 6.25 Tutorial: Maple-based Algorithmic Question Authoring - Maple T.A. 2016 Help Instructor
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## 6.25 Tutorial: Maple-based Algorithmic Question Authoring

Algorithmically generated variables are used to generate random numbers in questions and create multiple permutations of questions from a single template.

You can use either Maple T.A. or Maple to generate algorithmic variables. You can use either (or both) types of variables in any question type.

The syntax for a Maple-based variable definition is:

`<variable_i>=maple("<Maple_command>");`

### Using a Text or HTML Editor

To define an algorithmic variable in the plain-text script file, specify variable definitions (or other variable control sequences) in the algorithm field.

`algorithm=`
`<variable_definition_1>`
`...`
`<variable_definition_n>`
`@`

### Using the Question Editor

In the Question Editor, define variables by directly entering Maple-based variable definitions on the algorithm screen or using the Algorithm Designer.

### Tutorial 1

The following tutorial shows how to convert a static Maple Formula question to an algorithmically generated question by using variables assigned values by Maple commands.

Consider the following plain-text script question definition, which asks a student to enter an anti-derivative of x^3.

```qu.1.1.question=Enter an anti-derivative of x^3.@
qu.1.1.maple=evalb(diff(\$RESPONSE,x)=x^3)@
qu.1.1.type=formula@
qu.1.1.mode=Maple@
qu.1.1.allow2d=1@
qu.1.1.name=Maple AntiDerivative@
qu.1.1.comment=Any function of the form x^4/4 + C, where C is a constant, is an anti-derivative of x^3.@
qu.1.1.editing=useHTML@```

Notes:

1. This question uses Maple to verify that the derivative of the student response is equal to x^3. This is recommended in place of comparing the student response, which can have an additive constant, with the integral of x^3, that is evalb(\$RESPONSE=int(x^3,x)).
1. If the student enters an incorrect response, the system display the value in the comment field. In Maple-graded questions, if there is no comment field, the system returns the message Comment: No feedback is provided with this question.

To change this question to an algorithmic question, use the following plain-text script question definition.

```qu.1.2.question=Enter an anti-derivative of x^\$exponent + \${coeff}x.@
qu.1.2.maple=evalb(diff(\$RESPONSE,x)=x^\$exponent+\$coeff*x)@
qu.1.2.type=formula@
qu.1.2.mode=Maple@
qu.1.1.allow2d=1@
qu.1.2.name=Maple AntiDerivative@
qu.1.2.comment=Any function of the form \$answer + C, where C is a constant, is an anti-derivative of x^\$exponent + \${coeff}x.@
qu.1.2.editing=useHTML@
qu.1.2.algorithm=\$exponent=maple("randomize():rand(2..5)()");
\$coeff=maple("randomize():rand(2..9)()");
@```

Notes:

1. You must follow the variable naming conventions.
1. For a list of the guidelines for Maple commands in Maple-based variables, see The Algorithm Designer.
1. The variable \$exponent is assigned a value calculated by Maple using the rand function. rand() returns a random 12-digit positive integer rand(a)() returns a random integer in the range 0 ... a-1 (inclusive) rand(a..b)() returns a random integer in the range a ... b (inclusive) For information on other Maple commands, see your Maple documentation.
1. The Maple command: randomize(): is included so that a different value is generated for each question instantiation. You must include the randomize(): command in every Maple-based variable definition. That is, it is required in the definition of \$exponent and \$coeff.
1. The Maple command: int(x^\$exponent,x) calculates the correct answer, which is displayed using the comment statement if the student response is incorrect.
1. The examples in Tutorial 1 can be converted to Maple Syntax questions by changing the type field value from formula to maple, and changing allow2d to 0 for text-entry mode. For Maple Syntax questions, it is recommended that you attempt to prevent a student from calculating the correct answer using Maple commands. For more information, see Using Maple Code to Prevent Cheating in Maple Syntax Questions.

For an example plain-text script that defines a Maple question with Maple plotting of the student response, see Plotting a Student Response.

### Tutorial 2

You can also use Maple-based algorithmic variables in other question types.

#### Formula Question

The following plain-text script defines a Formula question that uses Maple-based variables.

```qu.1.3.question=What is the sum of \$a and \$b?@
qu.1.3.mode=Formula@
qu.1.3.name=Maple-based Variables in Formula@
qu.1.3.editing=useHTML@
qu.1.3.algorithm=\$a=maple("randomize():rand(100..200)()");
\$b=rint(10,50);