PREP 2014 Question Authoring - Archived

answerHints message doesn't appear

answerHints message doesn't appear

by Chrissy Safranski -
Number of replies: 2
What am I doing wrong?  Everything seems to be working as I want it to, except that I can't get the answer hint to show up for the denominator if students enter the first denominator times the second denominator, instead of the least common denominator.  

If I change the required input (where I have "$p") to a constant number, then it works and the message shows up.  But if I change it to 'x' or '6 x' or anything else, and try entering that as the denominator, it just says that it's incorrect, no customized message.  Why is it doing that?  
------------------------------------------------
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"contextLimitedPolynomial.pl",
"contextPolynomialFactors.pl",
"contextLimitedPowers.pl",
"answerHints.pl"
);

Context("Numeric");


$a=non_zero_random(3,6);
$aa=$a**2;
$b=non_zero_random(1,5);
if ($b==$a) {$b++};
$c=non_zero_random(2,5);
if ($c==$a) {$c++};


$denom=Compute("x^2-$aa");


Context("LimitedPolynomial-Strict");
$p[0]=$b+1;
$p[1]=-$c-$a*$b;
$num=Compute("$p[0] x+$p[1]")->reduce;

Context()->texStrings;
BEGIN_TEXT

$BBOLD Simplifying Rational Expressions. $EBOLD Understand how to 
manipulate rational expressions.  They work just like fractions!
$BR

\[\frac{x-$c}{x^2-$aa} + \frac{$b}{x+$a} = \frac{A}{B} \]
where \(A\) and \(B\) 
are polynomials of degree as low as possible 
and the leading coefficient of \(B\) is 1.
$BR
A= \{ ans_rule(15) \} $BR
B=\{ ans_rule(15) \}

$PAR
Your numerator should be simplified (multiplied out and combined), while your denominator can be simplified or left in factored form.  However, make sure that it has the lowest possible degree!
END_TEXT

Context()->normalStrings;

ANS($num->cmp->withPostFilter(sub { 
  my $ans = shift; 
  $ans->{ans_message} = 'This needs to be multiplied out and simplified.' 
    if $ans->{ans_message} eq "Multiplication can only be used between coefficients and variables";
  return $ans; 
}));

# $p =  Formula("(x^2-$aa)(x+$a)");

$aaa=$a**3;
$p = Formula("x^3-$aa x+$a x^2 -$aaa");

ANS($denom->cmp()->withPostFilter(AnswerHints(
 Formula("$p") => "This is not the lowest common denominator.",
  )));

----------------------------
The problem is with the last line.
In reply to Chrissy Safranski

Re: answerHints message doesn't appear

by Davide Cervone -
The problem is that the values for $denom and Formula("$p") are in two different contents, and you can only compare formulas when they are in the same context. So the comparison in AnswerHints fails (silently). So I'd recommend creating $p just below $denom, which will let you give it in the factored form as well.

There are a number of other small issues with the problem as well. For example, you can just use 

     $p => "This is not the lowest common denominator",
as $p is already a formula (no need to turn it into a string a re-parse it). Also, you can use the Context's {error}{msg} object to adjust the answer message for the numerator rather than having to provide a custom post filter (see below).

Here is a modified version that includes these changes. 

DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "contextLimitedPolynomial.pl",
  "answerHints.pl",
  "PGcourse.pl",
);

Context("Numeric");

$a=non_zero_random(3,6);
$b=non_zero_random(1,5);
if ($b==$a) {$b++};
$c=non_zero_random(2,5);
if ($c==$a) {$c++};

$denom=Compute("x^2-$a^2");
$p =  Formula("(x^2-$a^2)(x+$a)");

$aa = $a**2;

Context("LimitedPolynomial-Strict");
Context()->{error}{msg}
    {"Multiplication can only be used between coefficients and variables"} =
     "This needs to be multiplied out and simplified";

$A = $b+1;
$B = $c+$a*$b;
$num=Compute("$A x - $B")->reduce;

Context()->texStrings;
BEGIN_TEXT

$BBOLD Simplifying Rational Expressions. $EBOLD Understand how to 
manipulate rational expressions.  They work just like fractions!
$BR

\[\frac{x-$c}{x^2-$aa} + \frac{$b}{x+$a} = \frac{A}{B} \]
where \(A\) and \(B\) 
are polynomials of degree as low as possible 
and the leading coefficient of \(B\) is 1.
$BR
A= \{ ans_rule(15) \} $BR
B=\{ ans_rule(15) \}

$PAR
Your numerator should be simplified (multiplied out and 
combined), while your denominator can be simplified or left in 
factored form.  However, make sure that it has the lowest 
possible degree!
END_TEXT

Context()->normalStrings;

ANS($num->cmp);
ANS($denom->cmp()->withPostFilter(AnswerHints(
 $p => "This is not the lowest common denominator.",
)));

ENDDOCUMENT();
In reply to Davide Cervone

Re: answerHints message doesn't appear

by Chrissy Safranski -
Thank you!  I was going crazy, as I've used both the context error message and postfilter answer hints in many other problems without issue.  But guess I normally stay in Numeric context, so I wasn't fully realizing how those commands need to be in the right context to work.  

I had actually tried the Context error message for the numerator first, but I put it right below the Context("Numeric") line instead of after the Context("LimitedPolynomial-Strict") line, and so when it didn't work, that's when I switched to the postfilter error message, thinking that it was a type problem like we had discussed before.  But I understand my mistake now.

Thank you!