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Merge pull request #1261 from d-torrance/placement-test
Add placement test problems
2 parents 983a829 + 6497ddc commit 0dcfe1c

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‎Contrib/Piedmont/MathPlacementTest/mpt.1.2.pg‎

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#DESCRIPTION
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## Algebra problem: simplifying fraction
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##ENDDESCRIPTION
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## hcao tagged and PAID on 12-12-2003
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## slightly modified for Piedmont placement test
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## (smaller numbers) by Doug Torrance (2025-05-08)
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## DBsubject(Arithmetic)
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## DBchapter(Fractions/rational numbers)
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## DBsection(Multiple operations)
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## MLT(DivFollowedBySubtract)
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## MLTleader(1)
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## Date(6/3/2002)
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## Level(2)
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## TitleText1('College Algebra')
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## AuthorText1('Stewart, Redlin, Watson')
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## EditionText1('3')
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## Section1('1.2')
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## Problem1('15')
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## KEYWORDS('algebra', 'fraction')
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DOCUMENT(); # This should be the first executable line in the problem.
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loadMacros(
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"PGstandard.pl",
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"PGchoicemacros.pl",
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"PGcourse.pl"
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);
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TEXT(beginproblem());
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$showCorrectPartialAnswers = 1;
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$n1 = random(2,5,1);
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$n2 = random(1,5,1);
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do {$d2 = random(2,5,1)} until (gcd($n2, $d2) == 1);
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BEGIN_TEXT
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Combine the fractions, and reduce your answer.
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\[ \left($n1\div\frac{$n2}{$d2}\right)-\frac{$n2}{$d2} \]
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The reduced answer is \{ans_rule(5)\} / \{ans_rule(5)\}
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END_TEXT
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@factors = ();
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@commonfactors = ();
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$fac = $d2*$n2;
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for($i=2; $i<=($d2*$n2)/2; $i++){
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if($fac % $i == 0){
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$fac =$fac/$i;
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push @factors,$i;
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$i = $i-1;
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};
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};
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$fac = $n1*$d2*$d2-$n2*$n2;
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foreach $i (@factors){
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if($fac % $i == 0){
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$fac = $fac / $i;
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push @commonfactors,$i;
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};
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};
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$den = $d2*$n2;
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$num = $n1*$d2*$d2-$n2*$n2;
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foreach $i (@commonfactors){
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$num = $num / $i;
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$den = $den / $i;
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};
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ANS(num_cmp($num, mode=>"strict"));
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ANS(num_cmp($den, mode=>"strict"));
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ENDDOCUMENT(); # This should be the last executable line in the problem.

‎Contrib/Piedmont/MathPlacementTest/mpt.1.6.pg‎

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## DESCRIPTION
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## Solve a linear inequality
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## ENDDESCRIPTION
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## KEYWORDS('linear inequality')
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## DBsubject('Algebra')
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## DBchapter('Algebra of real numbers and simplifying expressions')
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## DBsection('Inequalities and intervals')
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## Date('2025-05-06')
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## Author('Doug Torrance')
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## Institution('Piedmont University')
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DOCUMENT();
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loadMacros(
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"PGstandard.pl", # Standard macros for PG language
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"PGML.pl", # PGML markup and Math Objects
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"PGcourse.pl", # Customization file for the course
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);
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$endpoint = random(-5, 5);
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$oper = random(0, 3);
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$opertex = ("<", "\leq", ">", "\geq")[$oper];
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$b = random(1, 10);
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$c = random(2, 10);
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$d = random(1, $endpoint + 10);
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$e = $b - $c*($endpoint - $d);
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Context()->variables->add(a => 'Real');
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$f = Formula("$b - $c(a - $d)");
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if ($oper == 0) {
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$ans = Interval("($endpoint, inf)");
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} elsif ($oper == 1) {
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$ans = Interval("[$endpoint, inf)");
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} elsif ($oper == 2) {
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$ans = Interval("(-inf, $endpoint)");
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} else {
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$ans = Interval("(-inf, $endpoint]");
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}
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BEGIN_PGML
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Solve this inequality.
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[``[$f] [$opertex] [$e]``]
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Enter your answer using interval notation. See [@helpLink('interval notation')@]*.
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[_]{$ans}
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END_PGML
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ENDDOCUMENT();

‎Contrib/Piedmont/MathPlacementTest/mpt.1.7.pg‎

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# WeBWorK problem written by Chris Hughes, 2013
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# Portland Community College
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#
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# Template:
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# Solve the following quadratic equation
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#
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# ac x^2 = - (ad + bc) x - bd
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#
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# This equation factors nicely
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#
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# (ax + b)(cx + d) = 0
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#
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# If you need to use the square root symbol,
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# as in x=sqrt{17}, type it like: *sqrt(17)*
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#
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# a is integer on [2,5], c = 1
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#
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# b = d are both positive.
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#
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# Last updated: Hughes 8/20/13
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#
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# ENDDESCRIPTION
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# Modified for Piedmont placement test
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# (smaller numbers, no sqrt note)
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# by Doug Torrance (2025-05-08)
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## DBCCSS('A-REI.4.b')
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## DBsubject('Algebra')
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## DBchapter('Basic Algebra')
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## DBsection('equations', 'Simplification')
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## KEYWORDS('solve','quadratic','equation','factor','zero product principle','fraction')
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## Author('Alex Jordan, Carl Yao, Chris Hughes')
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## Institution('PCC')
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##############################################
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DOCUMENT();
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loadMacros(
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"PGstandard.pl",
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"MathObjects.pl",
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"parserAssignment.pl",
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"answerHints.pl",
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"PGML.pl",
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"contextFraction.pl",
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"PCCmacros.pl",
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"PGcourse.pl",
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);
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##############################################
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Context("Numeric");
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# globally set the reductions one time
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# # so that we can then merely call ->reduce;
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Context()->noreduce('(-x)-y','(-x)+y');
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$var = "x";
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$a=10;
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$b=$a;
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$c=$a;
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$d=$a;
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while(gcd($a,$b)!=1 or gcd($c,$d)!=1 or (abs($a*$d+$b*$d)>20) or abs($b * $d) > 20)
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{
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$a = random(2,5,1);
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$b = random(1,12,1);
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$c = 1;
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$d = random(2,10,1);
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}
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$lhs = Formula("$a*$c*$var^2")->reduce->reduce;
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$rhs = Formula("-($b*$c+$a*$d)*$var-($b*$d)")->reduce->reduce;
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$questionFormula = Formula("$a*$c*$var^2+($b*$c+$a*$d)*$var+($b*$d)")->reduce->reduce;
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$questionFormula1 = Formula("($a*$var+$b)($c*$var+$d)")->reduce;
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Context("LimitedFraction")->flags->set(
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reduceFractions => 0,
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showMixedNumbers=>0,
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showExtraParens=>0 );
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parser::Assignment->Allow;
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Context()->operators->redefine(',',using=>',',from=>'Numeric');
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Context()->operators->redefine('or',using=>',',from=>'Numeric');
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Context()->operators->set(
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','=>{string=>' or ',TeX=>'\hbox{ or }'},
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'or'=>{string=>' or ',TeX=>'\hbox{ or }'}
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);
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Context()->lists->set(List => {separator => " or "});
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Context()->{error}{msg}{"Function 'sqrt' is not allowed in this context"}
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= "Please simplify your answer further";
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Context()->{error}{msg}{"Can't use '*' in this context"}
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= "Please simplify your answer further";
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Context()->{error}{msg}{"Can't use '+' in this context"}
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= "Please simplify your answer further";
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Context()->{error}{msg}{"Can't use '-' in this context"}
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= "Please simplify your answer further";
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# add solution strings to context- this means that if
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# students enter these (and they are not correct), then
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# WW will not give a Context warning
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Context()->strings->add("no real solutions"=>{},
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"no real solution"=>{alias=>'no real solutions'},
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"none"=>{alias=>'no real solutions'},
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);
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$soln1 = Fraction(-$b,$a);
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$soln2 = Fraction(-$d,$c);
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$ans = Compute("$var = $soln1, $var = $soln2");
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##############################################
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TEXT(beginproblem());
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BEGIN_PGML
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Solve the equation.
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[` [$lhs]=[$rhs]`]
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[__________________________]
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[@KeyboardInstructions("Enter multiple answers separated by commas, as in [|x=1, x=-1|]*.")@]**
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END_PGML
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##############################################
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$showPartialCorrectAnswers = 1;
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ANS($ans->cmp(
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entry_type => "a solution",
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checker => sub {
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my ($correct,$student,$ans,$nth,$value) = @_;
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if ($correct->type eq "Assignment") {
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my ($svar,$sfrac) = $student->value; # get the variable and fraction
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#return 0 unless Value::classMatch($sfrac,'Fraction') && $sfrac->isReduced;
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if(Value::classMatch($sfrac,'Fraction'))
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{
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return 0 unless $sfrac->isReduced;
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}
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}
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return $correct == $student;
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},
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extra => sub {
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my ($student,$ansHash,$nth,$value) = @_;
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if($student eq "no real solutions")
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{
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$student->context->setError("This equation does have some solutions- try using the square root method","",undef,undef,$Value::CMP_WARNING)
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unless $ans->{isPreview};
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return;
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}
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if ($student->type ne "Assignment" && $ansHash->{student_formula}->type ne "Assignment") {
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$student->context->setError("Your $nth solution should be written $var = $US$US$US","",undef,undef,$Value::CMP_WARNING)
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unless $ans->{isPreview};
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return;
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}
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my ($svar,$sfrac) = $student->value; # get the variable and fraction
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if (Value::classMatch($sfrac,'Fraction') && !$sfrac->isReduced) {
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$student->context->setError("Your $nth $value is not reduced","",undef,undef,$Value::CMP_WARNING)
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unless $ans->{isPreview};
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return;
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}
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return Value::Real->typeMatch($student);
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}
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)->withPostFilter(AnswerHints(
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["$var=$soln1","$var=$soln2"] => "Are you sure you have all the solutions?",
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[$soln1,$soln2] => ["Your solution is a correct one, but you should write $var = $US$US$US<br>Are you sure you have all the solutions?",replaceMessage=>1],
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["$soln1,$soln2","$soln2,$soln1"] => ["Your solutions are correct, but you should write $var = $US$US$US",replaceMessage=>1],
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)));
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##############################################
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$A = $a*$c;
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$B = $b*$c+$a*$d;
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$C = $b*$d;
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BEGIN_PGML_SOLUTION
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There are a few ways to solve quadratic equations- the easiest way to solve this particular
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type of problem is to use the _zero product principle_.
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[`
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\begin{aligned}
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[$lhs]=[$rhs] &\Rightarrow [$questionFormula]=0 \\
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&\Rightarrow [$questionFormula1]=0 \\
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& \Rightarrow [$ans]
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\end{aligned}
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`]
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This quadratic equation has two distinct, real solutions.
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The solutions can be checked by substituting them into the original equation- this is left as an exercise.
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END_PGML_SOLUTION
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##############################################
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ENDDOCUMENT();
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‎Contrib/Piedmont/MathPlacementTest/mpt.1.8.pg‎

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## DESCRIPTION
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## Simplify radical expression
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## ENDDESCRIPTION
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## KEYWORDS('radical expression')
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## DBsubject('Algebra')
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## DBchapter('Properties of exponents, rational exponents and radicals')
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## DBsection('Properties of rational exponents and radicals')
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## Date('2025-05-07')
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## Author('Doug Torrance')
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## Institution('Piedmont University')
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DOCUMENT();
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loadMacros(
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"PGstandard.pl", # Standard macros for PG language
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"PGML.pl", # PGML markup and Math Objects
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"PGcourse.pl", # Customization file for the course
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"contextLimitedRadical.pl",
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);
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# constant term = a^2 * b, where a and b are chosen from 2, 3, 5
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$a = list_random(2, 3, 5);
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do {$b = list_random(2, 3, 5);} until ($a != $b);
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$coeff = $a**2 * $b;
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$var_with_exp = random(0, 1);
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$a_exp = random(2, 4);
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$q_exp = 2 * $a_exp + 1;
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Context('LimitedRadical');
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Context()->variables->add(y => 'Real');
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if ($var_with_exp == 0) {
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$q = Formula("sqrt($coeff x^$q_exp y)");
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$ans = Formula("$a x^$a_exp sqrt($b x y)");
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} else {
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$q = Formula("sqrt($coeff x y^$q_exp)");
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$ans = Formula("$a y^$a_exp sqrt($b x y)");
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}
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BEGIN_PGML
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Simplify this expression. Assume all variables represent positive real numbers.
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[``[$q]``].
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[_]{$ans}
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END_PGML
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ENDDOCUMENT();

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