As you have seen in the input options section, it is possible to filter the showed options from the beginning, based on an analysis of the correct answer. Thus, only the most relevant options will appear, clearing the window of all the possibilities that the tool offers that may not be of interest.

However, you can always select the Show all options box if you want to take a look at all the entry possibilities. From here, if they are all displayed, the window is divided into four sections.

Comparison with student answer

Once you have decided what format you expect the student answer to be in, you have a few options for how their answer should be compared to the correct one.

You can see a detailed description of each option in the table below.

Comparison with student answer criteria
Literally equal This removes all mathematical interpretations from the comparison. The student's answer is only correct if it matches the correct answer exactly. For example, if the correct answer is 4 but the student writes 4.0, it will not be counted. This criterion is rarely recommended.
Mathematically equal This is the default comparison. It will detect if what the student has written is mathematically equal to the correct answer. For example, we don't need to worry if the student writes a + b or b + a. More details
Compare as sets This is a checkbox that is independent of the above options. When checked, order and repetition are ignored from lists. So, if the correct answer is the set {1,5,2}, then {5,5,5,2,1} (for example) would be accepted. More details
Equivalent equations This comparison is very similar to the mathematically equal option, but it is for the special case where the answer is an equation (e.g. the student could write y equals 2 x minus 5, or 2.5 equals x minus y over 2, or any equivalent form). More details
Any answer Anything that the student answers will be counted as correct. This is useful in some cases. More details
Grading function Define your own function to decide which answers are accepted, and how to grade them. This is an advanced feature. More details

Numbers

In the Numbers section we specify the tolerance criteria used for the comparison between the student's answer and the correct answer. These settings apply globally (to the entire question) and they are divided into four. Firstly, you need to choose if you want the answer to be symbolic or not.

If you select this option, any answer expressed with decimal numbers will be graded as correct. To do so, it must be a combination of operations, fractions, roots, and functions. If it's enabled, it will be the only option available.

Otherwise, you can specify the tolerance criteria used for the comparison between the student's answer and the correct answer.

You can choose between the three possible options:

  • Exact answer: This option requires the student's answer to be exactly equal to the correct answer.
  • Error margin: This option requires the student's answer to be strictly within the tolerance interval. You can define this margin as a percent error or as an absolute error. It's selected by default at 0,1 percent error.
  • Matching digits: This option requires the student's answer to match the first significant figures or decimal places with the correct answer.

You can see more details here. Below, you can choose the format in which you want to require the student's answer.

You can choose between the three possible options:

  • Scientific notation: This option requires the student's answer to be expressed in normalized scientific notation.
  • Decimal notation: This option requires the student's answer to be expressed in plain decimal notation.
  • Any notation: This option allows the student's answer to be expressed either in scientific or decimal notation. It's selected by default.

You can see more details here. Below, you can define a particular precision to require the student's answer. It allows you to check the minimum and the maximum number of significant figures or decimal places the student answer must have.

Simplification

Sometimes it's not just the value of the answer that's important, but also its form. This usually happens when you are teaching basic algebraic manipulation, and you want the answer in a very specific form.

You can see a detailed description of each option in the table below.

Specific property Examples
Correct Wrong
Simplified It checks whether the expression cannot be simplified. Includes fractions, powers and roots, polynomials... open parentheses square root of x close parentheses cubed open parentheses square root of x close parentheses to the power of 4
Expanded It checks whether all operations that can be done are performed 27 1 plus 1
Factorized It checks whether an integer or a polynomial is expressed as product of primes 2 to the power of 4 times 3 48
Common factors It checks whether the summands of the answer have no common factors 2 left parenthesis 2 plus 3 plus 4 right parenthesis 4 plus 6 plus 8
Common denominator It checks whether the answer has a single common denominator fraction numerator x plus 1 over denominator x minus 1 end fraction fraction numerator x plus 1 over denominator x minus 1 end fraction plus fraction numerator x minus 1 over denominator x plus 1 end fraction
Rationalized It checks whether the expression does not have square (or higher) roots in the denominator. It also checks whether the expression has a pure real denominator (in the case of complex numbers) fraction numerator square root of 2 over denominator 2 end fraction fraction numerator 1 over denominator square root of 2 end fraction
Minimal radicands It checks whether any present radicands are minimal 2 square root of 2 square root of 8
Match unit of measure It checks whether the unit of the answer is literally equal to the given one 3 text km end text, given text km end text 3 text m end text times text s end text to the power of negative 1 end exponent, given text m end text divided by text s end text

For a complete and advanced description of all the properties, see assertions.