Christian Lawson-Perfect

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

Two double integrals with numerical limits

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m-1}}mf(x^m+a)dy$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

3 Repeated integrals of the form $\int_a^b\;dx\;\int_c^{f(x)}g(x,y)\;dy$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Questions on adding, subtracting, multiplying and dividing numbers in standard form.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

Work with measurements of weight, mass and density.

Questions involving the calculation of the volumes of shapes.

Questions on manipulating logarithms.

Calculate a speed in m/s given distance and time taken, then convert that to km/hour

A collection of questions on working with units of measurement, mainly in the SI/metric system.

Several 'real-world' examples.

Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.

Some questions on working with surds.

Calculations and graphs involving measurements of speed.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.

Given five fractions, identify the odd fraction out. The denominators are mainly two or three digits long.

Estimate whether you can afford an extra item in a shop by rounding prices to the nearest 10p.

Estimate the number of buckets of paint to buy, by rounding measurements of a room up to the nearest metre and estimating the total area.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Choose the probability of getting a tails, from four options.

A bag contains balls of three different colours. You're told how many there are of each, and asked the probability of picking a ball of a particular colour.

Given the probability that a basketball shot misses the hoop, find the probability that it's on target - use the law of total probability.

Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

Questions on presenting data in charts or tables.

Questions on powers, the laws of indices, and exponential growth.

Identify the plane transformation performed to create a given diagram.

Questions to do with money.

Some questions to do with measures of distance and length.