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Which answer check methods are available in math exercises?
Which answer check methods are available in math exercises?
Written by Thijs Gillebaart
Updated over a week ago

Note
We are actively expanding the set of check-methods and are keen to receive feature requests for new ones. Are you missing a check-method? Let us know by providing

• a (short) example exercise

• description of the left-hand-side (student answer dependent value) and right-hand-side of the check-method

• a short description on how the left-hand-side and right-hand-side should be compared

• check-method name suggestion

We will quickly get back to you whether we can implement such a check-method.

# List of check-methods

Within the math exercise type you can use different type of check methods to create specific feedback. We currently support the following check-methods:

## Algebra

• Algebraically Equivalent (default)

• same Exact Form

• same Ordered Collection

## Specialised Linear Algebra methods

• Parallel Vector

• same Basis

• same Orthogonal Basis

• same Orthonormal Basis

• same Solution to System of Equations

• is Diagonal Matrix

## Other

• Defined

• Greater Than

• Greater Than or Equal To

• Less Than

• Less Than or Equal To

• Numerical

# Detailed descriptions

## Algebraically Equivalent (default)

If you want to check whether two expressions are mathematically equal, you should use this check. A simple example would be: "x+x" is considered algebraically equivalent to "2*x".

You can apply this method to:

• exact numbers (e.g. 3 or pi)

• formulas (e.g. 3x+4)

• vectors and matrices

• unordered collections/lists

## Same Exact Form

If you want to check whether two expressions are mathematically equal AND have the same exact form, you should use this check. A simple example would be: "2x+3" is considered to have the same exact form as "3+2x" but not as "x+x+3".

You can apply this method to:

• exact numbers (e.g. 3 or pi)

• formulas (e.g. 3x+4)

• vectors and matrices

• unordered collections/lists

If the form of the expression is not important, use the Algebraically Equivalent check.

## Same Ordered Collection

If you want to check whether the left-hand-side is the same ordered collection as the right-hand-side, you should use this check. A simple example would be: "[4, 2x]" is the same as "[2+2, x+x]" but not equal to "[2x, 4]".

A collection can contain

• numbers (e.g. 3 or pi)

• formulas (e.g. 3x+4)

• vectors/matrices

If the order of the collection is not important, use the Algebraically Equivalent check.

## Parallel Vector

Checks whether the vector given on the left-hand-side is parallel to the vector provided at the right-hand-side. A vector can be both a column or row vector. Vectors "v1" and "v2" are parallel if "v1 = a*v2", with "a" being a non-zero scalar value.

Examples which are equivalent:

• vector(1,2) is parallel to vector(2,4)

• vector(1,2) is parallel to vector(-1,-2)

• vector(0,0) is parallel to vector(0,0)

Examples which are not equivalent:

• vector(1,2) is not parallel to vector(1,3)

• vector(1,2) is not parallel to vector(-1,2)

• vector(0,0) is not parallel to vector(1,1)

• vector(0,0) is not parallel to vector(1,2)

## Same Basis

Checks whether the left-hand-side (student answer dependent value) describes the same basis as the right-hand-side. Both left- and right-hand-side need to be a basis. A basis is provided by a comma separated list of column vectors (optionally enclosed in braces: "{" and "}").

## Same Orthogonal Basis

This check is equivalent to "Same Basis" with in addition the check whether the column vectors are also Orthogonal.

## Same Orthonormal Basis

This check is equivalent to "Same Basis" with in addition the check whether the column vectors are also Orthonormal.

## Same Solution to System of Equations

Checks whether the left-hand-side describes the same solution to the system of equations as the right-hand-side.
Both left- and right-hand-side need to be a complete (but minimal) solution to a system of equations. A solution to a system of equations can

• have free variables

• be written as an equation with column vectors

• be written as a single matrix with free variables

## Is Diagonal Matrix

Checks whether all elements on the matrix that are not on the diagonal are zero.

## Defined

Checks whether the variable on the left-hand-side exists and has a value.
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## Greater/Less Than (or Equal To)

Checks how (all elements of) the variable on the left-hand-side compare to the numeric value on the right-hand-side. These four check all work in a similar manner, only the method to compare the elements differ.

## Numerical

Checks whether the variable on the left-hand-side evaluates to a (complex) number
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