<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="2d95f88eea6b11efb8100e0e3c45b88f" data-usage-id="block-v1:OCW+18.031+2019_Spring+type@vertical+block@edxtutorial-tab2" data-graded="False" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:OCW+18.031+2019_Spring" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">2. Example Problem Types</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.031+2019_Spring+type@html+block@edxtutorial-tab2-text1">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="2d95f88eea6b11efb8100e0e3c45b88f" data-usage-id="block-v1:OCW+18.031+2019_Spring+type@html+block@edxtutorial-tab2-text1" data-graded="False" data-has-score="False" data-runtime-version="1" data-block-type="html" data-init="XBlockToXModuleShim" data-course-id="course-v1:OCW+18.031+2019_Spring" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>
Take a moment to familiarize yourself with the main problem types we use in this course. </p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem1">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2d95f88eea6b11efb8100e0e3c45b88f" data-usage-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem1" data-graded="False" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:OCW+18.031+2019_Spring" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_edxtutorial-tab2-problem1" class="problems-wrapper" role="group"
aria-labelledby="edxtutorial-tab2-problem1-problem-title"
data-problem-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem1" data-url="/courses/course-v1:OCW+18.031+2019_Spring/xblock/block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem1/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="edxtutorial-tab2-problem1-problem-title" aria-describedby="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem1-problem-progress" tabindex="-1">
Checking and submitting an answer
</h3>
<div class="problem-progress" id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem1-problem-progress"></div>
<div class="problem">
<div>
<p>
This course was built using the <a href="https://open.edx.org/the-platform/">edX platform</a>, which is able to check your answers and give you immediate feedback. When you "check" a problem, it is automatically submitted for grading purposes. </p>
<p>
Depending on the type of the problem you may have access to the "show answer" button. In the lecture exercises as well as the part A and part B Homework assignments, this option to show the answer will appear only after the due date has passed, you have run out of problem attempts, or you have already submitted the correct answer. You will never get detailed solutions to the final exam. </p>
<p>
This problem has unlimited attempts. If you get an answer wrong, you can simply try again until you get it right. How many weeks will this course be? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_edxtutorial-tab2-problem1_2_1" class=" capa_inputtype textline">
<div class="unanswered ">
<input type="text" name="input_edxtutorial-tab2-problem1_2_1" id="input_edxtutorial-tab2-problem1_2_1" aria-describedby="status_edxtutorial-tab2-problem1_2_1" value=""/>
<span class="trailing_text" id="trailing_text_edxtutorial-tab2-problem1_2_1"/>
<span class="status unanswered" id="status_edxtutorial-tab2-problem1_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_edxtutorial-tab2-problem1_2_1" class="answer"/>
</div>
</div></div> <div class="solution-span">
<span id="solution_edxtutorial-tab2-problem1_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Checking and submitting an answer" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_edxtutorial-tab2-problem1" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_edxtutorial-tab2-problem1">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem1-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem1-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem1-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem2">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2d95f88eea6b11efb8100e0e3c45b88f" data-usage-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem2" data-graded="False" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:OCW+18.031+2019_Spring" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_edxtutorial-tab2-problem2" class="problems-wrapper" role="group"
aria-labelledby="edxtutorial-tab2-problem2-problem-title"
data-problem-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem2" data-url="/courses/course-v1:OCW+18.031+2019_Spring/xblock/block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem2/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="edxtutorial-tab2-problem2-problem-title" aria-describedby="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem2-problem-progress" tabindex="-1">
Resetting a Problem
</h3>
<div class="problem-progress" id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem2-problem-progress"></div>
<div class="problem">
<div>
<p>
Some problems involve randomized parameters, or other elements that you may wish to reset to the original configuration. Here is an example where the variables [mathjaxinline]x_1[/mathjaxinline] and [mathjaxinline]x_2[/mathjaxinline] are randomized. After one attempt, you can click reset to see the values change! </p>
<p>
Let [mathjaxinline]\ x_1 = 17 \ [/mathjaxinline] and [mathjaxinline] \ x_2 = 60 [/mathjaxinline].</p>
<p>
Enter the numeric value of [mathjaxinline]x_1+x_2[/mathjaxinline] in the answer box below. </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_edxtutorial-tab2-problem2_2_1" class=" capa_inputtype textline">
<div class="unanswered ">
<input type="text" name="input_edxtutorial-tab2-problem2_2_1" id="input_edxtutorial-tab2-problem2_2_1" aria-describedby="status_edxtutorial-tab2-problem2_2_1" value=""/>
<span class="trailing_text" id="trailing_text_edxtutorial-tab2-problem2_2_1"/>
<span class="status unanswered" id="status_edxtutorial-tab2-problem2_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_edxtutorial-tab2-problem2_2_1" class="answer"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_edxtutorial-tab2-problem2_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Resetting a Problem" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_edxtutorial-tab2-problem2" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_edxtutorial-tab2-problem2">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem2-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem2-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem2-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-3" data-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem3">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2d95f88eea6b11efb8100e0e3c45b88f" data-usage-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem3" data-graded="False" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:OCW+18.031+2019_Spring" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_edxtutorial-tab2-problem3" class="problems-wrapper" role="group"
aria-labelledby="edxtutorial-tab2-problem3-problem-title"
data-problem-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem3" data-url="/courses/course-v1:OCW+18.031+2019_Spring/xblock/block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem3/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="edxtutorial-tab2-problem3-problem-title" aria-describedby="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem3-problem-progress" tabindex="-1">
Limited Number of Attempts 1
</h3>
<div class="problem-progress" id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem3-problem-progress"></div>
<div class="problem">
<div>
<p>
Most of the time, you will have a limited number of times that you can attempt a problem. To save an answer and keep it there until you come back, use the save button. </p>
<p>
How much does it cost to take an edX course? </p>
<p>
(Enter a number.) <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_edxtutorial-tab2-problem3_2_1" class=" capa_inputtype textline">
<div class="unanswered ">
<input type="text" name="input_edxtutorial-tab2-problem3_2_1" id="input_edxtutorial-tab2-problem3_2_1" aria-describedby="status_edxtutorial-tab2-problem3_2_1" value=""/>
<span class="trailing_text" id="trailing_text_edxtutorial-tab2-problem3_2_1"/>
<span class="status unanswered" id="status_edxtutorial-tab2-problem3_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_edxtutorial-tab2-problem3_2_1" class="answer"/>
</div>
</div></div> </p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Limited Number of Attempts 1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_edxtutorial-tab2-problem3" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_edxtutorial-tab2-problem3">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem3-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem3-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem3-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-4" data-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem4">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="2d95f88eea6b11efb8100e0e3c45b88f" data-usage-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem4" data-graded="False" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:OCW+18.031+2019_Spring" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_edxtutorial-tab2-problem4" class="problems-wrapper" role="group"
aria-labelledby="edxtutorial-tab2-problem4-problem-title"
data-problem-id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem4" data-url="/courses/course-v1:OCW+18.031+2019_Spring/xblock/block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem4/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="edxtutorial-tab2-problem4-problem-title" aria-describedby="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem4-problem-progress" tabindex="-1">
Limited Number of Attempts 2
</h3>
<div class="problem-progress" id="block-v1:OCW+18.031+2019_Spring+type@problem+block@edxtutorial-tab2-problem4-problem-progress"></div>
<div class="problem">
<div>
<p>
Multiple choice problems will almost always have between 1 and 3 attempts. </p>
<p>
Which choice is correct? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_edxtutorial-tab2-problem4_2_1">
<fieldset aria-describedby="status_edxtutorial-tab2-problem4_2_1">
<div class="field">
<input type="radio" name="input_edxtutorial-tab2-problem4_2_1" id="input_edxtutorial-tab2-problem4_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="edxtutorial-tab2-problem4_2_1-choice_1-label" for="input_edxtutorial-tab2-problem4_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_edxtutorial-tab2-problem4_2_1">
<text> incorrect</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_edxtutorial-tab2-problem4_2_1" id="input_edxtutorial-tab2-problem4_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="edxtutorial-tab2-problem4_2_1-choice_2-label" for="input_edxtutorial-tab2-problem4_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_edxtutorial-tab2-problem4_2_1">
<text> correct</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_edxtutorial-tab2-problem4_2_1" id="input_edxtutorial-tab2-problem4_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="edxtutorial-tab2-problem4_2_1-choice_3-label" for="input_edxtutorial-tab2-problem4_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_edxtutorial-tab2-problem4_2_1">
<text> incorrect</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_edxtutorial-tab2-problem4_2_1" id="input_edxtutorial-tab2-problem4_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="edxtutorial-tab2-problem4_2_1-choice_4-label" for="input_edxtutorial-tab2-problem4_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_edxtutorial-tab2-problem4_2_1">
<text> incorrect</text>
</label>
</div>
<span id="answer_edxtutorial-tab2-problem4_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_edxtutorial-tab2-problem4_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Limited Number of Attempts 2" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_edxtutorial-tab2-problem4" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_edxtutorial-tab2-problem4">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem4-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem4-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="edxtutorial-tab2-problem4-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
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Formula Entry Problems
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<p>
This is a math class, which means we are going to be using formulas. And sometimes, we want you to find these formulas. There are some rules for entering formulas into the text entry box (which follows rules for ASCII math). </p>
<ul class="itemize">
<li>
<p>
Use [mathjaxinline]+[/mathjaxinline] to denote addition; e.g. 2+3. </p>
</li>
<li>
<p>
Use [mathjaxinline]-[/mathjaxinline] to denote subtraction; e.g. x-1. </p>
</li>
<li>
<p>
Use [mathjaxinline]*[/mathjaxinline] to denote multiplication; e.g. 2[mathjaxinline]*[/mathjaxinline]x. </p>
</li>
<li>
<p>
Use [mathjaxinline]\wedge[/mathjaxinline] to denote exponentiation; e.g. x[mathjaxinline]\wedge[/mathjaxinline]2 for [mathjaxinline]x^2[/mathjaxinline]. </p>
</li>
<li>
<p>
Use / to denote division; e.g. 7/x for [mathjaxinline]\displaystyle \frac{7}{x}[/mathjaxinline]. </p>
</li>
<li>
<p>
Type <b class="bf">pi</b> for the mathematical constant [mathjaxinline]\pi[/mathjaxinline]. </p>
</li>
<li>
<p>
Type <b class="bf">e</b> for the mathematical constant [mathjaxinline]e[/mathjaxinline]. </p>
</li>
<li>
<p>
Type <b class="bf">sqrt(x)</b>, <b class="bf">sin(x)</b>, <b class="bf">cos(x)</b>, <b class="bf">ln(x)</b>, <b class="bf">arccos(x)</b>, etc. for the known functions [mathjaxinline]\sqrt {x}[/mathjaxinline], [mathjaxinline]\sin {x}[/mathjaxinline], [mathjaxinline]\cos {x}[/mathjaxinline], [mathjaxinline]\ln {x}[/mathjaxinline], [mathjaxinline]\arccos {x}[/mathjaxinline] etc. Note that parentheses are required. </p>
</li>
<li>
<p>
Use parentheses ( ) to specify order of operations. </p>
</li>
</ul>
<p>
Each formula entry box will have a Formula Input Help button below the answer button, where you can find these facts about how to enter formulas. (See the button below.) </p>
<p>
<b class="bfseries">Example</b>
</p>
<p>
To see how the answer box works, enter the function [mathjaxinline]2e^{x-1} +\sqrt {y}[/mathjaxinline] using the rules above. (Type 2[mathjaxinline]*[/mathjaxinline]e[mathjaxinline]\wedge[/mathjaxinline](x-1)+sqrt(y) into the answer box.) </p>
<p>
Below the answer box, there is a display box that shows how the system interpreted your formula. (You will get an error if you try to enter variables, like [mathjaxinline]z[/mathjaxinline], that are unspecified in the problem. You will get an error as you are typing if you have only one half &#8220;(" of a parenthesis. Just continue typing, and when you enter the closing parenthesis &#8220;)", the error will go away.) </p>
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<th class="formulainput" scope="col">Allowable Entries</th>
<th class="formulainput" scope="col">Descriptions</th>
<th class="formulainput" scope="col">Example Entries</th>
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<th class="formulainput" scope="row" rowspan="3">Numbers</th>
<td class="formulainput">Integers</td>
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<font color="#0078b0">2520</font>
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<font color="#0078b0">2/3</font>
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<td class="formulainput">Decimals </td>
<td class="formulainput"><font color="#0078b0">3.14</font>, <font color="#0078b0">.98</font></td>
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<th class="formulainput" scope="row" rowspan="4">Operators</th>
<td class="formulainput">+ - * / (add, subtract, multiply, divide)</td>
<td class="formulainput">Enter <font color="#0078b0"> (x+2*y)/(x-1)</font> for \( \displaystyle \frac{x+2y}{x-1} \) </td>
</tr>
<tr class="formulainput">
<td class="formulainput">^ (raise to a power)</td>
<td class="formulainput">Enter <font color="#0078b0"> x^(n+1) </font> for \( x^{n+1} \)</td>
</tr>
<tr class="formulainput">
<td class="formulainput">_ (add a subscript)</td>
<td class="formulainput">Enter <font color="#0078b0"> v_0 </font> for \( v_0 \) </td>
</tr>
<tr class="formulainput">
<td class="formulainput">Use ( ) to clarify order of operations</td>
<td class="formulainput"> Enter <font color="#0078b0">(2+3)*2 </font> for 10 <br/>
Enter <font color="#0078b0"> 2+3*2 </font> for 8 </td>
</tr>
<tr class="formulainput">
<th class="formulainput" scope="row">Greek letters</th>
<td class="formulainput">Enter (english) name of letter</td>
<td class="formulainput">Enter <font color="#0078b0">alpha </font> for \( \alpha \)<br/>
Enter <font color="#0078b0">lambda </font> for \(\lambda \)
</td>
</tr>
<tr class="formulainput">
<th class="formulainput" scope="row">Mathematical <br/> constants</th>
<td class="formulainput">e, pi</td>
<td class="formulainput">Enter <font color="#0078b0">e^x </font> for \( e^x \)<br/>
Enter <font color="#0078b0">2*pi </font> for \( 2\pi \)
</td>
</tr>
<tr class="formulainput">
<th class="formulainput" scope="row">Basic functions</th>
<td class="formulainput">abs, ln, log, log_2, sqrt</td>
<td class="formulainput">Enter <font color="#0078b0">abs(x+y) </font> for \( \left|x+y \right| \)<br/>
Enter <font color="#0078b0">sqrt(x^2-y) </font> for \( \sqrt{x^2-y} \)
</td>
</tr>
<tr class="formulainput">
<th class="formulainput" scope="row" rowspan="3">Trigonometric <br/> functions</th>
<td class="formulainput">sin, cos, tan, sec, csc, cot</td>
<td class="formulainput">Enter <font color="#0078b0">sin(4*x+y)^2 </font> for \(\sin^2(4x+y) \)</td>
</tr>
<tr class="formulainput">
<td class="formulainput">arcsin, arccos, arctan, etc.</td>
<td class="formulainput">Enter <font color="#0078b0">arctan(x^2/3) </font> for \(\tan^{-1}\left(\frac{x^2}{3}\right) \)</td>
</tr>
<tr class="formulainput">
<td class="formulainput"> sinh, cosh, arcsinh, etc.</td>
<td class="formulainput">Enter <font color="#0078b0">cosh(4*x+y) </font> for \(\cosh(4x+y) \)</td>
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Drag and Drop Problems
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<p>
Drag and drop the elements to create the quadratic formula: </p>
<table id="a0000000002" class="equation" width="100%" cellspacing="0" cellpadding="7" style="table-layout:auto">
<tr>
<td class="equation" style="width:80%; border:none">[mathjax]\lambda = \frac{-b \pm \sqrt {b^2 - 4ac}}{2a}.[/mathjax]</td>
<td class="eqnnum" style="width:20%; border:none;text-align:right">(1.1)</td>
</tr>
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<p>
Use the arrows on the horizontal bar to see more options to drag into the formula. </p>
<p>
(You can see the answer after you make at least one attempt by clicking on the show answer button below.) </p>
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Sketch Response Problems
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<p>
We created this sketch input problem type because being able to sketch functions to reason through problems is a big part of applying calculus as a problem-solving tool. </p>
<p>
Try drawing a smiley face. The mouth should lie below the [mathjaxinline]x[/mathjaxinline]-axis, and the place an eye at the points [mathjaxinline](-1,2)[/mathjaxinline] and [mathjaxinline](1,2)[/mathjaxinline]. </p>
<p>
(To clear the sketching area, hit the reset button in the lower right corner.) </p>
<p>
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