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.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "contextLimitedPowers.pl" ); TEXT(beginproblem()); |
Initialization:
We need to include the macros file |
###########################
#
# 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). |
- POD documentation: contextLimitedPowers.pl
- PG macro: contextLimitedPowers.pl
