Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.

A quick practice set of problems for education students to take in preparation for their numeracy test.

Inverse and division of complex numbers.  Four parts.

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Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Inverse and division of complex numbers.  Four parts.

Finding the inverse of a function of the form $f(x)=\ln(ax)+b$ for $x>0$.

Finding the inverse of a function of the form $f(x)=e^{mx+c}$.

Finding the inverse of a function of the form $f(x)=\frac{x^2}{a}+b$ for $x \geq 0$.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x},\,x\neq0$.

Finding the inverse of a linear function $f(x)=mx+c$.

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Cofactors Determinant and inverse of a 3x3 matrix.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Inverse and division of complex numbers.  Four parts.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Educational calculation tool rather than "question".

This allows the student to input a square matrix (max rows 5). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a "calculator". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".