Compute the experimental probability of a particular score on a die given a sample of throws, and compare it with the theoretical probability.

The last part asks what you expect to happen to the experimental probability as the sample size increases.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Several quadratics are given and students are asked to complete the square.

Several quadratics are given and students are asked to complete the square.

No description given

Finding surface area and volume, given formulae.

Given the original formula the student enters the transformed formula

Given the original formula the student enters the transformed formula

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

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

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.

Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.

Integration by susbtitution, no hint given

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

Round numbers to a given number of significant figures.

Round numbers to a given number of significant figures.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

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

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Students are given a graph of a cubic, and are asked to find the equation for it.