Difference between revisions of "ExpandedPolynomial1"
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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_TRUNK/macros/contextLimitedPolynomial.pl.html contextLimitedPolynomial.pl.html] |
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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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Revision as of 13:49, 1 December 2010
Polynomial Multiplication (Expanding)
This PG code shows how to require students to expand polynomial multiplication.
- Download file: File:ExpandedPolynomial1.txt (change the file extension from txt to pg when you save it)
- File location in NPL:
NationalProblemLibrary/FortLewis/Authoring/Templates/Algebra/ExpandedPolynomial1.pg
| PG problem file | Explanation |
|---|---|
|
Problem tagging: |
|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "contextLimitedPolynomial.pl", ); TEXT(beginproblem()); |
Initialization: |
#
# 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: Everything is as expected. |
Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;
COMMENT('MathObject version.');
ENDDOCUMENT();
|
Solution: |
