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<html>
<head>
<title>Berechnete Fragen</title>
</head>
<body>
<p align="center"><b>Berechnete Fragen</b></p>
Calculated questions offers a way to create individual numerical
question by the use of wildcards that are substituted with
individual values when the quiz is taken.<br>
Below is a shrunken view of the main editing page with some
example inputs:<br>
<table>
<tbody>
<tr valign="top">
<td align="right">
<p><b>Question:</b></p>
</td>
<td>
<textarea id="questiontext" name="questiontext" rows="5" cols=
"40" wrap="virtual">
How much is {a} + {b} ?
</textarea></td>
</tr>
<tr valign="top">
<td align="right">
<p><b>Image to display:</b></p>
</td>
<td><select name="image">
<option value="" selected="selected">None</option>
<option value="grevture.gif">grevture.gif</option>
</select></td>
</tr>
<tr valign="top">
<td align="right">
<p><b>Correct Answer Formula:</b></p>
</td>
<td><input align="left" type="text" id="formula0" name="answer[]"
size="20" value="{a} + {b}">   <input type="hidden" name=
"fraction[]" value="1.0"></td>
</tr>
<tr valign="top">
<td align="right">
<p><b>Tolerance:</b></p>
</td>
<td><input align="left" type="text" id="tolerance0&quot;" name=
"tolerance[]" size="15" value="0.01">&#177;</td>
</tr>
<tr valign="top">
<td align="right">
<p><b>Tolerance Type:</b></p>
</td>
<td><select name="tolerancetype[]">
<option value="1" selected="selected">Relative</option>
<option value="2">Nominal</option>
<option value="3">Geometric</option>
</select></td>
</tr>
<tr valign="top">
<td align="right">
<p><b>Significant Figures:</b></p>
</td>
<td><select name="correctanswerlength[]">
<option value="1">1</option>
<option value="2" selected="selected">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
</select></td>
</tr>
</tbody>
</table>
<br>
In the question text input and "Correct Answer Formula" {a} and
{b} can be seen. These and any other {name} can be used as a
wildcard that is substituted by some value when the quiz is
taken. Also, the correct answer is calculated when the quiz is
submitted using the expression in "Correct Answer Formula", which
is calculated as a numerical expression after the substitution of
the wildcards. The possible wildcard values are set or generated
on a later page in "editing wizard" for calculated
questions...<br>
The example formula uses the operator +. Other accepted operators
are -*/ and % where % is the modulo operator. It is also possible
to use some PHP-style mathematical function. Among these there
are 24 single-argument function:<br>
<b>abs, acos, acosh, asin, asinh, atan, atanh, ceil, cos, cosh,
deg2rad, exp, expm1, floor, log, log10, log1p, rad2deg, round,
sin, sinh, sprt, tan, tanh</b><br>
and two two-argument functions<br>
<b>atan2, pow</b><br>
and the functions <b>min</b> and <b>max</b> that can take two or
more arguments. It is also possible to use the function <b>pi</b>
that takes no arguments but do not forget the use the parentheses
- the correct usage is <b>pi()</b>. Similary the other function
must have their argument(s) within parentheses. Possible usage is
for example <b>sin({a}) + cos({b}) * 2</b>. It should not be any
problem to wrap functions within eachother like
<b>cos(deg2rad({a} + 90))</b> etc.<br>
More details on how to use these PHP-style functions can be found
in the <a target="phpmathdoc" href=
"http://www.php.net/manual/en/ref.math.php">documentation at the
PHP web site</a><br>
<br>
As for numerical questions it is possible to allow a margin
within which all responses are accepted as correct. The
"Tolerance" field is used for this. However, there are three
different types of tolerances. These are <b>Relative, Nominal and
Geometric</b>. If we say that the correct answer at quiz time is
calculated to 200 and the tolerance is set to 0.5 then the
different tolerance types work like this:<br>
<br>
<b>Relative:</b> A tolerance interval is calculated by
multiplying the correct answer with 0.5, ie in this case we get
100 so for this tolerance the correct response must be between
100 and 300. (200 &#177; 100)<br>
This is useful if the magnitude of the correct answer can differ
greatly between different wildcard values.<br>
<br>
<b>Nominal:</b> This is the simpliest tolerance type but not very
powerful. The correct response must be between 199.5 and 200.5
(200 &#177; 0.5)<br>
This tolerance type can be useful if the differences between
different correct answers are small.<br>
<br>
<b>Geometric:</b> The upper limit of the tolerance interval is
calculated as 200 + 0.5*200 and is the same as for the relative
case. The lower limit is calculated as 200/(1 + 0.5). The correct
response must then be between 133.33 and 300.<br>
This is useful for complex calculation that must have great
tolerances where relative tolerances of 1 or more would be used
for the upper limit but clearly not acceptable for the lower
limit as it would make zero a correct answer for all cases.<br>
<br>
The field <b>Significant Figures</b> does only relate to how the
correct answer should be presented in the review or the reports.
Examples: If it is set to 3 then the correct answer 13.333 would
be presented as 13.3; 1236 would be presented as 1240; 23 would
be presented as 23.0 etc.<br>
<br>
The feedback field and the optional unit fields work just like
they do for numerical questions.<br>
</body>
</html>