View source for Fundamental Theorem of Calculus: storing answers, the eval method for formulas and eval-or-do blocks.

It is very often that we want to give partial credit to a student based on a previous answer. This example goes over this.

 <nowiki># Created by Nikola Kuzmanovski
# In this problem we ask the student to find the anti-derivative of a function.
# The +C is included at the end, so the student need not insert it.
# However, if the student enters an answer with a concrete constant we will still count this as correct.
# For example both x^4 and x^4+3 would be valid answers if the correct answer is x^4.
# We then ask the student to find the definite integral of the same function with certain bounds.
# We will award partial credit for the second part of the problem based on the students input for the first part.

########################################################################

DOCUMENT();      

loadMacros(
   "PGstandard.pl",     		# Standard macros for PG language
   "MathObjects.pl",			# Standard objects like real numbers, functions etc.	
);

# Print problem number and point value (weight) for the problem
TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect
$showPartialCorrectAnswers = 1;

##############################################################
#
#  Setup
#
#


Context("Numeric");	# Contains almost everything you need for real variable calculus

# The function to be integrated.
$f = Formula("x^4");


# The anti-derivative
$antiDiv = Formula("x^5/5");

# The limits of integration for the definite integral
$lowerLimit = 4;
$upperLimit = 10;

# The correct value for the definite integral
$area = $antiDiv->eval(x => $upperLimit) - $antiDiv->eval(x => $lowerLimit);

##############################################################
#
#  Text
#
#

Context()->texStrings;
BEGIN_TEXT
The is a problem on integration.
For the first part you need to find an anti-derivative.
Note that we have included that \(+ C\) at the end, so you need not worry about it.
In the second part you need to compute a definite integral.
$BR

One has
$BCENTER
\(\displaystyle \int  $f = \) \{ans_rule\} + \(C\).
$ECENTER

So, then we get
$BCENTER
\(\displaystyle \int_{$lowerLimit}^{$upperLimit}  $f = \) \{ans_rule\}.
$ECENTER


END_TEXT
Context()->normalStrings;

##############################################################
#
#  Answers
#
#

# We are going to store the answer and score for the first answer that the student provides.
$ans1 = Formula("");
$score1  = 0.0;

# Subroutine that will check the first answer and store the answer and score.
$checkAntiDiv = sub{
	my ($correctFunc, $studentFunc, $ansHash) = @_;	# Get correct answer, student answer and the answer hash.
	
	# Store the first answer.
	$ans1 = $studentFunc;
	
	# Check if the student got the correct answer.
	if($correctFunc == $studentFunc){
		# The student got the correct answer.
		# Store the score the student got.
		$score1 = 1.0;
		
		# Return the score and exit.
		return $score1;
	}
	
	# The student didn't get any credit.
	return $score1;
};

# Check the first answer.
# We make sure that if the student answer differs by a constant that it is still accepted.
ANS($antiDiv->cmp(upToConstant => 1, checker => $checkAntiDiv));

# Subroutine that will check if the computed the definite integral correctly.
$checkArea= sub {
	my ($correctArea, $studentAreaInput, $ansHash) = @_;	# Get correct answer, student answer and the answer hash.
	
	# Check if the student got everything correct.
	if($score1 && $correctArea == $studentAreaInput){
		# The student got everything correct.
		#Give full points and exit.
		return 1.0;
	} 
	
	# The student didn't get the first part correct.
	# However, we will give them points if they used the Fundamental Theorem of Calculus correctly.
	
	# The score to be given to the student.
	# Currently 0 because they haven't earned any credit.
	my $score = 0.0;
	
	# Try to compute the definite integral based on the first answer.
	eval{
		# Compute the definite integral
		my $studentAreaEval = $ans1->eval(x => $upperLimit) - $ans1->eval(x => $lowerLimit);
		
		# Check if the definite integral from the first answer and the input for the second answer match.
		if ($studentAreaEval == $studentAreaInput){
			# They match.
			# Give the student full points for the second part.
			$score = 1.0;
			# Tell the student why they got points.
			$ansHash->{ans_message} = "You didn't get the first part right. However, you used the Fundamental Theorem of Calculus correctly.";
		}
		
		# Report that there were no errors.
		1;
	} or do{
		# An error occurred when using formula->eval above.
		# Tell the student to double check things.
		$ansHash->{ans_message} = "It seems that the answer you gave for the antiderivative doesn't evaluate at the limit points for the second part of the problem.";
		$ansHash->{ans_message} = $ansHash->{ans_message} . " Try double checking your work for the first part and try again.";
		$ansHash->{ans_message} = $ansHash->{ans_message} . " Check for things like divison by 0 or negatives under a square root.";
	};
	
	# Give partial credit points to the student.
	return $score;
};


ANS($area->cmp(checker => $checkArea));


ENDDOCUMENT();        
</nowiki>

Exercises:
# Input 1/(x+10) for the first answer blank. What happens? 
# Remove the 1; in the eval block. What happens and why? Try inputting x for the first answer and 3 for the second answer.
# Modify the problem above to give partial credit when the student flips the limits of integration.
# Modify the problem from exercise two to give partial credit in at least four other situations.
# Modify the problem above to use [https://webwork.maa.org/wiki/MultiAnswerProblems parserMultiAnswer.pl].
## Try inputting 1/(x+10) for the first answer blank. If your program fails, fix it.
## Try Inputting x^5/5 for the first answer blank and the string blabla for the second answer blank. If the problem doesn't award full points for the first part then fix it. Look at [https://webwork.maa.org/pod/pg/lib/AnswerHash.html PreFilter]. A multi answer object is an array, the first things that it points to (when you check the answers) is the student input.
## Try inputting x^5/5 in the first answer blank and (0,0) in the second. What happens?
## Discuss design decisions between storing answers and [https://webwork.maa.org/wiki/MultiAnswerProblems parserMultiAnswer.pl].