Adding more sample problems and cleanup

tutorial/sample-problems/Algebra/SimpleFactoring.pg

@@ -0,0 +1,77 @@
+## DESCRIPTION
+## Factored polynomial
+## ENDDESCRIPTION
+
+## DBsubject(WeBWorK)
+## DBchapter(WeBWorK tutorial)
+## DBsection(PGML tutorial 2015)
+## Date(06/01/2015)
+## Institution(Hope College)
+## Author(Paul Pearson)
+## Static(1)
+## MO(1)
+## KEYWORDS('algebra', 'factored polynomial')
+
+#:% name = Simple factoring
+#:% type = Sample
+#:% subject = [algebra, precalculus]
+#:% categories = [polynomial]
+#:% see_also = [FactoredPolynomial.pg, ExpandedPolynomial.pg, FactoringAndExpanding.pg]
+
+#:% section = preamble
+DOCUMENT();
+
+loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
+#:% section = setup
+#: First, we create two random roots and then create the factors.  Note:
+#: the `->reduce` will help make `x-(-3)` into `x+3`.  In addition, we
+#: create the expanded form of the quadratic.
+#:
+#: Note that the argument of the List call are the objects in the list,
+#: which can be any MathObjects. Here we create a list of Formulas and a list
+#: of Reals (the numbers that we use in the second list will be promoted to
+#: Real MathObjects when the List is created).
+#:
+#: If, for example, there were no real roots, we should set
+#: `$roots = List("NONE");` so that students who enter a list of roots will not
+#: receive an error message about entering the wrong type of answer. If we were
+#: to use `$roots = String("NONE");` instead, students who enter anything
+#: other than a string (e.g., a list of numbers) will receive an error message.
+#:
+#: Similarly, if there were only one root at x=4, we would use
+#: `$roots = List(4);` instead of $roots = Real(4); to avoid sending error
+#: messages to students who enter multiple answers or NONE.
+($x0, $x1) = (non_zero_random(-6, 6), non_zero_random(-6, 6));
+$factor1 = Compute("x-$x0")->reduce;
+$factor2 = Compute("x-$x1")->reduce;
+$f       = Compute("x^2-($x0+$x1)x+$x0*$x1")->reduce;
+$factors = List($factor1, $factor2);
+$roots   = List($x0,      $x1);
+
+# If there were only one solution
+# $roots = List(4);
+
+# If there were no solutions
+# $roots = List("NONE");
+
+#:% section = statement
+BEGIN_PGML
+a) What are the factors of [`[$f]`]?
+
+    Factors = [__]{$factors}
+
+
+b) What are the roots of this equation?
+
+    Roots = [__]{$roots}
+
+_(Enter both answers as a comma-separated list.)_
+
+END_PGML
+
+#:% section = solution
+BEGIN_PGML_SOLUTION
+Solution explanation goes here.
+END_PGML_SOLUTION
+
+ENDDOCUMENT();

tutorial/sample-problems/Misc/EssayAnswer.pg

@@ -15,7 +15,7 @@
 # http://webworkgoehle.blogspot.com/2012/09/essay-answers-in-webwork.html
 
 #:% name = Essay Answer
-#:% type = Sample
+#:% type = [Sample, technique]
 #:% categories = [essay]
 
 #:% section = preamble

tutorial/sample-problems/Misc/Matching.pg

@@ -48,7 +48,7 @@ loadMacros(
 #: 'None of the above' answer that will be made last with `makeLast`.
 #: So the popup list must have 9 entries A through I.
 #:
-#: As an alternative, see PROBLINK('MatchingAlt.pl') for another way to write
+#: As an alternative, see PROBLINK('MatchingAlt.pg') for another way to write
 #: a matching problem.
 $showPartialCorrectAnswers = 0;
 

tutorial/sample-problems/Misc/MatchingGraphs.pg

@@ -0,0 +1,173 @@
+## DESCRIPTION
+## Matching problem with graphs
+## ENDDESCRIPTION
+
+## DBsubject(WeBWorK)
+## DBchapter(WeBWorK tutorial)
+## DBsection(PGML tutorial 2015)
+## Date(07/15/2023)
+## Institution(Fitchburg State University)
+## Author(Peter Staab)
+## MO(1)
+## KEYWORDS('matching', 'dynamic graph')
+
+#:% name = Matching Problem with Graphs
+#:% type = Sample
+#:% subject = [algebra, precalculus]
+#:% categories = [graph]
+
+#:% section = preamble
+#: The dynamic graph is generated with `PGtikz.pl`, so this is needed.
+#: The matching is done with popups, so `parserPopUp.pl` is need and lastly
+#: a `LayoutTable` is used from `niceTables.pl`.
+DOCUMENT();
+
+loadMacros(
+    'PGstandard.pl', 'PGML.pl', 'PGtikz.pl', 'parserPopUp.pl',
+    'niceTables.pl', 'PGcourse.pl'
+);
+
+#:% section = setup
+#: The array `@all_plots` contains the display form (f) of the function,
+#: the functional form (form) of the function needed in tikz format,
+#: the domain of the function and the alterative text.
+#:
+#: The graphs of all plots and then created by calling commands from `PGtikz.pl`.
+#: See PROBLINK('DynamicGraph.pg') for a simpler example using tikz. Note
+#: that alternate text is provided to the `image` command and for accessibility
+#: should always be considered and this should be provided.
+#:
+#: The dropdowns are created in the `@dropdown` array which pulls all
+#: options.
+#:
+#: The `LayoutTable` is used to make an accessible table that is nicely
+#: laid out.
+#:
+#: Although this matching problem creates graphs dynamically, these can use
+#: static images by changing the call to `image` to just pass in the
+#: image names.
+@all_plots = (
+    {
+        f      => 'x^2',
+        form   => '\x*\x',
+        domain => '-3:3',
+        alt    =>
+            'A graph of a curve with a minimum at the origin and opening '
+            . 'upward.'
+    },
+    {
+        f      => 'e^x',
+        form   => 'exp(\x)',
+        domain => '-6:3',
+        alt    => 'A graph of a curve starting near the negative x axis and '
+            . 'rising steeply toward the first quadrant.'
+    },
+    {
+        f      => 'x^3',
+        form   => '\x*\x*\x',
+        domain => '-2:2',
+        alt    => 'A graph of a curve from the third quadrant (where is it '
+            . 'concave down) to the first quadrant (where it is concave up).'
+    },
+    {
+        f      => 'ln(x)',
+        form   => 'ln(\x)',
+        domain => '0.1:6',
+        alt    => 'A graph of a curve that approaches the negative y-axis '
+            . 'and rises to the first quadrant and everywhere it is concave'
+            . 'down.'
+    },
+    {
+        f      => '3x+2',
+        form   => '3*\x+2',
+        domain => '-6:6',
+        alt    =>
+            'The graph of a line from the 3rd quadrant to the first quadrant'
+    },
+    {
+        f      => 'sin(x)',
+        form   => 'sin(\x r)',
+        domain => '-6:6',
+        alt    => 'A graph of a curve that osciallates and passes through the '
+            . 'origin'
+    },
+);
+
+for $i (0 .. $#all_plots) {
+    my $graph = createTikZImage();
+    $graph->tikzLibraries('arrows.meta');
+    $graph->BEGIN_TIKZ
+    \tikzset{>={Stealth[scale=1.5]}}
+    \filldraw[
+        draw=LightBlue,
+        fill=white,
+        rounded corners=10pt,
+        thick,use as bounding box
+    ] (-7,-7) rectangle (7,7);
+    \draw[->,thick] (-6,0) -- (6,0) node[above left,outer sep=3pt] {\(x\)};
+    \foreach \x in {-5,...,-1,1,2,...,5}
+        \draw(\x,5pt) -- (\x,-5pt) node [below] {\(\x\)};
+    \draw[->,thick] (0,-6) -- (0,6) node[below right,outer sep=3pt] {\(y\)};
+    \foreach \y in {-5,...,-1,1,2,...,5}
+        \draw (5pt,\y) -- (-5pt,\y) node[left] {\(\y\)};
+    \draw[blue,ultra thick] plot[domain=$all_plots[$i]->{domain},smooth] (\x,{$all_plots[$i]->{form}});
+END_TIKZ
+    $all_plots[$i]->{graph} = $graph;
+}
+
+@plots = random_subset(4, @all_plots);
+
+# sorted list of possible answers
+$list = [ lex_sort(map {"$_->{f}"} @all_plots) ];
+
+@dropdowns = map { DropDown($list, "$_->{f}") } @plots;
+
+$tab = LayoutTable(
+    [
+        [
+            map {
+                image(
+                    $plots[$_]->{graph},
+                    width           => 300,
+                    tex_size        => 400,
+                    extra_html_tags => "alt = '$plots[$_]->{alt}'"
+                )
+            } (0 .. 1)
+        ],
+        [ map { $dropdowns[$_]->menu } (0 .. 1) ],
+        [
+            map {
+                image(
+                    $plots[$_]->{graph},
+                    width           => 300,
+                    tex_size        => 400,
+                    extra_html_tags => "alt = '$plots[$_]->{alt}'"
+                )
+            } (2 .. 3)
+        ],
+        [ map { $dropdowns[$_]->menu } (2 .. 3) ]
+
+    ],
+    align => 'cc'
+);
+
+$showPartialCorrectAnswers = 0;
+
+#:% section = statement
+BEGIN_PGML
+Match the graph with the formula for the graph (Click on image for a larger view.)
+
+[$tab]*
+END_PGML
+
+#:% section = answer
+#: Because the dropdowns are created in the older fashion, we use the `ANS` form
+#: to check the answer
+ANS($dropdowns[$_]->cmp) for (0 .. 3);
+
+#:% section = solution
+BEGIN_PGML_SOLUTION
+Solution explanation goes here.
+END_PGML_SOLUTION
+
+ENDDOCUMENT();

tutorial/sample-problems/Parametric/ParametricEquationAnswers.pg

@@ -0,0 +1,111 @@
+## DESCRIPTION
+## Check student answers that are parametric equations
+## ENDDESCRIPTION
+
+## DBsubject(WeBWorK)
+## DBchapter(WeBWorK tutorial)
+## DBsection(PGML tutorial 2015)
+## Date(06/01/2015)
+## Institution(Hope College)
+## Author(Paul Pearson)
+## Static(1)
+## MO(1)
+## KEYWORDS('parametric equation', 'answer checker')
+
+#:% name = Parametric Equation Answer Checker
+#:% type = [Sample, technique]
+#:% subject = [differential calculus]
+#:% categories = [parametric, answer]
+
+#:% section = preamble
+#: Since there are multiple ways to parameterize, we use the `parserMultiAnswer.pl`
+#: macro.
+DOCUMENT();
+
+loadMacros('PGstandard.pl', 'PGML.pl', 'parserMultiAnswer.pl', 'PGcourse.pl');
+
+#:% section = setup
+#: We use a `MultiAnswer()` answer checker that will verify that the students
+#: answers satisfy the equation for the circle and have the required starting
+#: and ending points. This answer checker will allow students to enter any
+#: correct parametrization. For example, both
+#: x = \cos(t), y = sin(t), 0 ≤ t ≤ pi/3 and x = cos(2t), y = sin(2t),
+#: 0 ≤ t ≤ pi/6 will be marked correct.
+#:
+#: When evaluating student's answers, it is important not to use quotes. For
+#: example, if the code were `$xstu->eval(t=>"$t1stu")` with quotes, then if a
+#: student enters pi the answer checker will interpret it as the string "pi"
+#: which will need to be converted to a MathObject Real and numerical error
+#: will be introduced in the conversion. The correct code to use is
+#: `$xstu->eval(t=>$t1stu)` without quotes so that the answer is interpreted
+#: without a conversion that may introduce error.
+#:
+#: The first if statement is fully correct, that is the parametric functions
+#: are on the unit circle and the initial and final points are correct.
+#: The other three ifelse in the answer checker has either the second point,
+#: first point or both points wrong.
+Context("Numeric")->variables->are(t => "Real");
+Context()->variables->set(t => { limits => [ -5, 5 ] });
+
+$x  = Formula("cos(t)");
+$y  = Formula("sin(t)");
+$t0 = Compute("0");
+$t1 = Compute("pi/3");
+
+($x0, $y0) = (1, 0);
+($x1, $y1) = (1 / 2, sqrt(3) / 2);
+
+$multians = MultiAnswer($x, $y, $t0, $t1)->with(
+    singleResult => 0,
+    checker      => sub {
+        my ($correct, $student, $self) = @_;
+        my ($xstu, $ystu, $t0stu, $t1stu) = @{$student};
+        if ((($xstu**2 + $ystu**2) == 1)
+            && (($xstu->eval(t => $t0stu)) == $x0)
+            && (($ystu->eval(t => $t0stu)) == $y0)
+            && (($xstu->eval(t => $t1stu)) == $x1)
+            && (($ystu->eval(t => $t1stu)) == $y1))
+        {
+            return [ 1, 1, 1, 1 ];
+
+        } elsif ((($xstu**2 + $ystu**2) == 1)
+            && (($xstu->eval(t => $t0stu)) == $x0)
+            && (($ystu->eval(t => $t0stu)) == $y0))
+        {
+            return [ 1, 1, 1, 0 ];
+
+        } elsif ((($xstu**2 + $ystu**2) == 1)
+            && (($xstu->eval(t => $t1stu)) == $x1)
+            && (($ystu->eval(t => $t1stu)) == $y1))
+        {
+            return [ 1, 1, 0, 1 ];
+
+        } elsif ((($xstu**2 + $ystu**2) == 1)) {
+            return [ 1, 1, 0, 0 ];
+
+        } else {
+            return [ 0, 0, 0, 0 ];
+        }
+    }
+);
+#:% section = statement
+#: Since the correct answer depends on all answer blanks, the MathObject
+#: `$multians` is input into all answer blanks.
+BEGIN_PGML
+Find a parametrization of the unit circle from the point
+[` \big(1,0\big) `] to [` \big(\frac{1}{2},\frac{\sqrt{3}}{2}\big) `].
+Use [` t `] as the parameter for your answers.
+
+[` x(t) = `] [__]{$multians}
+
+[` y(t) = `] [__]{$multians}
+
+for [__]{$multians} to [__]{$multians}.
+END_PGML
+
+#:% section = solution
+BEGIN_PGML_SOLUTION
+Solution explanation goes here.
+END_PGML_SOLUTION
+
+ENDDOCUMENT();

tutorial/sample-problems/Parametric/PolarGraph.pg

@@ -12,7 +12,7 @@
 ## KEYWORDS('parametric', 'graph polar curve')
 
 #:% name = Polar Graph
-#:% type = Sample
+#:% type = [sample, technique]
 #:% subject = parametric
 
 #:% section = preamble