Old-style example template

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A First ~WeBWorK Sample Problem, Alternate Version

This sample problem shows the basic structure of a WeBWorK PG problem file and how it is constructed. This is different from the default first sample in that it uses "old-style" answer checkers instead of the more flexible MathObjects.

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.

Below, the contents of the PG problem file are shown to the left, with a second column to the right that explains the different parts of the problem that are indicated above.

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

## DBsubject('WeBWorK')
## DBchapter('Demos')
## DBsection('Problem')
## KEYWORDS('')
## 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')).

DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl",
);

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
# Context("Numeric");

$a = random(2,9,1);
$trigFuncTeX = "\sin($a x)";
$trigDeriv = "$a*cos($a*x)";
$trigDerivTeX = "$a \cos($a x)";

This is the problem set-up section of the problem. Here we're using old-style answer checkers, and so aren't using MathObjects. This means we don't need to worry about the Context setting, so that line is commented out. In many problems you will want to use MathObjects, however, so you will want to keep it in your files.

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. Here we define three strings, one that specifies the TeX formula for the function that we're differentiating, one that gives the formula of the derivative in a form that will be understood by the old-style answer checker, and one that gives the TeX form of the derivative.

TEXT(&beginproblem);
# Context()->texStrings;
BEGIN_TEXT
Find the derivative of the function \(f(x) = $trigFuncTeX\).
$PAR
\(\frac{df}{dx} = \) \{ ans_rule(35) \}
END_TEXT
# Context()->normalStrings;

This is the text section of the problem. The TEXT(&beginproblem); line displays a header for the problem. We're not using MathObjects in this problem, so we don't need the Context()->texStrings line, but in most cases we will, so we've left that in as a comment here. Everything between the BEGIN_TEXT and END_TEXT lines (each of which must appear alone on a line) delimit the text that 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 long.

ANS( fun_cmp($trigDeriv) );

# Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
$PAR SOLUTION $PAR
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
\[ \frac{d}{dx} $trigFuncTeX = $trigDerivTeX. \]
END_SOLUTION
# Context()->normalStrings;

ENDDOCUMENT();

This is the answer and solution section of the problem. The problem answer is set by the ANS( fun_cmp($trigDeriv) ); line, which simply says that the answer is marked by comparing the student's answer with the trigonometric function derivative that we defined before. The fun_cmp function is an "old-style" answer evaluator that checks a function. The other most common such answer evaluator is num_cmp, which checks a numerical answer.

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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