Volume2

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A Question with Weighted Answer Blanks and a Credit Answer

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This PG code shows how to construct a volume of solids of revolution question that allows students to set up the integral and earn partial credit, or to answer just the final question for full credit.


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PG problem file Explanation

Problem tagging data

Problem tagging:

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGunion.pl",
"answerHints.pl",
"weightedGrader.pl",
);

TEXT(beginproblem());

install_weighted_grader();

$showPartialCorrectAnswers = 1;

Initialization: We load weightedGrader.pl and install it. Customized answer hints for particular kinds of student answers are provided by answerHints.pl. We load PGunion.pl to get macros for formatting tables that will be used to get the answer blanks into the limits of integration.

Context("Numeric");
Context()->variables->are(
x=>"Real", dx=>"Real",
y=>"Real", dy=>"Real"
);

$f = Compute("x");
$g = Compute("x^2");

$upper = Real("1");
$lower = Real("0");
# answers below are intentionally wrong
$int = Compute("( pi x - pi x^2 ) dx");
$vol = Compute("pi"); 

@weights = (5,5,40,50);

#
#  Display the answer blanks properly in different modes
#
Context()->texStrings;
if ($displayMode eq 'TeX') {
   $integral =
   'Volume = \(\displaystyle' . 
     '\int_{'. 
     NAMED_ANS_RULE("lowerlimit",4). '}^{'. 
     NAMED_ANS_RULE("upperlimit",4). '}'. 
     NAMED_ANS_RULE("integrand",30). ' = '.
     ans_rule(10). 
   '\)';
  } else {
   $integral =
   BeginTable(center=>0).
     Row([
       'Volume = \(\displaystyle\int\)',
       NAMED_ANS_RULE("upperlimit",4).$BR.$BR.
       NAMED_ANS_RULE("lowerlimit",4),
       NAMED_ANS_RULE("integrand",30).$SPACE.' = '.$SPACE.
       ans_rule(10),
     ],separation=>2).
   EndTable();
}
Context()->normalStrings;

Setup: Notice that for the final answer (volume) we use ans_rule(width), while for the answer blanks that involve setting up the integral we use NAMED_ANS_RULE(name,width).

Context()->texStrings;
BEGIN_TEXT
Set up and evaluate an integral for the volume
of the solid of revolution obtained by rotating
the region bounded by \( y = $f \) and \( y = $g \)
about the \(x\)-axis.
$BR
$BR
$integral
END_TEXT
TEXT(MODES(TeX=>"",HTML=>
"${PAR}${BITALIC}${BBOLD}Note:${EBOLD} 
You can earn 
$weights[0]${PERCENT} for the upper limit of integration,
$weights[1]${PERCENT} for the lower limit of integration,
$weights[2]${PERCENT} for the integrand, and
$weights[3]${PERCENT} for the finding the volume.
If you find the correct volume, you will get full credit
no matter what your other answers are.
${EITALIC}"));
Context()->normalStrings;

Main Text: In HTML mode, we add an explanation of how the question will be graded, pointing out that full credit can be earned if the volume calculation is correct.

NAMED_WEIGHTED_ANS( "upperlimit" => $upper->cmp(), $weights[0] );
NAMED_WEIGHTED_ANS( "lowerlimit" => $lower->cmp(), $weights[1] );
NAMED_WEIGHTED_ANS( "integrand" =>  $int->cmp()
->withPostFilter(AnswerHints( 
  Formula("pi x - pi x^2 dx") => "Don't forget to multiply every 
                                  term in the integrand by dx",
  Formula("pi x - pi x^2") => "Don't forget the differential dx", 
  Formula("(pi x^2 - pi x)*dx") => "Is the parabola above the line?",
  Formula("pi x^2 - pi x") => "Is the parabola above the line?",
)),
$weights[2]
);
CREDIT_ANS( $vol->cmp(), ["upperlimit","lowerlimit","integrand"], $weights[3] );

Answer Evaluation: Notice that we use NAMED_WEIGHTED_ANS( "name" => $answer->cmp()->withPostFilter(), weight) for the questions that have named answer blanks above. For the final answer, which can provide full credit, we use CREDIT_ANS( $answer->cmp(), ["name1", "name2", ...], weight) for this answer to provide credit for the answers with names in the list ["name1", "name2", ...].

Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;


COMMENT('MathObject version.  Weights each answer blank separately, 
and the last answer provides full credit for all other answer blanks.');

ENDDOCUMENT();

Solution:

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