Difference between revisions of "ExpandedPolynomial1"
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<h2>Polynomial Multiplication (Expanding)</h2> |
<h2>Polynomial Multiplication (Expanding)</h2> |
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− | <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> |
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+ | [[File:ExpandedPolynomial1.png|300px|thumb|right|Click to enlarge]] |
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+ | <p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;"> |
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This PG code shows how to require students to expand polynomial multiplication. |
This PG code shows how to require students to expand polynomial multiplication. |
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− | <ul> |
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− | <li>Download file: [[File:ExpandedPolynomial1.txt]] (change the file extension from txt to pg when you save it)</li> |
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− | <li>File location in NPL: <code>NationalProblemLibrary/FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1.pg</code></li> |
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− | </ul> |
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</p> |
</p> |
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+ | * File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1.pg FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1.pg] |
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+ | * PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1_PGML.pg FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1_PGML.pg] |
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+ | <br clear="all" /> |
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<p style="text-align:center;"> |
<p style="text-align:center;"> |
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[[SubjectAreaTemplates|Templates by Subject Area]] |
[[SubjectAreaTemplates|Templates by Subject Area]] |
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<p> |
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<b>Initialization:</b> |
<b>Initialization:</b> |
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+ | We must load <code>contextLimitedPolynomial.pl</code> |
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<b>Setup:</b> |
<b>Setup:</b> |
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+ | The macro <code>contextLimitedPolynomial.pl</code> provides two contexts: |
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+ | <pre> |
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+ | Context("LimitedPolynomial"); |
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+ | Context("LimitedPolynomial-Strict"); |
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+ | </pre> |
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+ | The strict version does not allow any mathematical operations within coefficients, so <code>(5+3)x</code> must be simplified to <code>8x</code>. |
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+ | For more details, see [http://webwork.maa.org/pod/pg/macros/contextLimitedPolynomial.html contextLimitedPolynomial.pl] |
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+ | </p> |
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+ | <p> |
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We use the <code>LimitedPolynomial-Strict</code> context, construct the coefficients <code>$b</code> and <code>$c</code> as Perl reals, and then construct <code>$expandedform</code> using these pre-computed coefficients. This is because the LimitedPolynomial-Strict context balks at answers that are not already simplified completely. Notice that we called the <code>->reduce()</code> method on the expanded form of the polynomial, which will ensure that the polynomial will be displayed as <code>x^2 - 6x + 4</code> instead of <code>x^2 + -6x + 4</code>. |
We use the <code>LimitedPolynomial-Strict</code> context, construct the coefficients <code>$b</code> and <code>$c</code> as Perl reals, and then construct <code>$expandedform</code> using these pre-computed coefficients. This is because the LimitedPolynomial-Strict context balks at answers that are not already simplified completely. Notice that we called the <code>->reduce()</code> method on the expanded form of the polynomial, which will ensure that the polynomial will be displayed as <code>x^2 - 6x + 4</code> instead of <code>x^2 + -6x + 4</code>. |
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<b>Answer Evaluation:</b> |
<b>Answer Evaluation:</b> |
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− | Everything is as expected. |
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[[Category:Top]] |
[[Category:Top]] |
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− | [[Category: |
+ | [[Category:Sample Problems]] |
+ | [[Category:Subject Area Templates]] |
Revision as of 17:56, 7 April 2021
Polynomial Multiplication (Expanding)
This PG code shows how to require students to expand polynomial multiplication.
- File location in OPL: FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1.pg
- PGML location in OPL: FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1_PGML.pg
PG problem file | Explanation |
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Problem tagging: |
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DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "contextLimitedPolynomial.pl", ); TEXT(beginproblem()); |
Initialization:
We must load |
# # Vertex form # Context("Numeric"); $h = 3; $k = 5; $vertexform = Compute("(x-$h)^2-$k"); # # Expanded form # Context("LimitedPolynomial-Strict"); $b = -2 * $h; $c = $h**2 - $k; $expandedform = Formula("x^2 + $b x + $c")->reduce(); |
Setup:
The macro Context("LimitedPolynomial"); Context("LimitedPolynomial-Strict"); The strict version does not allow any mathematical operations within coefficients, so
We use the |
Context()->texStrings; BEGIN_TEXT The quadratic expression \( $vertexform \) is written in vertex form. Write the expression in expanded form \( ax^2 + bx + c \). $BR $BR \{ ans_rule(30) \} END_TEXT Context()->normalStrings; |
Main Text:
To help students understand how to format their answers, we give an example |
$showPartialCorrectAnswers = 1; ANS( $expandedform->cmp() ); |
Answer Evaluation: |
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT(); |
Solution: |