Implicit Equations Evaluators

Setup

Select the ImplicitEquation context, and define the equation for the answer. Note that the ImplicitEquation context contains the variables x and y by default. If other variables are needed, they will need to be added.

Its often important to set the limits for variables when working with equations. In this case the limits for the variable x are set to the interval [-2, 2] and the limits for the variable y are set to the interval [0, 4].

The ImplicitEquation checker attempts to locate the solutions for the given equation using a random search. This search can fail in some cases which will result in correct answers being marked incorrect, or incorrect answers being marked correct. Thus it is generally a good idea to specify some particular solutions. This can be done in the ImplicitEquation call, by passing the solutions option as is done in this example.

Also, for this type of answer checking it is likely that the student will represent the function in a form that exceeds the default problem checking tolerances, and so be marked as incorrect. To correct for this it may be necessary to specify a tolerance. An absolute tolerance can be set in the ImplicitEquation call, e.g.,

$eqn = ImplicitEquation("y = (x-1)^2", tolerance => 0.0001);

It is possible to remove the error message “Can’t find any solutions to your equation” by remapping it to another error message. The message has to be non-empty, but it can be the string containing one space " ", as in

Context()->{error}{msg}{"Can't find any solutions to your equation"} = " ";

However, this is not recommended as it can be confusing. Although no error message will be shown, the answer feedback button will still show a dot indicating a message is present.

A better way to remove the error message would be to use a post-filter to remove the message after the answer has been graded. The answerHints.pl file provides one way to do this. A post-filter can also be added manually for this as in the following example.

$ans = ImplicitEquation('y = (x-1)^2')->cmp->withPostFilter(sub {
   my $ans = shift;
   delete $ans->{ans_message}
       if $ans->{ans_message} eq "Can't find any solutions to your equation";
   return $ans;
});