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 Templates

• 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)
• Answers can be entered into several answer blanks in any order. Factoring using separate answer blanks and the unordered answer checker. (Uses unorderedAnswer.pl)
• Answer must be simplified using laws of logarithms. Typical laws of logarithms question that disables certain operations so students must simplify their answer.

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

• Domain and range of a function. Requires students to enter answers as inequalities using correct variables. (Uses contextInequalities.pl)
• Dynamically generated graph. A dynamically generated graph 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)
• Scaling and translating functions. Adding a named function to the context for a scaling and translating question. (Uses parserFunction.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 number or formula with units. A velocity question with units. (uses parserNumberWithUnits.pl and parserFormulaWithUnits.pl)
• Answer is a difference quotient. Students are required to simplify their difference quotient. (Uses parserDifferenceQuotient.pl)
• Numbers, parameters, constants, variables: http://webwork.maa.org/moodle/mod/forum/discuss.php?d=456

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. (Uses PGgraphmacros.pl and unionTables.pl)
• 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)
• Integrals that have domain issues.
• Volume of solids of revolution. (Uses weightedGrader.pl)

Sequences

• 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.
• Answer is an ordered list.

Multivariable Differential Calculus

• Answer is an equation for a plane (Uses parserImplicitPlane.pl)

Differential Equations

• General solutions to ODEs with arbitrary constants. http://webwork.maa.org/moodle/mod/forum/discuss.php?d=378 and http://webwork.maa.org/moodle/mod/forum/discuss.php?d=324
• Primes in formulas http://webwork.maa.org/moodle/mod/forum/discuss.php?d=442
• Using the Heaviside step function http://webwork.maa.org/moodle/mod/forum/discuss.php?d=458

Linear Algebra

• Matrices and matrix operations http://webwork.maa.org/moodle/mod/forum/discuss.php?d=354

Miscellaneous Topics

• Chemistry http://webwork.maa.org/moodle/mod/forum/discuss.php?d=449
• JavaScript graphing http://webwork.maa.org/moodle/mod/forum/discuss.php?d=431
• HTML input for dynamic problem adjustments http://webwork.maa.org/moodle/mod/forum/discuss.php?d=2351

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.