Difference between revisions of "ExplicitSequence1"

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(PGML example link)
(switch to PGML and remove answerFormatHelp.pl macro)
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This PG code shows how to evaluate answers that are (possibly alternating) sequences with explicit formulas.
  
This PG code shows how to evaluate answers that are (possibly alternating) sequences with explicit formulas.
 
</p>
  
</p>
−
* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/ExplicitSequence1.pg FortLewis/Authoring/Templates/Sequences/ExplicitSequence1.pg]
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<!--* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/ExplicitSequence1.pg FortLewis/Authoring/Templates/Sequences/ExplicitSequence1.pg]-->
 
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg]
  
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg]
   
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<tr valign="top">
  
<tr valign="top">
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<th> PG problem file </th>
 +
<th style="width: 50%"> PG problem file </th>
 
<th> Explanation </th>
  
<th> Explanation </th>
 
</tr>
  
</tr>
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DOCUMENT();
  
DOCUMENT();
   
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loadMacros(
  
  +
loadMacros('PGstandard.pl','MathObjects.pl','PGML.pl','PGcourse.pl');
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"PGstandard.pl",
  
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"MathObjects.pl",
  
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"AnswerFormatHelp.pl",
  
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);
  
−  
 
TEXT(beginproblem());
  
TEXT(beginproblem());
 
</pre>
  
</pre>
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<td style="background-color:#ffffdd;border:black 1px dashed;">
  
<td style="background-color:#ffffdd;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context("Numeric");
 +
Context('Numeric');
−
Context()->variables->are(n=>"Real");
 +
Context()->variables->are(n=>'Real');
   
 
$answer = Compute("(-1)^n / n!");
  
$answer = Compute("(-1)^n / n!");
 
$answer->{test_points} = [[1],[2],[3],[4],[5],[6]];
  
$answer->{test_points} = [[1],[2],[3],[4],[5],[6]];
   
−
@seq = (
  
  +
$sequence = 'a_0=1, a_1 = -1, a_2 = \frac{1}{2}, a_3 = -\frac{1}{6}'
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"a_0 = 1",
  
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. 'a_4 = \frac{1}{24}, a_5 = -\frac{1}{120}, \ldots';
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"a_1 = -1",
  
−
"a_2 = \frac{1}{2}",
  
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"a_3 = -\frac{1}{6}",
  
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"a_4 = \frac{1}{24}",
  
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"a_5 = -\frac{1}{120}",
  
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"\ldots"
  
−
);
  
−  
−
$sequence = join(", ", @seq);
  
 
</pre>
  
</pre>
 
</td>
  
</td>
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<b>Setup:</b>
 
<b>Setup:</b>
 
We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as <code>cos(pi * n) / n!</code>, you should still restrict the domain to positive integers, because some students may simplify this to <code>(-1)^n / n!</code> and receive errors because the answer checker is substituting things such as <code>n=0.5</code> into their formula.
  
We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as <code>cos(pi * n) / n!</code>, you should still restrict the domain to positive integers, because some students may simplify this to <code>(-1)^n / n!</code> and receive errors because the answer checker is substituting things such as <code>n=0.5</code> into their formula.
−
</p>
  
−
<p>
  
−
We create an array of strings <code>@seq</code> and use Perl's join function to paste the entries in this array together into one long string with entries separated by commas.
  
 
</p>
  
</p>
 
</td>
  
</td>
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<td style="background-color:#ffdddd;border:black 1px dashed;">
  
<td style="background-color:#ffdddd;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context()->texStrings;
  
  +
BEGIN_PGML
−
BEGIN_TEXT
  
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Find a formula for [` n^{th} `] term of the sequence [` [$sequence] `].
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Find a formula for \( n^{th} \) term of the sequence \( $sequence \).
  
  +
−
$BR
  
  +
[` a_n = `] [__________________]{$answer}
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$BR
  
  +
−
\( a_n = \)
  
  +
[@ helpLink('formulas') @]*
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\{ ans_rule(20) \}
  
  +
END_PGML
−
\{ AnswerFormatHelp("formulas") \}
  
−
END_TEXT
  
−
Context()->normalStrings;
  
 
</pre>
  
</pre>
 
<td style="background-color:#ffcccc;padding:7px;">
  
<td style="background-color:#ffcccc;padding:7px;">
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</td>
  
</td>
 
</tr>
  
</tr>
−  
−
<!-- Answer evaluation section -->
  
−  
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<tr valign="top">
  
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<td style="background-color:#eeddff;border:black 1px dashed;">
  
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<pre>
  
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$showPartialCorrectAnswers = 1;
  
−  
−
ANS( $answer->cmp() );
  
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</pre>
  
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<td style="background-color:#eeccff;padding:7px;">
  
−
<p>
  
−
<b>Answer Evaluation:</b>
  
−
</p>
  
−
</td>
  
−
</tr>
  
−  
 
<!-- Solution section -->
  
<!-- Solution section -->
   
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<td style="background-color:#ddddff;border:black 1px dashed;">
  
<td style="background-color:#ddddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context()->texStrings;
  
  +
BEGIN_PGML_SOLUTION
−
BEGIN_SOLUTION
  
 
Solution explanation goes here.
  
Solution explanation goes here.
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END_SOLUTION
  
  +
END_PGML_SOLUTION
−
Context()->normalStrings;
  
−  
−
COMMENT('MathObject version.');
  
   
 
ENDDOCUMENT();
  
ENDDOCUMENT();

Revision as of 09:55, 4 April 2023

Sequences with Explicit Formulas

Click to enlarge

This PG code shows how to evaluate answers that are (possibly alternating) sequences with explicit formulas.


Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();

loadMacros('PGstandard.pl','MathObjects.pl','PGML.pl','PGcourse.pl');
TEXT(beginproblem());

Initialization: 

Context('Numeric');
Context()->variables->are(n=>'Real');

$answer = Compute("(-1)^n / n!");
$answer->{test_points} = [[1],[2],[3],[4],[5],[6]];

$sequence = 'a_0=1, a_1 = -1, a_2 = \frac{1}{2}, a_3 = -\frac{1}{6}'
  . 'a_4 = \frac{1}{24}, a_5 = -\frac{1}{120}, \ldots';

Setup: We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as cos(pi * n) / n!, you should still restrict the domain to positive integers, because some students may simplify this to (-1)^n / n! and receive errors because the answer checker is substituting things such as n=0.5 into their formula. 

BEGIN_PGML
Find a formula for [` n^{th} `] term of the sequence [` [$sequence] `].

[` a_n = `] [__________________]{$answer}

[@ helpLink('formulas') @]*
END_PGML

Main Text: 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution:

Templates by Subject Area

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