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

We currently support the following check-methods in math exercises:

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

  • Is Defined
  • Greater Than
  • Greater Than or Equal To
  • Less Than
  • Less Than or Equal To

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

Read more about the default Algebraically Equivalent check here.

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.

Read more about the Exact Form check here.

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.

Read more about the Ordered Collection check here.

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)

Read more about the Parallel Vector check here.

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 "}").

Read more about the Basis check here.

Same Orthogonal Basis

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

Read more about the Basis check here.

Same Orthonormal Basis

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

Read more about the Basis check here.

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

Read more about the Solution to System of Equations check here.

Is Diagonal Matrix

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

Read more about the is Diagonal Matrix check here.

Is Defined

Checks whether the variable on the left-hand-side exists and has a value.

Read more about the Is 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. 

Read more about the Compared to checks here.

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