Formulas up to additive constants

Formulas up to additive constants.

Complete Code

POD for Macro Files

parserFormulaUpToConstant.pl

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',                'PGML.pl',
    'parserFormulaUpToConstant.pl', 'PGcourse.pl'
);

Preamble

There are two types of answers demonstrated here. One is “a particular antiderivative of f(x)”, and the other is “all antiderivatives of f(x)”. The former requires that a student enter an answer like F(x), F(x) + 1, or F(x) - sqrt(8), and the latter, that a student enter an answer like F(x) + C or F(x) + 5 - k.

To check the all antiderivatives of a function, that is, a formula up to an arbitrary additive constant, the parserFormulaUpToConstant.pl macro is used. To check a particular antiderivative of a function, that is, a formula that is unique up to a specific additive constant, this macro is not needed.

$func  = Formula('sin(x)');
$gfunc = FormulaUpToConstant('sin(x) + C');

Setup

Define a particular antiderivative $func and all antiderivatives $gfunc. For the latter it is not required to include + C. It would be equivalent to specify $gfunc = FormulaUpToConstant('sin(x)').

BEGIN_PGML
An antiderivative of [`\cos(x)`] is [_]{$func->cmp(upToConstant => 1)}

The most general antiderivative is [_]{$gfunc}
END_PGML

ENDDOCUMENT();

Statement

Call the MathObject cmp method and specify the upToConstant => 1 option. This allows the student answer to differ from the correct answer by any constant. Both sin(x) and sin(x) + 5 would be marked correct, but sin(x) + C is not correct since it is a family of answers and not a specific antiderivative. Note that for the formula up to an arbitrary constant the comparison will correctly mark student’s answers that have different arbitrary constants. Thus, a student answer to the second question of sin(x) + k will be marked correct as will sin(x) + c. Any letter can be used for the constant that is not a variable or predefined constant (like e) in the context.