Difference between revisions of "ExpandedPolynomial1"
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(Created page with '<h2>Polynomial Multiplication (Expanding)</h2> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> This PG code shows how to require students to expand poly…') |
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"MathObjects.pl", |
"MathObjects.pl", |
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"contextLimitedPolynomial.pl", |
"contextLimitedPolynomial.pl", |
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| − | "contextPolynomialFactors.pl", |
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| − | "contextLimitedPowers.pl", |
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); |
); |
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| Line 55: | Line 53: | ||
<p> |
<p> |
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<b>Initialization:</b> |
<b>Initialization:</b> |
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| − | We need all of these macros. |
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</p> |
</p> |
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</td> |
</td> |
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| Line 69: | Line 66: | ||
# |
# |
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Context("Numeric"); |
Context("Numeric"); |
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| − | $n = list_random(4,6); |
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| + | $h = 3; |
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| − | $ |
+ | $k = 5; |
| − | $b = ($a+$n); |
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| − | $h = ($b-$a)/2; |
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| − | $k = $h**2+$a*$b; |
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$vertexform = Compute("(x-$h)^2-$k"); |
$vertexform = Compute("(x-$h)^2-$k"); |
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| Line 77: | Line 74: | ||
# |
# |
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Context("LimitedPolynomial-Strict"); |
Context("LimitedPolynomial-Strict"); |
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| − | $ |
+ | $b = -2 * $h; |
| − | $ |
+ | $c = $h**2 - $k; |
| − | $expandedform = Formula("x^2 |
+ | $expandedform = Formula("x^2 + $b x + $c")->reduce(); |
| − | |||
| − | # |
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| − | # Factored form |
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| − | # |
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| − | Context("PolynomialFactors-Strict"); |
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| − | Context()->flags->set(singleFactors=>0); |
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| − | LimitedPowers::OnlyIntegers( |
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| − | minPower => 0, maxPower => 1, |
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| − | message => "either 0 or 1", |
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| − | ); |
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| − | $factoredform = Compute("(x+$a)(x-$b)"); |
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</pre> |
</pre> |
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</td> |
</td> |
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<p> |
<p> |
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<b>Setup:</b> |
<b>Setup:</b> |
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| − | To construct this quadratic, we choose a nice factored form <code>(x+$a)(x-$b)</code> and from it we construct its vertex form (a(x-h)^2+k) and expanded form (ax^2+bx+c). |
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| + | We use the <code>LimitedPolynomial-Strict</code> context, construct the coefficients <code>$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. |
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| − | </p> |
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| − | <p> |
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| − | For the expanded form we use the <code>LimitedPolynomial-Strict</code> context, construct the coefficients <code>$p[0]</code> and <code>$p[1]</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. |
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| − | </p> |
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| − | <p> |
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| − | For the factored form we need to change to the <code>PolynomialFactors-Strict</code> context and restrict the allowed powers to either 0 or 1 using the <code>LimitedPowers::OnlyIntegers</code> block of code. Note: restricting all exponents to 0 or 1 means that repeated factors will have to be entered in the form <code>k(ax+b)(ax+b)</code> instead of <code>k(ax+b)^2</code>. Also, restricting all exponents to 0 or 1 means that the polynomial must factor as a product of linear factors (no irreducible quadratic factors can appear). Of course, we could allow exponents to be 0, 1, or 2, but then students would be allowed to enter <i>reducible</i> quadratic factors. There are no restrictions on the coefficients, i.e., the quadratic could have any nonzero leading coefficient. We set <code>singleFactors=>0</code> so that repeated, non-simplified factors do not generate errors. |
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</p> |
</p> |
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</td> |
</td> |
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| Line 104: | Line 95: | ||
BEGIN_TEXT |
BEGIN_TEXT |
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The quadratic expression \( $vertexform \) |
The quadratic expression \( $vertexform \) |
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| − | is written in vertex form. |
+ | is written in vertex form. Write the |
| + | expression in expanded form |
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| + | \( ax^2 + bx + c \). |
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$BR |
$BR |
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| − | $BR |
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| − | (a) Write the expression in expanded form |
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| − | \( ax^2 + bx + c \). |
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$BR |
$BR |
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\{ ans_rule(30) \} |
\{ ans_rule(30) \} |
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| − | $BR |
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| − | $BR |
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| − | (b) Write the expression in factored form |
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| − | \( k(ax+b)(cx+d) \). |
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| − | $BR |
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| − | \{ ans_rule(30)\} |
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END_TEXT |
END_TEXT |
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Context()->normalStrings; |
Context()->normalStrings; |
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<p> |
<p> |
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<b>Main Text:</b> |
<b>Main Text:</b> |
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| − | + | To help students understand how to format their answers, we give an example <code>ax^2+bx+c</code> of what the answer should look like. |
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</p> |
</p> |
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</td> |
</td> |
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ANS( $expandedform->cmp() ); |
ANS( $expandedform->cmp() ); |
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| − | ANS( $factoredform->cmp() ); |
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</pre> |
</pre> |
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Revision as of 13:29, 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: |
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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:
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: |
