bigr\} \middle/ 365^3 \right.$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2014/w14m17.xml b/app/src/data/questions/comp2804/midterm-winter-2014/w14m17.xml new file mode 100644 index 00000000..1dffa4b4 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2014/w14m17.xml @@ -0,0 +1,11 @@ + + + + + Herbal tea + India Pale Ale + Poutine + None of the above, because Simon doesn't like beer + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m01.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m01.xml new file mode 100644 index 00000000..d58688c4 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m01.xml @@ -0,0 +1,14 @@ + + + + + $(n - 7) + {n \choose 7}$ + $n + {n \choose 7}$ + $(n - 7) \cdot {n \choose 7}$ + $n \cdot {n \choose 7}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m02.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m02.xml new file mode 100644 index 00000000..2852335f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m02.xml @@ -0,0 +1,12 @@ + + + + + $7^{15}$ + $15^7$ + $15!/7!$ + ${15 \choose 7}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m03.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m03.xml new file mode 100644 index 00000000..f2d46aa5 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m03.xml @@ -0,0 +1,12 @@ + + + + + $8 \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13 \cdot 14 \cdot 15$ + $9 \cdot 10 \cdot 11 \cdot 12 \cdot 13 \cdot 14 \cdot 15$ + $10 \cdot 11 \cdot 12 \cdot 13 \cdot 14 \cdot 15$ + $9 \cdot 10 \cdot 11 \cdot 12 \cdot 13 \cdot 14$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m04.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m04.xml new file mode 100644 index 00000000..1ccc17f6 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m04.xml @@ -0,0 +1,16 @@ + + + valid, + if no two consecutive characters are equal. Thus, $abacbac$ is valid, whereas $abaccac$ is not + valid.
    + + Let $n \geq 1$ be an integer and let $V_n$ be the number of valid strings of length $n$. Which of + the following is true? + ]]> +     + $V_n = 3 \cdot 2^{n-1}$ + $V_n = 3^n - (n - 1) \cdot 3$ + $V_n = 3^n - (n - 1) \cdot 3 \cdot 3^{n-2}$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m05.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m05.xml new file mode 100644 index 00000000..b8b653d1 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m05.xml @@ -0,0 +1,12 @@ + + + + + $3^{96} + 3^{96}$ + $3^{99} - 2 \cdot 3^{96}$ + $2 \cdot 3^{96} - 3^{93}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m06.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m06.xml new file mode 100644 index 00000000..89d25dea --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m06.xml @@ -0,0 +1,19 @@ + + + + $\newcommand{\Silly}{{\rm S \scriptsize ILLY}}$ + + + What does + $$ + \sum_{k=2}^{n-1} (k-1)(n-k) + $$ + count? + ]]> + + The number of 3-element subsets of an $(n-1)$-element set. + The number of 3-element subsets of an $n$-element set. + The number of 3-element subsets of an $(n+1)$-element set. + The number of times you fart when running algorithm $\Silly(n)$. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m07.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m07.xml new file mode 100644 index 00000000..7e66d076 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m07.xml @@ -0,0 +1,12 @@ + + + + + $365^2$ + $365^2 + 1$ + $2 \cdot 365$ + $2 \cdot 365 + 1$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m08.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m08.xml new file mode 100644 index 00000000..61e5b18f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m08.xml @@ -0,0 +1,11 @@ + + + + + $2^{16} \cdot 17^{82} \cdot {99 \choose 16}$ + $2^{17} \cdot 17^{82} \cdot {99 \choose 17}$ + $2^{82} \cdot 17^{17} \cdot {99 \choose 17}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m09.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m09.xml new file mode 100644 index 00000000..88dbcd57 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m09.xml @@ -0,0 +1,12 @@ + + + + + ${101 \choose 2}$ + ${101 \choose 3}$ + ${102 \choose 2}$ + ${102 \choose 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m10.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m10.xml new file mode 100644 index 00000000..ffaec5bf --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m10.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = 3n^{2} + 2n + 15$ + $f(n) = 3n^{2} - 2n + 15$ + $f(n) = 3n^{2} + n + 15$ + $f(n) = 3n^{2} - n + 15$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m11.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m11.xml new file mode 100644 index 00000000..42479d5f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m11.xml @@ -0,0 +1,13 @@ + + + valid, + if it does not contain the substring $aaa$. Let $S_n$ be the number of valid strings of length + $n$. Which of the following is true? + ]]> + + $S_n = 2 \cdot S_{n-1} + 2 \cdot S_{n-2}$ + $S_n = 2 \cdot S_{n-1} + 2 \cdot S_{n-2} + S_{n-3}$ + $S_n = 2 \cdot S_{n-1} + S_{n-2} + 2 \cdot S_{n-3}$ + $S_n = 2 \cdot S_{n-1} + 2 \cdot S_{n-2} + 2 \cdot S_{n-3}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m12.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m12.xml new file mode 100644 index 00000000..026bac49 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m12.xml @@ -0,0 +1,30 @@ + + + +
  • + the order in which the 1s and 2s occur in the sum matters, and +
    • +
  • + it is not allowed to have two consecutive 1s. +
    • + + For example, if $n = 7$, then + $$ + 7 = 1 + 2 + 1 + 2 + 1 + $$ is allowed, whereas + $$ + 7 = 1 + 2 + 1 + 1 + 2 + $$ + is not allowed.
    + + Which of the following is true? + ]]> +     + $S_n = S_{n-1} + S_{n-2}$ + $S_n = S_{n-1} + S_{n-3}$ + $S_n = S_{n-2} + S_{n-3}$ + $S_n = S_{n-1} + S_{n-2} + S_{n-3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m13.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m13.xml new file mode 100644 index 00000000..bb0c3c29 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m13.xml @@ -0,0 +1,27 @@ + + + + $\newcommand{\Fib}{{\rm F \scriptsize IB}}$ + + + Consider the following recursive algorithm $\Fib$, which takes as input an + integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ f = n$
    + $\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$
    + $\mathbf{endif};$
    + $\mathbf{return}\ f$
    +

    + + When running $\Fib(99)$, how many calls are there to $\Fib(95)$? + ]]> +     + 4 + 5 + 6 + 7 +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m14.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m14.xml new file mode 100644 index 00000000..2719e04e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m14.xml @@ -0,0 +1,31 @@ + + + + $\newcommand{\NationalAnthem}{{\rm N {\scriptsize ATIONAL} A {\scriptsize NTHEM}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the following recursive algorithm $\NationalAnthem$, which takes as input an integer $n \geq 1$, + which is a power of 2: + +

    + $\mathbf{Algorithm}\ \NationalAnthem(n)\mathrm{:}$
    + $\mathbf{if}\ n = 1$
    + $\mathbf{then}\ \mathrm{sing}\ {\it O\ Canada}\ \mathrm{once}$
    + $\mathbf{else}\ \NationalAnthem(n / 2);$
    + $\elsesp \mathrm{sing}\ {\it O\ Canada}\ \mathrm{once};$
    + $\elsesp \NationalAnthem(n / 2)$
    + $\mathbf{endif}$ +

    + + For $n$ a power of 2, let $S(n)$ be the number of times you sing O Canada when running algorithm + $\NationalAnthem(n)$. Which of the following is true?
    + (n.b., $\log$ denotes the base-2 logarithm) + ]]> +     + $S(n) = 1 + \log n$ + $S(n) = 1 + n \log n$ + $S(n) = 2n + 1$ + $S(n) = 2n - 1$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m15.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m15.xml new file mode 100644 index 00000000..4e1c1e67 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m15.xml @@ -0,0 +1,15 @@ + + + + + 3/8 + 4/8 + 5/8 + 6/8 + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m16.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m16.xml new file mode 100644 index 00000000..9f9f1285 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m16.xml @@ -0,0 +1,19 @@ + + + + + $\Pr(A) = \Pr(B)$ + $\Pr(A) < \Pr(B)$ + $\Pr(A) > \Pr(B)$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2015/w15m17.xml b/app/src/data/questions/comp2804/midterm-winter-2015/w15m17.xml new file mode 100644 index 00000000..8d5fd101 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2015/w15m17.xml @@ -0,0 +1,25 @@ + + + +
  • + There are 7 beers of the pilsner type. +
    • +
  • + There are 5 beers of the India pale ale type. +
    • +
  • + There are 4 beers of the German wheatbeer type. +
    • + + You order 4 different beers with at least one beer of each type. What is the number of ways in which + you can do this? (The order in which you order the beers does not matter.) + ]]> +     + ${16 \choose 4}$ + ${7 \choose 2} \cdot 5 \cdot 4 + 7 \cdot {5 \choose 2} \cdot 4 + 7 \cdot 5 \cdot {4 \choose 2}$ + ${16 \choose 4} - {7 \choose 3} - {5 \choose 3} - {4 \choose 3}$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m01.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m01.xml new file mode 100644 index 00000000..b3fb363e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m01.xml @@ -0,0 +1,16 @@ + + + + + $f \cdot {f+m-1 \choose 7}$ + $f + {f+m-1 \choose 5} + {f+m-6 \choose 2}$ + $f \cdot {f+m-1 \choose 5} \cdot {f+m-6 \choose 2}$ + $f \cdot {f+m \choose 5} \cdot {f+m \choose 2}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m02.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m02.xml new file mode 100644 index 00000000..9aafaf45 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m02.xml @@ -0,0 +1,12 @@ + + + + + $(b + g)!$ + $g \cdot (b + g - 1)!$ + $(b + g)! / b$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m03.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m03.xml new file mode 100644 index 00000000..2b6f2a1b --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m03.xml @@ -0,0 +1,12 @@ + + + + + $(b+g)!$ + $(b+g)! - b \cdot (b+g-1)! -\ $ $ g \cdot (b+g-1)!$ + $g \cdot (b+g-1)! + b \cdot (b+g-1)!\ -$ $ b \cdot g \cdot (b+g-1)!$ + $g \cdot (b+g-1)! + b \cdot (b+g-1)!\ -$ $ b \cdot g \cdot (b+g-2)!$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m04.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m04.xml new file mode 100644 index 00000000..53ea2ebe --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m04.xml @@ -0,0 +1,12 @@ + + + + + ${n \choose 12} \cdot {12 \choose 7}$ + ${n \choose 7} + {n \choose 5}$ + ${n \choose 7} + {n \choose 5} - {n \choose 5} \cdot {n - 5 \choose 7}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m05.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m05.xml new file mode 100644 index 00000000..12e49b2d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m05.xml @@ -0,0 +1,12 @@ + + + + + 79 + 80 + 81 + 82 + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m06.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m06.xml new file mode 100644 index 00000000..a6cf4752 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m06.xml @@ -0,0 +1,12 @@ + + + + + $4^{n}$ + $4^{n-1}$ + $4^{n-2}$ + $4^{n-3}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m07.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m07.xml new file mode 100644 index 00000000..067b46bf --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m07.xml @@ -0,0 +1,15 @@ + + + + + The number of ways to choose an ordered pair $(x,y)$ from a group consisting of $m$ men and $n$ women, where $x$ must be a man and $y$ must be a woman. + The number of ways to choose an ordered pair $(x,y)$ from a group consisting of $m$ men and $n$ women, where $x$ and $y$ cannot both be men. + The number of ways to choose an unordered pair of people from a group consisting of $m$ men and $n$ women, where at least one man must be chosen. + The number of ways to choose an unordered pair of people from a group consisting of $m$ men and $n$ women. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m08.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m08.xml new file mode 100644 index 00000000..60dff348 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m08.xml @@ -0,0 +1,15 @@ + + + + + What is the minimum number of students such that we can guarantee that at least two of them have the + same student number? + ]]> + + $1 + 10^{5}$ + $1 + 5^{10}$ + $1 + \frac{10!}{5!}$ + $1 + \frac{5!}{10!}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m09.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m09.xml new file mode 100644 index 00000000..24a4d334 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m09.xml @@ -0,0 +1,11 @@ + + + + + ${100 \choose 80} \cdot 7^{20} \cdot 13^{80}$ + $- {100 \choose 80} \cdot 7^{20} \cdot 13^{80}$ + ${100 \choose 20} \cdot 7^{80} \cdot 13^{20}$ + $- {100 \choose 20} \cdot 7^{80} \cdot 13^{20}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m10.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m10.xml new file mode 100644 index 00000000..4e416946 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m10.xml @@ -0,0 +1,14 @@ + + + + POOPERSCOOPER +

    + ]]> +     + $13!$ + ${13 \choose 4}{13 \choose 3}{13 \choose 2}{13 \choose 2}{13 \choose 1}$ + ${13 \choose 4}{9 \choose 3}{6 \choose 2}{4 \choose 2}$ + ${13 \choose 4}{9 \choose 3}{6 \choose 2}{4 \choose 2}{2 \choose 1}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m11.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m11.xml new file mode 100644 index 00000000..e7f8dfd4 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m11.xml @@ -0,0 +1,17 @@ + + + free if it does not contain two 0's next to each other. + In class, we have seen that for any $m \geq 1$, + the number of 00-free bitstrings of length $m$ is equal to the $(m+2)$-th Fibonacci number $f_{m+2}$.
    + + Let $n \geq 3$ be an integer. What is the number of 00-free bitstrings of length $3n-1$ that have 0 at position $n$ + and 1 at position $2n$? (The positions are numbered $1,2,\dots,3n-1)$.
    + (n.b., $f^2_x = f_x \cdot f_x$) + ]]> +     + ${f^2_{n+1}} \cdot f_n$ + ${f^2_{n}} \cdot f_{n+1}$ + ${f^2_{n+2}} \cdot f_{n+1}$ + ${f^2_{n+1}} \cdot f_{n+2}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m12.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m12.xml new file mode 100644 index 00000000..571c114d --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m12.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = \frac{2^{n}}{(n-1)^{2}}$ + $f(n) = \frac{2^{n-1}}{n^{2}}$ + $f(n) = \frac{2^{n}}{n^{2}}$ + $f(n) = \frac{n^{2}}{2^{n}}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m13.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m13.xml new file mode 100644 index 00000000..5062d61e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m13.xml @@ -0,0 +1,12 @@ + + + + + $B_n = n$ + $B_n = n+1$ + $B_n = f_{n+1}$, the $(n+1)$-st Fibonacci number. + $B_n = f_{n+2}$, the $(n+2)$-nd Fibonacci number. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m14.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m14.xml new file mode 100644 index 00000000..e5b634f5 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m14.xml @@ -0,0 +1,28 @@ + + + + + + $11$ + + $= 3 + 4 + 4 = 4 + 3 + 4$ + $= 4 + 4 + 3.$ + + + + + + Which of the following is true for any $n \geq 5$? + ]]> + + $S_n = 2 \cdot S_{n - 1}$ + $S_n = S_{n - 1} + S_{n - 2}$ + $S_n = S_{n - 2} + S_{n - 3}$ + $S_n = S_{n - 3} + S_{n - 4}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m15.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m15.xml new file mode 100644 index 00000000..0c05a838 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m15.xml @@ -0,0 +1,30 @@ + + + + $\newcommand{\Hello}{{\rm H {\scriptsize ELLO}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the recursive algorithm $\Hello$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \Hello(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \text{print ``hello''}$
    + $\mathbf{else}\ \mathbf{if}\ n\ \mathrm{is}\ \mathrm{even}$
    + $\elsesp \mathbf{then}\ \Hello(n / 2)$
    + $\elsesp \mathbf{else}\ \Hello(n - 1);$
    + $\elsesp \elsesp \Hello(n - 2)$
    + $\elsesp \mathbf{endif};$
    + $\mathbf{endif}$ +

    + + If we run algorithm $\Hello(7)$, how many times is the word "hello" printed? + ]]> +     + 4 + 5 + 6 + 7 +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m16.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m16.xml new file mode 100644 index 00000000..0c5b237c --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m16.xml @@ -0,0 +1,15 @@ + + + + + 1/2 + 1/4 + 1/6 + 1/8 + diff --git a/app/src/data/questions/comp2804/midterm-winter-2017/w17m17.xml b/app/src/data/questions/comp2804/midterm-winter-2017/w17m17.xml new file mode 100644 index 00000000..b64a296a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2017/w17m17.xml @@ -0,0 +1,16 @@ + + + + + $\left. n^2 \middle/ {2n \choose 2} \right.$ + $\left. {2n \choose 2} \middle/ n^2 \right.$ + $\left. n^2 \middle/ {n \choose 2} \right.$ + $\left. {n \choose 2} \middle/ n^2 \right.$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m01.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m01.xml new file mode 100644 index 00000000..105ebdfb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m01.xml @@ -0,0 +1,22 @@ + + + + + How many such strings have the property that +
      +
    • + each even position contains an element of $\{a,b,c\}$, and +
      • +
    • + each odd position contains an element of $\{d,e\}$? +
      • +
    + ]]> +     + $6^6$ + $5^{12}$ + $6^3 \cdot 6^2$ + None of the above. +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m02.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m02.xml new file mode 100644 index 00000000..57519780 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m02.xml @@ -0,0 +1,22 @@ + + + + + How many such strings have the property that +
      +
    • + each even position contains an element of $\{a, b, c\}$, or +
      • +
    • + each odd position contains an element of $\{d,e\}$? +
      • +
    + ]]> +     + $6^{3} \cdot 6^{5} + 6^{2} \cdot 6^{5}$ + $3^{6} \cdot 5^{6} + 2^{6} \cdot 5^{6}$ + $3^{6} \cdot 5^{6} + 2^{5} \cdot 5^{6} - 2^{6} \cdot 3^{6}$ + $6^{3} \cdot 6^{5} + 6^{2} \cdot 6^{5} - 6^{2} \cdot 6^{3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m03.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m03.xml new file mode 100644 index 00000000..ed926745 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m03.xml @@ -0,0 +1,14 @@ + + + + + How many such strings contain at least two $a$'s? + ]]> + + $5^{12} - 4^{12} - 12 \cdot 4^{11}$ + $5^{12} - 4^{12} - 12 \cdot 4^{12}$ + $12^{5} - 12^{4} - 12 \cdot 11^{4}$ + $12^{5} - 12^{4} - 12 \cdot 12^{4}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m04.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m04.xml new file mode 100644 index 00000000..6a0977ea --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m04.xml @@ -0,0 +1,16 @@ + + + + + In how many ways can Elisa place these orders, such that exactly 4 people get a beer? + ]]> + + ${6 \choose 4} \cdot b^{4} \cdot c^{2}$ + ${6 \choose 4} \cdot b^{4} \cdot c^{3}$ + ${7 \choose 4} \cdot b^{4} \cdot c^{3}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m05.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m05.xml new file mode 100644 index 00000000..e833c9ab --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m05.xml @@ -0,0 +1,20 @@ + + + +
  • + 60 do not like Donald Trump and do not like Kim Jong Un, and +
    • +
  • + 25 like Kim Jong Un. +
    • + + How many people in this group like Donald Trump and do not like Kim Jong Un? + ]]> +     + 10 + 15 + 20 + 25 +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m06.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m06.xml new file mode 100644 index 00000000..398cbda7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m06.xml @@ -0,0 +1,16 @@ + + + ShortLastName, every person has a last name consisting of one uppercase letter, + followed by two lowercase letters. No two letters in a last name can be equal. Thus, Lin + is a valid last name, whereas Xax is not a valid last name.
    + + What is the minimum size of the population of ShortLastName, such that there must be at least two people + who have the same last name? + ]]> +     + $1 + 26!$ + $1 + 26^{3}$ + $1 + \frac{24 \cdot 25 \cdot 26}{3!}$ + $1 + 24 \cdot 25 \cdot 26$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m07.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m07.xml new file mode 100644 index 00000000..d7ff1fc8 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m07.xml @@ -0,0 +1,17 @@ + + + + + The number of bitstrings of length $n$. + The number of bitstrings of length $\left. (n-2) \middle/ 2 \right.$. + The number of bitstrings of length $n$ having an odd number of 0's. + + The number of bitstrings of length $n$ in which the number of 0's plus the number of 1's is at most $\left. (n-1) \middle/ 2 \right.$. + + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m08.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m08.xml new file mode 100644 index 00000000..0a53bf73 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m08.xml @@ -0,0 +1,23 @@ + + + + + Consider subsets $X$ of $A \cup B$, such that $|X| = k, |X \cap A| = 17$, and all elements of $X \cap A$ are even.
    + + How many such subsets $X$ are there? + ]]> +     + ${m/2 \choose 17} \cdot {n \choose k-17}$ + ${m \choose 17} \cdot {n \choose k-17}$ + ${m+n \choose 17} \cdot {n \choose k-17}$ + ${m/2+n \choose 17} \cdot {n \choose k-17}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m09.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m09.xml new file mode 100644 index 00000000..85d89aea --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m09.xml @@ -0,0 +1,16 @@ + + + + + ${36 \choose 4}$ + ${36 \choose 3}$ + ${37 \choose 4}$ + ${37 \choose 3}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m10.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m10.xml new file mode 100644 index 00000000..31dce6eb --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m10.xml @@ -0,0 +1,21 @@ + + + + + Since having finished marking assignment 2, Nick has been working hard to improve his Spiderman-skills: + In one step, Nick can move up either two floors or three floors. (Nick lost his ability to move up one floor in one step.)
    + + Let $n \geq 2$ be an integer and consider a building with $n$ floors, numbered $1,2,\dots,n$. (The first floor has number 1; + this is not the ground floor.) Nick is standing in front of this building, at the ground level.
    + + Let $N_n$ be the number of different ways in which Nick can climb to the $n$-th floor. + Which of the following is true for any $n \geq 5$? + ]]> +     + $N_n = N_{n-1} + N_{n-2} + N_{n-3}$ + $N_n = N_{n-1} + N_{n-2}$ + $N_n = N_{n-1} + N_{n-3}$ + $N_n = N_{n-2} + N_{n-3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m11.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m11.xml new file mode 100644 index 00000000..4518855a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m11.xml @@ -0,0 +1,16 @@ + + + free, if it does not contain two 0's next to each other. + In class, we have seen that for any $m \geq 1$, + the number of 00-free bitstrings of length $m$ is equal to the $(m+2)$-th Fibonacci number $f_{m+2}$.
    + + What is the number of 00-free bitstrings of length 55 that have 0 at position 9, and 1 at position 40? + (The positions are numbered $1,2,\dots,55$.) + ]]> +     + $f_7 \cdot f_{29} \cdot f_{15}$ + $f_8 \cdot f_{30} \cdot f_{16}$ + $f_9 \cdot f_{31} \cdot f_{17}$ + $f_{10} \cdot f_{32} \cdot f_{18}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m12.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m12.xml new file mode 100644 index 00000000..6d9d760e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m12.xml @@ -0,0 +1,21 @@ + + + + + $7^{2n}$ + $7^{n}$ + $(2n)^{7}$ + $n^{7}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m13.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m13.xml new file mode 100644 index 00000000..d15ec03a --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m13.xml @@ -0,0 +1,15 @@ + + + ccc-free, if it does not contain ccc.
    + + For any integer $n \geq 4$, let $B_n$ be the number of ccc-free bitstrings of length $n$. + Which of the following is true? + ]]> +     + $B_n = B_{n-1} + B_{n-2} + B_{n-3}$ + $B_n = 2 \cdot B_{n-1} + 2 \cdot B_{n-2} + 2 \cdot B_{n-3}$ + $B_n = 2 \cdot B_{n-1} + 2 \cdot B_{n-2} + B_{n-3}$ + $B_n = B_{n-1} + B_{n-2} + 2 \cdot B_{n-3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m14.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m14.xml new file mode 100644 index 00000000..9eb38703 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m14.xml @@ -0,0 +1,30 @@ + + + + $\newcommand{\IFeelLikeSinging}{{\rm IF {\scriptsize EEL} L {\scriptsize IKE} S {\scriptsize INGING}}} + \newcommand{\elsesp}{\phantom{\mathbf{else}\ }}$ + + + Consider the recursive algorithm $\IFeelLikeSinging$, which takes as input an integer $n \geq 0$: + +

    + $\mathbf{Algorithm}\ \IFeelLikeSinging(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \mathrm{sing}\ {\it O\ Canada}$
    + $\mathbf{else}\ \mathbf{if}\ n\ \text{is odd}$
    + $\elsesp \mathbf{then}\ \IFeelLikeSinging(n + 1)$
    + $\elsesp \mathbf{else}\ \IFeelLikeSinging(\frac{n}{2});$
    + $\elsesp \elsesp \IFeelLikeSinging(\frac{n}{2} - 1)$
    + $\elsesp \mathbf{endif};$
    + $\mathbf{endif}$ +

    + + If you run algorithm $\IFeelLikeSinging(9)$, how many times do you sing O Canada? + ]]> +     + 6 + 7 + 8 + 9 +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m15.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m15.xml new file mode 100644 index 00000000..36fbd3c7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m15.xml @@ -0,0 +1,15 @@ + + + + + ${12 \choose 2} \cdot \left. 5^{10} \middle/ 6^{12} \right.$ + $12^{2} \cdot \left. 5^{10} \middle/ 6^{12} \right.$ + ${12 \choose 2} \cdot \left. 5^{12} \middle/ 6^{12} \right.$ + $12^{2} \cdot \left. 5^{12} \middle/ 6^{12} \right.$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2018/w18m16.xml b/app/src/data/questions/comp2804/midterm-winter-2018/w18m16.xml new file mode 100644 index 00000000..e896e1a4 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2018/w18m16.xml @@ -0,0 +1,19 @@ + + + + + Nick buys 25 bananas at Alexa's Banana Emporium (ABE) and 30 bananas at Shelly's Fruit Market (SFM). + Nick chooses, uniformly at random, a 15-element subset of these bananas. Define the event + [defs] + A = "the subset chosen by Nick contains exactly 7 bananas from ABE". + [/defs] + What is $\Pr(A)$? + ]]> + + $\frac{{25 \choose 8} + {30 \choose 7}}{55 \choose 15}$ + $\frac{{25 \choose 8} \cdot {30 \choose 7}}{55 \choose 15}$ + $\frac{{25 \choose 7} + {30 \choose 8}}{55 \choose 15}$ + $\frac{{25 \choose 7} \cdot {30 \choose 8}}{55 \choose 15}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m01.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m01.xml new file mode 100644 index 00000000..6f301d16 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m01.xml @@ -0,0 +1,12 @@ + + + + + 32 + 64 + 128 + 256 + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m02.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m02.xml new file mode 100644 index 00000000..e9957c2c --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m02.xml @@ -0,0 +1,12 @@ + + + + How many such permutations are there? + ]]> + + $7! - 6!$ + $7! - 5!$ + $7! - 4!$ + $7! - 3!$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m03.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m03.xml new file mode 100644 index 00000000..304b400f --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m03.xml @@ -0,0 +1,12 @@ + + + + + $52^{15} - 26^{15}$ + $52^{15} - 2 \cdot 26^{15}$ + $52^{15} - 3 \cdot 26^{15}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m04.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m04.xml new file mode 100644 index 00000000..a6de04dd --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m04.xml @@ -0,0 +1,13 @@ + + + + + ${n \choose k} - {n/2 \choose k - 1} - \frac{n}{2} \cdot {n/2 \choose k}$ + ${n \choose k} - {n/2 \choose k - 1} - \frac{n}{2} \cdot {n/2 \choose k - 1}$ + ${n \choose k} - {n/2 \choose k} - \frac{n}{2} \cdot {n/2 \choose k}$ + ${n \choose k} - {n/2 \choose k} - \frac{n}{2} \cdot {n/2 \choose k - 1}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m05.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m05.xml new file mode 100644 index 00000000..9a6891b9 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m05.xml @@ -0,0 +1,23 @@ + + + +
  • + 37 students like beer, +
    • +
  • + 18 students like cider, +
    • +
  • + 55 students do not like beer and do not like cider. +
    • + + How many students like beer and cider? + ]]> +     + 8 + 9 + 10 + 11 +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m06.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m06.xml new file mode 100644 index 00000000..fb8d956e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m06.xml @@ -0,0 +1,13 @@ + + + + What is the minimum value for $n$, such that there must be at least four students who receive the same grade? + ]]> + + 14 + 15 + 16 + 17 + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m07.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m07.xml new file mode 100644 index 00000000..05bfcbc7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m07.xml @@ -0,0 +1,12 @@ + + + + How many such subsets have the property that the largest element in the subset is equal to 30? + ]]> + + ${{29}\choose{16}}$ + ${29 \choose 17}$ + ${30 \choose 16}$ + ${30 \choose 17}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m08.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m08.xml new file mode 100644 index 00000000..5adedbec --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m08.xml @@ -0,0 +1,27 @@ + + + + + + + (beer bottle, cider bottle, wine bottle) +

    + in a set consisting of $n$ beer bottles, $n$ cider bottles, and $n$ wine bottles. + ]]> +     + + The number of ways to choose a 3-element subset of a set consisting of $n$ beer bottles, $n$ cider bottles, and $n$ wine bottles. + + + The number of ways to choose 3 elements (with repetitions allowed) in a set consisting of $n$ beer bottles, $n$ cider bottles, and $n$ wine bottles. + + None of the above. +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m09.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m09.xml new file mode 100644 index 00000000..fd8b472e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m09.xml @@ -0,0 +1,24 @@ + + + +
  • + each character is an element of $\{a, b, c\}$, +
    • +
  • + the number of $a$'s is equal to $k$, and +
    • +
  • + each $a$ is at an even position. +
    • + + How many such strings are there? + ]]> +     + ${n/2 \choose k} \cdot 2^{n-k}$ + ${n/2 \choose k} \cdot 2^{n/2}$ + ${n \choose k} \cdot 2^{n-k}$ + ${n \choose k} \cdot 2^{n/2}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m10.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m10.xml new file mode 100644 index 00000000..7a5ea8e1 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m10.xml @@ -0,0 +1,15 @@ + + + free, if it does not contain two 0's next to each other. + In class, we have seen that for any $m \geq 1$, + the number of 00-free bitstrings of length $m$ is equal to the $(m+2)$-th Fibonacci number + $f_{m+2}$.
    + What is the number of 00-free bitstrings of length 77 that have 0 at position 59? (The positions are numbered $1,2,\dots,77$.) + ]]> +     + $f_{17} \cdot f_{57}$ + $f_{18} \cdot f_{58}$ + $f_{19} \cdot f_{59}$ + $f_{20} \cdot f_{60}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m11.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m11.xml new file mode 100644 index 00000000..8d0161f7 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m11.xml @@ -0,0 +1,18 @@ + + + + + $f(n) = 6 \cdot 4^{n} - 2^{n}$ + $f(n) = 7 \cdot 4^{n} - 2^{n}$ + $f(n) = 8 \cdot 4^{n} - 2^{n+1}$ + None of the above. + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m12.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m12.xml new file mode 100644 index 00000000..e9c68100 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m12.xml @@ -0,0 +1,14 @@ + + + awesome, if it does not contain $aa$, and does not contain $aba$, and does not contain $abb$.
    + For any integer $n \geq 1$, let $A_n$ be the number of awesome strings of length $n$.
    + Which of the following is true for any integer $n \geq 4$? + ]]> +     + $A_n = A_{n-1} + 2 \cdot A_{n-2} + 2 \cdot A_{n-3}$ + $A_n = A_{n-1} + 2 \cdot A_{n-2} + A_{n-3}$ + $A_n = 2 \cdot A_{n-1} + A_{n-2} + 2 \cdot A_{n-3}$ + $A_n = 2 \cdot A_{n-1} + A_{n-2} + A_{n-3}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m13.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m13.xml new file mode 100644 index 00000000..c19e2fbc --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m13.xml @@ -0,0 +1,23 @@ + + + $1 \atop 1$-column, + if both bits in the column are 1.
    + For any integer $n \geq 1$ and integer $k$ with $0 \leq k \leq n$, let $M(n,k)$ be the number of binary $2 \times n$ matrices +
      +
    • + that do not contain any $1 \atop 1$-column, and +
      • +
    • + contain exactly $k$ many 1's. +
      • +
    + Which of the following is true for all integers $n \geq 2$ and $k$ with $1 \leq k \leq n-1$? + ]]> +     + $M(n,k) = M(n-1,k)\ +$$\ M(n-1,k-1)$ + $M(n,k) = M(n-1,k)\ +$$\ 2 \cdot M(n-1,k-1)$ + $M(n,k) = M(n,k-1)\ +$$\ M(n-1,k-1)$ + $M(n,k) = M(n,k-1)\ +$$\ 2 \cdot M(n-1,k-1)$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m14.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m14.xml new file mode 100644 index 00000000..27f07e22 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m14.xml @@ -0,0 +1,26 @@ + + + $\newcommand{\HelloWorld}{{\rm H {\scriptsize ELLO} W {\scriptsize ORLD}}}$ + + Consider the recursive algorithm $\HelloWorld$, which takes as input an integer $n \geq 0$: +

    + $\mathbf{Algorithm}\ \HelloWorld(n)\mathrm{:}$
    + $\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$
    + $\mathbf{then}\ \mathrm{print}\ \mathit{Hello}\ \mathit{World}$
    + $\mathbf{else}\ \mathbf{if}\ n \text{ is a multiple of } 3$
    + $\qquad \mathbf{then}\ \HelloWorld\left( n \middle/ 3 \right);$
    + $\qquad \qquad \ \ \mathrm{print}\ \mathit{Hello}\ \mathit{World};$
    + $\qquad \qquad \ \ \HelloWorld\left( 2n \middle/ 3 \right)$
    + $\qquad \mathbf{else}\ \HelloWorld(n + 1)$
    + $\qquad \mathbf{endif};$
    + $\mathbf{endif}$ +

    + Which of the following is correct? + ]]> +     + For any integer $n \geq 0$, algorithm $\HelloWorld(n)$ terminates. + There exists an integer $n \geq 0$, for which algorithm $\HelloWorld(n)$ does not terminate. + All of the above. + None of the above. +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m15.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m15.xml new file mode 100644 index 00000000..102fa33e --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m15.xml @@ -0,0 +1,30 @@ + + + +
  • + Porterhouse Brewing Co. Oyster Stout, +
    • +
  • + Guinness Extra Stout, +
    • +
  • + Magners Original Irish Cider. +
    • + + There is an unlimited supply for each of these types.
    + There are 75 students at the party, and each of them gets one drink, which is chosen uniformly at random from these three types.
    + Let $A$ be the event + [defs] + A = "exactly 50 students get Magners Original Irish Cider". + [/defs] + What is $\Pr(A)$? + ]]> +     + $\frac{{ 75 \choose 50 } \cdot 2^{25}}{3^{75}}$ + $\frac{3^{75}}{{75 \choose 50} \cdot 2^{25}}$ + $\frac{75 \choose 50}{3^{75}}$ + $\frac{{75 \choose 50} \cdot 3^{25}}{3^{75}}$ +     diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m16.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m16.xml new file mode 100644 index 00000000..7c7245cf --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m16.xml @@ -0,0 +1,15 @@ + + + + + $1 - {\frac{8 \cdot 5^{7}}{6^{8}}}$ + $1 - {\frac{6^{8}}{5^{8} + 8 \cdot 5^{7}}}$ + $1 - {\frac{5^{8} + 8 \cdot 5^{7}}{6^{8}}}$ + $1 - {\frac{8^{5} + 8 \cdot 7^{5}}{8^{6}}}$ + diff --git a/app/src/data/questions/comp2804/midterm-winter-2019/w19m17.xml b/app/src/data/questions/comp2804/midterm-winter-2019/w19m17.xml new file mode 100644 index 00000000..b284aaa0 --- /dev/null +++ b/app/src/data/questions/comp2804/midterm-winter-2019/w19m17.xml @@ -0,0 +1,17 @@ + + + + Let A be the event + [defs] + A = "you answer at least 16 questions correctly". + [/defs] + What is $\Pr(A)$? + ]]> + + $\frac{4^{17}}{52}$ + $\frac{51}{4^{17}}$ + $\frac{49}{4^{17}}$ + $\frac{52}{4^{17}}$ + diff --git a/app/src/data/tests/comp1805/midterm-fall-2013.json b/app/src/data/tests/comp1805/midterm-fall-2013.json new file mode 100644 index 00000000..49b0902a --- /dev/null +++ b/app/src/data/tests/comp1805/midterm-fall-2013.json @@ -0,0 +1,6 @@ +{ + "id": "midterm-fall-2013", + "title": "TEMPORARY", + "author": "Michiel Smid", + "questions": ["comp2804/midterm-fall-2013/f13m01.xml"] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2013.json b/app/src/data/tests/comp2804/exam-fall-2013.json new file mode 100644 index 00000000..70281ffb --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2013.json @@ -0,0 +1,40 @@ +{ + "id": "exam-fall-2013", + "title": "Fall 2013 Exam", + "author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2013/f13f01.xml", + "comp2804/exam-fall-2013/f13f02.xml", + "comp2804/exam-fall-2013/f13f03.xml", + "comp2804/exam-fall-2013/f13f04.xml", + "comp2804/exam-fall-2013/f13f05.xml", + "comp2804/exam-fall-2013/f13f06.xml", + "comp2804/exam-fall-2013/f13f07.xml", + "comp2804/exam-fall-2013/f13f08.xml", + "comp2804/exam-fall-2013/f13f09.xml", + "comp2804/exam-fall-2013/f13f10.xml", + "comp2804/exam-fall-2013/f13f11.xml", + "comp2804/exam-fall-2013/f13f12.xml", + "comp2804/exam-fall-2013/f13f13.xml", + "comp2804/exam-fall-2013/f13f14.xml", + "comp2804/exam-fall-2013/f13f15.xml", + "comp2804/exam-fall-2013/f13f16.xml", + "comp2804/exam-fall-2013/f13f17.xml", + "comp2804/exam-fall-2013/f13f18.xml", + "comp2804/exam-fall-2013/f13f19.xml", + "comp2804/exam-fall-2013/f13f20.xml", + "comp2804/exam-fall-2013/f13f21.xml", + "comp2804/exam-fall-2013/f13f22.xml", + "comp2804/exam-fall-2013/f13f23.xml", + "comp2804/exam-fall-2013/f13f24.xml", + "comp2804/exam-fall-2013/f13f25.xml", + "comp2804/exam-fall-2013/f13f26.xml", + "comp2804/exam-fall-2013/f13f27.xml", + "comp2804/exam-fall-2013/f13f28.xml", + "comp2804/exam-fall-2013/f13f29.xml", + "comp2804/exam-fall-2013/f13f30.xml", + "comp2804/exam-fall-2013/f13f31.xml", + "comp2804/exam-fall-2013/f13f32.xml", + "comp2804/exam-fall-2013/f13f33.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2014.json b/app/src/data/tests/comp2804/exam-fall-2014.json new file mode 100644 index 00000000..e942eff9 --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2014.json @@ -0,0 +1,32 @@ +{ + "id": "exam-fall-2014", + "title": "Fall 2014 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2014/f14f01.xml", + "comp2804/exam-fall-2014/f14f02.xml", + "comp2804/exam-fall-2014/f14f03.xml", + "comp2804/exam-fall-2014/f14f04.xml", + "comp2804/exam-fall-2014/f14f05.xml", + "comp2804/exam-fall-2014/f14f06.xml", + "comp2804/exam-fall-2014/f14f07.xml", + "comp2804/exam-fall-2014/f14f08.xml", + "comp2804/exam-fall-2014/f14f09.xml", + "comp2804/exam-fall-2014/f14f10.xml", + "comp2804/exam-fall-2014/f14f11.xml", + "comp2804/exam-fall-2014/f14f12.xml", + "comp2804/exam-fall-2014/f14f13.xml", + "comp2804/exam-fall-2014/f14f14.xml", + "comp2804/exam-fall-2014/f14f15.xml", + "comp2804/exam-fall-2014/f14f16.xml", + "comp2804/exam-fall-2014/f14f17.xml", + "comp2804/exam-fall-2014/f14f18.xml", + "comp2804/exam-fall-2014/f14f19.xml", + "comp2804/exam-fall-2014/f14f20.xml", + "comp2804/exam-fall-2014/f14f21.xml", + "comp2804/exam-fall-2014/f14f22.xml", + "comp2804/exam-fall-2014/f14f23.xml", + "comp2804/exam-fall-2014/f14f24.xml", + "comp2804/exam-fall-2014/f14f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2015.json b/app/src/data/tests/comp2804/exam-fall-2015.json new file mode 100644 index 00000000..a9b2f71d --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2015.json @@ -0,0 +1,32 @@ +{ + "id": "exam-fall-2015", + "title": "Fall 2015 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2015/f15f01.xml", + "comp2804/exam-fall-2015/f15f02.xml", + "comp2804/exam-fall-2015/f15f03.xml", + "comp2804/exam-fall-2015/f15f04.xml", + "comp2804/exam-fall-2015/f15f05.xml", + "comp2804/exam-fall-2015/f15f06.xml", + "comp2804/exam-fall-2015/f15f07.xml", + "comp2804/exam-fall-2015/f15f08.xml", + "comp2804/exam-fall-2015/f15f09.xml", + "comp2804/exam-fall-2015/f15f10.xml", + "comp2804/exam-fall-2015/f15f11.xml", + "comp2804/exam-fall-2015/f15f12.xml", + "comp2804/exam-fall-2015/f15f13.xml", + "comp2804/exam-fall-2015/f15f14.xml", + "comp2804/exam-fall-2015/f15f15.xml", + "comp2804/exam-fall-2015/f15f16.xml", + "comp2804/exam-fall-2015/f15f17.xml", + "comp2804/exam-fall-2015/f15f18.xml", + "comp2804/exam-fall-2015/f15f19.xml", + "comp2804/exam-fall-2015/f15f20.xml", + "comp2804/exam-fall-2015/f15f21.xml", + "comp2804/exam-fall-2015/f15f22.xml", + "comp2804/exam-fall-2015/f15f23.xml", + "comp2804/exam-fall-2015/f15f24.xml", + "comp2804/exam-fall-2015/f15f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2016.json b/app/src/data/tests/comp2804/exam-fall-2016.json new file mode 100644 index 00000000..df49ceda --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2016.json @@ -0,0 +1,32 @@ +{ + "id": "exam-fall-2016", + "title": "Fall 2016 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2016/f16f01.xml", + "comp2804/exam-fall-2016/f16f02.xml", + "comp2804/exam-fall-2016/f16f03.xml", + "comp2804/exam-fall-2016/f16f04.xml", + "comp2804/exam-fall-2016/f16f05.xml", + "comp2804/exam-fall-2016/f16f06.xml", + "comp2804/exam-fall-2016/f16f07.xml", + "comp2804/exam-fall-2016/f16f08.xml", + "comp2804/exam-fall-2016/f16f09.xml", + "comp2804/exam-fall-2016/f16f10.xml", + "comp2804/exam-fall-2016/f16f11.xml", + "comp2804/exam-fall-2016/f16f12.xml", + "comp2804/exam-fall-2016/f16f13.xml", + "comp2804/exam-fall-2016/f16f14.xml", + "comp2804/exam-fall-2016/f16f15.xml", + "comp2804/exam-fall-2016/f16f16.xml", + "comp2804/exam-fall-2016/f16f17.xml", + "comp2804/exam-fall-2016/f16f18.xml", + "comp2804/exam-fall-2016/f16f19.xml", + "comp2804/exam-fall-2016/f16f20.xml", + "comp2804/exam-fall-2016/f16f21.xml", + "comp2804/exam-fall-2016/f16f22.xml", + "comp2804/exam-fall-2016/f16f23.xml", + "comp2804/exam-fall-2016/f16f24.xml", + "comp2804/exam-fall-2016/f16f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2017.json b/app/src/data/tests/comp2804/exam-fall-2017.json new file mode 100644 index 00000000..7d0edcf0 --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2017.json @@ -0,0 +1,32 @@ +{ + "id": "exam-fall-2017", + "title": "Fall 2017 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2017/f17f01.xml", + "comp2804/exam-fall-2017/f17f02.xml", + "comp2804/exam-fall-2017/f17f03.xml", + "comp2804/exam-fall-2017/f17f04.xml", + "comp2804/exam-fall-2017/f17f05.xml", + "comp2804/exam-fall-2017/f17f06.xml", + "comp2804/exam-fall-2017/f17f07.xml", + "comp2804/exam-fall-2017/f17f08.xml", + "comp2804/exam-fall-2017/f17f09.xml", + "comp2804/exam-fall-2017/f17f10.xml", + "comp2804/exam-fall-2017/f17f11.xml", + "comp2804/exam-fall-2017/f17f12.xml", + "comp2804/exam-fall-2017/f17f13.xml", + "comp2804/exam-fall-2017/f17f14.xml", + "comp2804/exam-fall-2017/f17f15.xml", + "comp2804/exam-fall-2017/f17f16.xml", + "comp2804/exam-fall-2017/f17f17.xml", + "comp2804/exam-fall-2017/f17f18.xml", + "comp2804/exam-fall-2017/f17f19.xml", + "comp2804/exam-fall-2017/f17f20.xml", + "comp2804/exam-fall-2017/f17f21.xml", + "comp2804/exam-fall-2017/f17f22.xml", + "comp2804/exam-fall-2017/f17f23.xml", + "comp2804/exam-fall-2017/f17f24.xml", + "comp2804/exam-fall-2017/f17f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2018.json b/app/src/data/tests/comp2804/exam-fall-2018.json new file mode 100644 index 00000000..d4c0f39d --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2018.json @@ -0,0 +1,32 @@ +{ + "id": "exam-fall-2018", + "title": "Fall 2018 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2018/f18f01.xml", + "comp2804/exam-fall-2018/f18f02.xml", + "comp2804/exam-fall-2018/f18f03.xml", + "comp2804/exam-fall-2018/f18f04.xml", + "comp2804/exam-fall-2018/f18f05.xml", + "comp2804/exam-fall-2018/f18f06.xml", + "comp2804/exam-fall-2018/f18f07.xml", + "comp2804/exam-fall-2018/f18f08.xml", + "comp2804/exam-fall-2018/f18f09.xml", + "comp2804/exam-fall-2018/f18f10.xml", + "comp2804/exam-fall-2018/f18f11.xml", + "comp2804/exam-fall-2018/f18f12.xml", + "comp2804/exam-fall-2018/f18f13.xml", + "comp2804/exam-fall-2018/f18f14.xml", + "comp2804/exam-fall-2018/f18f15.xml", + "comp2804/exam-fall-2018/f18f16.xml", + "comp2804/exam-fall-2018/f18f17.xml", + "comp2804/exam-fall-2018/f18f18.xml", + "comp2804/exam-fall-2018/f18f19.xml", + "comp2804/exam-fall-2018/f18f20.xml", + "comp2804/exam-fall-2018/f18f21.xml", + "comp2804/exam-fall-2018/f18f22.xml", + "comp2804/exam-fall-2018/f18f23.xml", + "comp2804/exam-fall-2018/f18f24.xml", + "comp2804/exam-fall-2018/f18f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-fall-2019.json b/app/src/data/tests/comp2804/exam-fall-2019.json new file mode 100644 index 00000000..1365b818 --- /dev/null +++ b/app/src/data/tests/comp2804/exam-fall-2019.json @@ -0,0 +1,32 @@ +{ + "id": "exam-fall-2019", + "title": "Fall 2019 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-fall-2019/f19f01.xml", + "comp2804/exam-fall-2019/f19f02.xml", + "comp2804/exam-fall-2019/f19f03.xml", + "comp2804/exam-fall-2019/f19f04.xml", + "comp2804/exam-fall-2019/f19f05.xml", + "comp2804/exam-fall-2019/f19f06.xml", + "comp2804/exam-fall-2019/f19f07.xml", + "comp2804/exam-fall-2019/f19f08.xml", + "comp2804/exam-fall-2019/f19f09.xml", + "comp2804/exam-fall-2019/f19f10.xml", + "comp2804/exam-fall-2019/f19f11.xml", + "comp2804/exam-fall-2019/f19f12.xml", + "comp2804/exam-fall-2019/f19f13.xml", + "comp2804/exam-fall-2019/f19f14.xml", + "comp2804/exam-fall-2019/f19f15.xml", + "comp2804/exam-fall-2019/f19f16.xml", + "comp2804/exam-fall-2019/f19f17.xml", + "comp2804/exam-fall-2019/f19f18.xml", + "comp2804/exam-fall-2019/f19f19.xml", + "comp2804/exam-fall-2019/f19f20.xml", + "comp2804/exam-fall-2019/f19f21.xml", + "comp2804/exam-fall-2019/f19f22.xml", + "comp2804/exam-fall-2019/f19f23.xml", + "comp2804/exam-fall-2019/f19f24.xml", + "comp2804/exam-fall-2019/f19f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-winter-2014.json b/app/src/data/tests/comp2804/exam-winter-2014.json new file mode 100644 index 00000000..f229ceee --- /dev/null +++ b/app/src/data/tests/comp2804/exam-winter-2014.json @@ -0,0 +1,32 @@ +{ + "id": "exam-winter-2014", + "title": "Winter 2014 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-winter-2014/w14f01.xml", + "comp2804/exam-winter-2014/w14f02.xml", + "comp2804/exam-winter-2014/w14f03.xml", + "comp2804/exam-winter-2014/w14f04.xml", + "comp2804/exam-winter-2014/w14f05.xml", + "comp2804/exam-winter-2014/w14f06.xml", + "comp2804/exam-winter-2014/w14f07.xml", + "comp2804/exam-winter-2014/w14f08.xml", + "comp2804/exam-winter-2014/w14f09.xml", + "comp2804/exam-winter-2014/w14f10.xml", + "comp2804/exam-winter-2014/w14f11.xml", + "comp2804/exam-winter-2014/w14f12.xml", + "comp2804/exam-winter-2014/w14f13.xml", + "comp2804/exam-winter-2014/w14f14.xml", + "comp2804/exam-winter-2014/w14f15.xml", + "comp2804/exam-winter-2014/w14f16.xml", + "comp2804/exam-winter-2014/w14f17.xml", + "comp2804/exam-winter-2014/w14f18.xml", + "comp2804/exam-winter-2014/w14f19.xml", + "comp2804/exam-winter-2014/w14f20.xml", + "comp2804/exam-winter-2014/w14f21.xml", + "comp2804/exam-winter-2014/w14f22.xml", + "comp2804/exam-winter-2014/w14f23.xml", + "comp2804/exam-winter-2014/w14f24.xml", + "comp2804/exam-winter-2014/w14f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-winter-2015.json b/app/src/data/tests/comp2804/exam-winter-2015.json new file mode 100644 index 00000000..e0b4db3b --- /dev/null +++ b/app/src/data/tests/comp2804/exam-winter-2015.json @@ -0,0 +1,32 @@ +{ + "id": "exam-winter-2015", + "title": "Winter 2015 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-winter-2015/w15f01.xml", + "comp2804/exam-winter-2015/w15f02.xml", + "comp2804/exam-winter-2015/w15f03.xml", + "comp2804/exam-winter-2015/w15f04.xml", + "comp2804/exam-winter-2015/w15f05.xml", + "comp2804/exam-winter-2015/w15f06.xml", + "comp2804/exam-winter-2015/w15f07.xml", + "comp2804/exam-winter-2015/w15f08.xml", + "comp2804/exam-winter-2015/w15f09.xml", + "comp2804/exam-winter-2015/w15f10.xml", + "comp2804/exam-winter-2015/w15f11.xml", + "comp2804/exam-winter-2015/w15f12.xml", + "comp2804/exam-winter-2015/w15f13.xml", + "comp2804/exam-winter-2015/w15f14.xml", + "comp2804/exam-winter-2015/w15f15.xml", + "comp2804/exam-winter-2015/w15f16.xml", + "comp2804/exam-winter-2015/w15f17.xml", + "comp2804/exam-winter-2015/w15f18.xml", + "comp2804/exam-winter-2015/w15f19.xml", + "comp2804/exam-winter-2015/w15f20.xml", + "comp2804/exam-winter-2015/w15f21.xml", + "comp2804/exam-winter-2015/w15f22.xml", + "comp2804/exam-winter-2015/w15f23.xml", + "comp2804/exam-winter-2015/w15f24.xml", + "comp2804/exam-winter-2015/w15f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-winter-2017.json b/app/src/data/tests/comp2804/exam-winter-2017.json new file mode 100644 index 00000000..ebedc2d5 --- /dev/null +++ b/app/src/data/tests/comp2804/exam-winter-2017.json @@ -0,0 +1,32 @@ +{ + "id": "exam-winter-2017", + "title": "Winter 2017 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-winter-2017/w17f01.xml", + "comp2804/exam-winter-2017/w17f02.xml", + "comp2804/exam-winter-2017/w17f03.xml", + "comp2804/exam-winter-2017/w17f04.xml", + "comp2804/exam-winter-2017/w17f05.xml", + "comp2804/exam-winter-2017/w17f06.xml", + "comp2804/exam-winter-2017/w17f07.xml", + "comp2804/exam-winter-2017/w17f08.xml", + "comp2804/exam-winter-2017/w17f09.xml", + "comp2804/exam-winter-2017/w17f10.xml", + "comp2804/exam-winter-2017/w17f11.xml", + "comp2804/exam-winter-2017/w17f12.xml", + "comp2804/exam-winter-2017/w17f13.xml", + "comp2804/exam-winter-2017/w17f14.xml", + "comp2804/exam-winter-2017/w17f15.xml", + "comp2804/exam-winter-2017/w17f16.xml", + "comp2804/exam-winter-2017/w17f17.xml", + "comp2804/exam-winter-2017/w17f18.xml", + "comp2804/exam-winter-2017/w17f19.xml", + "comp2804/exam-winter-2017/w17f20.xml", + "comp2804/exam-winter-2017/w17f21.xml", + "comp2804/exam-winter-2017/w17f22.xml", + "comp2804/exam-winter-2017/w17f23.xml", + "comp2804/exam-winter-2017/w17f24.xml", + "comp2804/exam-winter-2017/w17f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-winter-2018.json b/app/src/data/tests/comp2804/exam-winter-2018.json new file mode 100644 index 00000000..8a988d79 --- /dev/null +++ b/app/src/data/tests/comp2804/exam-winter-2018.json @@ -0,0 +1,32 @@ +{ + "id": "exam-winter-2018", + "title": "Winter 2018 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-winter-2018/w18f01.xml", + "comp2804/exam-winter-2018/w18f02.xml", + "comp2804/exam-winter-2018/w18f03.xml", + "comp2804/exam-winter-2018/w18f04.xml", + "comp2804/exam-winter-2018/w18f05.xml", + "comp2804/exam-winter-2018/w18f06.xml", + "comp2804/exam-winter-2018/w18f07.xml", + "comp2804/exam-winter-2018/w18f08.xml", + "comp2804/exam-winter-2018/w18f09.xml", + "comp2804/exam-winter-2018/w18f10.xml", + "comp2804/exam-winter-2018/w18f11.xml", + "comp2804/exam-winter-2018/w18f12.xml", + "comp2804/exam-winter-2018/w18f13.xml", + "comp2804/exam-winter-2018/w18f14.xml", + "comp2804/exam-winter-2018/w18f15.xml", + "comp2804/exam-winter-2018/w18f16.xml", + "comp2804/exam-winter-2018/w18f17.xml", + "comp2804/exam-winter-2018/w18f18.xml", + "comp2804/exam-winter-2018/w18f19.xml", + "comp2804/exam-winter-2018/w18f20.xml", + "comp2804/exam-winter-2018/w18f21.xml", + "comp2804/exam-winter-2018/w18f22.xml", + "comp2804/exam-winter-2018/w18f23.xml", + "comp2804/exam-winter-2018/w18f24.xml", + "comp2804/exam-winter-2018/w18f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/exam-winter-2019.json b/app/src/data/tests/comp2804/exam-winter-2019.json new file mode 100644 index 00000000..f16a39f0 --- /dev/null +++ b/app/src/data/tests/comp2804/exam-winter-2019.json @@ -0,0 +1,32 @@ +{ + "id": "exam-winter-2019", + "title": "Winter 2019 Exam", + "Author": "Michiel Smid", + "questions": [ + "comp2804/exam-winter-2019/w19f01.xml", + "comp2804/exam-winter-2019/w19f02.xml", + "comp2804/exam-winter-2019/w19f03.xml", + "comp2804/exam-winter-2019/w19f04.xml", + "comp2804/exam-winter-2019/w19f05.xml", + "comp2804/exam-winter-2019/w19f06.xml", + "comp2804/exam-winter-2019/w19f07.xml", + "comp2804/exam-winter-2019/w19f08.xml", + "comp2804/exam-winter-2019/w19f09.xml", + "comp2804/exam-winter-2019/w19f10.xml", + "comp2804/exam-winter-2019/w19f11.xml", + "comp2804/exam-winter-2019/w19f12.xml", + "comp2804/exam-winter-2019/w19f13.xml", + "comp2804/exam-winter-2019/w19f14.xml", + "comp2804/exam-winter-2019/w19f15.xml", + "comp2804/exam-winter-2019/w19f16.xml", + "comp2804/exam-winter-2019/w19f17.xml", + "comp2804/exam-winter-2019/w19f18.xml", + "comp2804/exam-winter-2019/w19f19.xml", + "comp2804/exam-winter-2019/w19f20.xml", + "comp2804/exam-winter-2019/w19f21.xml", + "comp2804/exam-winter-2019/w19f22.xml", + "comp2804/exam-winter-2019/w19f23.xml", + "comp2804/exam-winter-2019/w19f24.xml", + "comp2804/exam-winter-2019/w19f25.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2013.json b/app/src/data/tests/comp2804/midterm-fall-2013.json new file mode 100644 index 00000000..49b0902a --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2013.json @@ -0,0 +1,6 @@ +{ + "id": "midterm-fall-2013", + "title": "TEMPORARY", + "author": "Michiel Smid", + "questions": ["comp2804/midterm-fall-2013/f13m01.xml"] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2014.json b/app/src/data/tests/comp2804/midterm-fall-2014.json new file mode 100644 index 00000000..eb30bd7a --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2014.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-fall-2014", + "title": "Fall 2014 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-fall-2014/f14m01.xml", + "comp2804/midterm-fall-2014/f14m02.xml", + "comp2804/midterm-fall-2014/f14m03.xml", + "comp2804/midterm-fall-2014/f14m04.xml", + "comp2804/midterm-fall-2014/f14m05.xml", + "comp2804/midterm-fall-2014/f14m06.xml", + "comp2804/midterm-fall-2014/f14m07.xml", + "comp2804/midterm-fall-2014/f14m08.xml", + "comp2804/midterm-fall-2014/f14m09.xml", + "comp2804/midterm-fall-2014/f14m10.xml", + "comp2804/midterm-fall-2014/f14m11.xml", + "comp2804/midterm-fall-2014/f14m12.xml", + "comp2804/midterm-fall-2014/f14m13.xml", + "comp2804/midterm-fall-2014/f14m14.xml", + "comp2804/midterm-fall-2014/f14m15.xml", + "comp2804/midterm-fall-2014/f14m16.xml", + "comp2804/midterm-fall-2014/f14m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2015.json b/app/src/data/tests/comp2804/midterm-fall-2015.json new file mode 100644 index 00000000..96978c94 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2015.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-fall-2015", + "title": "Fall 2015 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-fall-2015/f15m01.xml", + "comp2804/midterm-fall-2015/f15m02.xml", + "comp2804/midterm-fall-2015/f15m03.xml", + "comp2804/midterm-fall-2015/f15m04.xml", + "comp2804/midterm-fall-2015/f15m05.xml", + "comp2804/midterm-fall-2015/f15m06.xml", + "comp2804/midterm-fall-2015/f15m07.xml", + "comp2804/midterm-fall-2015/f15m08.xml", + "comp2804/midterm-fall-2015/f15m09.xml", + "comp2804/midterm-fall-2015/f15m10.xml", + "comp2804/midterm-fall-2015/f15m11.xml", + "comp2804/midterm-fall-2015/f15m12.xml", + "comp2804/midterm-fall-2015/f15m13.xml", + "comp2804/midterm-fall-2015/f15m14.xml", + "comp2804/midterm-fall-2015/f15m15.xml", + "comp2804/midterm-fall-2015/f15m16.xml", + "comp2804/midterm-fall-2015/f15m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2016.json b/app/src/data/tests/comp2804/midterm-fall-2016.json new file mode 100644 index 00000000..684795e2 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2016.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-fall-2016", + "title": "Fall 2016 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-fall-2016/f16m01.xml", + "comp2804/midterm-fall-2016/f16m02.xml", + "comp2804/midterm-fall-2016/f16m03.xml", + "comp2804/midterm-fall-2016/f16m04.xml", + "comp2804/midterm-fall-2016/f16m05.xml", + "comp2804/midterm-fall-2016/f16m06.xml", + "comp2804/midterm-fall-2016/f16m07.xml", + "comp2804/midterm-fall-2016/f16m08.xml", + "comp2804/midterm-fall-2016/f16m09.xml", + "comp2804/midterm-fall-2016/f16m10.xml", + "comp2804/midterm-fall-2016/f16m11.xml", + "comp2804/midterm-fall-2016/f16m12.xml", + "comp2804/midterm-fall-2016/f16m13.xml", + "comp2804/midterm-fall-2016/f16m14.xml", + "comp2804/midterm-fall-2016/f16m15.xml", + "comp2804/midterm-fall-2016/f16m16.xml", + "comp2804/midterm-fall-2016/f16m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2017.json b/app/src/data/tests/comp2804/midterm-fall-2017.json new file mode 100644 index 00000000..5847c917 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2017.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-fall-2017", + "title": "Fall 2017 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-fall-2017/f17m01.xml", + "comp2804/midterm-fall-2017/f17m02.xml", + "comp2804/midterm-fall-2017/f17m03.xml", + "comp2804/midterm-fall-2017/f17m04.xml", + "comp2804/midterm-fall-2017/f17m05.xml", + "comp2804/midterm-fall-2017/f17m06.xml", + "comp2804/midterm-fall-2017/f17m07.xml", + "comp2804/midterm-fall-2017/f17m08.xml", + "comp2804/midterm-fall-2017/f17m09.xml", + "comp2804/midterm-fall-2017/f17m10.xml", + "comp2804/midterm-fall-2017/f17m11.xml", + "comp2804/midterm-fall-2017/f17m12.xml", + "comp2804/midterm-fall-2017/f17m13.xml", + "comp2804/midterm-fall-2017/f17m14.xml", + "comp2804/midterm-fall-2017/f17m15.xml", + "comp2804/midterm-fall-2017/f17m16.xml", + "comp2804/midterm-fall-2017/f17m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2018.json b/app/src/data/tests/comp2804/midterm-fall-2018.json new file mode 100644 index 00000000..6ab11405 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2018.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-fall-2018", + "title": "Fall 2018 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-fall-2018/f18m01.xml", + "comp2804/midterm-fall-2018/f18m02.xml", + "comp2804/midterm-fall-2018/f18m03.xml", + "comp2804/midterm-fall-2018/f18m04.xml", + "comp2804/midterm-fall-2018/f18m05.xml", + "comp2804/midterm-fall-2018/f18m06.xml", + "comp2804/midterm-fall-2018/f18m07.xml", + "comp2804/midterm-fall-2018/f18m08.xml", + "comp2804/midterm-fall-2018/f18m09.xml", + "comp2804/midterm-fall-2018/f18m10.xml", + "comp2804/midterm-fall-2018/f18m11.xml", + "comp2804/midterm-fall-2018/f18m12.xml", + "comp2804/midterm-fall-2018/f18m13.xml", + "comp2804/midterm-fall-2018/f18m14.xml", + "comp2804/midterm-fall-2018/f18m15.xml", + "comp2804/midterm-fall-2018/f18m16.xml", + "comp2804/midterm-fall-2018/f18m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-fall-2019.json b/app/src/data/tests/comp2804/midterm-fall-2019.json new file mode 100644 index 00000000..b52a8a16 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-fall-2019.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-fall-2019", + "title": "Fall 2019 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-fall-2019/f19m01.xml", + "comp2804/midterm-fall-2019/f19m02.xml", + "comp2804/midterm-fall-2019/f19m03.xml", + "comp2804/midterm-fall-2019/f19m04.xml", + "comp2804/midterm-fall-2019/f19m05.xml", + "comp2804/midterm-fall-2019/f19m06.xml", + "comp2804/midterm-fall-2019/f19m07.xml", + "comp2804/midterm-fall-2019/f19m08.xml", + "comp2804/midterm-fall-2019/f19m09.xml", + "comp2804/midterm-fall-2019/f19m10.xml", + "comp2804/midterm-fall-2019/f19m11.xml", + "comp2804/midterm-fall-2019/f19m12.xml", + "comp2804/midterm-fall-2019/f19m13.xml", + "comp2804/midterm-fall-2019/f19m14.xml", + "comp2804/midterm-fall-2019/f19m15.xml", + "comp2804/midterm-fall-2019/f19m16.xml", + "comp2804/midterm-fall-2019/f19m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-winter-2014.json b/app/src/data/tests/comp2804/midterm-winter-2014.json new file mode 100644 index 00000000..5a1c2b94 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-winter-2014.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-winter-2014", + "title": "Winter 2014 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-winter-2014/w14m01.xml", + "comp2804/midterm-winter-2014/w14m02.xml", + "comp2804/midterm-winter-2014/w14m03.xml", + "comp2804/midterm-winter-2014/w14m04.xml", + "comp2804/midterm-winter-2014/w14m05.xml", + "comp2804/midterm-winter-2014/w14m06.xml", + "comp2804/midterm-winter-2014/w14m07.xml", + "comp2804/midterm-winter-2014/w14m08.xml", + "comp2804/midterm-winter-2014/w14m09.xml", + "comp2804/midterm-winter-2014/w14m10.xml", + "comp2804/midterm-winter-2014/w14m11.xml", + "comp2804/midterm-winter-2014/w14m12.xml", + "comp2804/midterm-winter-2014/w14m13.xml", + "comp2804/midterm-winter-2014/w14m14.xml", + "comp2804/midterm-winter-2014/w14m15.xml", + "comp2804/midterm-winter-2014/w14m16.xml", + "comp2804/midterm-winter-2014/w14m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-winter-2015.json b/app/src/data/tests/comp2804/midterm-winter-2015.json new file mode 100644 index 00000000..e263a01e --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-winter-2015.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-winter-2015", + "title": "Winter 2015 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-winter-2015/w15m01.xml", + "comp2804/midterm-winter-2015/w15m02.xml", + "comp2804/midterm-winter-2015/w15m03.xml", + "comp2804/midterm-winter-2015/w15m04.xml", + "comp2804/midterm-winter-2015/w15m05.xml", + "comp2804/midterm-winter-2015/w15m06.xml", + "comp2804/midterm-winter-2015/w15m07.xml", + "comp2804/midterm-winter-2015/w15m08.xml", + "comp2804/midterm-winter-2015/w15m09.xml", + "comp2804/midterm-winter-2015/w15m10.xml", + "comp2804/midterm-winter-2015/w15m11.xml", + "comp2804/midterm-winter-2015/w15m12.xml", + "comp2804/midterm-winter-2015/w15m13.xml", + "comp2804/midterm-winter-2015/w15m14.xml", + "comp2804/midterm-winter-2015/w15m15.xml", + "comp2804/midterm-winter-2015/w15m16.xml", + "comp2804/midterm-winter-2015/w15m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-winter-2017.json b/app/src/data/tests/comp2804/midterm-winter-2017.json new file mode 100644 index 00000000..69498445 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-winter-2017.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-winter-2017", + "title": "Winter 2017 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-winter-2017/w17m01.xml", + "comp2804/midterm-winter-2017/w17m02.xml", + "comp2804/midterm-winter-2017/w17m03.xml", + "comp2804/midterm-winter-2017/w17m04.xml", + "comp2804/midterm-winter-2017/w17m05.xml", + "comp2804/midterm-winter-2017/w17m06.xml", + "comp2804/midterm-winter-2017/w17m07.xml", + "comp2804/midterm-winter-2017/w17m08.xml", + "comp2804/midterm-winter-2017/w17m09.xml", + "comp2804/midterm-winter-2017/w17m10.xml", + "comp2804/midterm-winter-2017/w17m11.xml", + "comp2804/midterm-winter-2017/w17m12.xml", + "comp2804/midterm-winter-2017/w17m13.xml", + "comp2804/midterm-winter-2017/w17m14.xml", + "comp2804/midterm-winter-2017/w17m15.xml", + "comp2804/midterm-winter-2017/w17m16.xml", + "comp2804/midterm-winter-2017/w17m17.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-winter-2018.json b/app/src/data/tests/comp2804/midterm-winter-2018.json new file mode 100644 index 00000000..3214bb08 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-winter-2018.json @@ -0,0 +1,23 @@ +{ + "id": "midterm-winter-2018", + "title": "Winter 2018 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-winter-2018/w18m01.xml", + "comp2804/midterm-winter-2018/w18m02.xml", + "comp2804/midterm-winter-2018/w18m03.xml", + "comp2804/midterm-winter-2018/w18m04.xml", + "comp2804/midterm-winter-2018/w18m05.xml", + "comp2804/midterm-winter-2018/w18m06.xml", + "comp2804/midterm-winter-2018/w18m07.xml", + "comp2804/midterm-winter-2018/w18m08.xml", + "comp2804/midterm-winter-2018/w18m09.xml", + "comp2804/midterm-winter-2018/w18m10.xml", + "comp2804/midterm-winter-2018/w18m11.xml", + "comp2804/midterm-winter-2018/w18m12.xml", + "comp2804/midterm-winter-2018/w18m13.xml", + "comp2804/midterm-winter-2018/w18m14.xml", + "comp2804/midterm-winter-2018/w18m15.xml", + "comp2804/midterm-winter-2018/w18m16.xml" + ] +} diff --git a/app/src/data/tests/comp2804/midterm-winter-2019.json b/app/src/data/tests/comp2804/midterm-winter-2019.json new file mode 100644 index 00000000..6c114604 --- /dev/null +++ b/app/src/data/tests/comp2804/midterm-winter-2019.json @@ -0,0 +1,24 @@ +{ + "id": "midterm-winter-2019", + "title": "Winter 2019 Midterm", + "Author": "Michiel Smid", + "questions": [ + "comp2804/midterm-winter-2019/w19m01.xml", + "comp2804/midterm-winter-2019/w19m02.xml", + "comp2804/midterm-winter-2019/w19m03.xml", + "comp2804/midterm-winter-2019/w19m04.xml", + "comp2804/midterm-winter-2019/w19m05.xml", + "comp2804/midterm-winter-2019/w19m06.xml", + "comp2804/midterm-winter-2019/w19m07.xml", + "comp2804/midterm-winter-2019/w19m08.xml", + "comp2804/midterm-winter-2019/w19m09.xml", + "comp2804/midterm-winter-2019/w19m10.xml", + "comp2804/midterm-winter-2019/w19m11.xml", + "comp2804/midterm-winter-2019/w19m12.xml", + "comp2804/midterm-winter-2019/w19m13.xml", + "comp2804/midterm-winter-2019/w19m14.xml", + "comp2804/midterm-winter-2019/w19m15.xml", + "comp2804/midterm-winter-2019/w19m16.xml", + "comp2804/midterm-winter-2019/w19m17.xml" + ] +} diff --git a/app/src/layouts/BaseLayout.astro b/app/src/layouts/BaseLayout.astro new file mode 100644 index 00000000..52cceefb --- /dev/null +++ b/app/src/layouts/BaseLayout.astro @@ -0,0 +1,27 @@ +--- +export interface Props { + title: string; +} + +import "../styles.scss"; + +const { title } = Astro.props as Props; +--- + + + + + + + + {title} + + + + + + diff --git a/app/src/layouts/CourseLayout.astro b/app/src/layouts/CourseLayout.astro new file mode 100644 index 00000000..d7c453b0 --- /dev/null +++ b/app/src/layouts/CourseLayout.astro @@ -0,0 +1,27 @@ +--- +import BaseLayout from "./BaseLayout.astro"; +import { CourseNavbar } from "../components"; +--- + + +
    + +
    + +
    +
    +     + + diff --git a/app/src/layouts/ExaminationLayout.astro b/app/src/layouts/ExaminationLayout.astro new file mode 100644 index 00000000..b8346436 --- /dev/null +++ b/app/src/layouts/ExaminationLayout.astro @@ -0,0 +1,15 @@ +--- +import CourseLayout from "./CourseLayout.astro"; +--- + + +
    + +
    +     + + diff --git a/app/src/layouts/HomeLayout.astro b/app/src/layouts/HomeLayout.astro new file mode 100644 index 00000000..8aa6f229 --- /dev/null +++ b/app/src/layouts/HomeLayout.astro @@ -0,0 +1,40 @@ +--- +import "../styles.scss"; + +const currentDate: Date = new Date(); +--- + +
    + +
    + © {currentDate.getFullYear()} Carleton Computer Science Society + +
    +
    + + diff --git a/app/src/pages/[course].astro b/app/src/pages/[course].astro new file mode 100644 index 00000000..c8647fd5 --- /dev/null +++ b/app/src/pages/[course].astro @@ -0,0 +1,66 @@ +--- +import CourseLayout from "../layouts/CourseLayout.astro"; +import { Repository } from "../data"; +import Graph from "../apps/Graphs/Graph.svelte"; +import { ContentCard } from "../components"; + +export function getStaticPaths() { + return [ + { params: { course: "comp1805" } }, + { params: { course: "comp2804" } }, + ]; +} + +const { course } = Astro.params; +const data = new Repository().fetchCourse(course); +--- + + +
    +

    {data.code}: {data.title}

    +

    {data.description}

    + +
    + {data.tests.map((test) => ( + + + + ))} +
    +

    Labs:

    +
    + {data.labs.map((lab) => ( + + + + ))} +
    +
    +

    Temporary Graph Demo:

    + +
    +     + + diff --git a/app/src/pages/[course]/labs/[lab].astro b/app/src/pages/[course]/labs/[lab].astro new file mode 100644 index 00000000..d1fca5db --- /dev/null +++ b/app/src/pages/[course]/labs/[lab].astro @@ -0,0 +1,20 @@ +--- +import ExaminationLayout from "../../../layouts/ExaminationLayout.astro"; +import { Lab } from "../../../apps"; +import { Repository } from "../../../data"; + +// TODO: move params data into data folder? +export function getStaticPaths() { + return [ + { params: { course: "comp1805", lab: "asymtopic-analysis" } }, + { params: { course: "comp2804", lab: "how-many-functions" } }, + ]; +} + +const { course, lab } = Astro.params; +const data = new Repository().fetchLab(`${course}/${lab}`); +--- + + + + diff --git a/app/src/pages/[course]/tests/[test].astro b/app/src/pages/[course]/tests/[test].astro new file mode 100644 index 00000000..cade0a2c --- /dev/null +++ b/app/src/pages/[course]/tests/[test].astro @@ -0,0 +1,42 @@ +--- +import ExaminationLayout from "../../../layouts/ExaminationLayout.astro"; +import { Test } from "../../../apps"; +import { Repository } from "../../../data"; + +// TODO: move params data into data folder? +export function getStaticPaths() { + return [ + { params: { course: "comp2804", test: "midterm-fall-2013" } }, + { params: { course: "comp2804", test: "midterm-winter-2014" } }, + { params: { course: "comp2804", test: "midterm-fall-2014" } }, + { params: { course: "comp2804", test: "midterm-winter-2015" } }, + { params: { course: "comp2804", test: "midterm-fall-2015" } }, + { params: { course: "comp2804", test: "midterm-fall-2016" } }, + { params: { course: "comp2804", test: "midterm-winter-2017" } }, + { params: { course: "comp2804", test: "midterm-fall-2017" } }, + { params: { course: "comp2804", test: "midterm-winter-2018" } }, + { params: { course: "comp2804", test: "midterm-fall-2018" } }, + { params: { course: "comp2804", test: "midterm-winter-2019" } }, + { params: { course: "comp2804", test: "midterm-fall-2019" } }, + { params: { course: "comp2804", test: "exam-fall-2013" } }, + { params: { course: "comp2804", test: "exam-winter-2014" } }, + { params: { course: "comp2804", test: "exam-fall-2014" } }, + { params: { course: "comp2804", test: "exam-winter-2015" } }, + { params: { course: "comp2804", test: "exam-fall-2015" } }, + { params: { course: "comp2804", test: "exam-fall-2016" } }, + { params: { course: "comp2804", test: "exam-winter-2017" } }, + { params: { course: "comp2804", test: "exam-fall-2017" } }, + { params: { course: "comp2804", test: "exam-winter-2018" } }, + { params: { course: "comp2804", test: "exam-fall-2018" } }, + { params: { course: "comp2804", test: "exam-winter-2019" } }, + { params: { course: "comp2804", test: "exam-fall-2019" } }, + ]; +} + +const { course, test } = Astro.params; +const data = new Repository().fetchTest(`${course}/${test}`); +--- + + + + diff --git a/app/src/pages/index.astro b/app/src/pages/index.astro new file mode 100644 index 00000000..be2693e1 --- /dev/null +++ b/app/src/pages/index.astro @@ -0,0 +1,92 @@ +--- +import BaseLayout from "../layouts/BaseLayout.astro"; +import HomeLayout from "../layouts/HomeLayout.astro"; +import { Button } from "../components"; +--- + + + +
    +
    + DiscreteMath.ca +
    Learn Without Limits.
    +
    + Built by Carleton students, for Carleton students. DiscreteMath.ca is + an interactive platform built specifically for content from Carleton's + discrete mathematics courses. +
    +
    + + +
    +
    +
    +
    + +     +     + + diff --git a/app/src/styles.scss b/app/src/styles.scss new file mode 100644 index 00000000..ad1ccb42 --- /dev/null +++ b/app/src/styles.scss @@ -0,0 +1,12 @@ +body { + margin: 0; + padding: 0; + background-color: #ffffff; + overflow-x: hidden; + font-size: 1rem; +} + +:root { + --color-main: #ffab40; + --color-main-dark: #d68110; +} diff --git a/app/src/utilities/index.js b/app/src/utilities/index.js new file mode 100644 index 00000000..efa0a905 --- /dev/null +++ b/app/src/utilities/index.js @@ -0,0 +1 @@ +export * from "./mathjax"; diff --git a/app/src/utilities/mathjax.js b/app/src/utilities/mathjax.js new file mode 100644 index 00000000..4dc8a3c2 --- /dev/null +++ b/app/src/utilities/mathjax.js @@ -0,0 +1,21 @@ +import "mathjax/es5/tex-svg-full.js"; + +const mathjaxLoad = () => { + if (!window.MathJax.config.tex.inlineMath) { + window.MathJax.config.tex.inlineMath = [ + ["$", "$"], + ["\\(", "\\)"], + ]; + window.MathJax.config.tex.displayMath = [ + ["$$", "$$"], + ["\\[", "\\]"], + ]; + window.MathJax.startup.getComponents(); + } +}; + +const mathjaxTypeset = () => { + window.MathJax.typeset(); +}; + +export { mathjaxLoad, mathjaxTypeset }; diff --git a/app/src/utilities/xml.js b/app/src/utilities/xml.js new file mode 100644 index 00000000..a8a6bf75 --- /dev/null +++ b/app/src/utilities/xml.js @@ -0,0 +1,21 @@ +import { Parser } from "xml2js"; +import { readFileSync } from "fs"; + +const parseXmlToJson = (file) => { + let parser = new Parser(); + let xmlString = readFileSync(`./src/data/${file}`, "utf8"); + let result; + + // TODO: error handling + parser.parseString(xmlString, function (error, data) { + if (error === null) { + result = data; + } else { + console.log(error); + } + }); + + return result; +}; + +export { parseXmlToJson }; diff --git a/app/tsconfig.json b/app/tsconfig.json new file mode 100644 index 00000000..7ac81809 --- /dev/null +++ b/app/tsconfig.json @@ -0,0 +1,15 @@ +{ + "compilerOptions": { + // Enable top-level await, and other modern ESM features. + "target": "ESNext", + "module": "ESNext", + // Enable node-style module resolution, for things like npm package imports. + "moduleResolution": "node", + // Enable JSON imports. + "resolveJsonModule": true, + // Enable stricter transpilation for better output. + "isolatedModules": true, + // Add type definitions for our Vite runtime. + "types": ["vite/client"] + } +} diff --git a/client/yarn.lock b/client/yarn.lock index 2ffa74de..bd3cde44 100644 --- a/client/yarn.lock +++ b/client/yarn.lock @@ -3120,13 +3120,13 @@ abab@^2.0.3, abab@^2.0.5: resolved "https://registry.yarnpkg.com/abab/-/abab-2.0.5.tgz#c0b678fb32d60fc1219c784d6a826fe385aeb79a" integrity sha512-9IK9EadsbHo6jLWIpxpR6pL0sazTXV6+SQv25ZB+F7Bj9mJNaOc4nCRabwd5M/JwmUa8idz6Eci6eKfJryPs6Q== -accepts@~1.3.7: - 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version "1.19.0" - resolved "https://registry.yarnpkg.com/body-parser/-/body-parser-1.19.0.tgz#96b2709e57c9c4e09a6fd66a8fd979844f69f08a" - integrity sha512-dhEPs72UPbDnAQJ9ZKMNTP6ptJaionhP5cBb541nXPlW60Jepo9RV/a4fX4XWW9CuFNK22krhrj1+rgzifNCsw== +body-parser@1.20.1: + version "1.20.1" + resolved "https://registry.yarnpkg.com/body-parser/-/body-parser-1.20.1.tgz#b1812a8912c195cd371a3ee5e66faa2338a5c668" + integrity sha512-jWi7abTbYwajOytWCQc37VulmWiRae5RyTpaCyDcS5/lMdtwSz5lOpDE67srw/HYe35f1z3fDQw+3txg7gNtWw== dependencies: - bytes "3.1.0" + bytes "3.1.2" content-type "~1.0.4" debug "2.6.9" - depd "~1.1.2" - http-errors "1.7.2" + depd "2.0.0" + destroy "1.2.0" + http-errors "2.0.0" iconv-lite "0.4.24" - on-finished "~2.3.0" - qs "6.7.0" - raw-body "2.4.0" - type-is "~1.6.17" + on-finished "2.4.1" + qs "6.11.0" + raw-body "2.5.1" + type-is "~1.6.18" + unpipe "1.0.0" boolbase@^1.0.0, boolbase@~1.0.0: version "1.0.0" @@ -4300,10 +4302,10 @@ byline@5.0.0: resolved "https://registry.yarnpkg.com/byline/-/byline-5.0.0.tgz#741c5216468eadc457b03410118ad77de8c1ddb1" integrity sha1-dBxSFkaOrcRXsDQQEYrXfejB3bE= -bytes@3.1.0: - version "3.1.0" - resolved "https://registry.yarnpkg.com/bytes/-/bytes-3.1.0.tgz#f6cf7933a360e0588fa9fde85651cdc7f805d1f6" - integrity sha512-zauLjrfCG+xvoyaqLoV8bLVXXNGC4JqlxFCutSDWA6fJrTo2ZuvLYTqZ7aHBLZSMOopbzwv8f+wZcVzfVTI2Dg== +bytes@3.1.2: + version "3.1.2" + resolved "https://registry.yarnpkg.com/bytes/-/bytes-3.1.2.tgz#8b0beeb98605adf1b128fa4386403c009e0221a5" + integrity sha512-/Nf7TyzTx6S3yRJObOAV7956r8cr2+Oj8AC5dt8wSP3BQAoeX58NoHyCU8P8zGkNXStjTSi6fzO6F0pBdcYbEg== cacache@^12.0.2: version "12.0.4" @@ -4925,12 +4927,12 @@ contains-path@^0.1.0: resolved "https://registry.yarnpkg.com/contains-path/-/contains-path-0.1.0.tgz#fe8cf184ff6670b6baef01a9d4861a5cbec4120a" integrity sha1-/ozxhP9mcLa67wGp1IYaXL7EEgo= -content-disposition@0.5.3: - version "0.5.3" - resolved "https://registry.yarnpkg.com/content-disposition/-/content-disposition-0.5.3.tgz#e130caf7e7279087c5616c2007d0485698984fbd" - integrity sha512-ExO0774ikEObIAEV9kDo50o+79VCUdEB6n6lzKgGwupcVeRlhrj3qGAfwq8G6uBJjkqLrhT0qEYFcWng8z1z0g== +content-disposition@0.5.4: + version "0.5.4" + resolved "https://registry.yarnpkg.com/content-disposition/-/content-disposition-0.5.4.tgz#8b82b4efac82512a02bb0b1dcec9d2c5e8eb5bfe" + integrity sha512-FveZTNuGw04cxlAiWbzi6zTAL/lhehaWbTtgluJh4/E95DqMwTmha3KZN1aAWA8cFIhHzMZUvLevkw5Rqk+tSQ== dependencies: - safe-buffer "5.1.2" + safe-buffer "5.2.1" content-type@^1.0.4, content-type@~1.0.4: version "1.0.4" @@ -4947,12 +4949,12 @@ convert-source-map@^1.4.0, convert-source-map@^1.5.0, convert-source-map@^1.6.0, cookie-signature@1.0.6: version "1.0.6" resolved "https://registry.yarnpkg.com/cookie-signature/-/cookie-signature-1.0.6.tgz#e303a882b342cc3ee8ca513a79999734dab3ae2c" - integrity sha1-4wOogrNCzD7oylE6eZmXNNqzriw= + integrity sha512-QADzlaHc8icV8I7vbaJXJwod9HWYp8uCqf1xa4OfNu1T7JVxQIrUgOWtHdNDtPiywmFbiS12VjotIXLrKM3orQ== -cookie@0.4.0: - version "0.4.0" - resolved "https://registry.yarnpkg.com/cookie/-/cookie-0.4.0.tgz#beb437e7022b3b6d49019d088665303ebe9c14ba" - integrity sha512-+Hp8fLp57wnUSt0tY0tHEXh4voZRDnoIrZPqlo3DPiI4y9lwg/jqx+1Om94/W6ZaPDOUbnjOt/99w66zk+l1Xg== +cookie@0.5.0: + version "0.5.0" + resolved "https://registry.yarnpkg.com/cookie/-/cookie-0.5.0.tgz#d1f5d71adec6558c58f389987c366aa47e994f8b" + integrity sha512-YZ3GUyn/o8gfKJlnlX7g7xq4gyO6OSuhGPKaaGssGB2qgDUS0gPgtTvoyZLTt9Ab6dC4hfc9dV5arkvc/OCmrw== copy-concurrently@^1.0.0: version "1.0.5" @@ -5282,9 +5284,9 @@ decimal.js@^10.2.1: integrity sha512-KaL7+6Fw6i5A2XSnsbhm/6B+NuEA7TZ4vqxnd5tXz9sbKtrN9Srj8ab4vKVdK8YAqZO9P1kg45Y6YLoduPf+kw== decode-uri-component@^0.2.0: - version "0.2.0" - resolved "https://registry.yarnpkg.com/decode-uri-component/-/decode-uri-component-0.2.0.tgz#eb3913333458775cb84cd1a1fae062106bb87545" - integrity sha1-6zkTMzRYd1y4TNGh+uBiEGu4dUU= + version "0.2.2" + resolved "https://registry.yarnpkg.com/decode-uri-component/-/decode-uri-component-0.2.2.tgz#e69dbe25d37941171dd540e024c444cd5188e1e9" + integrity sha512-FqUYQ+8o158GyGTrMFJms9qh3CqTKvAqgqsTnkLI8sKu0028orqBhxNMFkFen0zGyg6epACD32pjVk58ngIErQ== dedent-js@^1.0.1: version "1.0.1" @@ -5355,10 +5357,10 @@ delegates@^1.0.0: resolved "https://registry.yarnpkg.com/delegates/-/delegates-1.0.0.tgz#84c6e159b81904fdca59a0ef44cd870d31250f9a" integrity sha1-hMbhWbgZBP3KWaDvRM2HDTElD5o= -depd@~1.1.2: - version "1.1.2" - resolved "https://registry.yarnpkg.com/depd/-/depd-1.1.2.tgz#9bcd52e14c097763e749b274c4346ed2e560b5a9" - integrity sha1-m81S4UwJd2PnSbJ0xDRu0uVgtak= +depd@2.0.0: + version "2.0.0" + resolved "https://registry.yarnpkg.com/depd/-/depd-2.0.0.tgz#b696163cc757560d09cf22cc8fad1571b79e76df" + integrity sha512-g7nH6P6dyDioJogAAGprGpCtVImJhpPk/roCzdb3fIh61/s/nPsfR6onyMwkCAR/OlC3yBC0lESvUoQEAssIrw== des.js@^1.0.0: version "1.0.1" @@ -5368,10 +5370,10 @@ des.js@^1.0.0: inherits "^2.0.1" minimalistic-assert "^1.0.0" -destroy@~1.0.4: - version "1.0.4" - resolved "https://registry.yarnpkg.com/destroy/-/destroy-1.0.4.tgz#978857442c44749e4206613e37946205826abd80" - integrity sha1-l4hXRCxEdJ5CBmE+N5RiBYJqvYA= +destroy@1.2.0: + version "1.2.0" + resolved "https://registry.yarnpkg.com/destroy/-/destroy-1.2.0.tgz#4803735509ad8be552934c67df614f94e66fa015" + integrity sha512-2sJGJTaXIIaR1w4iJSNoN0hnMY7Gpc/n8D4qSCJw8QqFWXf7cuAgnEHxBpweaVcPevC2l3KpjYCx3NypQQgaJg== detab@2.0.4: version "2.0.4" @@ -5626,7 +5628,7 @@ ecc-jsbn@~0.1.1: ee-first@1.1.1: version "1.1.1" resolved "https://registry.yarnpkg.com/ee-first/-/ee-first-1.1.1.tgz#590c61156b0ae2f4f0255732a158b266bc56b21d" - integrity sha1-WQxhFWsK4vTwJVcyoViyZrxWsh0= + integrity sha512-WMwm9LhRUo+WUaRN+vRuETqG89IgZphVSNkdFgeb6sS/E4OrDIN7t48CAewSHXc6C8lefD8KKfr5vY61brQlow== electron-to-chromium@^1.3.564, electron-to-chromium@^1.3.723: version "1.3.725" @@ -5695,7 +5697,7 @@ emotion-theming@^10.0.27: encodeurl@~1.0.2: version "1.0.2" resolved "https://registry.yarnpkg.com/encodeurl/-/encodeurl-1.0.2.tgz#ad3ff4c86ec2d029322f5a02c3a9a606c95b3f59" - integrity sha1-rT/0yG7C0CkyL1oCw6mmBslbP1k= + integrity sha512-TPJXq8JqFaVYm2CWmPvnP2Iyo4ZSM7/QKcSmuMLDObfpH5fi7RUGmd/rTDf+rut/saiDiQEeVTNgAmJEdAOx0w== end-of-stream@^1.0.0, end-of-stream@^1.1.0: version "1.4.4" @@ -5855,7 +5857,7 @@ escalade@^3.0.2, escalade@^3.1.1: escape-html@~1.0.3: version "1.0.3" resolved "https://registry.yarnpkg.com/escape-html/-/escape-html-1.0.3.tgz#0258eae4d3d0c0974de1c169188ef0051d1d1988" - integrity sha1-Aljq5NPQwJdN4cFpGI7wBR0dGYg= + integrity sha512-NiSupZ4OeuGwr68lGIeym/ksIZMJodUGOSCZ/FSnTxcrekbvqrgdUxlJOMpijaKZVjAJrWrGs/6Jy8OMuyj9ow== escape-string-regexp@1.0.5, escape-string-regexp@^1.0.2, escape-string-regexp@^1.0.5: version "1.0.5" @@ -6137,7 +6139,7 @@ esutils@^2.0.2: etag@~1.8.1: version "1.8.1" resolved "https://registry.yarnpkg.com/etag/-/etag-1.8.1.tgz#41ae2eeb65efa62268aebfea83ac7d79299b0887" - integrity sha1-Qa4u62XvpiJorr/qg6x9eSmbCIc= + integrity sha512-aIL5Fx7mawVa300al2BnEE4iNvo1qETxLrPI/o05L7z6go7fCw1J6EQmbK4FmJ2AS7kgVF/KEZWufBfdClMcPg== events@^3.0.0: version "3.3.0" @@ -6216,37 +6218,38 @@ expect@^26.6.2: jest-regex-util "^26.0.0" express@^4.17.1: - version "4.17.1" - resolved "https://registry.yarnpkg.com/express/-/express-4.17.1.tgz#4491fc38605cf51f8629d39c2b5d026f98a4c134" - integrity sha512-mHJ9O79RqluphRrcw2X/GTh3k9tVv8YcoyY4Kkh4WDMUYKRZUq0h1o0w2rrrxBqM7VoeUVqgb27xlEMXTnYt4g== + version "4.18.2" + resolved "https://registry.yarnpkg.com/express/-/express-4.18.2.tgz#3fabe08296e930c796c19e3c516979386ba9fd59" + integrity sha512-5/PsL6iGPdfQ/lKM1UuielYgv3BUoJfz1aUwU9vHZ+J7gyvwdQXFEBIEIaxeGf0GIcreATNyBExtalisDbuMqQ== dependencies: - accepts "~1.3.7" + accepts "~1.3.8" array-flatten "1.1.1" - body-parser "1.19.0" - content-disposition "0.5.3" + body-parser "1.20.1" + content-disposition "0.5.4" content-type "~1.0.4" - cookie "0.4.0" + cookie "0.5.0" cookie-signature "1.0.6" debug "2.6.9" - depd "~1.1.2" + depd "2.0.0" encodeurl "~1.0.2" escape-html "~1.0.3" etag "~1.8.1" - finalhandler "~1.1.2" + finalhandler "1.2.0" fresh "0.5.2" + http-errors "2.0.0" merge-descriptors "1.0.1" methods "~1.1.2" - on-finished "~2.3.0" + on-finished "2.4.1" parseurl "~1.3.3" path-to-regexp "0.1.7" - proxy-addr "~2.0.5" - qs "6.7.0" + proxy-addr "~2.0.7" + qs "6.11.0" range-parser "~1.2.1" - safe-buffer "5.1.2" - send "0.17.1" - serve-static "1.14.1" - setprototypeof "1.1.1" - statuses "~1.5.0" + safe-buffer "5.2.1" + send "0.18.0" + serve-static "1.15.0" + setprototypeof "1.2.0" + statuses "2.0.1" type-is "~1.6.18" utils-merge "1.0.1" vary "~1.1.2" @@ -6448,17 +6451,17 @@ filter-obj@^1.1.0: resolved "https://registry.yarnpkg.com/filter-obj/-/filter-obj-1.1.0.tgz#9b311112bc6c6127a16e016c6c5d7f19e0805c5b" integrity sha1-mzERErxsYSehbgFsbF1/GeCAXFs= -finalhandler@~1.1.2: - version "1.1.2" - resolved "https://registry.yarnpkg.com/finalhandler/-/finalhandler-1.1.2.tgz#b7e7d000ffd11938d0fdb053506f6ebabe9f587d" - integrity sha512-aAWcW57uxVNrQZqFXjITpW3sIUQmHGG3qSb9mUah9MgMC4NeWhNOlNjXEYq3HjRAvL6arUviZGGJsBg6z0zsWA== +finalhandler@1.2.0: + version "1.2.0" + resolved "https://registry.yarnpkg.com/finalhandler/-/finalhandler-1.2.0.tgz#7d23fe5731b207b4640e4fcd00aec1f9207a7b32" + integrity sha512-5uXcUVftlQMFnWC9qu/svkWv3GTd2PfUhK/3PLkYNAe7FbqJMt3515HaxE6eRL74GdsriiwujiawdaB1BpEISg== dependencies: debug "2.6.9" encodeurl "~1.0.2" escape-html "~1.0.3" - on-finished "~2.3.0" + on-finished "2.4.1" parseurl "~1.3.3" - statuses "~1.5.0" + statuses "2.0.1" unpipe "~1.0.0" find-cache-dir@^2.0.0, find-cache-dir@^2.1.0: @@ -6620,10 +6623,10 @@ format@^0.2.0: resolved "https://registry.yarnpkg.com/format/-/format-0.2.2.tgz#d6170107e9efdc4ed30c9dc39016df942b5cb58b" integrity sha1-1hcBB+nv3E7TDJ3DkBbflCtctYs= -forwarded@~0.1.2: - version "0.1.2" - resolved "https://registry.yarnpkg.com/forwarded/-/forwarded-0.1.2.tgz#98c23dab1175657b8c0573e8ceccd91b0ff18c84" - integrity sha1-mMI9qxF1ZXuMBXPozszZGw/xjIQ= +forwarded@0.2.0: + version "0.2.0" + resolved "https://registry.yarnpkg.com/forwarded/-/forwarded-0.2.0.tgz#2269936428aad4c15c7ebe9779a84bf0b2a81811" + integrity sha512-buRG0fpBtRHSTCOASe6hD258tEubFoRLb4ZNA6NxMVHNw2gOcwHo9wyablzMzOA5z9xA9L1KNjk/Nt6MT9aYow== fragment-cache@^0.2.1: version "0.2.1" @@ -6635,7 +6638,7 @@ fragment-cache@^0.2.1: fresh@0.5.2: version "0.5.2" resolved "https://registry.yarnpkg.com/fresh/-/fresh-0.5.2.tgz#3d8cadd90d976569fa835ab1f8e4b23a105605a7" - integrity sha1-PYyt2Q2XZWn6g1qx+OSyOhBWBac= + integrity sha512-zJ2mQYM18rEFOudeV4GShTGIQ7RbzA7ozbU9I/XBpm7kqgMywgmylMwXHxZJmkVoYkna9d2pVXVXPdYTP9ej8Q== from2@^2.1.0: version "2.3.0" @@ -6785,7 +6788,16 @@ get-caller-file@^2.0.1: resolved "https://registry.yarnpkg.com/get-caller-file/-/get-caller-file-2.0.5.tgz#4f94412a82db32f36e3b0b9741f8a97feb031f7e" integrity sha512-DyFP3BM/3YHTQOCUL/w0OZHR0lpKeGrxotcHWcqNEdnltqFwXVfhEBQ94eIo34AfQpo0rGki4cyIiftY06h2Fg== -get-intrinsic@^1.0.2, get-intrinsic@^1.1.0, get-intrinsic@^1.1.1: +get-intrinsic@^1.0.2: + version "1.1.3" + resolved "https://registry.yarnpkg.com/get-intrinsic/-/get-intrinsic-1.1.3.tgz#063c84329ad93e83893c7f4f243ef63ffa351385" + integrity sha512-QJVz1Tj7MS099PevUG5jvnt9tSkXN8K14dxQlikJuPt4uD9hHAHjLyLBiLR5zELelBdD9QNRAXZzsJx0WaDL9A== + dependencies: + function-bind "^1.1.1" + has "^1.0.3" + has-symbols "^1.0.3" + +get-intrinsic@^1.1.0, get-intrinsic@^1.1.1: version "1.1.1" resolved "https://registry.yarnpkg.com/get-intrinsic/-/get-intrinsic-1.1.1.tgz#15f59f376f855c446963948f0d24cd3637b4abc6" integrity sha512-kWZrnVM42QCiEA2Ig1bG8zjoIMOgxWwYCEeNdwY6Tv/cOSeGpcoX4pXHfKUxNKVoArnrEr2e9srnAxxGIraS9Q== @@ -7163,6 +7175,11 @@ has-symbols@^1.0.1, has-symbols@^1.0.2: resolved "https://registry.yarnpkg.com/has-symbols/-/has-symbols-1.0.2.tgz#165d3070c00309752a1236a479331e3ac56f1423" integrity sha512-chXa79rL/UC2KlX17jo3vRGz0azaWEx5tGqZg5pO3NUyEJVB17dMruQlzCCOfUvElghKcm5194+BCRvi2Rv/Gw== +has-symbols@^1.0.3: + version "1.0.3" + resolved "https://registry.yarnpkg.com/has-symbols/-/has-symbols-1.0.3.tgz#bb7b2c4349251dce87b125f7bdf874aa7c8b39f8" + integrity sha512-l3LCuF6MgDNwTDKkdYGEihYjt5pRPbEg46rtlmnSPlUbgmB8LOIrKJbYYFBSbnPaJexMKtiPO8hmeRjRz2Td+A== + has-unicode@^2.0.0: version "2.0.1" resolved "https://registry.yarnpkg.com/has-unicode/-/has-unicode-2.0.1.tgz#e0e6fe6a28cf51138855e086d1691e771de2a8b9" @@ -7419,27 +7436,16 @@ http-call@^5.2.2: parse-json "^4.0.0" tunnel-agent "^0.6.0" -http-errors@1.7.2: - 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toidentifier "1.0.0" + setprototypeof "1.2.0" + statuses "2.0.1" + toidentifier "1.0.1" http-signature@~1.2.0: version "1.2.0" @@ -8835,9 +8841,9 @@ loader-utils@2.0.0, loader-utils@^2.0.0: json5 "^2.1.2" loader-utils@^1.2.3, loader-utils@^1.4.0: - version "1.4.0" - resolved "https://registry.yarnpkg.com/loader-utils/-/loader-utils-1.4.0.tgz#c579b5e34cb34b1a74edc6c1fb36bfa371d5a613" - integrity sha512-qH0WSMBtn/oHuwjy/NucEgbx5dbxxnxup9s4PVXJUDHZBQY+s0NWA9rJf53RBnQZxfch7euUui7hpoAPvALZdA== + version "1.4.2" + resolved "https://registry.yarnpkg.com/loader-utils/-/loader-utils-1.4.2.tgz#29a957f3a63973883eb684f10ffd3d151fec01a3" + integrity sha512-I5d00Pd/jwMD2QCduo657+YM/6L3KZu++pmX9VFncxaxvHcru9jx1lBaFft+r4Mt2jK0Yhp41XlRAihzPxHNCg== dependencies: big.js "^5.2.2" emojis-list "^3.0.0" @@ -9146,7 +9152,7 @@ mdurl@^1.0.0: media-typer@0.3.0: version "0.3.0" resolved "https://registry.yarnpkg.com/media-typer/-/media-typer-0.3.0.tgz#8710d7af0aa626f8fffa1ce00168545263255748" - integrity sha1-hxDXrwqmJvj/+hzgAWhUUmMlV0g= + integrity sha512-dq+qelQ9akHpcOl/gUVRTxVIOkAJ1wR3QAvb4RsVjS8oVoFjDGTc679wJYmUmknUF5HwMLOgb5O+a3KxfWapPQ== memfs@^3.1.2: version "3.2.2" @@ -9181,7 +9187,7 @@ memory-fs@^0.5.0: merge-descriptors@1.0.1: version "1.0.1" resolved "https://registry.yarnpkg.com/merge-descriptors/-/merge-descriptors-1.0.1.tgz#b00aaa556dd8b44568150ec9d1b953f3f90cbb61" - 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version "2.3.0" - resolved "https://registry.yarnpkg.com/on-finished/-/on-finished-2.3.0.tgz#20f1336481b083cd75337992a16971aa2d906947" - integrity sha1-IPEzZIGwg811M3mSoWlxqi2QaUc= +on-finished@2.4.1: + version "2.4.1" + resolved "https://registry.yarnpkg.com/on-finished/-/on-finished-2.4.1.tgz#58c8c44116e54845ad57f14ab10b03533184ac3f" + integrity sha512-oVlzkg3ENAhCk2zdv7IJwd/QUD4z2RxRwpkcGY8psCVcCYZNq4wYnVWALHM+brtuJjePWiYF/ClmuDr8Ch5+kg== dependencies: ee-first "1.1.1" @@ -10104,7 +10127,7 @@ path-parse@^1.0.6: path-to-regexp@0.1.7: version "0.1.7" resolved "https://registry.yarnpkg.com/path-to-regexp/-/path-to-regexp-0.1.7.tgz#df604178005f522f15eb4490e7247a1bfaa67f8c" - integrity sha1-32BBeABfUi8V60SQ5yR6G/qmf4w= + integrity sha512-5DFkuoqlv1uYQKxy8omFBeJPQcdoE07Kv2sferDCrAq1ohOU+MSDswDIbnx3YAM60qIOnYa53wBhXW0EbMonrQ== path-type@^2.0.0: version "2.0.0" @@ -10428,12 +10451,12 @@ protocols@^1.1.0, protocols@^1.4.0: resolved "https://registry.yarnpkg.com/protocols/-/protocols-1.4.8.tgz#48eea2d8f58d9644a4a32caae5d5db290a075ce8" integrity sha512-IgjKyaUSjsROSO8/D49Ab7hP8mJgTYcqApOqdPhLoPxAplXmkp+zRvsrSQjFn5by0rhm4VH0GAUELIPpx7B1yg== -proxy-addr@~2.0.5: - version "2.0.6" - resolved "https://registry.yarnpkg.com/proxy-addr/-/proxy-addr-2.0.6.tgz#fdc2336505447d3f2f2c638ed272caf614bbb2bf" - integrity sha512-dh/frvCBVmSsDYzw6n926jv974gddhkFPfiN8hPOi30Wax25QZyZEGveluCgliBnqmuM+UJmBErbAUFIoDbjOw== +proxy-addr@~2.0.7: + version "2.0.7" + resolved "https://registry.yarnpkg.com/proxy-addr/-/proxy-addr-2.0.7.tgz#f19fe69ceab311eeb94b42e70e8c2070f9ba1025" + integrity sha512-llQsMLSUDUPT44jdrU/O37qlnifitDP+ZwrmmZcoSKyLKvtZxpyV0n2/bD/N4tBAAZ/gJEdZU7KMraoK1+XYAg== dependencies: - forwarded "~0.1.2" + forwarded "0.2.0" ipaddr.js "1.9.1" prr@~1.0.1: @@ -10498,22 +10521,17 @@ punycode@^2.1.0, punycode@^2.1.1: resolved "https://registry.yarnpkg.com/punycode/-/punycode-2.1.1.tgz#b58b010ac40c22c5657616c8d2c2c02c7bf479ec" integrity sha512-XRsRjdf+j5ml+y/6GKHPZbrF/8p2Yga0JPtdqTIY2Xe5ohJPD9saDJJLPvp9+NSBprVvevdXZybnj2cv8OEd0A== -qs@6.7.0: - version "6.7.0" - resolved "https://registry.yarnpkg.com/qs/-/qs-6.7.0.tgz#41dc1a015e3d581f1621776be31afb2876a9b1bc" - integrity sha512-VCdBRNFTX1fyE7Nb6FYoURo/SPe62QCaAyzJvUjwRaIsc+NePBEniHlvxFmmX56+HZphIGtV0XeCirBtpDrTyQ== - -qs@^6.10.0, qs@^6.9.4: - version "6.10.1" - resolved "https://registry.yarnpkg.com/qs/-/qs-6.10.1.tgz#4931482fa8d647a5aab799c5271d2133b981fb6a" - integrity sha512-M528Hph6wsSVOBiYUnGf+K/7w0hNshs/duGsNXPUCLH5XAqjEtiPGwNONLV0tBH8NoGb0mvD5JubnUTrujKDTg== +qs@6.11.0, qs@^6.10.0, qs@^6.9.4: + version "6.11.0" + resolved "https://registry.yarnpkg.com/qs/-/qs-6.11.0.tgz#fd0d963446f7a65e1367e01abd85429453f0c37a" + integrity sha512-MvjoMCJwEarSbUYk5O+nmoSzSutSsTwF85zcHPQ9OrlFoZOYIjaqBAJIqIXjptyD5vThxGq52Xu/MaJzRkIk4Q== dependencies: side-channel "^1.0.4" qs@~6.5.2: - version "6.5.2" - resolved "https://registry.yarnpkg.com/qs/-/qs-6.5.2.tgz#cb3ae806e8740444584ef154ce8ee98d403f3e36" - integrity sha512-N5ZAX4/LxJmF+7wN74pUD6qAh9/wnvdQcjq9TZjevvXzSUo7bfmw91saqMjzGS2xq91/odN2dW/WOl7qQHNDGA== + version "6.5.3" + resolved "https://registry.yarnpkg.com/qs/-/qs-6.5.3.tgz#3aeeffc91967ef6e35c0e488ef46fb296ab76aad" + integrity sha512-qxXIEh4pCGfHICj1mAJQ2/2XVZkjCDTcEgfoSQxc/fYivUZxTkk7L3bDBJSoNrEzXI17oUO5Dp07ktqE5KzczA== query-string@^6.13.8: version "6.14.1" @@ -10570,13 +10588,13 @@ range-parser@^1.2.1, range-parser@~1.2.1: resolved "https://registry.yarnpkg.com/range-parser/-/range-parser-1.2.1.tgz#3cf37023d199e1c24d1a55b84800c2f3e6468031" integrity sha512-Hrgsx+orqoygnmhFbKaHE6c296J+HTAQXoxEF6gNupROmmGJRoyzfG3ccAveqCBrwr/2yxQ5BVd/GTl5agOwSg== -raw-body@2.4.0: - version "2.4.0" - resolved "https://registry.yarnpkg.com/raw-body/-/raw-body-2.4.0.tgz#a1ce6fb9c9bc356ca52e89256ab59059e13d0332" - integrity sha512-4Oz8DUIwdvoa5qMJelxipzi/iJIi40O5cGV1wNYp5hvZP8ZN0T+jiNkL0QepXs+EsQ9XJ8ipEDoiH70ySUJP3Q== +raw-body@2.5.1: + version "2.5.1" + resolved "https://registry.yarnpkg.com/raw-body/-/raw-body-2.5.1.tgz#fe1b1628b181b700215e5fd42389f98b71392857" + integrity sha512-qqJBtEyVgS0ZmPGdCFPWJ3FreoqvG4MVQln/kCgF7Olq95IbOp0/BWyMwbdtn4VTvkM8Y7khCQ2Xgk/tcrCXig== dependencies: - bytes "3.1.0" - http-errors "1.7.2" + bytes "3.1.2" + http-errors "2.0.0" iconv-lite "0.4.24" unpipe "1.0.0" @@ -11279,16 +11297,16 @@ safe-buffer@5.1.1: resolved "https://registry.yarnpkg.com/safe-buffer/-/safe-buffer-5.1.1.tgz#893312af69b2123def71f57889001671eeb2c853" integrity sha512-kKvNJn6Mm93gAczWVJg7wH+wGYWNrDHdWvpUmHyEsgCtIwwo3bqPtV4tR5tuPaUhTOo/kvhVwd8XwwOllGYkbg== -safe-buffer@5.1.2, safe-buffer@~5.1.0, safe-buffer@~5.1.1: - version "5.1.2" - resolved "https://registry.yarnpkg.com/safe-buffer/-/safe-buffer-5.1.2.tgz#991ec69d296e0313747d59bdfd2b745c35f8828d" - integrity sha512-Gd2UZBJDkXlY7GbJxfsE8/nvKkUEU1G38c1siN6QP6a9PT9MmHB8GnpscSmMJSoF8LOIrt8ud/wPtojys4G6+g== - -safe-buffer@^5.0.1, safe-buffer@^5.1.0, safe-buffer@^5.1.1, safe-buffer@^5.1.2, safe-buffer@^5.2.0, safe-buffer@~5.2.0: +safe-buffer@5.2.1, safe-buffer@^5.0.1, safe-buffer@^5.1.0, safe-buffer@^5.1.1, safe-buffer@^5.1.2, safe-buffer@^5.2.0, safe-buffer@~5.2.0: version "5.2.1" resolved "https://registry.yarnpkg.com/safe-buffer/-/safe-buffer-5.2.1.tgz#1eaf9fa9bdb1fdd4ec75f58f9cdb4e6b7827eec6" integrity sha512-rp3So07KcdmmKbGvgaNxQSJr7bGVSVk5S9Eq1F+ppbRo70+YeaDxkw5Dd8NPN+GD6bjnYm2VuPuCXmpuYvmCXQ== +safe-buffer@~5.1.0, safe-buffer@~5.1.1: + version "5.1.2" + resolved "https://registry.yarnpkg.com/safe-buffer/-/safe-buffer-5.1.2.tgz#991ec69d296e0313747d59bdfd2b745c35f8828d" + integrity sha512-Gd2UZBJDkXlY7GbJxfsE8/nvKkUEU1G38c1siN6QP6a9PT9MmHB8GnpscSmMJSoF8LOIrt8ud/wPtojys4G6+g== + safe-regex@^1.1.0: version "1.1.0" resolved "https://registry.yarnpkg.com/safe-regex/-/safe-regex-1.1.0.tgz#40a3669f3b077d1e943d44629e157dd48023bf2e" @@ -11411,24 +11429,24 @@ semver@^6.0.0, semver@^6.1.0, semver@^6.1.1, semver@^6.1.2, semver@^6.3.0: resolved "https://registry.yarnpkg.com/semver/-/semver-6.3.0.tgz#ee0a64c8af5e8ceea67687b133761e1becbd1d3d" integrity sha512-b39TBaTSfV6yBrapU89p5fKekE2m/NwnDocOVruQFS1/veMgdzuPcnOM34M6CwxW8jH/lxEa5rBoDeUwu5HHTw== -send@0.17.1: - version "0.17.1" - resolved "https://registry.yarnpkg.com/send/-/send-0.17.1.tgz#c1d8b059f7900f7466dd4938bdc44e11ddb376c8" - integrity sha512-BsVKsiGcQMFwT8UxypobUKyv7irCNRHk1T0G680vk88yf6LBByGcZJOTJCrTP2xVN6yI+XjPJcNuE3V4fT9sAg== +send@0.18.0: + version "0.18.0" + resolved "https://registry.yarnpkg.com/send/-/send-0.18.0.tgz#670167cc654b05f5aa4a767f9113bb371bc706be" + integrity sha512-qqWzuOjSFOuqPjFe4NOsMLafToQQwBSOEpS+FwEt3A2V3vKubTquT3vmLTQpFgMXp8AlFWFuP1qKaJZOtPpVXg== dependencies: debug "2.6.9" - depd "~1.1.2" - destroy "~1.0.4" + depd "2.0.0" + destroy "1.2.0" encodeurl "~1.0.2" escape-html "~1.0.3" etag "~1.8.1" fresh "0.5.2" - http-errors "~1.7.2" + http-errors "2.0.0" mime "1.6.0" - ms "2.1.1" - on-finished "~2.3.0" + ms "2.1.3" + on-finished "2.4.1" range-parser "~1.2.1" - statuses "~1.5.0" + statuses "2.0.1" sentence-case@^3.0.4: version "3.0.4" @@ -11464,15 +11482,15 @@ serve-favicon@^2.5.0: parseurl "~1.3.2" safe-buffer "5.1.1" -serve-static@1.14.1: - version "1.14.1" - resolved "https://registry.yarnpkg.com/serve-static/-/serve-static-1.14.1.tgz#666e636dc4f010f7ef29970a88a674320898b2f9" - integrity sha512-JMrvUwE54emCYWlTI+hGrGv5I8dEwmco/00EvkzIIsR7MqrHonbD9pO2MOfFnpFntl7ecpZs+3mW+XbQZu9QCg== +serve-static@1.15.0: + version "1.15.0" + resolved "https://registry.yarnpkg.com/serve-static/-/serve-static-1.15.0.tgz#faaef08cffe0a1a62f60cad0c4e513cff0ac9540" + integrity sha512-XGuRDNjXUijsUL0vl6nSD7cwURuzEgglbOaFuZM9g3kwDXOWVTck0jLzjPzGD+TazWbboZYu52/9/XPdUgne9g== dependencies: encodeurl "~1.0.2" escape-html "~1.0.3" parseurl "~1.3.3" - send "0.17.1" + send "0.18.0" set-blocking@^2.0.0, set-blocking@~2.0.0: version "2.0.0" @@ -11494,10 +11512,10 @@ setimmediate@^1.0.4: resolved "https://registry.yarnpkg.com/setimmediate/-/setimmediate-1.0.5.tgz#290cbb232e306942d7d7ea9b83732ab7856f8285" integrity sha1-KQy7Iy4waULX1+qbg3Mqt4VvgoU= -setprototypeof@1.1.1: - version "1.1.1" - resolved "https://registry.yarnpkg.com/setprototypeof/-/setprototypeof-1.1.1.tgz#7e95acb24aa92f5885e0abef5ba131330d4ae683" - integrity sha512-JvdAWfbXeIGaZ9cILp38HntZSFSo3mWg6xGcJJsd+d4aRMOqauag1C63dJfDw7OaMYwEbHMOxEZ1lqVRYP2OAw== +setprototypeof@1.2.0: + version "1.2.0" + resolved "https://registry.yarnpkg.com/setprototypeof/-/setprototypeof-1.2.0.tgz#66c9a24a73f9fc28cbe66b09fed3d33dcaf1b424" + integrity sha512-E5LDX7Wrp85Kil5bhZv46j8jOeboKq5JMmYM3gVGdGH8xFpPWXUMsNrlODCrkoxMEeNi/XZIwuRvY4XNwYMJpw== sha.js@^2.4.0, sha.js@^2.4.11, sha.js@^2.4.8: version "2.4.11" @@ -11839,10 +11857,10 @@ static-extend@^0.1.1: define-property "^0.2.5" object-copy "^0.1.0" -"statuses@>= 1.5.0 < 2", statuses@~1.5.0: - version "1.5.0" - resolved "https://registry.yarnpkg.com/statuses/-/statuses-1.5.0.tgz#161c7dac177659fd9811f43771fa99381478628c" - integrity sha1-Fhx9rBd2Wf2YEfQ3cfqZOBR4Yow= +statuses@2.0.1: + version "2.0.1" + resolved "https://registry.yarnpkg.com/statuses/-/statuses-2.0.1.tgz#55cb000ccf1d48728bd23c685a063998cf1a1b63" + integrity sha512-RwNA9Z/7PrK06rYLIzFMlaF+l73iwpzsqRIFgbMLbTcLD6cOao82TaWefPXQvB2fOC4AjuYSEndS7N/mTCbkdQ== stealthy-require@^1.1.1: version "1.1.1" @@ -12449,10 +12467,10 @@ toggle-selection@^1.0.6: resolved "https://registry.yarnpkg.com/toggle-selection/-/toggle-selection-1.0.6.tgz#6e45b1263f2017fa0acc7d89d78b15b8bf77da32" integrity sha1-bkWxJj8gF/oKzH2J14sVuL932jI= -toidentifier@1.0.0: - version "1.0.0" - resolved "https://registry.yarnpkg.com/toidentifier/-/toidentifier-1.0.0.tgz#7e1be3470f1e77948bc43d94a3c8f4d7752ba553" - integrity sha512-yaOH/Pk/VEhBWWTlhI+qXxDFXlejDGcQipMlyxda9nthulaxLZUNcUqFxokp0vcYnvteJln5FNQDRrxj3YcbVw== +toidentifier@1.0.1: + version "1.0.1" + resolved "https://registry.yarnpkg.com/toidentifier/-/toidentifier-1.0.1.tgz#3be34321a88a820ed1bd80dfaa33e479fbb8dd35" + integrity sha512-o5sSPKEkg/DIQNmH43V0/uerLrpzVedkUh8tGNvaeXpfpuwjKenlSox/2O/BTlZUtEe+JG7s5YhEz608PlAHRA== totalist@^1.0.0: version "1.1.0" @@ -12655,7 +12673,7 @@ type-fest@^0.8.1: resolved "https://registry.yarnpkg.com/type-fest/-/type-fest-0.8.1.tgz#09e249ebde851d3b1e48d27c105444667f17b83d" integrity sha512-4dbzIzqvjtgiM5rw1k5rEHtBANKmdudhGyBEajN01fEyhaAIhsoKNy6y7+IN93IfpFtwY9iqi7kD+xwKhQsNJA== -type-is@~1.6.17, type-is@~1.6.18: +type-is@~1.6.18: version "1.6.18" resolved "https://registry.yarnpkg.com/type-is/-/type-is-1.6.18.tgz#4e552cd05df09467dcbc4ef739de89f2cf37c131" integrity sha512-TkRKr9sUTxEH8MdfuCSP7VizJyzRNMjj2J2do2Jr3Kym598JVdEksuzPQCnlFPW4ky9Q+iA+ma9BGm06XQBy8g== @@ -12838,7 +12856,7 @@ universalify@^2.0.0: unpipe@1.0.0, unpipe@~1.0.0: version "1.0.0" resolved "https://registry.yarnpkg.com/unpipe/-/unpipe-1.0.0.tgz#b2bf4ee8514aae6165b4817829d21b2ef49904ec" - integrity sha1-sr9O6FFKrmFltIF4KdIbLvSZBOw= + integrity sha512-pjy2bYhSsufwWlKwPc+l3cN7+wuJlK6uz0YdJEOlQDbl6jo/YlPi4mb8agUkVC8BF7V8NuzeyPNqRksA3hztKQ== unquote@^1.1.0: version "1.1.1" @@ -12981,7 +12999,7 @@ utila@~0.4: utils-merge@1.0.1: version "1.0.1" resolved "https://registry.yarnpkg.com/utils-merge/-/utils-merge-1.0.1.tgz#9f95710f50a267947b2ccc124741c1028427e713" - integrity sha1-n5VxD1CiZ5R7LMwSR0HBAoQn5xM= + integrity sha512-pMZTvIkT1d+TFGvDOqodOclx0QWkkgi6Tdoa8gC8ffGAAqz9pzPTZWAybbsHHoED/ztMtkv/VoYTYyShUn81hA== uuid-browser@^3.1.0: version "3.1.0" @@ -13023,7 +13041,7 @@ validate-npm-package-license@^3.0.1: vary@~1.1.2: version "1.1.2" resolved "https://registry.yarnpkg.com/vary/-/vary-1.1.2.tgz#2299f02c6ded30d4a5961b0b9f74524a18f634fc" - integrity sha1-IpnwLG3tMNSllhsLn3RSShj2NPw= + integrity sha512-BNGbWLfd0eUPabhkXUVm0j8uuvREyTh5ovRa/dyow/BqAbZJyC+5fU+IzQOzmAKzYqYRAISoRhdQr3eIZ/PXqg== verror@1.10.0: version "1.10.0" diff --git a/test_output backup b/test_output backup deleted file mode 100644 index 6ab96db7..00000000 --- a/test_output backup +++ /dev/null @@ -1,99 +0,0 @@ -""" This file contains tools for test_main.py to use. """ - -def check_mathjax_compatible(output_string): - # for now, checks that the answers start and end with the "$" to be conventionally compatible with mathjax - # could change the conditions to accommodate more types of mathjax compatible examples ... - return output_string[0] == "$" and output_string[len(output_string)-1] == "$" - -# returns True if the output dictionary is a valid output for the "ruby side" interpretation -def test_output(out): - - bodyFormat_options = ["text", "mathjax"] # can add more options in the future - - if type(out) != type({}): - return False - else: - - answer_type = { - "title": "", - "body": "", - "bodyFormat": "text", # or "mathjax" - "pseudocode": "", - "multipleChoiceAnswers": [ - { - "body": "", - "bodyFormat": "mathjax", - "correct": "true", - }, - { - "body": "", - "bodyFormat": "mathjax", - "correct": "false", - }, - { - "body": "", - "bodyFormat": "mathjax", - "correct": "false", - }, - { - "body": "", - "bodyFormat": "mathjax", - "correct": "false", - } - ] - } - - - keys_list = list(answer_type.keys()) # the list of keys from the template answer_type dictionary - out_list = list(out.keys()) # the list of keys from the output dictionary that we are testing - - # checks if the output dictionary that is being tested has the correct type of keys as in the answer_type - for i in range(len(out_list)): - if not out_list[i] in keys_list: - return False - - # if there is "title" key in the ouput dictionary, check that the item of "title" is string type - if "title" in out_list: - if not type(out["title"])==type(""): - return False - - # check that the item of the key, "body", is string type - if not type(out["body"])==type(""): - return False - - # checks "bodyFormat" key has the correct item types available as in the bodyFormat_options - if not (out["bodyFormat"] in bodyFormat_options): - return False - - # if there is "pseudocode" key in the output dictionary, check that the item of "pseudocode" is a string type - if "pseudocode" in out_list: - if not type(out["pseudocode"])==type(""): - return False - - # tests the item of "multipleChoiceAnswers" key - mult_choice_answers = out[keys_list[4]] - if len(mult_choice_answers) != 4: - return False - else: - - for i in range(0,4): - - if type(mult_choice_answers[i]) != type({}): - return False - elif len(mult_choice_answers[i]) != 3: - return False - - for j in range(len(list(mult_choice_answers[i].keys()))): - if not (list(mult_choice_answers[i].keys())[j] in ["body", "bodyFormat", "correct"]): - return False - - if not check_mathjax_compatible(mult_choice_answers[i]["body"]): - return False - - if not (mult_choice_answers[i]["bodyFormat"] in bodyFormat_options): - return False - - if not (mult_choice_answers[i]["correct"]=="true" or mult_choice_answers[i]["correct"]=="false"): - return False - - return True