Thompson Rivers University added 7 problems to Contrib

Contrib/TRU/README.md

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+Thompson Rivers University Problem Authors:
+
+Kyle Schlitt; email kschlitt@tru.ca; GitHub: kyleschlitt

Contrib/TRU/math1070/comparingSimpleCompound.pg

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+## DBsubject(Financial mathematics)
+## DBchapter(Interest)
+## DBsection(Compound interest)
+## Level(2)
+## KEYWORDS('simple interest rate', 'compound interest')
+## Author(Kyle Schlitt)
+## Institution(TRU)
+## Language(en)
+
+DOCUMENT();
+
+loadMacros(
+  'PGstandard.pl',
+  'PGML.pl',
+  'contextCurrency.pl',
+  'parserPopUp.pl'
+);
+
+Context("Currency");
+
+Context()->flags->set(
+  tolerance => 0.01,
+  tolType => "absolute",
+);
+
+# what is the compounding frequency
+@frequencies = (1,2,4,6,12,24,52,365);
+
+@compounding_type = (
+  "annually",
+  "semi-annually",
+  "quarterly",
+  "bi-monthly",
+  "monthly",
+  "semi-monthly",
+  "weekly",
+  "daily"
+);
+
+do {
+  $P = Currency(10000 + 1000 * random(0,10,1));
+  $t = random(15,20,1);
+
+  $simple_r = 0.07 + 0.01 * random(0,3,1);
+  $simple_r_percent = $simple_r * 100;
+  $compound_r = $simple_r - 0.02;
+  $compound_r_percent = $compound_r * 100;
+
+  $k = random(0,7,1);
+  $m = $frequencies[$k];
+  $m_word = @compounding_type[$k];
+
+  $n = $m*$t;
+  $i = $compound_r/$m;
+
+  $simple_amount = $P * (1 + $simple_r*$t);
+  $simple_interest = $simple_amount - $P;
+
+  $compound_amount = $P * (1 + $i)**($n);
+  $compound_interest = $compound_amount - $P;
+
+  if ($compound_amount > $simple_amount) {
+    $correct_choice = "Option #2";
+  } else { # unlikely
+    $correct_choice = "Option #1";
+  }
+
+  $final_choice = DropDown(
+    ["Option #1", "Option #2"],
+    $correct_choice,
+    placeholder => "Select One"
+  );
+
+} while ($compound_amount == $simple_amount);
+
+BEGIN_PGML
+
+You plan to invest [$P] in a retirement fund for [$t] years, and you are offered two investment options:
+
+**Option #1:** Simple interest at an annual rate of [$simple_r_percent]%.
+
+**Option #2:** Compound interest at an annual rate of [$compound_r_percent]%, compounded [$m_word].
+
+How much interest will each investment option yield?  After comparing the two plans, which option should be chosen?
+
+----
+
+**Answer**:
+
+Under simple interest, the investment will earn [_]{$simple_interest} in interest, growing to a total of [_]{$simple_amount}.
+
+Under compound interest, the investment will earn [_]{$compound_interest} in interest, growing to a total of [_]{$compound_amount}.
+
+[_]{$final_choice} should be chosen.
+
+END_PGML
+
+ENDDOCUMENT();

Contrib/TRU/math1070/convenienceStore.pg

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+## DBsubject(Algebra)
+## DBchapter(Linear equations and functions)
+## DBsection(Applications and models)
+## Level(2)
+## KEYWORDS('supply', 'demand', 'price')
+## Author(Kyle Schlitt)
+## Institution(TRU)
+## Language(en)
+
+DOCUMENT();
+
+loadMacros(
+  "PGstandard.pl",
+  "PGML.pl",
+  "contextCurrency.pl",
+  "parserImplicitEquation.pl"
+);
+
+$slope_num = -(1 + random(5,20,1));
+$slope_den = 100;
+$m = $slope_num/$slope_den;
+
+$data_q_1 = random(10,20,1);
+$data_p_1 = 4 + 0.01*random(0,50,1);
+
+$b = $data_p_1 - $m*$data_q_1;
+$q_intercept = $data_q_1 - $data_p_1/$m;
+
+$data_q_2 = $data_q_1 + random(4,10,1);
+$data_p_2 = $slope_num/$slope_den*($data_q_2 - $data_q_1) + $data_p_1;
+
+$target_quantity = int($data_q_2 + int(($q_intercept - $data_q_2)/random(2,3,1)));
+
+$target_price = $m*($target_quantity - $data_q_2) + $data_p_2;
+
+$specified_price = -1;
+
+while ($specified_price < 0 || $specified_price == $target_price) {
+  $random_multiplier = random(5,15,1);
+  $specified_quantity = $data_q_2 + $random_multiplier;
+  $specified_price = $data_p_2 + $m * $random_multiplier;
+}
+
+Context("Currency");
+
+BEGIN_PGML
+
+A store-owner is marketing a brand new energy drink at a local convenience store.  He observes that [`[$data_q_1]`] cans per day are sold if the price per can is set to [`[@ Currency($data_p_1) @]`], but [`[$data_q_2]`] cans per day are sold if the price is set at [`[@ Currency($data_p_2) @]`] per can.
+
+Assuming there is a linear relationship between
+
+* [`p =`] the price per can, and
+* [`q =`] the number of cans sold per day,
+
+find the demand equation, expressed as a relationship between the variables [`p`] and [`q`].
+
+END_PGML
+
+Context("ImplicitEquation");
+
+Context()->variables->add(q => 'Real', p => 'Real');
+
+Context()->variables->set(
+  q => { limits => [-10,10]},
+  p => { limits => [-10,10]}
+);
+
+$demand_equation = ImplicitEquation("p=$m*q + $b");
+
+BEGIN_PGML
+
+**Answer:** [_]{$demand_equation}
+
+----
+
+END_PGML
+
+Context("Currency");
+
+BEGIN_PGML
+
+What should the price be set to in order to sell [`[$target_quantity]`] cans per day -- be sure to include units!
+
+**Answer:** The price should be set to [_]{Currency($target_price)} per can.
+
+----
+
+If the price per can is set to [`[@ Currency($specified_price) @]`], how many cans should the store-owner expect to sell per day?
+
+**Answer:** The store will sell [_]{$specified_quantity} cans per day.
+
+END_PGML
+
+ENDDOCUMENT();

Contrib/TRU/math1070/domainInterceptsRationalFunction.pg

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+## DBsubject(Algebra)
+## DBchapter(Functions)
+## DBsection(Graphs)
+## Level(2)
+## KEYWORDS('domain', 'range', 'intercepts', 'rational function', 'rational functions')
+## Author(Kyle Schlitt)
+## Institution(TRU)
+## Language(en)
+
+DOCUMENT();
+
+loadMacros(
+  "PGstandard.pl",
+  "PGML.pl",
+  "parserMultiAnswer.pl",
+  "parserPopUp.pl",
+  "contextFraction.pl"
+);
+
+Context("Fraction");
+
+# choose the x-intercepts of f
+$xintercept1num = random(1,4,1);
+$xintercept1den = 5;
+$xintercept1 = Fraction($xintercept1num, $xintercept1den)->reduce;
+
+$xintercept2 = random(2,5);
+
+# build the numerator of f so it has the desired xintercepts
+$f_num_a = $xintercept1den;
+$f_num_b = -($xintercept1den*$xintercept2 + $xintercept1num);
+$f_num_c = $xintercept1num*$xintercept2;
+$f_num = Compute("$f_num_a x^2 + $f_num_b x + $f_num_c")->reduce;
+
+# choose the points at which f will not be defined
+$singularity1 = random(5,9,1);
+
+do {
+  $singularity2 = random(1,7,1);
+} while ($singularity2 == $singularity1);
+
+# build the denominator of f so it has the desired singularities
+$f_den_a = 1;
+$f_den_b = -($singularity1 + $singularity2);
+$f_den_c = $singularity1*$singularity2;
+
+$f_den = Compute("$f_den_a x^2 + $f_den_b x + $f_den_c")->reduce;
+
+$f = $f_num/$f_den;
+
+$popup = DropDown(['a polynomial', 'a rational function', 'an exponential function', 'a quadratic function'], 'a rational function', placeholder => 'Select One');
+
+BEGIN_PGML
+
+Consider the function [`f(x) = \displaystyle{[$f]}`].
+
+What type of function is [`f`]? 
+
+**Answer:** [`f`] is [_]{$popup}.
+----
+
+END_PGML
+
+Context("Interval");
+
+$a = 0;$b = 0;
+
+if ($singularity1 < $singularity2) {
+  $a = $singularity1; $b = $singularity2;
+} else {
+  $a = $singularity2; $b = $singularity1;
+}
+
+$domain = Union("(-infinity, $a) U ($a, $b) U ($b, infinity)");
+
+BEGIN_PGML
+
+What is the domain of [`f`]?  Express your answer using interval notation.
+
+**Answer:** [`\text{dom}(f)=`] [_]{$domain}
+
+----
+
+END_PGML
+
+$intercepts = MultiAnswer($xintercept1, $xintercept2)->with(
+  singleResult => 0,
+  checker => sub {
+    my ($correct, $student, $self) = @_;
+    my ($x1stu, $x2stu) = @{$student};
+    my ($x1, $x2) = @{$correct};
+
+    if (($x1 == $x1stu && $x2 == $x2stu) || ($x1 == $x2stu && $x2 == $x1stu)) {
+      return [1,1];
+    } elsif ($x1 == $x1stu || $x2 == $x1stu) {
+      return [1,0];
+    } elsif ($x1 == $x2stu || $x2 == $x2stu) {
+      return [0,1];
+    } else {
+      return [0,0];
+    }
+  }
+);
+
+BEGIN_PGML
+
+What are the [`x`]-intercepts of the graph of [`f`]?
+
+**Answer:** [`x =`] [_]{$intercepts} and [`x = `] [_]{$intercepts}
+
+----
+END_PGML
+
+Context("Fraction");
+
+$yintercept = Fraction("$f_num_c/$f_den_c")->reduce;
+
+BEGIN_PGML
+
+What is the [`y`]-intercept of the graph of [`f`]?
+
+**Answer:** [`y =`] [_]{$yintercept}
+
+END_PGML
+
+ENDDOCUMENT();