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A First WeBWorK Sample Problem

This sample problem shows the basic structure of a WeBWorK PG problem file and how it is constructed.

A standard WeBWorK PG file has five sections:

  1. A tagging and description section, that describes the problem for future users and authors,
  2. An initialization section, that loads required macros for the problem,
  3. A problem set-up section that sets variables specific to the problem,
  4. A text section, that gives the text that is shown to the student, and
  5. An answer and solution section, that specifies how the answer(s) to the problem is(are) marked for correctness, and gives a solution that may be shown to the student after the problem set is complete.

The sample file attached to this page shows this; below the file is shown to the left, with a second column on its right that explains the different parts of the problem that are indicated above.

PG problem file Explanation
# A simple sample problem that asks students to 
# differentiate a trigonometric function.
# WeBWorK problem written by Gavin LaRose, 
# <glarose(at)umich(dot)edu>

## DBsubject('WeBWorK')
## DBchapter('Demos')
## DBsection('Problem')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
## Author('Gavin LaRose')
## Institution('UMich')

This is the tagging and description section of the problem. Note that any line that begins with a "#" character is a comment for other authors who read the problem, and is not interpreted by !WeBWorK.

The description is provided to give a quick summary of the problem so that someone reading it later knows what it does without having to read through all of the problem code.

All of the tagging information exists to allow the problem to be easily indexed. Because this is a sample problem there isn't a textbook per se, and we've used some default tagging values. There is an on-line list of current chapter and section names and a similar list of keywords. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).


This is the initialization section of the problem. The first executed line of the problem must be the DOCUMENT(); command. Note that every command must end with a semicolon.

The loadMacros command loads information that works behind the scenes. For our purposes we can usually just load the macros shown here and not worry about things further.

# make sure we're in the context we want

$a = random(2,9,1);
$trigFunc = Formula("sin($a x)");
$trigDeriv = $trigFunc->D();

This is the problem set-up section of the problem. Context("Numeric"); sets the "context", which determines how variables are interpreted. Contexts and context explanations are given on this help page.

The bulk of the set-up section defines variables that we use in the rest of the problem. All scalar variables are prefaced with a dollar sign: thus $a is a variable that has a (non-vector, non-array) value. We also define $trigFunc to be a MathObject Formula, which means that it knows things about itself, in particular, how to find its own derivative, which we find with the expression $trigFunc->D().

Find the derivative of the function \(f(x) = $trigFunc\).
\(\frac{df}{dx} = \) \{ ans_rule(35) \}

This is the text section of the problem. The TEXT(beginproblem()); line displays a header for the problem, and the Context()->texStrings line sets how formulas are displayed in the text, and we reset this after the text section. Everything between the BEGIN_TEXT and END_TEXT lines (each of which must appear alone on a line) is shown to the student.

Mathematical equations are delimited by \( \) (for inline equations) or \[ \] (for displayed equations); in these contexts inserted text is assumed to be TeX code.

There are a number of variables that set formatting: $PAR is a paragraph break (like \par in TeX). This page gives a list of variables like this. Finally, \{ \} sets off code that will be executed in the problem text. Here, ans_rule(35) is a function that inserts an answer blank 35 characters wide.

ANS( $trigDeriv->cmp() );

We find the derivative to this using the 
chain rule.  The inside function is \($a x\), 
so that its derivative is \($a\), and the 
outside function is \(\sin(x)\), which has 
derivative \(\cos(x)\).  Thus the solution is
\[ \frac{d}{dx} $trigFunc = $trigDeriv. \]


This is the answer and solution section of the problem. The problem answer is set by the ANS( $trigDeriv->cmp() ); line, which simply says that the answer is marked by comparing the student's answer with the trigonometric function derivative that we defined before.

Then, we explain the solution to the student. This solution will show up when the student clicks the "show solution" checkbox after they've finished the problem set.

The ENDDOCUMENT(); command is the last command in the file.

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