Calculated quiz question

Calculated questions are used to create mathematical questions by substituting randomly generated values into a formula using wildcards (e.g. {x} , {y}). This randomisation allows each learner to have a individualised calculated quiz question during an attempt.

For example, a question could be 'Calculate the area of a rectangle where its width = {width} and the height = {height}'. When displayed to the Learner, {width} and {height} would be replaced with randomly selected numerical values - e.g. 'Calculate the area of a rectangle where its width = 18cm and the height = 7cm'.

You can also specify the units required for the answers (e.g. cm).

To set up a calculated quiz question, follow these steps:

1. In the quiz activity, click Add, then select a new question.
2. Select Calculated, then click Add.
3. Give the question a name, then enter the question in the Question text field. The question text must include the wildcards you will use in the answer formula, with each one inside a set of curly brackets. For example:
   'A rectangle has a width of {width} and a height of {height}. What is the area of this rectangle?'
4. Set the Default mark, i.e. how many marks the Learner will be awarded if they answer correctly.
5. In the Answer 1 formula field, enter the formula that will be used to calculated the correct answer based on the wildcards that are randomly generated. For example, entering {width}*{height} would mean the correct answer would be calculated by multiplying two wildcards: {height} and {width}. See Answer formula syntax for more information. You can configure additional answers by clicking Blanks for 1 more answer.
6. Set the grade weighting for each answer.
7. Set the error tolerance and how many decimal places or significant figures will be displayed.
8. Either enter feedback for each answer, or use the General feedback field.
9. If required, configure the Units and Unit handling sections.
10. If required, configure the Multiple tries and Tags sections.
11. Click Save changes.
12. Set which dataset you wish to use for the wildcards, and set whether data is synchronised with other questions in the quiz.
13. Click Next page.
14. Manually add wildcard values by entering values in the Wild card {x} fields, then clicking Add. If you want Totara to generate the values, you can additionally enter the Minimum and Maximum for the Range of values, set the number of decimal places, and select which distribution to use (Uniform means all values in the range are equally likely, while Loguniform means higher values are less likely to be generated). Note that you can generate multiple wildcards at once using the dropdown next to the Add button.
15. Click Save changes.

Answer formula syntax

• There is no need to use an equals symbol in the formula.
• As a general rule, enter formulas as you would on a calculator e.g. 3 + 5 * sin(3/{x}. Exponentiation should be entered as pow({x}, y).
• Any special mathematical function must have parentheses around its values.
• Use an asterisk (*) for multiplication.

Tolerance

You can set the acceptable tolerance for error within the Learner's response and the type of tolerance allowed. The specified tolerance value and the tolerance type selected combine to generate a range of acceptable scores.

If tolerance = t, correct answer = x and the difference between the user's answer and the correct answer is cx, then the tolerance types are as follows: 

• Nominal: Mark correct if cx <= t 
• Relative: Mark correct if cx / x <= t 
• Geometric: Mark correct if cx² / x² <= t²

Units and unit handling

In the Units section you can configure any units that should be accounted for in the Learner's response. These can be visible in a dropdown list or radio buttons, or the user can enter a unit as part of their answer. You can set up multiple units and use multipliers to allow for multiple correct answers, such as 5kg and 5000g. For this example, you could set up one unit as 'g' with a multiplier of 1, and a second unit as 'kg' with a multiplier of 0.001.

There are several settings to configure in the Unit handling section if your question requires units.

Wildcards

Wildcards are placeholders for the numbers, values and/or measurements used in a calculated question formula. Wildcards (such as {width} and {height} from the above example) can be saved within a wildcard bank within a quiz category and reused across quizzes and quiz questions. 

After adding a wildcard to a calculated question and saving, select the wildcard datasets available for this question.

Wildcard datasets defines the range of numerical values available for each wildcard, specifies the number of different datasets (values) available for random selection, and determines the wildcard values for each of the datasets available.

For the Next 'Item to Add' field you can choose to either reuse previously generated wildcard values, or regenerate all or only non-shared wildcards.