SimplifiedSquareRoots

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Simplified Square Roots in Student Answers


This PG code shows how to require student answers to be completely reduced square roots.

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).

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