Multiply two numbers in standard form, then divide two numbers in standard form.

Needs marking algorithm to allow equal values in standard form to gain equal marks

Solve a quadratic equation by completing the square. The roots are not pretty!

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

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.

Quiz covering basic arithmetic with complex numbers and solving roots for a quadratic with complex solutions

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Differentiate $\displaystyle \frac{ax+b}{cx+d}$.

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

Questions on rearranging expressions, expanding brackets and collecting like terms.

Some questions of relevance to consumers.

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

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

Find the original price before a discount by dividing the new price by the percentage discount.

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

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. 

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. 

Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

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r digits are picked at random (with replacement) from the set $\{0,\;1,\;2,\ldots,\;n\}$. Probabilities that 1) all $\lt k$, 2) largest is $k$?

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Version I. Graph is quadratic

Version II. Graph is horizontal

Version III. Graph is cubic

Version IV. Graph is sinusoidal

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

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

Calculation of the length and alternative form of the parameteric representation of a curve.