A worksheet of 6 geometrical questions using complex numbers with solutions.

1 hour revision lesson including the following: Mathematical content - Differentiation (in particular, stationary points), integration, straight lines, curve sketching, hidden quadratics, surds, repeated roots,… Also - Problem-solving, using graphing software, conjecturing and generalisation, almost certainly a bit of proof…

Examples and Questions

This is a short investigation using graphing software to investigate how the gradient of exponential graphs y=a^x, a>1 changes with y. By establishing direct proportionality it then allows for e to be introduced as the value for which the constant of proportionality is 1.

A simple geometric proof for the sin and cos double angle identities using a circle theorem.

This is a lovely integration result involving algebraic division and inverse trig functions, perfect for your A-level Further Maths students.

A selection of questions about objects in lifts, with solutions

An activity to develop the students skills at curve sketching, using inverse trig functions

This is an activity leading the students through a proof of a lovely result using the Factor Formulae. Perfect for A-level Further Maths students.

An activity that uses integration by substitution to prove the laws of logarithms. With solutions.

A matching activity to make connections

This is a revision activity to practise forming and solving quadratics and rationalising surds within an interesting context.

An interesting way to practise basic complex number arithmetic with a look at generating the Mandelbrot set.

This resource is a worksheet in which the students explore the links between matrices and trig identities.

This is a set of pictorial problems to accompany the teaching of the natural number series. The three different versions are the same but formatted differently.