[LON-CAPA-users] Maxima is being fussy

[Seema Ali]

Hi,

I have a graph transformation question, that recognizes correct answers most of the time.  I was wondering if it could recognize it all of the time.

Example: y = 8 + (x-12)^3
New graph is vertically compressed by 1/3 and shifted horizontally to the left by 9 units.

A possible solution:  1/3 * (8 + (x -3)^3)
This solutions was marked wrong as was:
(8 + (x -3)^3)/3

The solution that was marked correctly was:
8/3 + ((x-3)^3)/3

I'm not sure why Maxima did not mark the other 2 correctly.  Below is the code for the problem. 

Also is there something that I'm missing?  I am worried that for the algebra response questions that I created students may be marked incorrectly when they are right.  

Thanks.


<problem>
<script type="loncapa/perl">$origA = &random(5,9,1);
$origB = &random(10,15,1);
$origC = &random(16,20,1);

#pick a function
$index = &random(1,3,1);
$function = &choose($index, "sqrt($origA-(x-$origB)^2)",  "$origA + (x-$origB)^3", "$origA / (x-$origB) + $origC");
$functionL= &choose($index, "\\sqrt{$origA-(x-$origB)^2}", "$origA + (x-$origB)^3", "\\Large\\frac{$origA}{x-$origB} \\normalsize + $origC");

#set the types of translations
$temp = &random(1,2,1);
$compression = &choose($temp,"horizontal ", "vertical ");

$temp = &random(1,2,1);
$compression = $compression.&choose($temp,"expansion", "compression");

$compressionAmount = &random(2,9,1);


$temp = &random(1,2,1);
$translation = &choose($temp, "horizontal translation", "vertical translation");

$temp = &random(1,2,1)+ ($temp-1)*2;
$translationDirection = &choose($temp, "left", "right", "up", "down");

do
{
   $translationAmount = &random(2,9,1);
}while($compressionAmount==$translationAmount);


#set the constants for $a and $b
if($compression eq "horizontal expansion")
{
  $a = 1;
  $b = 1/$compressionAmount;
  $texcomp = $compressionAmount;
}
elsif($compression eq "horizontal compression")
{
  $a = 1;
  $b = $compressionAmount;
  $texcomp =  "\\frac{1}{$compressionAmount}";
}
elsif($compression eq "vertical compression")
{
  $a = 1/$compressionAmount;
  $b = 1;
  $texcomp = "\\frac{1}{$compressionAmount}";
}
else
{
  $a = $compressionAmount;
  $b = 1;
  $texcomp = $compressionAmount;
}


#set values to $c and $d
if($translation eq "horizontal translation" && $translationDirection eq "left")
{
  $c = -1*$translationAmount;
  $d = 0;
}
elsif($translation eq "horizontal translation" && $translationDirection eq "right")
{
  $c = $translationAmount;
  $d = 0;
}
elsif($translation eq "vertical translation" && $translationDirection eq "up")
{
  $c = 0;
  $d = $translationAmount;
}
elsif($translation eq "vertical translation" && $translationDirection eq "down")
{
  $c = 0;
  $d = -1*$translationAmount;
}






@args = ($function, $a, $b, $c, $d);</script><startouttext /><p>
What is the equation of <m eval="on"> $ y= $functionL$ </m> after a 
$compression by a factor of <m eval="on">$ $texcomp $</m> and
$translation $translationAmount units $translationDirection?
</p>
Instructions: <br />
<ul>
  <li>Use * for multiplication, / for division, ^ for exponent and brackets</li>
  <li>For example to represent <m>$y=\Large\frac{(x^3-4)^5}{2}$</m>you would type: ((x^3-4)^5)/2</li>
  <li>If you enter a formula, double check your formula by clicking on the pencil icon to get a 
      different representation of your formula </li>
  <li>Another example to represent <m>$\sqrt{x^2+3} - 5$</m> you would type:  sqrt(x^2 + 3) - 5</li>
</ul>

<br />
<br />


Answer:  <m>$y =$</m><endouttext />
<mathresponse cas="maxima" args="@args" id="11">
    <answer>f(x) := LONCAPALIST[1];
a:LONCAPALIST[2];
b:LONCAPALIST[3];
c:LONCAPALIST[4];
d:LONCAPALIST[5];
g(x) := LONCAPALIST[2]*f(LONCAPALIST[3]*(x-LONCAPALIST[4]))+LONCAPALIST[5];
is(trigsimp(trigreduce(RESPONSE[1]-g(x)))=0);</answer>
    <textline readonly="no" />
    
</mathresponse>
</problem>



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