version 1.6, 2013/06/26 08:14:55
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version 1.7, 2016/08/20 17:48:11
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Overview - This box is used to create a rule that determines whether or not a submitted graph is correct. In general, it takes the form of testing the function, its integral, or its first or second derivative over a given set of x-values. The test can be to see if it equals, is greater than, or less than a specified value. Anywhere a number is needed, a variable can also be used. (Skip to the bottom for examples of rules.) |
Overview - This box is used to create a rule that determines whether or not a submitted graph is correct. In general, it takes the form of testing the function, its integral, or its first or second derivative over a given set of x-values. The test can be to see if it equals, is greater than, or less than a specified value. Anywhere a number is needed, a variable can also be used. (Skip to the bottom for examples of rules.) |
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\begin{itemize} |
\begin{itemize} |
\item ``Index/Name" - This is an internal label for the rule. Something must be entered here, and it must be different for each rule. This same value will be used to add a conditional hint. |
\item ``Index/Name'' - This is an internal label for the rule. Something must be entered here, and it must be different for each rule. This same value will be used to add a conditional hint. |
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\item ``Function" - This determines what the server will be testing. For instance, choose 'First derivative' causes the server to evaluate the derivative of the entered answer over the given domain. |
\item ``Function'' - This determines what the server will be testing. For instance, choose `First derivative' causes the server to evaluate the derivative of the entered answer over the given domain. |
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\item ``Initial x-value'' and ``Initial x-value label'' - A value must be entered for one of these. Either choose a numerical value for x (the first option), or choose the beginning of the submitted answer, the end, or a previously chosen named point (see below). |
\item ``Initial x-value'' and ``Initial x-value label'' - A value must be entered for one of these. Either choose a numerical value for x (the first option), or choose the beginning of the submitted answer, the end, or a previously chosen named point (see below). |
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Line 17 Overview - This box is used to create a
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Line 17 Overview - This box is used to create a
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\item ``Relationship'' - The heart of the rule. This choice determines whether the chosen `Function' is greater than, less than, equal to, etc. a certain `Value'. |
\item ``Relationship'' - The heart of the rule. This choice determines whether the chosen `Function' is greater than, less than, equal to, etc. a certain `Value'. |
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\item ``Value'' - Enter the number you wish to compare to. It is also possible to choose 'not defined', in the event the answer should not have a value for the given domain. Within the value argument, the function itself can be evaluated using \&fpr\_f(), its derivative using \&fpr\_dfdx(), and its second derivative using \&fpr\_d2fdx2(). This allows for a comparison of two points on the graph. The value of a previously defined label can be retrieved using the function \&fpr\_val(), e.g., \&fpr\_val(`positive'). Previous defined values from script blocks can also be retrieved as normal variables, e.g., \$x. |
\item ``Value'' - Enter the number you wish to compare to. It is also possible to choose `not defined', in the event the answer should not have a value for the given domain. Within the value argument, the function itself can be evaluated using \&fpr\_f(), its derivative using \&fpr\_dfdx(), and its second derivative using \&fpr\_d2fdx2(). This allows for a comparison of two points on the graph. The value of a previously defined label can be retrieved using the function \&fpr\_val(), e.g., \&fpr\_val(`positive'). Previous defined values from script blocks can also be retrieved as normal variables, e.g., \$x. |
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\item ``Percent error'' - This allows for a margin of error in the y-direction. For instance, if the rule requires that the derivative be equal to 5, the server will accept values close enough to 5 that are within the percent error defined here. Note: Choosing 10\% would not mean that the answer is correct as long as it is within the range 4.5-5.5. Instead, the percent corresponds to the total size of the graph. For the function itself, the `percent error' is multiplied by the ymax-ymin; for the first derivative, it's multiplied by (ymax-ymin)/(xmax-xmin); for the second derivative, it's multiplied by (ymax-ymin)/(xmax-xmin)$^2$; and for the integral, it's multiplied by (ymax-ymin)*(xmax-xmin). |
\item ``Percent error'' - This allows for a margin of error in the y-direction. For instance, if the rule requires that the derivative be equal to 5, the server will accept values close enough to 5 that are within the percent error defined here. Note: Choosing 10\% would not mean that the answer is correct as long as it is within the range 4.5-5.5. Instead, the percent corresponds to the total size of the graph. For the function itself, the `percent error' is multiplied by the ymax-ymin; for the first derivative, it's multiplied by (ymax-ymin)/(xmax-xmin); for the second derivative, it's multiplied by (ymax-ymin)/(xmax-xmin)$^2$; and for the integral, it's multiplied by (ymax-ymin)*(xmax-xmin). |
\end{itemize} |
\end{itemize} |
Line 32 The figure below shows some examples of
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Line 32 The figure below shows some examples of
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\item Checks that the second derivative at $x=$\$time1 is $0$. |
\item Checks that the second derivative at $x=$\$time1 is $0$. |
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\item Checks that the value of the function $>7$ from ``Start of Graph" to $x=5$. |
\item Checks that the value of the function $>7$ from ``Start of Graph'' to $x=5$. |
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\item Checks that the function is $0$ from $x=0$ until the function is no longer $0$, labeling this new point `notzero'. |
\item Checks that the function is $0$ from $x=0$ until the function is no longer $0$, labeling this new point `notzero'. |
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