diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.1.2.pg b/Contrib/Piedmont/MathPlacementTest/mpt.1.2.pg
new file mode 100644
index 0000000000..7ebd324773
--- /dev/null
+++ b/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($den, mode=>"strict"));
+
+ENDDOCUMENT();        # This should be the last executable line in the problem.
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.1.6.pg b/Contrib/Piedmont/MathPlacementTest/mpt.1.6.pg
new file mode 100644
index 0000000000..25605c4c09
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.1.6.pg
@@ -0,0 +1,54 @@
+## DESCRIPTION
+## Solve a linear inequality
+## ENDDESCRIPTION
+
+## KEYWORDS('linear inequality')
+
+## DBsubject('Algebra')
+## DBchapter('Algebra of real numbers and simplifying expressions')
+## DBsection('Inequalities and intervals')
+## Date('2025-05-06')
+## Author('Doug Torrance')
+## Institution('Piedmont University')
+
+DOCUMENT();
+
+loadMacros(
+    "PGstandard.pl",    # Standard macros for PG language
+    "PGML.pl",          # PGML markup and Math Objects
+    "PGcourse.pl",      # Customization file for the course
+);
+
+$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')@]*.
+
+[_]{$ans}
+END_PGML
+ 
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.1.7.pg b/Contrib/Piedmont/MathPlacementTest/mpt.1.7.pg
new file mode 100644
index 0000000000..ada82a1fe3
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.1.7.pg
@@ -0,0 +1,191 @@
+# WeBWorK problem written by Chris Hughes, 2013
+# Portland Community College
+#
+# Template:
+# Solve the following quadratic equation
+#
+#       ac x^2 = - (ad + bc) x - bd
+# 
+# This equation factors nicely
+#
+#       (ax + b)(cx + d) = 0
+#
+# If you need to use the square root symbol, 
+# as in x=sqrt{17}, type it like: *sqrt(17)*
+#
+# a is integer on [2,5], c = 1
+#
+# b = d are both positive.
+#
+# Last updated: Hughes 8/20/13
+#
+# ENDDESCRIPTION
+
+# Modified for Piedmont placement test
+# (smaller numbers, no sqrt note)
+# by Doug Torrance (2025-05-08)
+
+## DBCCSS('A-REI.4.b')
+## DBsubject('Algebra')
+## DBchapter('Basic Algebra')
+## DBsection('equations', 'Simplification')
+## KEYWORDS('solve','quadratic','equation','factor','zero product principle','fraction')
+## Author('Alex Jordan, Carl Yao, Chris Hughes')
+## Institution('PCC')
+
+
+##############################################
+DOCUMENT();
+loadMacros(
+     "PGstandard.pl",
+     "MathObjects.pl",
+     "parserAssignment.pl",
+     "answerHints.pl",
+     "PGML.pl",
+     "contextFraction.pl",
+  "PCCmacros.pl",
+  "PGcourse.pl",
+);
+
+##############################################
+
+Context("Numeric");
+# globally set the reductions one time
+# # so that we can then merely call ->reduce;
+Context()->noreduce('(-x)-y','(-x)+y');
+
+$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 [$ans]
+       \end{aligned}
+    `]
+
+This quadratic equation has two distinct, real solutions.
+
+The solutions can be checked by substituting them into the original equation- this is left as an exercise.
+END_PGML_SOLUTION
+
+##############################################
+
+ENDDOCUMENT();
+
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.1.8.pg b/Contrib/Piedmont/MathPlacementTest/mpt.1.8.pg
new file mode 100644
index 0000000000..3490b18531
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.1.8.pg
@@ -0,0 +1,51 @@
+## DESCRIPTION
+## Simplify radical expression
+## ENDDESCRIPTION
+
+## KEYWORDS('radical expression')
+
+## DBsubject('Algebra')
+## DBchapter('Properties of exponents, rational exponents and radicals')
+## DBsection('Properties of rational exponents and radicals')
+## Date('2025-05-07')
+## Author('Doug Torrance')
+## Institution('Piedmont University')
+
+DOCUMENT();
+
+loadMacros(
+    "PGstandard.pl",    # Standard macros for PG language
+    "PGML.pl",          # PGML markup and Math Objects
+    "PGcourse.pl",      # Customization file for the course
+    "contextLimitedRadical.pl",
+);
+
+# constant term = a^2 * b, where a and b are chosen from 2, 3, 5
+$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();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.1.9.pg b/Contrib/Piedmont/MathPlacementTest/mpt.1.9.pg
new file mode 100644
index 0000000000..e78a8af914
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.1.9.pg
@@ -0,0 +1,126 @@
+## DESCRIPTION
+## Exponent rules
+## ENDDESCRIPTION
+
+# Modified for Piedmont placement test (fewer
+# parts) by Doug Torrance (2025-05-08)
+
+## DBsubject(Arithmetic)
+## DBchapter(Integers)
+## DBsection(Exponentiation)
+## Date(01/01/10)
+## Institution(Fort Lewis College)
+## Author(Paul Pearson)
+## Level(2)
+## MO(1)
+## TitleText1('Functions Modeling Change')
+## TitleText2('Functions Modeling Change')
+## TitleText3('Functions Modeling Change')
+## AuthorText1('Connally')
+## AuthorText2('Connally')
+## AuthorText3('Connally')
+## EditionText1('3')
+## EditionText2('4')
+## EditionText3('5')
+## Section1(3.Tools)
+## Section2('4.Skills')
+## Section3('4.Skills')
+## Problem1(21 22 26)
+## Problem2(16 19)
+## Problem3(16 19)
+## KEYWORDS('exponents')
+
+
+DOCUMENT();
+
+loadMacros(
+  "PGstandard.pl",
+  "MathObjects.pl",
+  "PGcourse.pl",
+  "contextLimitedNumeric.pl",
+  "contextLimitedFactor.pl",
+  "contextFraction.pl",
+);
+
+TEXT(beginproblem());
+
+##############################################
+#  Setup
+
+Context("LimitedNumeric");
+
+$a1 = random(-5,-3,1);
+$b1 = random(3,5,1);
+$answera = Real($a1 * $b1**2);
+
+$a2 = random(3,7,1);
+$b2 = random(3,7,1);
+$answerb = Real("1");
+
+$a3 = random(2, 9.9, 0.1);
+$c3 = random(3,5,1);
+$answerc = Real($a3 * 10**($c3));
+
+Context("LimitedFactor");
+Context()->variables->add(y => 'Real');
+
+$db = random(2, 10);
+$da = $db * random(2, 10);
+$dc = random(2, 10);
+$dd = $dc + random(2, 10);
+$de = random(2, 10);
+$df = random(2, 10);
+$answerd = Formula($da/$db . "y^" . ($de + $df) . "/x^" . ($dd - $dc));
+
+Context()->variables->add(t => 'Real');
+
+$ea = random(2, 10);
+do {$eb = random(2, 10)} until (gcd($ea, $eb) == 1);
+$ec = random(2, 10);
+$answere = Formula("$ea t^2 / (" . ($eb**2) . "x^" . (2*$ec) . ")");
+
+Context("LimitedFraction");
+$a = random(2,4,1);
+$aaa = $a**3;
+
+$b = random(2,4,1);
+while ($b==$a) { $b=random(2,4,1); }
+$bbb = $b**3;
+
+$answerf = Fraction("$b","$a");
+
+##############################################
+#  Main text
+
+Context()->texStrings;
+BEGIN_TEXT
+
+Evaluate the following without a calculator.
+Simplify your answers as much as possible, without using negative exponents.  Do not include commas in any large numbers.
+$BR
+$BR
+(a) \( ($a1)\cdot$b1^2 = \)
+\{ans_rule(10)\}
+$BR
+$BR
+(b) \( \displaystyle \left( \frac{$aaa}{$bbb} \right)^{-1/3} = \)
+\{ans_rule(10)\}
+$BR
+$BR
+(c) \(\dfrac{$da x^{$dc}y^{$de}}{$db x^{$dd}y^{-$df}} = \)
+\{ans_rule(10)\}
+
+END_TEXT
+
+##################################################
+#  Answer evaluation
+
+#install_problem_grader(~~&std_problem_grader);
+
+$showPartialCorrectAnswers = 1;
+
+ANS($answera->cmp());
+ANS($answerf->cmp());
+ANS($answerd->cmp());
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.1.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.1.pg
new file mode 100644
index 0000000000..b7d8320114
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.1.pg
@@ -0,0 +1,42 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 1 - Difference quotient
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Functions)
+## DBsection(Difference quotient)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$b = non_zero_random(-5, 5);
+$c = non_zero_random(-5, 5);
+
+$f = Formula("x^2 + $b x + $c");
+
+Context()->variables->add(h => 'Real');
+Context()->operators->undefine("/");
+
+$ans = Formula("2x + $b + h");
+
+BEGIN_TEXT
+
+Suppose \(x\) and \(h\) are variables and \(f(x) = \{$f->reduce->TeX\}\).  Simplify the following expression.
+$PAR
+
+\(\dfrac{f(x+h)-f(x)}{h}\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($ans->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.10.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.10.pg
new file mode 100644
index 0000000000..7681927927
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.10.pg
@@ -0,0 +1,56 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 10 - Application of exponential/logarithmic functions (half-life)
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Exponential and logarithmic expressions and functions)
+## DBsection(Applications and models - radioactive decay)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",
+   "MathObjects.pl"
+);
+
+$half_amount = 8 * random(1, 10);
+$initial_amount = 2 * $half_amount;
+$half_life = random(1, 10);
+
+$r = Compute("1/$half_life * ln(1/2)");
+
+$t = $half_life * random(2, 4);
+
+$ans = Compute("$initial_amount * (1/2)^($t/$half_life)");
+
+BEGIN_TEXT
+
+Suppose that an initial amount of $initial_amount g of some radioactive isotype decays to $half_amount g after $half_life hours.
+$PAR
+
+(a) If the amount of of this isotype is modeled by the function \(f(t) = Pe^{rt}\), where \(t\) represents the time in hours, then find the decay constant \(r\).
+$PAR
+
+Do not give a decimal approximation.  You may leave your answers in terms of logarithms.
+$PAR
+
+\(r\) = \{ans_rule\}
+$PAR
+
+(b) Determine how much of the isotype remains after $t hours.
+$PAR
+
+\(f($t)\) = \{ans_rule\} g
+$PAR
+
+END_TEXT
+
+ANS($r->cmp);
+ANS($ans->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.2.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.2.pg
new file mode 100644
index 0000000000..e0968406e6
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.2.pg
@@ -0,0 +1,38 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 2 - Complete the square (vertex form)
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Quadratic equations and functions)
+## DBsection(Forms: vertex, factored, general)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$h = non_zero_random(-10, 10);
+$k = non_zero_random(-10, 10);
+
+$f = Formula("x^2 + " . (-2*$h) . "x + " . ($h**2 + $k));
+
+BEGIN_TEXT
+
+Consider the parabola \(y = \{$f->reduce->TeX\}\).  Complete the square to find its equation in vertex form.
+$PAR
+
+\(y\) = \((x - \)\{ans_rule\}\()^2 + \)\{ans_rule\}
+
+END_TEXT
+
+ANS(Compute($h)->cmp);
+ANS(Compute($k)->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.3.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.3.pg
new file mode 100644
index 0000000000..0db8a15632
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.3.pg
@@ -0,0 +1,92 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 3 - Transformation of parabola
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Quadratic equations and functions)
+## DBsection(Graphs)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+   "parserGraphTool.pl"
+);
+
+$gt_checker = sub {
+    my ($correct, $student, $ans, $value) = @_;
+    return 0 if $ans->{isPreview};
+
+    my $score = 0;
+    my @errors;
+    my $count = 1;
+
+    my ($h, $k) = $correct->[0]->extract(4)->value;
+    my ($px, $py) = $correct->[0]->extract(5)->value;
+    my $a = ($py - $k) / ($px - $h)**2;
+
+    my $pointOnParabola= sub {
+        my $point = shift;
+        my ($x, $y) = $point->value;
+        return $y == $a * ($x - $h)**2 + $k;
+    };
+
+    for (@$student) {
+        my $nth = Value::List->NameForNumber($count++);
+        
+        $score += 1, next
+        if ($_->extract(1) eq $correct->[0]->extract(1) &&
+            $_->extract(3) == $correct->[0]->extract(3) &&
+            $_->extract(4) == $correct->[0]->extract(4) &&
+            $pointOnParabola->($_->extract(5)));
+            
+        push(@errors, "The $nth object graphed is not a parabola"),
+        next if ($_->extract(1) ne $correct->[0]->extract(1));
+
+        push(@errors, "The $nth parabola graphed should be " .
+                      $correct->[0]->extract(3)),
+        next if ($_->extract(3) ne $correct->[0]->extract(3));
+        
+        push(@errors, "The $nth parabola graphed should have vertex " .
+                      $correct->[0]->extract(4)),
+        next if ($_->extract(4) ne $correct->[0]->extract(4));
+        
+        push(@errors, "The $nth parabola graphed should not contain the point " .
+            $_->extract(5));
+    }
+
+    return ($score, @errors);
+};
+
+
+Context()->noreduce('(-x)-y');
+
+$sgn = non_zero_random(-1, 1);
+$h = non_zero_random(-5, 5);
+$k = non_zero_random(-5, 5);
+$f = Formula("$sgn*(x - $h)^2 + $k");
+
+$y1 = $f->eval(x => $h);
+$y2 = $f->eval(x => $h + 1);
+
+$gt = GraphTool("{parabola, solid, vertical, ($h, $y1), ($h + 1, $y2)}")->with(
+    cmpOptions => { list_checker => $gt_checker });
+
+BEGIN_TEXT
+
+Sketch the parabola \(y = \{$f->reduce->TeX\}\).
+$PAR
+
+\{$gt->ans_rule()\}
+
+END_TEXT
+
+ANS($gt->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.4.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.4.pg
new file mode 100644
index 0000000000..f535ecf021
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.4.pg
@@ -0,0 +1,44 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 4 - Polynomial division
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Operations on polynomial and rational expressions)
+## DBsection(Polynomials: divide)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+   "parserGraphTool.pl"
+);
+
+$a = non_zero_random(-5, 5);
+$b = non_zero_random(-5, 5);
+$c = non_zero_random(-5, 5);
+$r = non_zero_random(-5, 5);
+
+$f = Formula("x^3 + " . ($a + $b) . "x^2 + " . ($a * $b + $c) . "x + " . ($a * $c + $r));
+$g = Formula("x + $a");
+
+$q = Formula("x^2 + $b x + $c");
+
+BEGIN_TEXT
+
+Find the quotient and remainder when dividing \(\{$f->reduce->TeX\}\) by \(\{$g->reduce->TeX\}\).
+$PAR
+
+\(\{$f->reduce->TeX\}\) = \((\)\{ans_rule\}\()(\{$g->reduce->TeX\}) + \)\{ans_rule\}
+
+END_TEXT
+
+ANS($q->cmp);
+ANS(Compute($r)->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.5.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.5.pg
new file mode 100644
index 0000000000..e934c503cc
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.5.pg
@@ -0,0 +1,43 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 4 - Polynomial division
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Polynomial equations and functions)
+## DBsection(Polynomial equations)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl"
+);
+
+$a = non_zero_random(-5, 5);
+do {$b = random(1, 5)} until (abs($a) != $b);
+
+# (x - a)(x - b)(x + b)
+$f = Formula("x^3 - $a x^2 - " . $b**2 . "x + " . ($a * $b**2));
+
+$roots = List($a, $b, -$b);
+
+BEGIN_TEXT
+
+Solve the cubic equation \(\{$f->reduce->TeX\} = 0\).
+$PAR
+
+If there are multiple solutions, then separate them with commas.
+$PAR
+
+\(x\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($roots->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.6.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.6.pg
new file mode 100644
index 0000000000..17cf3d9a07
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.6.pg
@@ -0,0 +1,68 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 4 - Polynomial division
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Polynomial equations and functions)
+## DBsection(Inequalities involving polynomials)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl"
+);
+
+$a = random(-5, -1);
+$b = random(1, 5);
+
+# x^2 * (x - a) * (x - b)
+$f = Formula("x^4 - " . ($a + $b) . "x^3 + " . ($a * $b) . "x^2");
+
+$roots = List(0, $a, $b);
+$pos = Interval("(-infinity, $a) U ($b, infinity)");
+$neg = Interval("[$a, $b]");
+
+BEGIN_TEXT
+
+Consider the quartic polynomial function \(f(x)=\{$f->reduce->TeX\}\).
+$PAR
+
+(a) Find all solutions to the equation \(f(x) = 0\).
+$PAR
+
+If there are multiple solutions, then separate them with commas.  If any solution has multiplicity greater than 1, then just enter it once.
+$PAR
+
+\(x\) = \{ans_rule\}
+$PAR
+
+(b) Find all solutions to the inequality \(f(x) > 0\).
+$PAR
+
+Give your answer in \{helpLink('interval')\} notation.
+$PAR
+
+\(x\in\) \{ans_rule\}
+$PAR
+
+(c) Find all solutions to the inequality \(f(x) \leq 0\).
+$PAR
+
+Give your answer in \{helpLink('interval')\} notation.
+$PAR
+
+\(x\in\) \{ans_rule\}
+
+END_TEXT
+
+ANS($roots->cmp);
+ANS($pos->cmp);
+ANS($neg->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.7.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.7.pg
new file mode 100644
index 0000000000..1fe4a5ab0d
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.7.pg
@@ -0,0 +1,64 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 7 - Graph of rational function
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Rational equations and functions)
+## DBsection(Graphs of rational functions)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",
+   "MathObjects.pl"
+);
+
+$a = non_zero_random(-5, 5);
+$b = non_zero_random(-5, 5);
+do {$c = non_zero_random(-5, 5)} until ($c != $a);
+
+# x^2 * (x - a) * (x - b)
+$f = Formula("($b x - " . ($b * $c) . ") / (x - $a)");
+
+BEGIN_TEXT
+
+Consider the hyperbola \(y=\{$f->reduce->TeX\}\).
+$PAR
+
+(a) Find the vertical asymptote.
+$PAR
+
+\(x\) = \{ans_rule\}
+$PAR
+
+(b) Find the horizontal asymptote.
+$PAR
+
+\(y\) = \{ans_rule\}
+$PAR
+
+(c) Find the \(x\)-intercept.
+$PAR
+
+\(x\) = \{ans_rule\}
+$PAR
+
+(d) Find the \(y\)-intercept.
+$PAR
+
+\(y\) = \{ans_rule\}
+$PAR
+
+END_TEXT
+
+ANS(Compute($a)->cmp);
+ANS(Compute($b)->cmp);
+ANS(Compute($c)->cmp);
+ANS(Compute($b * $c / $a)->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.8.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.8.pg
new file mode 100644
index 0000000000..6262ab98c5
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.8.pg
@@ -0,0 +1,64 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 8 - Evaluate logarithms
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Exponential and logarithmic expressions and functions)
+## DBsection(Logarithmic functions)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",
+   "MathObjects.pl"
+);
+
+# largest logarithm we might expect a student to do by hand
+sub max_log {
+    my $b = shift;
+    return 6 if ($b == 2);  # 2^6 = 64
+    return 4 if ($b == 3);  # 3^4 = 81
+    return 3 if ($b <= 5);  # 4^3 = 64, 5^3 = 125
+    return 2;
+}
+
+$b1 = random(2, 9);
+
+$b2 = random(2, 9);
+$e2 = random(2, max_log($b2));
+
+$b3 = random(2, 9);
+$e3 = random(2, max_log($b3));
+
+$b4 = random(2, 9);
+$e4 = random(2, max_log($b4));
+
+BEGIN_TEXT
+
+Evaluate the following logarithms.
+$PAR
+
+(a) \(\log_$b1 1\) = \{ans_rule\}
+$PAR
+
+(b) \(\log_$b2 \{$b2 ** $e2\}\)= \{ans_rule\}
+$PAR
+
+(c) \(\log_{\{$b3 ** $e3\}} $b3\) = \{ans_rule\}
+$PAR
+
+(d) \(\log_$b4\frac{1}{\{$b4 ** $e4\}}\) = \{ans_rule\}
+
+END_TEXT
+
+ANS(Compute(0)->cmp);
+ANS(Compute($e2)->cmp);
+ANS(Compute(1/$e3)->cmp);
+ANS(Compute(-$e4)->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.2.9.pg b/Contrib/Piedmont/MathPlacementTest/mpt.2.9.pg
new file mode 100644
index 0000000000..b9639bee54
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.2.9.pg
@@ -0,0 +1,42 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 2
+## Problem 9 - Logarithmic properties
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Exponential and logarithmic expressions and functions)
+## DBsection(Properties of logarithms)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",
+   "MathObjects.pl"
+);
+
+$a = random(2, 9);
+$b = random(2, 9);
+$c = random(2, 9);
+
+Context()->variables->add(y => "Real", z => "Real");
+
+$f = Compute("$a ln x + $b ln y - $c ln z");
+$ans = Compute("x^$a * y^$b / z^$c");
+
+BEGIN_TEXT
+
+Simplify the expression \(\{$f->reduce->TeX\}\) using a single logarithm.
+$PAR
+
+\(\{$f->reduce->TeX\} = \ln\Bigl(\) \{ans_rule\} \(\Bigr)\)
+
+
+END_TEXT
+
+ANS($ans->cmp);
+
+ENDDOCUMENT();
\ No newline at end of file
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.1.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.1.pg
new file mode 100644
index 0000000000..d1a470691e
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.1.pg
@@ -0,0 +1,58 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 1 - Function composition
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Functions)
+## DBsection(Compositions and combinations of functions)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$a = non_zero_random(-5, 5);
+$b = non_zero_random(-5, 5);
+$c = non_zero_random(-5, 5);
+$d = non_zero_random(-5, 5);
+
+$f = Formula("$a + $b x^2");
+$g = Formula("$c x + $d");
+
+$part_a = $f->eval(x => $g->eval(x => 0));
+$part_b = $g->eval(x => $f->eval(x => 0));
+$part_c = $f->substitute(x => $f);
+$part_d = $g->substitute(x => $g);
+
+BEGIN_TEXT
+
+Suppose \(f(x) = \{$f->reduce->TeX\}\) and \(g(x) = \{$g->reduce->TeX\}\).  Find the following
+$PAR
+
+(a) \((f\circ g)(0)\) = \{ans_rule\}
+$PAR
+
+(b) \((g\circ f)(0)\) = \{ans_rule\}
+$PAR
+
+(c) \((f\circ f)(x)\) = \{ans_rule\}
+$PAR
+
+(d) \((g\circ g)(x)\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($part_a->cmp);
+ANS($part_b->cmp);
+ANS($part_c->cmp);
+ANS($part_d->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.10.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.10.pg
new file mode 100644
index 0000000000..62a7050b6b
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.10.pg
@@ -0,0 +1,83 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 10 - Transformations of sine curve
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Triangle trigonometry)
+## DBsection(Applications of special triangles & right triangles)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+   "parserRadioButtons.pl",
+   "PGgraphmacros.pl",
+   "PGchoicemacros.pl"
+);
+
+sub func_str {
+    my ($a, $b, $c) = @_;
+    return "$a * sin(pi * x /$b) + $c";
+}
+
+sub sketch_graph {
+    my $str = shift;
+    my $gr = init_graph(-10, -10, 10, 10, axes => [0, 0], grid => [20, 20], size => [400, 400]);
+    add_functions($gr, "$str for x in <-10, 10> using color:blue");
+    return $gr;
+}
+
+$a = non_zero_random(-5, 5);
+$b = random(2, 5);
+$c = non_zero_random(-5, 5);
+
+$fstr = func_str($a, $b, $c);
+$f = Compute($fstr);
+
+@strings = ($fstr, func_str($a, $b, -$c), func_str(-$a, $b, $c), func_str(-$a, $b, -$c))[shuffle(4)];
+
+@options = ['(i)', '(ii)', '(iii)', '(iv)'];
+$correct = 0;
+while ($strings[$correct] ne $fstr) {
+    $correct++;
+}
+
+@gr = ();
+for ($i = 0; $i < 4; $i++) {
+    push(@gr, sketch_graph($strings[$i]));
+}
+
+$buttons = RadioButtons(@options, $correct);
+
+BEGIN_TEXT
+
+Identify the graph of the curve \(y = \{$f->reduce->TeX\}\).
+$PAR
+
+
+(i) \{ image(insertGraph($gr[0]), width => 400, height => 400)\}
+$PAR
+
+(ii) \{ image(insertGraph($gr[1]), width => 400, height => 400)\}
+$PAR
+
+(iii) \{ image(insertGraph($gr[2]), width => 400, height => 400)\}
+$PAR
+
+(iv) \{ image(insertGraph($gr[3]), width => 400, height => 400)\}
+$PAR
+
+\{$buttons->buttons\}
+
+END_TEXT
+
+ANS($buttons->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.2.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.2.pg
new file mode 100644
index 0000000000..46a11cf288
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.2.pg
@@ -0,0 +1,40 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 2 - Inverse functions
+##ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Functions)
+## DBsection(Compositions and combinations of functions)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$a = non_zero_random(-9, 9);
+$b = non_zero_random(-9, 9);
+$c = non_zero_random(-9, 9);
+
+$f = Formula("($a + $b x) / $c");
+$finv = Formula("($c x - $a) / $b");
+
+BEGIN_TEXT
+
+Suppose \(f(x) = \{$f->reduce->TeX\}\).  Find the inverse of \(f\).
+$PAR
+
+\(f^{-1}(x)\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($finv->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.3.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.3.pg
new file mode 100644
index 0000000000..f24074844a
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.3.pg
@@ -0,0 +1,49 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 2 - Inverse functions
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Analytic trigonometry)
+## DBsection(Using and proving basic identities)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+   "contextFraction.pl"
+);
+
+$opp = non_zero_random(-9, 9);
+$adj = non_zero_random(-9, 9);
+$hyp = sqrt($opp**2 + $adj**2);
+
+Context("Fraction");
+$tan = Compute("$opp / $adj");
+$ineq = ($opp > 0) ? ">" : "<";
+
+$cos = Compute("$adj / $hyp");
+$sin = Compute("$opp / $hyp");
+
+BEGIN_TEXT
+
+If \(\tan\theta = \{$tan->TeX\}\) and \(\sin\theta $ineq 0\), then find the following.
+$PAR
+
+(a) \(\cos\theta\) = \{ans_rule\}
+$PAR
+
+(b) \(\sin\theta\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($cos->cmp);
+ANS($sin->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.4.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.4.pg
new file mode 100644
index 0000000000..04773f0698
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.4.pg
@@ -0,0 +1,88 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 2 - Inverse functions
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Analytic trigonometry)
+## DBsection(Using and proving basic identities)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+   "contextFraction.pl"
+);
+
+Context("Fraction");
+
+sub pretty_sqrt {
+    my $x = shift;
+    if ($x == 1 || $x == 4 || $x == 9 || $x == 16) {
+        return sqrt($x);
+    } elsif ($x % 4 == 0) {
+        return "2\sqrt " . ($x / 4);
+    } elsif ($x == 18) {
+        return "3\sqrt 2";
+    } else {
+        return "\sqrt $x";
+    }
+}
+
+sub pretty_frac {
+    my $frac = shift;
+    my $sgn = shift;
+    my ($num, $den) = $frac->value;
+    my $result = "\frac{" . pretty_sqrt($num) . "}{ " . pretty_sqrt($den) . "}";
+    if ($sgn < 0) {
+        $result = "-" . $result;
+    }
+    return $result;
+}
+
+$a = random(1, 9);
+$b = random(1, 9);
+$c = $a + $b;
+
+$cossgn = non_zero_random(-1, 1);
+$sinsgn = non_zero_random(-1, 1);
+
+$cos2 = Compute("$a / $c");
+$sin2 = Compute("$b / $c");
+
+$cosstr = pretty_frac($cos2, $cossgn);
+$sinstr = pretty_frac($sin2, $sinsgn);
+
+$cos = Compute("$cossgn * sqrt($a / $c)");
+$sin = Compute("$sinsgn * sqrt($b / $c)");
+$tan = Compute("$cossgn * $sinsgn * sqrt($b / $a)");
+
+BEGIN_TEXT
+
+Suppose the angle \(\theta\) in standard position meets the unit circle at \(\left($cosstr, $sinstr\right)\).
+$PAR
+
+Find the following.
+$PAR
+
+(a) \(\cos\theta\) = \{ans_rule\}
+$PAR
+
+(b) \(\sin\theta\) = \{ans_rule\}
+$PAR
+
+(c) \(\tan\theta\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($cos->cmp);
+ANS($sin->cmp);
+ANS($tan->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.5.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.5.pg
new file mode 100644
index 0000000000..849945898c
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.5.pg
@@ -0,0 +1,44 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 2 - Inverse functions
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Analytic trigonometry)
+## DBsection(Using and proving general identities)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$a = random(1, 9);
+$b = random(1, 9);
+$c = random(1, 9);
+$d = random(1, 9);
+
+$orig = Compute("($a + $b sin x) / ($c - $d sin x)");
+
+Context()->functions->disable("Trig");
+Context()->functions->redefine("csc");
+$ans = Compute("($a csc x + $b) / ($c csc x - $d)");
+
+BEGIN_TEXT
+
+Find an expression involving only \(\csc x\) that is equal to \(\{$orig->reduce->TeX\}\).
+$PAR
+
+\(\{$orig->reduce->TeX\}\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($ans->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.6.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.6.pg
new file mode 100644
index 0000000000..2aa150e16f
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.6.pg
@@ -0,0 +1,43 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 6 - Trigonmetric identities
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Analytic trigonometry)
+## DBsection(Using and proving general identities)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$a = random(1, 9);
+$b = non_zero_random(-9, 9);
+
+$orig = Compute("($a tan x + $b cot x)^2");
+
+Context()->functions->disable("Trig");
+Context()->functions->redefine("sec");
+Context()->functions->redefine("csc");
+$ans = Compute("$a^2 (sec x)^2 + ($b)^2 (csc x)^2 - ($a - $b)^2");
+
+BEGIN_TEXT
+
+Find an expression involving only \(\sec x\) and/or \(\csc x\) that is equal to \(\{$orig->reduce->TeX\}\).
+$PAR
+
+\(\{$orig->reduce->TeX\}\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($ans->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.7.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.7.pg
new file mode 100644
index 0000000000..206f56340e
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.7.pg
@@ -0,0 +1,43 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 7 - Trigonmetric equations
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Analytic trigonometry)
+## DBsection(Solving trigonometric equations exactly)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$a = non_zero_random(-9, 9);
+do {$b = non_zero_random(-9, 9)} until ($a + $b != 0);
+
+$x = non_zero_random(-1, 1);
+
+$lhs = Compute("$b cos x + " . ($a * $x + $a + $b));
+$rhs = Compute(($a + $b) . "(cos x + 1)");
+
+$ans = Compute(-90 * ($x - 1));
+
+BEGIN_TEXT
+
+Solve \(\{$lhs->reduce->TeX\} = \{$rhs->reduce->TeX\}\), \(0^\circ \leq x < 360^\circ\).
+$PAR
+
+\(x\) = \{ans_rule\}\(^\circ\)
+
+END_TEXT
+
+ANS($ans->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.8.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.8.pg
new file mode 100644
index 0000000000..279076c259
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.8.pg
@@ -0,0 +1,45 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 8 - Trigonmetric equations
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Analytic trigonometry)
+## DBsection(Solving trigonometric equations exactly)
+## Author(Shahryar Heydari)
+## Author(Doug Torrance)
+## Institution(Piedmont)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+$a = non_zero_random(-1, 1);
+$b = random(-1, 1);
+
+$rhs = Compute(($a + 2*$b) . "sin x - " . ($a * $b));
+
+$ans1 = Compute("$a * pi/6");
+$ans2 = Compute("$b * pi/2");
+$ans = List($ans1, $ans2);
+
+BEGIN_TEXT
+
+Solve \(2\sin^2 x = \{$rhs->reduce->TeX\}\), \(-\frac{\pi}{2}\leq x \leq\frac{\pi}{2}\).
+$PAR
+
+If there are multiple solutions, then separate them with a comma.
+$PAR
+
+\(x\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($ans->cmp);
+
+ENDDOCUMENT();
diff --git a/Contrib/Piedmont/MathPlacementTest/mpt.3.9.pg b/Contrib/Piedmont/MathPlacementTest/mpt.3.9.pg
new file mode 100644
index 0000000000..4ba8cba45a
--- /dev/null
+++ b/Contrib/Piedmont/MathPlacementTest/mpt.3.9.pg
@@ -0,0 +1,38 @@
+##DESCRIPTION
+## Piedmont Math Placement Test Part 3
+## Problem 9 - Right triangle trigonometry
+##ENDDESCRIPTION
+
+## DBsubject(Trigonometry)
+## DBchapter(Triangle trigonometry)
+## DBsection(Applications of special triangles & right triangles)
+## Institution(Piedmont)
+## Author(Doug Torrance)
+
+########################################################################
+
+DOCUMENT();
+
+loadMacros(
+   "PGstandard.pl",     # Standard macros for PG language
+   "MathObjects.pl",
+);
+
+# 30/60/90 or 45/45/90 right triangle
+$angleA = 15 * random(2, 4);
+$angleB = 90 - $angleA;
+$sideAB = random(1, 20);
+$sideBC = Compute("$sideAB * sin($angleA * pi/180)");
+
+BEGIN_TEXT
+
+In a triangle \(ABC\) with \(m\angle A = $angleA^\circ\), \(m\angle B = $angleB^\circ\), and \(AB = $sideAB\), find \(BC\).
+$PAR
+
+\(BC\) = \{ans_rule\}
+
+END_TEXT
+
+ANS($sideBC->cmp);
+
+ENDDOCUMENT();