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

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

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

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

Determine the way in which an image A has been reflected onto an image B.

Identify the centre of enlargement and the scale factor in a transformation of an image A to an image B

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

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Substitute given values into formulas.

Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.

Solve a linear equation of the form $ax+b = c$, where $a$, $b$ and $c$ are integers.

The answer is always an integer.

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

Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.

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.

Work with lower and upper bounds for estimates of weight.

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.

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

Round numbers to a given number of significant figures.

Round numbers to a given number of decimal places.

Round some large integers to the a given power of ten.

Estimate the result of an arithmetic operation by first rounding numbers to given significant figures

Calculate relative frequencies in a variety of scenarios.

Given some coordinates, recognise which quadrant a point lies in, or which axis a point lies upon.