Find the force required to produce a given moment, or vice-versa.

Solving a separable differential equation that describes the rate of decay of radioactive isotopes over time with a known initial condition to calculate the mass of the isotope after a given time and the time taken for the mass to reach $m$ grams. 

Decay Constant - Radioactivity - Nuclear Power (nuclear-power.com)

The student is shown a diagram containing a line between two points. They're given a gradient and $y$-intercept.

They must manipulate the line or the points so that the line has the given gradient and $y$-intercept.

The student is shown a diagram containing a single point at the origin. They must move the point to the given integer coordinates.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Given a number evaluate simple power, negative power, to one half.

Interpreting a p-value given the hypothesis.  Common misconceptions. 

This exercise will help you rearrange a linear equation to find the value of a given variable

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

Given a linear or a quadratic function and asked whether it is continuous. Part of HELM Book 2.4.

This shows how to take an expression given by the student and plot the implicit curve of points where it equals zero.

Find the unit vectors in the direction of four 3-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

given Voltage and loads calculated all the line currents

Given the position vectors of three 2-dimensional points $A$, $B$ and $C$, find the coordinates of a fourth point $D$ such that $ABCD$ forms a parallelogram. 

Find the unit vectors in the direction of four 2-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

(a) Read subscript notation to identify an element in a 3x3 matrix; (b) chose the correct subscripted name from a list for a given element in a 3x3 matrix.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Calculating the amount of money in a savings account after a given amount of time, and calculating how long it will take for the amount of savings to exceed a given value. 

A random dataset given by a linear function with noise (gradient and y-intercept of the linear function are randomised as is distribution of x values).

Given a point and a line, determine the distance between them.

Find forces required to hold a particle in equilibrium when subjected to a downward load.  Directions of the reactions are given.