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Merge pull request #1288 from kyleschlitt/main
Thompson Rivers University added 7 problems to Contrib
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‎Contrib/TRU/README.md‎

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Thompson Rivers University Problem Authors:
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Kyle Schlitt; email [email protected]; GitHub: kyleschlitt

‎Contrib/TRU/math1070/comparingSimpleCompound.pg‎

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

‎Contrib/TRU/math1070/convenienceStore.pg‎

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

‎Contrib/TRU/math1070/domainInterceptsRationalFunction.pg‎

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

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