Make sure you can confidently answer questions on all the topics listed in the posts How to get a Grade B at GCSE Maths and How to get a Grade C at GCSE Mathematics. Below is a list of additional topics that you need to know well if you want to get a grade A at GCSE Maths.

Number

• Simplifying and calculating with surds, rationalising surds
• Using π and/or surds in exact calculations and exact answers
• Carrying out calculations involving upper and lower bounds
• Using direct and inverse proportion

Algebra

• Forming and solving equations from a worded problem and/or diagram
• Factorising quadratics using the difference of two squares
• Simplifying algebraic fractions
• Rearranging more complex formulae
• Using the rules of indices with negative and fractional indices
• Solving equations graphically
• Solving linear inequalities graphically
• Knowing and using the fact that the product of the gradients of perpendicular lines is –1
• Sketching curves – cubic, exponential and reciprocal functions

Shape and Geometry

• Sketching and using the graphs of the sine, cosine and tangent functions
• Using the sine rule and cosine rule
• Finding the area of a triangle using ½ ab sin c
• Working with congruent triangles
• Calculating the lengths of arcs and areas of sectors
• Calculating the surface areas and volumes of cylinders, cones, pyramids and spheres
• Understanding the effect of enlargement on area and volume
• Working with vectors
• Be able to prove the circle theorems, the alternate segment theorem, the ruler and compass constructions of perpendicular bisectors and angle bisectors

Data

• Choosing which average to use and giving a reason
• Understanding the effect of sampling method and sample size on the reliability of conclusions
• Working with stratified sampling and calculating sample sizes
• Applying probabilities, and understanding the difference between mutually exclusive and independent events

Now you know what you need to revise if you want to get a grade A at GCSE Mathematics. Try to do practice questions on as many of the topics as you can, to make sure you not only understand the topic but can use your knowledge to answer questions.