Space Curve

Parametric equations: parametric curve in space

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Complete Code

Download file: Spacecurve.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

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

$showPartialCorrectAnswers = 0;

Preamble

These standard macros need to be loaded. 
Context()->variables->are(t => 'Real');
Context()->variables->set(t => { limits => [ 0, 10 ] });

$a = random(-5, -2);
$x = Formula("$a * t^2");
$y = Formula('0');
$z = Formula('t');

$multians = MultiAnswer($x, $y, $z)->with(
    singleResult => 1,
    checker      => sub {
        my ($correct, $student, $self) = @_;
        my ($xstu,    $ystu,    $zstu) = @$student;
        return 0 unless $xstu->isFormula;
        return $xstu == $a * $zstu**2 && $ystu == 0 ? 1 : 0;
    }
);

Setup

The parserMultiAnswer.pl is used to check the answers together since they are interdependent.

The option singleResult => 1 is used since it doesn’t make sense to say that x(t) is correct but z(t) is incorrect since they depend on one another.

The checker first ensures that the student has not given a bogus constant solution such as x = y = z = 0 by requiring the x-coordinate to be a non-constant formula via

return 0 unless $xstu->isFormula;

Then, it checks that the student answers satisfy the curve equation.

BEGIN_PGML
Find a parametrization of the curve [`x = [$a]z^2`] in the [`xz`]-plane.  Use
[`t`] for the parameter.

[`x(t) =`] [_]{$multians}{15}

[`y(t) =`] [_]{$multians}{15}

[`z(t) =`] [_]{$multians}{15}
END_PGML

Statement

Notice that $multians is used for the answer for all answer rules.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.