Learn how to use the remainder and factor theorems and then apply them to factoring polynomials and solving equations. Simplifying algebraic fractions either by long division or by comparing coefficients.

Use circle theorems. Use geometric information to find the equations of circles or use the equation to find the radius and centre of circles. Decide whether or not two given circles intersect. Find the equation of the tangent or normal to a given circle.

Learn about exponential graphs. Learn and use the laws of logarithms to any base, including the change of base formula. Apply these laws to solving exponential equations.

Find the sum of geometric series and the sum of convergent infinite geometric series. Use the binomial expansion to simplify binomial expressions.

Explore the circular functions and important trigonometrical identities, and solve triangles using trigonometry. This will include the functions sine, cosine and tan, the inverse functions arcsin, arccos and arctan and their graphs. Use radian measure to find arc lengths and sector areas. Use the sine and cosine rules are used to solve triangles.

How to use the first and second derivatives to identify stationary points (maxima and minima) on curves. Relate this to curve sketching. Solve maxima and minima problems set in a practical context.

Evaluate definite integrals and use them to find the area contained by a curve. Find approximations to the area under a curve by using the trapezium rule.