You can enter point awards and custom feedback in the spaces provided for correct and incorrect participant responses. In order for this feedback to be shown, the appropriate options in Step#4 - Submit Actions must be set. That is, you must enable the issuing of feedback for your assessment. Point awards must be positive integer numbers.

If this assessment is being offered a question-at-a-time and you have enabled branching, additional popup menus are shown to permit defining to which question to branch upon the correctness of a participant's response. Note that the branch is executed based upon the correctness of the response and not the content of the response. This behavior is unique to fill-in-the-blank questions. It is generally recommended to first define all questions before setting up branching. The presentation of the popup menus is nearly identical to that of yes/no questions as shown below.

Formula Specification

Answers may be specified as a formula. That is, the correct answer could be the result of a calculation. Mathematical operators can be used as follows:

• 1 + 1
  
  
• 5 - 2
  
  
• 5 + 9 -3
  
  
• 2 * 3 indicates the product of 2 and 3
  
  
• (10-3) * 5 note that an * must be inserted to indicate multiplication - implied multiplication is not allowed
  
  
• 10 * 3 + 5 standard mathematical precedence is respected, thus the multiplication is carried out first
  
  
• 3^2 the ^ operator is for raising a number to a power - in this case three squared or nine
  
  
• 6 % 4 the % operator represents modulo or the remainder of a division - in this case the remainder of 6 divided by 4 or 2

In addition, Test Pilot has a complete mathematical function library including the following constants and functions.

• abs(..) - absolute value
• ceil(..) - Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. Example: ceil( 3.2 ) = 4.0 , ceil( 9.9 ) = 10.0
• exponential functions
  • euler - the constant e or exp(1)
  • exp(..) constant e raised to..
  • ln(..) the natural logaritm
  • [base]log(..) - any logaritm. Example: 10log(10) = 1.0, exp(1)log(exp(1)) = 1.0
• fac(..) - factorial of... n*(n-1)*(n-2)*..*1
• floor(..) - Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. Example: floor( 3.2 ) = 3.0 , floor( 9.9 ) = 9.0
• fpart(..) - returns the decimalvalue of its argument Example: fpart(2.345) = 0.345, fpart(4) = 0.0 etc.
• round(..) - rounds the argument to the closest mathematical integer. Example: round( 3.4 ) = 3.0, round( 4.99 ) = 5.0 etc.
• sfac(..) - semifactorial of.. n*(n-2)*(n-4)*..*4*2 if n is even n*(n-2)*(n-4)*..*3*1 if n is not even
• sqrt(..) - square root
• trigonometric functions (arguments must be in radians)
  • pi - the constant pi
  • sin(..) - the sine function
  • cos(..) - the cosine function
  • tan(..) - the tangent function
  • cotan(..) - the cotangent function
  • asin(..) - the arc sine function
  • acos(..) - the arc cosine function
  • atan(..) - the arc tangent function
  • acotan(..) - the arc cotangent function
  • hyperbolic functions
    • sinh(..) - the hyperbolic sine function
    • cosh(..) - the hyperbolic cosine function
    • tanh(..) - the hyperbolic tangent function

For example:

• sin( pi/2 ) - the sine of pi over 2 radians or 1
• sqrt( 2 ) - the square root of 2 or 1.414...

Random Variables

One of Test Pilot's most powerful features is its ability to generate random numbers for use in numeric questions. This permits the generation of unique questions each time a participant requests an assessment. In a computer laboratory environment, this means that each student could get a different test. This drastically reduces the efficacy of copying your neighbor's responses. What it has meant to Purdue University's Electrical Engineering Technology department was that students stopped asking each other What did you get for #...? and now they ask How did you get your answer? - a much more productive question and one geared productively towards learning.

Test Pilot supports two categories of random variables: local and global. Global variables are shared by all questions on an assessment. That is, you may construct multiple questions referring to the same set of random data. Local variables are unique to a specific question and are not accessible for use in other questions. There is no limit on the number of global or local random variables that may be defined.

Random variables may be defined as follows:

In this sample global variable definition four variables have been defined. Variable names can only consist of alphabetic letters a-z and numbers 0-9. (e.g. x, xx, var2, aVeryLongVariable ) You can use any name that is not reserved by an operator or a predefined constant, as a variable name. You should avoid beginning a variable name with a number, like 3x or 1var. Care should be taken to avoid confusion between a number in scientific notation and a variable name. (e.g. use 2.0E+5 instead of 2E5) You may specify integer or decimal real numbers as start, end and increment values. You may also use scientific notation.

Each variable is assigned a starting value, and ending value and an increment value. Note the sample list at the end of each row. These are example of calculated values for each of these variables and are typical of the assignments that will be made at assessment time for the participant. Please note that the assignment of these values occurs at assessment time. None of our competitors offer this powerful capability.

Pooled random variables

In addition to calculated random variables such as shown above, Test Pilot includes the capability to define a pool of numbers to be used to select from. If you enter a series of numbers separated by commas in the start field of a random variable definition, you create a pooled random variable.

In this example local random variable definition a pooled random variable named pooledVar is defined to be the set of the first eight non-negative prime numbers. Purdue's EET Department uses pooled random variables to define a set of resistance values common to electronic circuit construction. This lends an aura of realism for their use in Test Pilot for circuit design problems.

Using Random Variables in Questions and Formulae

For this example, we want to create a problem which asks the participant to calculate the circumference of a circle of a given radius. The value assigned to the radius will be a randomly generated quantity. We start the construction of the problem by creating a new fill-in-the-blank question and specifying that the response should be numeric. We then define our random variable for the radius as follows:

Here we define a variable r which will range in value from 2 to 7 by an increment of 1. That is, it will be able to take on values from the set [2,3,4,5,6,7].

Next, we'll define the text of the question to include the generated value for r. We do this with the special notation of including the variable's name in brackets:

The brackets tell Test Pilot to substitute the generated value for r at the appropriate location in the question's text. Thus, when the assessment is generated, participants will see, for example:

What is the circumference of a circle of radius 7?

or

What is the circumference of a circle of radius 3?

Finally, we need to specify the correct answer to the question. Since we don't know what value will be assigned when Test Pilot generates the assessment, we must specify the correct answer as a function applied to the random variable. In this case, a circles circumference is determined by multiplying pi times twice the radius. In this question's formula box, the following could be entered:

Note that upon updating, a sample evaluation of the formula is shown below the formula. A quick test with a calculator indicates that the value was calculated correctly.

Question Chaining

Quite often in instruction, you want to define your problems in steps and to identify which steps are causing particular students problems. Yet, if problems occur at an early step and the results of one step is used in the next, errors compound quickly and it is very hard to determine whether succeeding steps were performed correctly. Test Pilot is unique among it competition at addressing this issue. It allows you to compose formulae using the correct answer of any problem. That is, if a student gets step #2 wrong, step #3's question is based upon a correct response to step #2. This is incredibly useful in developing powerful arithmetic, scientific and engineering tutorials. The syntax for referencing the correct answer to a problem involves enclosing it's id preceded by a Q in brackets:

Test Pilot's mathematical capabilities are unparalleled in the world of online assessment. For mathematical, scientific and engineering assessment online, Test Pilot is the best and only choice.