SimplifiedSquareRoots

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).

Problem Techniques Index

• POD documentation: contextLimitedPowers.pl
• PG macro: contextLimitedPowers.pl