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Adding more sample problems and cleanup
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‎tutorial/sample-problems/Algebra/SimpleFactoring.pg

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## DESCRIPTION
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## Factored polynomial
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## ENDDESCRIPTION
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## DBsubject(WeBWorK)
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## DBchapter(WeBWorK tutorial)
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## DBsection(PGML tutorial 2015)
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## Date(06/01/2015)
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## Institution(Hope College)
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## Author(Paul Pearson)
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## Static(1)
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## MO(1)
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## KEYWORDS('algebra', 'factored polynomial')
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#:% name = Simple factoring
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#:% type = Sample
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#:% subject = [algebra, precalculus]
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#:% categories = [polynomial]
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#:% see_also = [FactoredPolynomial.pg, ExpandedPolynomial.pg, FactoringAndExpanding.pg]
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#:% section = preamble
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DOCUMENT();
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loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
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#:% section = setup
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#: First, we create two random roots and then create the factors. Note:
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#: the `->reduce` will help make `x-(-3)` into `x+3`. In addition, we
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#: create the expanded form of the quadratic.
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#:
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#: Note that the argument of the List call are the objects in the list,
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#: which can be any MathObjects. Here we create a list of Formulas and a list
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#: of Reals (the numbers that we use in the second list will be promoted to
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#: Real MathObjects when the List is created).
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#:
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#: If, for example, there were no real roots, we should set
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#: `$roots = List("NONE");` so that students who enter a list of roots will not
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#: receive an error message about entering the wrong type of answer. If we were
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#: to use `$roots = String("NONE");` instead, students who enter anything
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#: other than a string (e.g., a list of numbers) will receive an error message.
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#:
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#: Similarly, if there were only one root at x=4, we would use
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#: `$roots = List(4);` instead of $roots = Real(4); to avoid sending error
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#: messages to students who enter multiple answers or NONE.
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($x0, $x1) = (non_zero_random(-6, 6), non_zero_random(-6, 6));
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$factor1 = Compute("x-$x0")->reduce;
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$factor2 = Compute("x-$x1")->reduce;
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$f = Compute("x^2-($x0+$x1)x+$x0*$x1")->reduce;
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$factors = List($factor1, $factor2);
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$roots = List($x0, $x1);
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# If there were only one solution
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# $roots = List(4);
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# If there were no solutions
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# $roots = List("NONE");
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#:% section = statement
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BEGIN_PGML
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a) What are the factors of [`[$f]`]?
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Factors = [__]{$factors}
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b) What are the roots of this equation?
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Roots = [__]{$roots}
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_(Enter both answers as a comma-separated list.)_
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END_PGML
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#:% section = solution
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BEGIN_PGML_SOLUTION
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Solution explanation goes here.
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END_PGML_SOLUTION
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ENDDOCUMENT();

‎tutorial/sample-problems/Misc/EssayAnswer.pg

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# http://webworkgoehle.blogspot.com/2012/09/essay-answers-in-webwork.html
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#:% name = Essay Answer
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#:% type = Sample
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#:% type = [Sample, technique]
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#:% categories = [essay]
2020

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#:% section = preamble

‎tutorial/sample-problems/Misc/Matching.pg

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#: 'None of the above' answer that will be made last with `makeLast`.
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#: So the popup list must have 9 entries A through I.
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#:
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#: As an alternative, see PROBLINK('MatchingAlt.pl') for another way to write
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#: As an alternative, see PROBLINK('MatchingAlt.pg') for another way to write
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#: a matching problem.
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$showPartialCorrectAnswers = 0;
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‎tutorial/sample-problems/Misc/MatchingGraphs.pg

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## DESCRIPTION
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## Matching problem with graphs
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## ENDDESCRIPTION
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## DBsubject(WeBWorK)
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## DBchapter(WeBWorK tutorial)
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## DBsection(PGML tutorial 2015)
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## Date(07/15/2023)
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## Institution(Fitchburg State University)
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## Author(Peter Staab)
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## MO(1)
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## KEYWORDS('matching', 'dynamic graph')
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#:% name = Matching Problem with Graphs
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#:% type = Sample
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#:% subject = [algebra, precalculus]
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#:% categories = [graph]
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#:% section = preamble
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#: The dynamic graph is generated with `PGtikz.pl`, so this is needed.
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#: The matching is done with popups, so `parserPopUp.pl` is need and lastly
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#: a `LayoutTable` is used from `niceTables.pl`.
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DOCUMENT();
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loadMacros(
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'PGstandard.pl', 'PGML.pl', 'PGtikz.pl', 'parserPopUp.pl',
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'niceTables.pl', 'PGcourse.pl'
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);
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#:% section = setup
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#: The array `@all_plots` contains the display form (f) of the function,
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#: the functional form (form) of the function needed in tikz format,
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#: the domain of the function and the alterative text.
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#:
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#: The graphs of all plots and then created by calling commands from `PGtikz.pl`.
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#: See PROBLINK('DynamicGraph.pg') for a simpler example using tikz. Note
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#: that alternate text is provided to the `image` command and for accessibility
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#: should always be considered and this should be provided.
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#:
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#: The dropdowns are created in the `@dropdown` array which pulls all
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#: options.
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#:
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#: The `LayoutTable` is used to make an accessible table that is nicely
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#: laid out.
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#:
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#: Although this matching problem creates graphs dynamically, these can use
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#: static images by changing the call to `image` to just pass in the
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#: image names.
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@all_plots = (
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{
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f => 'x^2',
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form => '\x*\x',
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domain => '-3:3',
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alt =>
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'A graph of a curve with a minimum at the origin and opening '
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. 'upward.'
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},
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{
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f => 'e^x',
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form => 'exp(\x)',
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domain => '-6:3',
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alt => 'A graph of a curve starting near the negative x axis and '
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. 'rising steeply toward the first quadrant.'
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},
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{
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f => 'x^3',
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form => '\x*\x*\x',
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domain => '-2:2',
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alt => 'A graph of a curve from the third quadrant (where is it '
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. 'concave down) to the first quadrant (where it is concave up).'
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},
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{
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f => 'ln(x)',
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form => 'ln(\x)',
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domain => '0.1:6',
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alt => 'A graph of a curve that approaches the negative y-axis '
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. 'and rises to the first quadrant and everywhere it is concave'
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. 'down.'
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},
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{
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f => '3x+2',
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form => '3*\x+2',
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domain => '-6:6',
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alt =>
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'The graph of a line from the 3rd quadrant to the first quadrant'
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},
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{
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f => 'sin(x)',
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form => 'sin(\x r)',
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domain => '-6:6',
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alt => 'A graph of a curve that osciallates and passes through the '
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. 'origin'
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},
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);
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for $i (0 .. $#all_plots) {
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my $graph = createTikZImage();
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$graph->tikzLibraries('arrows.meta');
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$graph->BEGIN_TIKZ
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\tikzset{>={Stealth[scale=1.5]}}
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\filldraw[
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draw=LightBlue,
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fill=white,
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rounded corners=10pt,
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thick,use as bounding box
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] (-7,-7) rectangle (7,7);
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\draw[->,thick] (-6,0) -- (6,0) node[above left,outer sep=3pt] {\(x\)};
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\foreach \x in {-5,...,-1,1,2,...,5}
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\draw(\x,5pt) -- (\x,-5pt) node [below] {\(\x\)};
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\draw[->,thick] (0,-6) -- (0,6) node[below right,outer sep=3pt] {\(y\)};
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\foreach \y in {-5,...,-1,1,2,...,5}
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\draw (5pt,\y) -- (-5pt,\y) node[left] {\(\y\)};
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\draw[blue,ultra thick] plot[domain=$all_plots[$i]->{domain},smooth] (\x,{$all_plots[$i]->{form}});
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END_TIKZ
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$all_plots[$i]->{graph} = $graph;
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}
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@plots = random_subset(4, @all_plots);
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# sorted list of possible answers
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$list = [ lex_sort(map {"$_->{f}"} @all_plots) ];
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@dropdowns = map { DropDown($list, "$_->{f}") } @plots;
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$tab = LayoutTable(
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[
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[
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map {
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image(
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$plots[$_]->{graph},
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width => 300,
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tex_size => 400,
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extra_html_tags => "alt = '$plots[$_]->{alt}'"
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)
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} (0 .. 1)
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],
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[ map { $dropdowns[$_]->menu } (0 .. 1) ],
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[
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map {
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image(
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$plots[$_]->{graph},
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width => 300,
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tex_size => 400,
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extra_html_tags => "alt = '$plots[$_]->{alt}'"
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)
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} (2 .. 3)
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],
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[ map { $dropdowns[$_]->menu } (2 .. 3) ]
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],
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align => 'cc'
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);
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$showPartialCorrectAnswers = 0;
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#:% section = statement
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BEGIN_PGML
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Match the graph with the formula for the graph (Click on image for a larger view.)
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[$tab]*
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END_PGML
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#:% section = answer
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#: Because the dropdowns are created in the older fashion, we use the `ANS` form
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#: to check the answer
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ANS($dropdowns[$_]->cmp) for (0 .. 3);
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#:% section = solution
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BEGIN_PGML_SOLUTION
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Solution explanation goes here.
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END_PGML_SOLUTION
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ENDDOCUMENT();

‎tutorial/sample-problems/Parametric/ParametricEquationAnswers.pg

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## DESCRIPTION
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## Check student answers that are parametric equations
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## ENDDESCRIPTION
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## DBsubject(WeBWorK)
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## DBchapter(WeBWorK tutorial)
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## DBsection(PGML tutorial 2015)
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## Date(06/01/2015)
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## Institution(Hope College)
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## Author(Paul Pearson)
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## Static(1)
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## MO(1)
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## KEYWORDS('parametric equation', 'answer checker')
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#:% name = Parametric Equation Answer Checker
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#:% type = [Sample, technique]
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#:% subject = [differential calculus]
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#:% categories = [parametric, answer]
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#:% section = preamble
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#: Since there are multiple ways to parameterize, we use the `parserMultiAnswer.pl`
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#: macro.
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DOCUMENT();
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loadMacros('PGstandard.pl', 'PGML.pl', 'parserMultiAnswer.pl', 'PGcourse.pl');
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#:% section = setup
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#: We use a `MultiAnswer()` answer checker that will verify that the students
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#: answers satisfy the equation for the circle and have the required starting
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#: and ending points. This answer checker will allow students to enter any
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#: correct parametrization. For example, both
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#: x = \cos(t), y = sin(t), 0 ≤ t ≤ pi/3 and x = cos(2t), y = sin(2t),
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#: 0 ≤ t ≤ pi/6 will be marked correct.
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#:
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#: When evaluating student's answers, it is important not to use quotes. For
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#: example, if the code were `$xstu->eval(t=>"$t1stu")` with quotes, then if a
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#: student enters pi the answer checker will interpret it as the string "pi"
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#: which will need to be converted to a MathObject Real and numerical error
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#: will be introduced in the conversion. The correct code to use is
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#: `$xstu->eval(t=>$t1stu)` without quotes so that the answer is interpreted
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#: without a conversion that may introduce error.
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#:
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#: The first if statement is fully correct, that is the parametric functions
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#: are on the unit circle and the initial and final points are correct.
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#: The other three ifelse in the answer checker has either the second point,
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#: first point or both points wrong.
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Context("Numeric")->variables->are(t => "Real");
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Context()->variables->set(t => { limits => [ -5, 5 ] });
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$x = Formula("cos(t)");
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$y = Formula("sin(t)");
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$t0 = Compute("0");
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$t1 = Compute("pi/3");
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($x0, $y0) = (1, 0);
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($x1, $y1) = (1 / 2, sqrt(3) / 2);
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$multians = MultiAnswer($x, $y, $t0, $t1)->with(
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singleResult => 0,
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checker => sub {
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my ($correct, $student, $self) = @_;
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my ($xstu, $ystu, $t0stu, $t1stu) = @{$student};
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if ((($xstu**2 + $ystu**2) == 1)
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&& (($xstu->eval(t => $t0stu)) == $x0)
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&& (($ystu->eval(t => $t0stu)) == $y0)
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&& (($xstu->eval(t => $t1stu)) == $x1)
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&& (($ystu->eval(t => $t1stu)) == $y1))
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{
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return [ 1, 1, 1, 1 ];
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} elsif ((($xstu**2 + $ystu**2) == 1)
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&& (($xstu->eval(t => $t0stu)) == $x0)
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&& (($ystu->eval(t => $t0stu)) == $y0))
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{
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return [ 1, 1, 1, 0 ];
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} elsif ((($xstu**2 + $ystu**2) == 1)
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&& (($xstu->eval(t => $t1stu)) == $x1)
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&& (($ystu->eval(t => $t1stu)) == $y1))
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{
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return [ 1, 1, 0, 1 ];
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} elsif ((($xstu**2 + $ystu**2) == 1)) {
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return [ 1, 1, 0, 0 ];
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} else {
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return [ 0, 0, 0, 0 ];
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}
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}
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);
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#:% section = statement
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#: Since the correct answer depends on all answer blanks, the MathObject
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#: `$multians` is input into all answer blanks.
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BEGIN_PGML
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Find a parametrization of the unit circle from the point
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[` \big(1,0\big) `] to [` \big(\frac{1}{2},\frac{\sqrt{3}}{2}\big) `].
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Use [` t `] as the parameter for your answers.
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[` x(t) = `] [__]{$multians}
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[` y(t) = `] [__]{$multians}
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for [__]{$multians} to [__]{$multians}.
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END_PGML
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#:% section = solution
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BEGIN_PGML_SOLUTION
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Solution explanation goes here.
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END_PGML_SOLUTION
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ENDDOCUMENT();

‎tutorial/sample-problems/Parametric/PolarGraph.pg

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## KEYWORDS('parametric', 'graph polar curve')
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#:% name = Polar Graph
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#:% type = Sample
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#:% type = [sample, technique]
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#:% subject = parametric
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#:% section = preamble

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