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
Note: these checks are only available for the math exercise type. More information about other question types can be found in this article.
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.
Read more about the Defined check here.
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
Read more about the Numerical check here.