Difference between revisions of "IdentitiesAsAnswers"

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<h2>Trigonometric Identities</h2>
  
  +
<h2>Identities As Answers (Trig Identities, Laws of Logarithms and Exponents, etc.)</h2>
   
 
<!-- Header for these sections -- no modification needed -->
 
<!-- Header for these sections -- no modification needed -->
   
 
<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
  
<p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
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<em>This code shows how to prevent students from receiving credit for entering exactly what they were given, while at the same time allowing the correct answer to be entered for credit, even when what the students were given and the correct answer are the same function.</em>
 +
<em>This code shows how to prevent students from receiving credit for entering exactly what they were given, while at the same time allowing the correct answer to be entered for credit, even when what the students were given and the correct answer are identical functions written in different ways (such as trig identities, laws of logarithms, laws of exponents, etc).</em>
 
</p>
  
</p>
   
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"MathObjects.pl",
  
"MathObjects.pl",
 
"PGcourse.pl",
  
"PGcourse.pl",
  +
"answerHints.pl",
 
);
  
);
   
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it will still appear as the tangent function. (The student will have no clue
  
it will still appear as the tangent function. (The student will have no clue
 
that the tangent function has been redefined.) Of course, we have to choose
  
that the tangent function has been redefined.) Of course, we have to choose
−
carefully which functions we would like to redefine.
 +
carefully which functions we would like to redefine, and also redefine them as a
  +
function that a student is unlikely to type in (such as exchanging a trig function
  +
for an exponential function).
 
</p>
  
</p>
 
</td>
  
</td>
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$showPartialCorrectAnswers = 1;
  
$showPartialCorrectAnswers = 1;
   
−
ANS( Formula("sin(x)")->cmp() );
 +
ANS( Formula("sin(x)")->cmp()
  +
->withPostFilter(AnswerHints(
  +
Formula("tan(x)*cos(x)") =>
  +
"No credit for entering what you were given.",
  +
))
  +
);
   
 
COMMENT("Prevents students from entering trivial
 
COMMENT("Prevents students from entering trivial
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<p>
  
<p>
 
<b>Answer Evaluation:</b>
  
<b>Answer Evaluation:</b>
  +
We use an answer hint to tell students that the cannot enter what they were given and receive credit.
 
We include a comment visible only to instructors when they view the problem via the Library Browser that lets others know that this question won't allow students to enter exactly what they were given and earn credit.
  
We include a comment visible only to instructors when they view the problem via the Library Browser that lets others know that this question won't allow students to enter exactly what they were given and earn credit.
 
</p>
  
</p>

Latest revision as of 15:19, 14 May 2010

Identities As Answers (Trig Identities, Laws of Logarithms and Exponents, etc.)


This code shows how to prevent students from receiving credit for entering exactly what they were given, while at the same time allowing the correct answer to be entered for credit, even when what the students were given and the correct answer are identical functions written in different ways (such as trig identities, laws of logarithms, laws of exponents, etc).

Problem Techniques Index

PG problem file Explanation 
DOCUMENT();  

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl",
"answerHints.pl",
);

TEXT(beginproblem());

Initialization: Use MathObjects. 

Context("Numeric");

Context()->functions->remove("tan");
package NewFunc;
# this next line makes the function a 
# function from reals to reals
our @ISA = qw(Parser::Function::numeric);
sub tan {
  shift; my $x = shift;
  return CORE::exp($x*3.1415926535);
}
package main;
# Make it work on formulas as well as numbers
sub tan {Parser::Function->call('tan',@_)} 
#  Add the new functions to the Context
Context()->functions->add( tan => {class => 'NewFunc', TeX => '\tan'}, );

Setup: We internally redefine the tangent function to be e^(pi*x) so that if a student enters tan(x) cos(x), WeBWorK will evaluate it as the function e^(pi x) cos(x). Since e^(pi x) cos(x) does not equal sin(x), if the student enters tan(x) cos(x) it will be marked incorrect. We have redefined the value of the function named tangent, though not given it a different name, so to the student it will still appear as the tangent function. (The student will have no clue that the tangent function has been redefined.) Of course, we have to choose carefully which functions we would like to redefine, and also redefine them as a function that a student is unlikely to type in (such as exchanging a trig function for an exponential function). 

BEGIN_TEXT
Simplify the expression as much as possible.
$BR
$BR
\( \tan(x) \cos(x) \) = \{ ans_rule(20) \}
END_TEXT

Main Text: The problem text section of the file is as we'd expect. 

$showPartialCorrectAnswers = 1;

ANS( Formula("sin(x)")->cmp() 
->withPostFilter(AnswerHints(
  Formula("tan(x)*cos(x)") => 
  "No credit for entering what you were given.",
))
);

COMMENT("Prevents students from entering trivial 
identities (entering what they were given)");

ENDDOCUMENT();

Answer Evaluation: We use an answer hint to tell students that the cannot enter what they were given and receive credit. We include a comment visible only to instructors when they view the problem via the Library Browser that lets others know that this question won't allow students to enter exactly what they were given and earn credit.

Problem Techniques Index

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