# FormulaTestPoints

When the solution to a problem is a formula, WeBWorK compares student answers to the given solution by evaluating them at a set of randomly chosen test points. If for all test points, neither the correct answer nor the student's evaluate to anything, an error "Can't generate enough valid points for comparison" is signaled. Thus, it is important that the test points be chosen from an interval contained in the domain of the correct answer. For instance, if a Real variable is going to have its logarithm taken, or raised to a non-integer power, then it should always be positive (**NB:** even *rational exponents with odd denominator* such as cube roots, which mathematically apply unproblematically to negative numbers, should have their domains restricted to positive numbers, since floating-point arithmetic is not reliable about being able to do such computations.) The default range from which these points are chosen is -2 to 2 for MathObjects (and -1 to 1 for the traditional checkers); this page explains how to change it.

## Formula Test Points for Evaluation: PG Code Snippet

*This code snippet shows the essential PG code to specify the points on which a formula is evaluated when a student's answer is checked. Note that these are insertions, not a complete PG file. This code will have to be incorporated into the problem file on which you are working.*

This can, of course, be done with new and old-style answer evaluators. An example of the latter appears below. Also note that we may want to do this in two different ways: either by setting the *domain* on which the formula is evaluated (that is, the *limits of evaluation*), or by setting specific *test points* on which the formula should be considered. These are both shown below.

PG problem file | Explanation |
---|---|

Context("Numeric"); Context()->variables->set(x=>{limits=>[-1,1]}); $func = Compute("sqrt(x+1)"); ## Alternately: Context()->flags->set(limits=>[2,5]); # $func = Compute("sqrt(x-1)"); ## Or, setting the limits only for the given ## formula, we don't need to reset the Context, ## and just include # $func = Compute("sqrt(x-1)"); # $func->{limits} = [2,5]; $gunc = Compute("sqrt(x^2 - 4)"); $gunc->{test_points} = [[-3],[-2],[2],[3],[4]]; #$gunc->{test_at} = [[-3],[-2],[2],[3],[4]]; |
We don't have to change anything in the documentation and tagging or initialization sections of the PG file. In the problem set-up, we can specify the limits on which all Formulas are evaluated by setting the
It is also possible to specify the actual points on which the Formula will be evaluated. This is an attribute of the Formula itself; the call is shown for our formula
It is possible to test at points that are not defined in the correct solution (e.g., to verify that a student didn't enter
Note: if the formula is a function of more than one variable and we're specifying limits in the formula, we need to specify the limits for all variables. Thus, we'd have something like
Also note that your test points must contain one value per variable, even if it doesn't appear in the formula; for instance, if
If you are trying to set test points for a function you have added to the context (e.g., using loadMacros("parserFunction.pl"); Context("Numeric"); parserFunction("m(x)" => "log(x/2)" ); $h = Formula("5 m(x)+2"); $answer = $h->with(test_at => [[1],[2]]);
If you want to add a variable Context()->variables->add(n => ['Real', limits=>[1,20], resolution=>1]); |

BEGIN_TEXT Enter \( $func \): \{ ans_rule(35) \} $BR Enter \( $gunc \): \{ ans_rule(35) \} END_TEXT |
The text portion of the file is the same as usual. |

ANS( $func->cmp() ); ANS( $gunc->cmp() ); |
And the answer evaluation is as we'd expect. |

With old-style answer evaluators, we can do the same thing:

PG problem file | Explanation |
---|---|

$func = "sqrt(x+1)"; $gunc = "sqrt(x^2 - 4)"; |
We define the functions as expected in the problem set-up section of the file. |

BEGIN_TEXT Enter \( \sqrt{x+1} \): \{ ans_rule(35) \} $BR Enter \( \sqrt{x^2 - 4} \): \{ ans_rule(35) \} END_TEXT |
And the text portion of the file is similarly mundane. |

ANS(fun_cmp($func, limits=>[-1,1])); ANS(fun_cmp($gunc, test_points=>[-3,-2,2,3,4])); |
The limits or test points are specified in the |