View of /trunk/NationalProblemLibrary/Union/setMVfunctions/an13_1_b.pg

    1 DOCUMENT();        # This should be the first executable line in the problem.
    2 
    3 loadMacros(
    4   "PGstandard.pl",
    5   "PGunion.pl",
    6   "alignedChoice.pl",
    7   "Parser.pl",
    8   "PGcourse.pl"
    9 );
   10 
   11 
   12 TEXT(beginproblem());
   13 BEGIN_PROBLEM();
   14 
   15 ##############################################
   16 #  Setup
   17 
   18 Context("Vector")->variables->are(
   19   x=>'Real', y=>'Real', s=>'Real', t=>'Real',
   20 );
   21 
   22 #
   23 #  The function to use
   24 #
   25 $f = Formula("(x^2-y^2,2xy,x^3)");
   26 $f->perlFunction('f');
   27 
   28 #
   29 #  some points to evaluate it at
   30 #
   31 $a = non_zero_random(-6,6,1);
   32 $b = non_zero_random(-6,6,1); $b++ if ($b == $a);
   33 $c = non_zero_random(-6,6,1);
   34 
   35 $at = Formula("$a t")->reduce;
   36 
   37 #
   38 #  The questions and answers
   39 #
   40 Context()->texStrings;
   41 $al = new_aligned_list(ans_rule_len=>35);
   42 $al->qa(
   43   "\(f($a,$b)\)",    f($a,$b)->cmp,
   44   "\(f($b,$a)\)",    f($b,$a)->cmp,
   45   "\(f(0,$c)\)",     f(0,$c)->cmp,
   46   "\(f(t^2,$at)\)",  Formula("(t^4-($a t)^2,2*$a*t^3,t^6)")->reduce->cmp,
   47   "\(f(s+t,s-t)\)",  Formula("(4st,2(s^2-t^2),(s-t)^3)")->cmp,
   48 );
   49 Context()->normalStrings;
   50 
   51 ##############################################
   52 #  Main text
   53 
   54 Context()->texStrings;
   55 BEGIN_TEXT
   56 
   57 Suppose \(f(x,y)=$f\).  Compute the following values:
   58 $PAR
   59 
   60 $BBLOCKQUOTE
   61 \{$al->print_q\}
   62 $EBLOCKQUOTE
   63 
   64 END_TEXT
   65 Context()->normalStrings;
   66 
   67 ##############################################
   68 # Answers
   69 
   70 ANS($al->correct_ans);
   71 $showPartialCorrectAnswers = 1;
   72 
   73 ##############################################
   74 
   75 END_PROBLEM();
   76 ENDDOCUMENT();        # This should be the last executable line in the problem.