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## Respondus 4 - About Arithmetic and Numerical Answer Questions

Learn how to create Arithmetic and Numerical Answer Questions in Respondus 4.

### Introduction

Arithmetic and Numerical Answer questions require students to apply a mathematical formula to answer the question. These questions are designed using variables. Random values, based on a specified range, are automatically generated for each variable in the question. Thus, Arithmetic and Numerical Answer questions can be unique for each student, as illustrated in this example where values are inserted for {x} and {y}.

Example: If a car is traveling {x} miles per hour for {y} hours, how far does it travel (in miles)?

The Respondus editor for these questions contains the following sections that need to be completed:

- Question Wording
- Formula
- Variable Properties
- Answer Properties
- Value/Answer Sets

### Question Wording

In the Question Wording section, enter the text of the question just as you would for any other question type. However, instead of using specific numerical values to define the details of the question, instead use variables by specifying a name enclosed in curly brackets for each one. For example: “How long does it take to travel {x} miles at a speed of {y} mph?”

Variable names can only contain letters and digits (the characters 0-9, a-z, and A-Z), and the “_” (underscore) character. In addition, the first character of a variable name cannot be a number.

You can use as many different variables as you need to define the question, and you can use the same variable name multiple times if necessary.

Note that adding images, complex HTML, etc. to the question wording will significantly increase the file size of the Flash object generated for the question, thereby limiting the number of different value/answer sets that will be available for random selection.

### Formula

In the Formula section, enter the mathematical formula associated with the question. This is the same formula that the student will be expected to use, and the same one that will be used to automatically calculate the correct answer for grading purposes. The same variables specified in the question wording will be used to indicate where each value should go in the formula.

The formula can be typed into the edit field directly, or entered by selecting options from the pull-down lists provided for Variables, Functions, Operators, and Constants. Selected options will appear in the edit field at the current cursor location, and will overwrite the current selection (if any).

- abs(x) Absolute value of x. abs(-3) = 3.
- atan(x) Arc-tangent of x in radians
- cos(x) Cosine of x in radians
- cosec(x) Cosecant of x in radians
- cotan(x) Cotangent of x in radians
- exp(x) Base e (Euler’s constant) raised to the power of x
- factorial(x) Factorial of x. fact(3) = 6.
- ln(x) Base e natural logarithm of x
- log(x) Same as ln(x)
- sec(x) Secant of x in radians
- sin(x) Sine of x in radians
- sqr(x) Square root. sqrt(9) = 3.
- tan(x) Tangent of x in radians

Note that the values for trigonometric functions are expressed in radians, not degrees. For conversion purposes, Pi radians = 180 degrees. Also, for all formulas that have two correct answers (for example, the square root of 9 is +3 and -3), only the positive number will be treated as correct.

After selecting a function from the list, the formula must be edited to replace the argument list with numbers or variables. For example, “round(d,x)” might be edited to specify a fixed number of decimal places and a variable to round, as in “round(3,{y})”, which would round the variable {y} to 3 decimal places.

Functions can also be nested within a formula, as in “sqrt(abs({x}))”. In this case, the absolute value of {x} is evaluated first, followed by the square root of the result. Functions can be nested as deeply as necessary to properly calculate the answer.

- 3.2E4 equals 32000
- -2E0 equals -2
- 3.14E-2 equals 0.0314

- - = Subtraction
- % = Modulus or remainder. For example, 5%2 = 1.
- () = Parentheses used to group elements for precedence
- * = Multiplication
- ^ = Power or exponent. For example, 2^3 = 8.
- / = Division
- + = Addition

- _e - Base e or Euler’s constant (2.71828…)
- _pi - Pi – the circle ratio (3.14159…)

- Question: How long does it take to travel {x} miles at a speed of {y} mph?

Formula: {x}/{y} - Question: What is the positive square root of {x}?

Formula: sqrt({x}) - Question: Compute sin(x) where x = {x} degrees.

Formula: sin({x}/180*_pi)

### Variable Properties

Clicking the “Variable Properties” button in the Formula section displays the Variable Properties dialog. Here, each variable in the question wording and formula is listed by name, along with Minimum, Maximum, and Precision values for that variable.

The Minimum and Maximum define the range of values each variable can be assigned, and the Precision specifies the number of decimal places each value should be allowed before the value is rounded off.

You can click each cell in the grid to edit the specific minimum, maximum, or precision value you want to change (the variable names cannot be edited). In general, for a given variable the minimum must be less than or equal to the maximum, and the precision must be greater than or equal to 0 and less than or equal to 5.

### Answer Properties

Clicking the “Answer Properties” button in the Formula section displays the Answer Properties dialog. Here you can specify values for answer precision and acceptable tolerance, as well as a unit name if required.

Answer precision can be specified in Decimal Places or Significant Figures. If the precision is specified in decimal places, the value must be greater than or equal to 0 and less than or equal to 5, just as with the precision values specified in the Variable Properties dialog. If the precision is specified in significant figures, the minimum value is 1.

Answer tolerance is the amount that the student’s answer can deviate from the calculated answer and still be considered correct. It can be specified as a fixed number of units or as a percentage of the answer value.

If you choose to require a unit name, comparisons with the name entered by the student will be case-insensitive and space-insensitive.

### Value/Answer Sets

Clicking the “Value/Answer Sets” button below the Formula section displays the Value/Answer Sets dialog. Here you can generate sets of variable values and calculate the associated answers using the formula previously entered. When the Arithmetic question is presented to the student, one of these value sets will be randomly chosen to populate the variables in the question wording and the formula, and the associated answer will be used to grade the student’s response.

The grid displays a list of numbered value/answer sets. The number of sets available can be selected from the “Number of Sets” pull-down list. The contents of this list will vary, depending upon the complexity of the question wording. For each set, the generated values for each variable are shown, and the individual cells can be clicked to edit those values. Note that any manually-entered values must be within the range specified by the variable minimum and maximum in the Variable Properties dialog. The answers cannot be edited; instead, the “Update Answers” button can be clicked to recalculate the answers for all value sets.

Note: Canvas refers to Arithmetic questions as Numerical Answer, they are the exact same question type.