Add placement test problems

Contrib/Piedmont/MathPlacementTest/mpt.1.2.pg

@@ -0,0 +1,69 @@
+#DESCRIPTION
+##  Algebra problem: simplifying fraction
+##ENDDESCRIPTION
+
+## hcao tagged and PAID on 12-12-2003
+
+## slightly modified for Piedmont placement test
+## (smaller numbers) by Doug Torrance (2025-05-08)
+
+## DBsubject(Arithmetic)
+## DBchapter(Fractions/rational numbers)
+## DBsection(Multiple operations)
+## MLT(DivFollowedBySubtract)
+## MLTleader(1)
+## Date(6/3/2002)
+## Level(2)
+## TitleText1('College Algebra')
+## AuthorText1('Stewart, Redlin, Watson')
+## EditionText1('3')
+## Section1('1.2')
+## Problem1('15')
+## KEYWORDS('algebra', 'fraction')
+DOCUMENT();        # This should be the first executable line in the problem.
+
+loadMacros(
+  "PGstandard.pl",
+  "PGchoicemacros.pl",
+  "PGcourse.pl"
+);
+TEXT(beginproblem());
+$showCorrectPartialAnswers = 1;
+
+$n1 = random(2,5,1);
+$n2 = random(1,5,1);
+do {$d2 = random(2,5,1)} until (gcd($n2, $d2) == 1);
+
+BEGIN_TEXT
+Combine the fractions, and reduce your answer. 
+             \[ \left($n1\div\frac{$n2}{$d2}\right)-\frac{$n2}{$d2} \]
+The reduced answer is \{ans_rule(5)\} / \{ans_rule(5)\}
+END_TEXT
+@factors = ();
+@commonfactors = ();
+$fac = $d2*$n2;
+for($i=2; $i<=($d2*$n2)/2; $i++){
+	if($fac % $i == 0){
+		$fac =$fac/$i;
+		push @factors,$i;
+                $i = $i-1;
+	};
+};
+$fac = $n1*$d2*$d2-$n2*$n2;
+foreach $i (@factors){
+	if($fac % $i == 0){
+		$fac = $fac / $i;
+		push @commonfactors,$i;
+	};
+};
+$den = $d2*$n2;
+$num = $n1*$d2*$d2-$n2*$n2;
+foreach $i (@commonfactors){
+	$num = $num / $i;
+	$den = $den / $i;
+};
+
+ANS(num_cmp($num, mode=>"strict"));
+ANS(num_cmp($den, mode=>"strict"));
+
+ENDDOCUMENT();        # This should be the last executable line in the problem.

Contrib/Piedmont/MathPlacementTest/mpt.1.6.pg

@@ -0,0 +1,54 @@
+## DESCRIPTION
+## Solve a linear inequality
+## ENDDESCRIPTION
+
+## KEYWORDS('linear inequality')
+
+## DBsubject('Algebra')
+## DBchapter('Algebra of real numbers and simplifying expressions')
+## DBsection('Inequalities and intervals')
+## Date('2025-05-06')
+## Author('Doug Torrance')
+## Institution('Piedmont University')
+
+DOCUMENT();
+
+loadMacros(
+    "PGstandard.pl",    # Standard macros for PG language
+    "PGML.pl",          # PGML markup and Math Objects
+    "PGcourse.pl",      # Customization file for the course
+);
+
+$endpoint = random(-5, 5);
+$oper = random(0, 3);
+$opertex = ("<", "\leq", ">", "\geq")[$oper];
+$b = random(1, 10);
+$c = random(2, 10);
+$d = random(1, $endpoint + 10);
+$e = $b - $c*($endpoint - $d);
+
+Context()->variables->add(a => 'Real');
+$f = Formula("$b - $c(a - $d)");
+
+if ($oper == 0) {
+  $ans = Interval("($endpoint, inf)");
+} elsif ($oper == 1) {
+  $ans = Interval("[$endpoint, inf)");
+} elsif ($oper == 2) {
+  $ans = Interval("(-inf, $endpoint)");
+} else {
+  $ans = Interval("(-inf, $endpoint]");
+}
+
+BEGIN_PGML
+
+Solve this inequality.
+
+[``[$f] [$opertex] [$e]``]
+
+Enter your answer using interval notation.  See [@helpLink('interval notation')@]*.
+
+[_]{$ans}
+END_PGML
+
+ENDDOCUMENT();

Contrib/Piedmont/MathPlacementTest/mpt.1.7.pg

@@ -0,0 +1,191 @@
+# WeBWorK problem written by Chris Hughes, 2013
+# Portland Community College
+#
+# Template:
+# Solve the following quadratic equation
+#
+#       ac x^2 = - (ad + bc) x - bd
+# 
+# This equation factors nicely
+#
+#       (ax + b)(cx + d) = 0
+#
+# If you need to use the square root symbol, 
+# as in x=sqrt{17}, type it like: *sqrt(17)*
+#
+# a is integer on [2,5], c = 1
+#
+# b = d are both positive.
+#
+# Last updated: Hughes 8/20/13
+#
+# ENDDESCRIPTION
+
+# Modified for Piedmont placement test
+# (smaller numbers, no sqrt note)
+# by Doug Torrance (2025-05-08)
+
+## DBCCSS('A-REI.4.b')
+## DBsubject('Algebra')
+## DBchapter('Basic Algebra')
+## DBsection('equations', 'Simplification')
+## KEYWORDS('solve','quadratic','equation','factor','zero product principle','fraction')
+## Author('Alex Jordan, Carl Yao, Chris Hughes')
+## Institution('PCC')
+
+
+##############################################
+DOCUMENT();
+loadMacros(
+     "PGstandard.pl",
+     "MathObjects.pl",
+     "parserAssignment.pl",
+     "answerHints.pl",
+     "PGML.pl",
+     "contextFraction.pl",
+  "PCCmacros.pl",
+  "PGcourse.pl",
+);
+
+##############################################
+
+Context("Numeric");
+# globally set the reductions one time
+# # so that we can then merely call ->reduce;
+Context()->noreduce('(-x)-y','(-x)+y');
+
+$var = "x";
+$a=10;
+$b=$a;
+$c=$a;
+$d=$a;
+
+while(gcd($a,$b)!=1 or gcd($c,$d)!=1 or (abs($a*$d+$b*$d)>20) or abs($b * $d) > 20)
+{
+    $a = random(2,5,1);
+    $b = random(1,12,1);
+    $c = 1;
+    $d = random(2,10,1);
+}
+
+$lhs = Formula("$a*$c*$var^2")->reduce->reduce;
+$rhs = Formula("-($b*$c+$a*$d)*$var-($b*$d)")->reduce->reduce;
+$questionFormula = Formula("$a*$c*$var^2+($b*$c+$a*$d)*$var+($b*$d)")->reduce->reduce;
+$questionFormula1 = Formula("($a*$var+$b)($c*$var+$d)")->reduce;
+
+Context("LimitedFraction")->flags->set(
+                        reduceFractions => 0,
+                        showMixedNumbers=>0,
+                        showExtraParens=>0 );
+parser::Assignment->Allow;
+Context()->operators->redefine(',',using=>',',from=>'Numeric');
+Context()->operators->redefine('or',using=>',',from=>'Numeric');
+Context()->operators->set(
+  ','=>{string=>' or ',TeX=>'\hbox{ or }'},
+  'or'=>{string=>' or ',TeX=>'\hbox{ or }'}
+);
+Context()->lists->set(List => {separator => " or "});
+Context()->{error}{msg}{"Function 'sqrt' is not allowed in this context"} 
+  = "Please simplify your answer further";
+Context()->{error}{msg}{"Can't use '*' in this context"} 
+  = "Please simplify your answer further";
+Context()->{error}{msg}{"Can't use '+' in this context"} 
+  = "Please simplify your answer further";
+Context()->{error}{msg}{"Can't use '-' in this context"} 
+  = "Please simplify your answer further";
+
+# add solution strings to context- this means that if
+# students enter these (and they are not correct), then 
+# WW will not give a Context warning
+Context()->strings->add("no real solutions"=>{},
+  "no real solution"=>{alias=>'no real solutions'}, 
+  "none"=>{alias=>'no real solutions'}, 
+  );
+
+$soln1 = Fraction(-$b,$a);
+$soln2 = Fraction(-$d,$c);
+$ans = Compute("$var = $soln1, $var = $soln2");
+
+##############################################
+
+TEXT(beginproblem());
+BEGIN_PGML
+Solve the equation.
+
+    [` [$lhs]=[$rhs]`]
+
+    [__________________________]
+
+[@KeyboardInstructions("Enter multiple answers separated by commas, as in [|x=1, x=-1|]*.")@]**
+END_PGML
+
+##############################################
+$showPartialCorrectAnswers = 1;
+ANS($ans->cmp(
+  entry_type => "a solution",
+  checker => sub {
+    my ($correct,$student,$ans,$nth,$value) = @_;
+    if ($correct->type eq "Assignment") {
+      my ($svar,$sfrac) = $student->value; # get the variable and fraction
+      #return 0 unless Value::classMatch($sfrac,'Fraction') && $sfrac->isReduced;
+      if(Value::classMatch($sfrac,'Fraction'))
+      {
+        return 0 unless $sfrac->isReduced;
+      }
+    }
+    return $correct == $student;
+  },
+  extra => sub {
+    my ($student,$ansHash,$nth,$value) = @_;
+    if($student eq "no real solutions")
+    {
+         $student->context->setError("This equation does have some solutions- try using the square root method","",undef,undef,$Value::CMP_WARNING)
+         unless $ans->{isPreview};
+         return;
+    }
+    if ($student->type ne "Assignment" && $ansHash->{student_formula}->type ne "Assignment") {
+      $student->context->setError("Your $nth solution should be written $var = $US$US$US","",undef,undef,$Value::CMP_WARNING)
+         unless $ans->{isPreview};
+      return;
+    }
+    my ($svar,$sfrac) = $student->value; # get the variable and fraction
+    if (Value::classMatch($sfrac,'Fraction') && !$sfrac->isReduced) {
+      $student->context->setError("Your $nth $value is not reduced","",undef,undef,$Value::CMP_WARNING)
+         unless $ans->{isPreview};
+      return;
+    }
+    return Value::Real->typeMatch($student);
+  }
+)->withPostFilter(AnswerHints(
+  ["$var=$soln1","$var=$soln2"] => "Are you sure you have all the solutions?",
+  [$soln1,$soln2] => ["Your solution is a correct one, but you should write $var = $US$US$US<br>Are you sure you have all the solutions?",replaceMessage=>1],
+  ["$soln1,$soln2","$soln2,$soln1"] => ["Your solutions are correct, but you should write $var = $US$US$US",replaceMessage=>1],
+)));
+
+##############################################
+
+$A = $a*$c;
+$B = $b*$c+$a*$d;
+$C = $b*$d;
+
+BEGIN_PGML_SOLUTION
+There are a few ways to solve quadratic equations- the easiest way to solve this particular 
+type of problem is to use the _zero product principle_. 
+
+    [`
+       \begin{aligned}
+                     [$lhs]=[$rhs]               &\Rightarrow [$questionFormula]=0 \\
+                                    &\Rightarrow [$questionFormula1]=0 \\
+                                    & \Rightarrow [$ans]
+       \end{aligned}
+    `]
+
+This quadratic equation has two distinct, real solutions.
+
+The solutions can be checked by substituting them into the original equation- this is left as an exercise.
+END_PGML_SOLUTION
+
+##############################################
+
+ENDDOCUMENT();
+

Contrib/Piedmont/MathPlacementTest/mpt.1.8.pg

@@ -0,0 +1,51 @@
+## DESCRIPTION
+## Simplify radical expression
+## ENDDESCRIPTION
+
+## KEYWORDS('radical expression')
+
+## DBsubject('Algebra')
+## DBchapter('Properties of exponents, rational exponents and radicals')
+## DBsection('Properties of rational exponents and radicals')
+## Date('2025-05-07')
+## Author('Doug Torrance')
+## Institution('Piedmont University')
+
+DOCUMENT();
+
+loadMacros(
+    "PGstandard.pl",    # Standard macros for PG language
+    "PGML.pl",          # PGML markup and Math Objects
+    "PGcourse.pl",      # Customization file for the course
+    "contextLimitedRadical.pl",
+);
+
+# constant term = a^2 * b, where a and b are chosen from 2, 3, 5
+$a = list_random(2, 3, 5);
+do {$b = list_random(2, 3, 5);} until ($a != $b);
+$coeff = $a**2 * $b;
+
+$var_with_exp = random(0, 1);
+$a_exp = random(2, 4);
+$q_exp = 2 * $a_exp + 1;
+
+Context('LimitedRadical');
+Context()->variables->add(y => 'Real');
+
+if ($var_with_exp == 0) {
+  $q = Formula("sqrt($coeff x^$q_exp y)");
+  $ans = Formula("$a x^$a_exp sqrt($b x y)");
+} else {
+  $q = Formula("sqrt($coeff x y^$q_exp)");
+  $ans = Formula("$a y^$a_exp sqrt($b x y)");
+}
+
+BEGIN_PGML
+Simplify this expression.  Assume all variables represent positive real numbers.
+
+[``[$q]``].
+
+[_]{$ans}
+END_PGML
+
+ENDDOCUMENT();