Difference between revisions of "Category:Subject Area Templates"

Complete Problem Authoring Templates by Subject Area

Miscellaneous Templates

• Answer is a number or a function. The most commonly used template file.
• Answer is a function with domain issues. We show how to set the domain and test points for evaluation and give customized answer hints. (Uses answerHints.pl)
• 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.
• An essay question paired with a multiple choice popup. There is a menu of choices followed by an essay answer that is graded manually by the professor.
• 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 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 any solution to an equation. Checks whether the student answer is a solution to an equation. (Uses parserSolutionFor.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 1. 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 2. 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)
• Linear approximation. Gives hints to students who enter a number instead of an equation for a line. (Uses answerHints.pl and parserAssignment.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. (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)
• Volume of solids of revolution 1. Requires students to set up an integral and the answer blanks are weighted. (Uses weightedGrader.pl)
• Volume of solids of revolution 2. Requires students to set up an integral, the answer blanks are weighted, and the final answer provides full credit. (Uses weightedGrader.pl)
• Volume of solids of revolution 3. Requires students to set up an integral and all answers must be correct for any credit to be awarded.

Sequences and Series

• Answer is an ordered list. The answer is a sequence of numbers.
• 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.
• Series tests. Requiring students to justify their answers for a series test. (Uses parserMultiAnswer.pl, PGgraders.pl, and unionTables.pl)

Parametric Equations and Vector Parametric Equations

• Graphing a parametric curve in 2D. Plotting a polar curve in the plane.
• Graphing a parametric curve in 3D. Plotting a parametric curve in 3D space. (Uses LiveGraphicsParametricCurve3D.pl)
• Graphing a parametric surface in 3D. Plotting a parametric surface in 3D space. (Uses LiveGraphicsParametricSurface3D.pl)
• Answer is a parametric curve in space. Uses three separate answer blanks that are controlled by MultiAnswer. (Uses parserMultiAnswer.pl)
• Answer is a vector parametric curve in the plane. Requires students to enter a vector parametric curve with correct domain. (Uses parserMultiAnswer.pl and parserVectorUtils.pl)
• Answer involves a vector parametric curve and its derivatives. Shows how to get the components of a vector-valued function, and uses a custom answer checker. (Uses parserVectorUtils.pl)
• Answer is a vector parametric line. Shows how to require a particular parametrization or allow any parametrization. (Uses parserVectorUtils.pl and parserParametricLine.pl)

Multivariable Differential Calculus

• Answer is an equation for a line (in 2D) or a plane (in 3D). The answer can be any linear (affine) equation. (Uses parserImplicitPlane.pl)
• Contour plots. Shows how to construct a contour plot with a color gradient and labeled contours.
• Interactive 3D graph of a function in rectangular coordinates. Uses LiveGraphics3D Java applet to display an interactive graph. (Uses LiveGraphicsRectangularPlot3D.pl)
• Interactive 3D graph of a function in cylindrical coordinates. Uses LiveGraphics3D Java applet to display an interactive graph. (Uses LiveGraphicsCylindricalPlot3D.pl)

Multivariable Integral Calculus

• Setting up a double integral. Allows a double integral to be set up in either order. (Uses parserMultiAnswer.pl)

Vector Calculus

• Vector operations. Dot product, cross product, length, unit vectors, parallel vectors. (Uses parserVectorUtils.pl and unionLists.pl)
• Graphing a vector field in 2D. Plotting a vector field in the plane. (Uses PGgraphmacros.pl and VectorField2D.pl)
• Graphing a vector field in 3D. Plotting a vector field in space. (Uses LiveGraphicsVectorField3D.pl)

Differential Equations

• Using the Heaviside step function We show how to evaluate answers involving the Heaviside step function. (Uses parserFunction.pl)
• Graphing a slope field.
• 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

Linear Algebra

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

Complex Analysis

Miscellaneous Topics

• HTML iframe embedded content. A Google slideshow embedded using an iframe.
• 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

Graphing

• Dynamically generated graph. A dynamically generated graph placed side-by-side with text. (Uses PGgraphmacros.pl and unionTables.pl)
• 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)
• Interactive GeoGebra applet for the Fundamental Theorem of Calculus. Shows how to construct and include a GeoGebra (Java) applet. (Uses AppletObjects.pl)
• Graphing a parametric curve in 2D. Plotting a polar curve in the plane.
• Graphing a parametric curve in 3D. Plotting a parametric curve in 3D space. (Uses LiveGraphicsParametricCurve3D.pl)
• Graphing a parametric surface in 3D. Plotting a parametric surface in 3D space. (Uses LiveGraphicsParametricSurface3D.pl)
• Contour plots. Shows how to construct a contour plot with a color gradient and labeled contours.
• Interactive 3D graph of a function in rectangular coordinates. Uses LiveGraphics3D Java applet to display an interactive graph. (Uses LiveGraphicsRectangularPlot3D.pl)
• Interactive 3D graph of a function in cylindrical coordinates. Uses LiveGraphics3D Java applet to display an interactive graph. (Uses LiveGraphicsCylindricalPlot3D.pl)
• Graphing a vector field in 2D. Plotting a vector field in the plane. (Uses PGgraphmacros.pl and VectorField2D.pl)
• Graphing a vector field in 3D. Plotting a vector field in space. (Uses LiveGraphicsVectorField3D.pl)

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.