Difference between revisions of "SimplifiedSquareRoots"

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(New page: <h2>Your title here: PG Code Snippet</h2> <!-- Header for these sections -- no modification needed --> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> <em>Thi...)
 
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<pre>
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# code essentially from Davide Cervone 4/25/10
  
 
###########################
  
###########################
 
#
  
#
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#
  
#
 
LimitedPowers::OnlyPositiveIntegers();
  
LimitedPowers::OnlyPositiveIntegers();
  +
  +
$expr = "\sqrt{12 x^2}";
   
 
$f = Compute("x*sqrt(6)");
  
$f = Compute("x*sqrt(6)");
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<p>
  
<p>
 
<b>Setup:</b>
 
<b>Setup:</b>
−
We specify that the Context should be <code>......</code>, and define the answer to be a formula.
 
  +
This code is from Davide Cervone (4/25/10). See the discussion [[http://webwork.maa.org/moodle/mod/forum/discuss.php?d=6416 simplifying radical expressions]] for more information.
 
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<p>
  
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Notes: on using this and related Contexts.
  
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</p>
  
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<pre>
  
<pre>
 
BEGIN_TEXT
  
BEGIN_TEXT
−
Simplify \( \sqrt{6 x^2} \) assuming that \( x \geq 0 \).
 +
Simplify \( $expr \) assuming that \( x \geq 0 \).
  +
Do not enter fractional exponents.
 
$BR
  
$BR
 
$BR
  
$BR
−
\( \sqrt{6 x^2} \) = \{ans_rule(20)\}
 +
\( $expr \) = \{ans_rule(20)\}
 
END_TEXT
  
END_TEXT
   
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$showPartialCorrectAnswers = 1;
  
$showPartialCorrectAnswers = 1;
   
−
#
  
−
# Use a custom checker to check that the answers are equivalent
  
−
# and that they are still equivalent when sqrt() is replaced by 1
  
−
# (so the stuff outside the sqrt() is equal in both)
  
−
#
  
 
ANS( $f-> cmp( checker => sub {
  
ANS( $f-> cmp( checker => sub {
 
my ($correct,$student,$ans) = @_;
  
my ($correct,$student,$ans) = @_;
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<p>
  
<p>
 
<b>Answer Evaluation:</b>
  
<b>Answer Evaluation:</b>
−
As is the answer.
  
  +
Use a custom checker to check that the answers are equivalent
  +
and that they are still equivalent when sqrt() is replaced by 1
  +
(so the stuff outside the sqrt() is equal in both).
 
</p>
  
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Revision as of 16:14, 25 April 2010

Your title here: PG Code Snippet


This PG code shows how to check student answers that are equations. Note that this is an insertion, not a complete PG file. This code will have to be incorporated into the problem file on which you are working.

Problem Techniques Index

PG problem file Explanation 
DOCUMENT(); 

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"contextLimitedPowers.pl"
);

TEXT(beginproblem());

Initialization: We need to include the macros file contextLimitedPowers.pl. 

###########################
#
# Subclass the numeric functions
#
package my::Function::numeric;
our @ISA = ('Parser::Function::numeric');

#
# Override sqrt() to return a special value (usually 1) when evaluated
# effectively eliminating it from the product.
#
sub sqrt {
  my $self = shift;
  my $value = $self->context->flag("setSqrt");
  return $value+1 if $value && $_[0] == 1; # force sqrt(1) to be incorrect
  return $value if $value;
  return $self->SUPER::sqrt(@_);
}

#
# end of subclass
#
package main;

###########################

Context("Numeric")->variables->are(
x => ["Real", limits => [0,2]],    # only needed if x is used in the square roots
);
#
# make sqrt() use our subclass
#
Context()->functions->set(sqrt=>{class=>'my::Function::numeric'});
Context()->flags->set(reduceConstantFunctions=>0);
#
# Don't allow fractional powers (avoids 1/2 power)
# [Could subclass exponentiation to handle that as well]
#
LimitedPowers::OnlyPositiveIntegers();

$expr = "\sqrt{12 x^2}";

$f = Compute("x*sqrt(6)");

Setup: This code is from Davide Cervone (4/25/10). See the discussion [simplifying radical expressions] for more information. 

BEGIN_TEXT
Simplify \( $expr \) assuming that \( x \geq 0 \).
Do not enter fractional exponents.
$BR
$BR
\( $expr \) = \{ans_rule(20)\}
END_TEXT

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

$showPartialCorrectAnswers = 1;

ANS( $f-> cmp( checker => sub {
  my ($correct,$student,$ans) = @_;
  return 0 if $ans->{isPreview} || $correct != $student;
  #
  #  Get parsed formula for student and correct answers
  #
  $student = $ans->{student_formula};
  $correct = $correct->{original_formula} if defined $correct->{original_formula};
  #
  # check if equal when sqrt's are replaced by 1
  #
  Context()->flags->set(setSqrt => 1);
  delete $correct->{test_values}, $student->{test_values};
  my $OK = ($correct == $student);
  Context()->flags->set(setSqrt => 0);
  #
  Value::Error("Check to see if your answer is simplified.") unless $OK;
  return $OK;
  }, formatStudentAnswer=>"reduced"
  )
);

ENDDOCUMENT();

Answer Evaluation: Use a custom checker to check that the answers are equivalent and that they are still equivalent when sqrt() is replaced by 1 (so the stuff outside the sqrt() is equal in both).

Problem Techniques Index


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