FactoringAndExpanding

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Factored Answers


This is the PG code to check answers that require students to factor an expression into two pieces that may have a constant factor that could be moved from one piece to another.

Problem Techniques Index

PG problem file Explanation 
DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserMultiAnswer.pl",
);

TEXT(beginproblem());

Initialization: We need to include the parserMultiAnswer.pl answer checker so we can take student answers from multiple answer blanks and check them as a whole. 

Context("Numeric");

$fac1 = Compute("(2 x + 3)");
$fac2 = Compute("(8 x + 12)");

$multians = MultiAnswer($fac1,$fac2)->with(
   singleResult => 0,
   allowBlankAnswers => 1,

#  singleResult => 1,  
#  separator => " * ",
#  tex_separator => " \cdot ",

  checker => sub {
    my $correct = shift; my $student = shift; my $self = shift;
    my ($F,$G) = @{$correct};
    my ($f,$g) = @{$student};

    Value::Error('Neither factor can be constant')
    unless $f->isFormula && $g->isFormula;

    Value::Error('Your product does not equal the original (it is incomplete)') 
    unless $F*$G == $f*$g;
#    return 0 unless $F*$G == $f*$g;

    #  use an adaptive parameter 'a'
    my $context = Context()->copy;
    $context->flags->set(no_parameters=>0);
    $context->variables->add('a'=>'Parameter');
    my $a = Formula($context,'a');
    $f = Formula($context,$f);
    my $result = ($a*$F == $f || $a*$G == $f);
    Value::Error('Factor as the product of two linear functions') 
    unless ($result == 1);
    return $result;

  }

);

Setup: This is a standard factoring problem for a non-monic polynomial (where the leading coefficient is not 1 or -1). The MultiAnswer answer checker allows us to collect student answers from several answer blanks and perform answer evaluation on several answer blanks simultaneously. Since it is possible to factor 16 x^2 + 48 x + 36 as (2x + 3) (8x + 12) or (4x + 6) (4x + 6), we need to use an adaptive parameter to allow both of these answers to be marked correct.

The MultiAnswer makes sure that neither factor is constant and that the product of the student's factors equals the product of the correct factors. Then, it creates a copy of the current context as a local context, and creates an adaptive parameter in this local context. The adaptive parameter will allow us to determine whether each factor in the student's answer is equal to a constant multiple of some factor of the correct answer. 

Context()->texStrings;
BEGIN_TEXT
Factor the following expression.
$BR
$BR
\( 16 t^2 + 48 t + 36 = \big( \) 
\{$multians->ans_rule(10)\}
\( \big) \big( \) 
\{$multians->ans_rule(10)\}
\( \big) \)
\{ AnswerFormatHelp("formulas") \}
END_TEXT
Context()->normalStrings;

Main Text: Each answer blank must be a method of the $multians object, which is why we use $multians->ans_rule(10). The big parentheses will help students understand what the format of the answer should be. 

$showPartialCorrectAnswers = 1;

ANS( $multians->cmp() );

ENDDOCUMENT();

Answer Evaluation: Everything is as expected.

Problem Techniques Index


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