# 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.

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.

### 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 $\mathrm{e}$ | $\mathrm{\pi}$ |

Imaginary $\mathrm{i}$ | Imaginary $\mathrm{j}$ |

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.

## 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.

## 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*.

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

### 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 $a,b\in \mathrm{\mathbb{R}}\cup \{\pm \infty \}$, 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.

### 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 ($\wedge ,\vee $), set constants... Below you can see all the supported logic and sets notations.

Supported logic and sets expressions | |
---|---|

true and false values | Logical and $\wedge $ |

Logical or $\vee $ | 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.

## 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.

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.

## 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*.

## 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*

### Tip

You can see a complete list here.