SubjectAreaTemplates

Any additions to the problems below should use the format of the full problem template. Also, your example should illustrate the technique without giving away the answer to an existing WeBWorK question.

Complete Problem Authoring Templates by Subject Area

This page has complete examples of problem templates organized by subject area. Within each subject, we give an explicit and brief description of the essential characteristics of each type of question. To keep overlap to a minimum, we try to give an example of each problem technique exactly once, which means you may need to look for a particular problem technique under other subject headings until you find it. We try to give a fairly complete list of techniques, rather than a complete list of types of questions that one might ask in each subject. All of these questions exist in the National Problem Library (NPL) at NationalProblemLibrary/FortLewis/Authoring/Templates/ A detailed list of code snippets for specific problem techniques has it's own category: index of problem techniques.

Miscellaneous

• Answer is a number or a function. The most commonly used template file.
• A multiple choice question with radio buttons. There is only one correct answer and all choices are shown.
• A multiple choice question with a popup menu. There is only one correct answer and the choices are hidden until the menu is clicked on.
• A multiple choice question with checkboxes. There is possibly more than one correct answer and all choices are shown.
• A list of many multiple choice questions with popup menus. For several multiple choice questions that share common answers. (Uses PGgraders.pl)
• A matching question with popup menus. A matching question in two-column format. (Uses unionTables.pl and PGgraders.pl)

Algebra

• Answer is a fraction (rational number). This question requires students to simplify their answer. (Uses contextFraction.pl)
• Answer is an algebraic fraction. Uses two answer blanks for the fraction and requires students simplify their answer. (Uses parserMultiAnswer.pl)
• Answer blank in the exponent. For questions about simplifying exponents.
• Answer is a an equation that defines a function. The answer is an equation of the form y = f(x). (Uses parserAssignment.pl)
• Answer is an equation that implicitly defines a function. An equation for a circle. (Uses parserImplicitEquation.pl)
• Answer is an inequality. Standard solve an inequality question. (Uses contextInequalities.pl)
• Answer is a fully expanded and simplified polynomial. Multiplying two linear terms together and collecting like terms. (Uses contextLimitedPolynomial.pl)
• Answer is a factored polynomial. Standard factoring a quadratic question. (Uses contextPolynomialFactors.pl and contextLimitedPowers.pl)
• Multiple answers that can be entered in any order. Factoring using separate answer blanks and the unordered answer checker. (Uses unorderedAnswer.pl)

Trigonometry

• Answers that are periodic. The student answer is evaluated modulo the period.
• Disabling functions so students must simplify answers. Unit circle trig question requiring students enter fractional answers. (Uses contextFraction.pl)
• Trig functions in degrees. Trig functions are redefined to be in degrees.
• Requiring trig identities be used. Cleverly redefining functions so that students must apply trig identities.
• Proving trig identities. A multi-part question that walks students through proving a trig identity. All parts are revealed sequentially and shown on the same page.
• Proving trig identities. The same multi-part question, but with each part shown on its own page. (Uses compoundProblem.pl)

Precalculus

• Dynamically generated graph. A randomized graph generated that is placed side-by-side with text. (Uses PGgraphmacros.pl and unionTables.pl)
• Function decomposition. Write a given function as a composition of two non-identity functions. (Uses answerComposition.pl)
• Table of values for a function. Fill in a table of values for a function.
• Answer could be a string, or a number, or a function, etc. For when a single answer could be a string or one of several other data types.
• Answer is a function up to multiplication. Answer is any quadratic with the specified roots. Uses a custom answer checker and adaptive parameters.
• Answer is a point or list of points. Finding the x-intercepts and y-intercepts of function, with lists of points as answers. (Uses contextLimitedPoint.pl)

Differential Calculus

• Differentiating and evaluating a function. Differentiating functions and controlling how they are evaluated and answers are displayed. (Uses unionLists.pl)
• Answer is a difference quotient. Students are required to simplify their difference quotient. (Uses parserDifferenceQuotient.pl)

Integral Calculus

• Dynamically generated graphs with Riemann sums. Has graphs with shaded (filled) regions. (Uses weightedGrader.pl and PGgraphmacros.pl)
• Find the area of the shaded region. A dynamically generated graph with a shaded region.
• Indefinite integrals and general antiderivatives. Checks whether a student's answer differs from the correct answer by a constant. (Uses parserFormulaUpToConstant.pl)
• Interactive GeoGebra applet for the Fundamental Theorem of Calculus. Shows how to construct and include a GeoGebra (Java) applet. (Uses AppletObjects.pl)
• Answer blanks in the limits of integration. Uses tables cleverly to put answer blanks into the limits of integration. (Uses PGunion.pl and answerHints.pl)
• Integral of 1/x and domain issues.
• Sequences and recursively defined functions. We add a named function (dummy function) to the context for a recursively defined function. (Uses parserFunction.pl)
• Sequences with explicit formulas. Restricts the domain of the formula to positive integers to avoid errors in answer evaluation.

Links to Documentation

• MathObjects documentation Written by Davide Cervone
• POD documentation (POD - Plain Old Documentation)
• PG macro files Source code for pg/macros files.
• PG library files Source code for pg/lib files.