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

Identify elements by their subscript notation from given matrices.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down. 

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

Recovering original function given some information such as derivative and value at some point.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

 Students must derive the shear and bending moment functions for beam loaded with a parabolic distributed load described with a loading function.  Diagrams are given, but the students must derive the equations by integration.

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Given the specifications of two vectors, draw the parallelogram representing their sum, then estimate length of the diagonal. 

Given three vectors with integer components, find the corresponding magnitude and direction.

Find the magnitude and direction of a force given its scalar components.

3D equilibrium of a particle problem.  Rectangular steel plate supported by three cables, dimensions and density given.

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

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

Given a linear programming problem in standard form, write down the dual problem.

Multiple choice of hyperbolic functions (image of graph given).

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 $p,\;q$.