InequalityEvaluators

Inequalities as Answers

This is the essential code for having inequalities as student answers.

Problem Techniques Index

PG problem file	Explanation
DOCUMENT(); loadMacros( "PGstandard.pl", "contextInequalities.pl", "PGcourse.pl", ); TEXT(beginproblem());	Initialization: Include the macro file contextInequalities.pl, which automatically loads MathObjects.pl.
Context("Inequalities-Only"); Context()->variables->add(y=>"Real"); # Context()->constants->add(EmptySet => Set()); # Context()->flags->set(noneWord=>"EmptySet"); # Context()->flags->set(ignoreEndpointTypes=>1); # f(x) = x^2 - 16 on -1 <= x <= 5 $f = Formula("x^2 - 16"); $range = Compute("-16 <= y <= 9"); Context()->variables->remove("x");	Setup: Using Context("Inequalities-Only"), if the student enters the inequality -16 <= y <= 9 their answer will be marked correct, but the equivalent interval [-16,9] would be incorrect. If we had used Context("Inequalities") instead, both the inequality and the interval be marked correct. Uncommenting the lines containing EmptySet creates an empty set as a named constant and uses that name. Uncommenting Context()->flags->set(ignoreEndpointTypes=>1); would also mark the student answers -16 < y < 9 or -16 <= y < 9 or -16 < y <= 9 correct. As of January 2010, the inequality is not variable-specific. If we had not removed the default variable x from the context using Context()->variables->remove("x");, then the student answer -16 <= x <= 9 would also be marked correct. Note that we removed the variable x from the context after we defined the formula $f that uses this variable (otherwise there would be errors and PG file would not work).
Context()->texStrings; BEGIN_TEXT What is the range of \( y = f(x) = $f \) on the domain \( -1 \leq x \leq 5 \)? $BR $BR Range: \{ ans_rule(20) \} Enter your answer using inequalities (not intervals). END_TEXT Context()->normalStrings;	Main Text: The problem text section of the file is as we'd expect.
ANS( $range->cmp() ); ENDDOCUMENT();	Answer Evaluation: As is the answer.

Problem Techniques Index

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