Equation

WirisQuizzes is mainly thought to validate mathematical expressions, including those involving units and currencies. You need to select the default answer type mode named Equation to enable the mathematical validation system.

WirisQuizzes Studio interface when Text answer type is selected

This documentation page intends to describe the set of mathematical expressions that can be correctly parsed by the WirisQuizzes mathematical engine. We cannot guarantee that all notations used worldwide for a listed expression are supported, but the most common forms are.

Some expressions will not be recognized with the default grammar settings because they may have an ambiguous meaning in a general context. You can use the Input Options menu to configure the context used to parse the corresponding correct answers and student answers.

Note

Suppose your integration does not use the WirisQuizzes Studio. In that case, you can do so by adding parameters to the syntax assertion (see the technical reference for the detailed instructions on that).

Basic expressions

The most basic expressions are recognized by default by WirisQuizzes evaluation engine. Below you can see a list of them.

Supported basic expressions
Sums	Substractions
Products	Divisions
Fractions	Exponents
Roots	Decimal points
Periodic decimal numbers	Absolute values
Plus-Minus symbol	Thousands separator
Infinity	Subindices

It's also possible to combine them into a single expression, and it will also be recognized.

$Example of the validation of a basic expression combining the plus-minus symbol with fractions and square roots$

Tip

The accepted subindices can be both numeric or algebraic. In the latter case, they must be single-character for the system to interpret them correctly. You can see more details here.

Constants

Several constants are defined in WirisQuizzes by default, and the students can use them in their answers. Below you can see a list of them.

Supported constants
Number $e$	$π$
Imaginary $i$	Imaginary $j$
Custom constants (defined in the question algorithm)

To do so, you need the select the corresponding constants in Input options > Input syntax. If you want to define a custom constant (for example, $g = 9.8$ ), you have to create a variable in CalcMe by clicking Define a new constant and checking it in the same panel.

Selecting the corresponding constants in the input options section

Functions

WirisQuizzes engine also recognizes a wide range of functions and their equivalences. Below you can see a list of them.

Supported functions
Exponentials	Logarithms
Hyperbolic functions	Trigonometric functions
Inverse functions	Arithmetic functions

It's also possible to combine different function types into the same answer, and the system will consider all its properties.

Example of the validation of two equivalent ways of expressing a function

Equations and inequations

With WirisQuizzes is possible to interpret the set of solutions of an equation and check if it's the same as the one defined by the correct answer. To do so, you need to check Equivalent equations in Validation options > Comparison with the student answer.

Example of the validation of two ways of expressing the same equation

Besides, you can also create questions involving univariate o multivariate inequations, and the validation system will consider the generated set of solutions.

Example of the validation of two ways of expressing the same inequation

Tip

If you want to see more information about Equivalent equations, see its dedicated page.

Intervals

Students can also use intervals in answers, and the system will understand them as their equivalent inequality to compare it with the correct answer. Let $a, b \in ℝ \cup {\pm \infty}$ , the following intervals are supported.

Supported intervals
Interval type	Expression
Open	$(a, b)$
Open-close	$(a, b]$
Close-open	$[a, b)$
Close	$[a, b]$

Notice

We can also use the reversed notation to exclude the endpoints from the corresponding set. Thus, for instance, $[a, b [$ will also be accepted.

Besides, you can also allow students to answer either intervals or inequations.

Example of the validation of two ways of expressing the same interval

Tip

If you want to see more information regarding how to create questions with intervals, see its dedicated page.

Logic and sets

Furthermore, WirisQuizzes also understand logic expressions as true and false values, the logical and or or symbols ( $\land, \lor$ ), set constants... Below you can see all the supported logic and sets notations.

Supported logic and sets expressions
true and false values	Logical and $\land$
Logical or $\lor$	Chain of inequalities
Sequences of elements	Set constants: naturals, integers...
Empty set	Set union
Set intersection	Set subtraction

Thus, it's possible to combine the intervals or inequations previously analyzed in single answers.

Example of the validation of two ways of expressing the union of two intervals

Vectors and matrices

The mathematical evaluation engine also recognizes vectors and matrices. You have to take into account parenthesis notation () is understood for points (or intervals if enabled) and square brackets [] for vectors.

Select the square brackets from the MathType editor toolbar

For instance, it's possible to answer with a matrix or a sum, subtraction or product of several of them. Besides, using a grading function, you can accept proportional vectors, for example.

Example of the validation of two ways of expressing a not unitary vector

Mixed fractions

Another accepted syntax is those involving mixed fractions. To do so, you need to select the corresponding check box in Input options > Allowed constructions.

$Selecting the corresponding option to enable mixed fractions notation in the input options section$

Ratios

Similarly, we can define answers like $2 : 3 : 5$ to be interpreted as ratios. To do so, you need to select the corresponding check box in Input options > Allowed constructions.

Units and currencies

Finally, as WirisQuizzes understands units of measurement, it's also appropriate for physics, chemistry, biology, economics, and more. To do so, it understands a wide range of units of measurement and currencies besides their equivalences. You need to enable this option in Validation options > Units of measure

Selecting the corresponding option to allow answers with other prefixes in the validation options section

Tip

You can see a complete list here.

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