Plus/Minus Operator

It is possible to perform computations with the plus-or-minus operator, as explained here. Therefore, the student is allowed to use the plus-or-minus symbol too. Recall that the result of the plus-or-minus operator is a list (not a set!).

Example 1: Simple equation

Let us start with an easy example: solve the equation x squared minus 2 equals 0. We simply write as correct answer plus-or-minus square root of 2

As we already mentioned, it is interpreted as a list: plus-or-minus square root of 2 equals open curly brackets square root of 2 comma negative square root of 2 close curly brackets; this means that the order matters and both options are enclosed in braces. Therefore, we have to change the default settings to allow the students to answer with any correct syntax:

  • Braces are not necessary: Validation > Options for general > Lists always need curly brackets "{}"

  • The order is not important: Validation > Comparison with student answer > Compare as sets

Finally, we can test the behavior.

Example 2: Complex expression

A well-known expression is the formula for solving the second order degree polynomial. For instance, the roots of the polynomial x squared plus b x plus c are given by fraction numerator negative b plus-or-minus square root of b squared minus 4 c end root over denominator 2 end fraction. Let us ask the student to write this expression.

The correct answer will be

As before, we have to change the default settings to allow the students to answer with any correct syntax:

  • Braces are not necessary: Validation > Options for general > Lists always need curly brackets "{}"

  • The order is not important: Validation > Comparison with student answer > Compare as sets

Finally, we can test the behavior.