As well as being able to do all the items listed in the posts How to get a Grade A at GCSE Maths, How to get a Grade B at GCSE Maths and How to get a Grade C at GCSE Mathematics. If you want to get a grade A* at GCSE Mathematics, you also need to understand and be able to:


  • Calculate and work with negative and fractional indices
  • Expand brackets involving surds
  • Solve more complex, multi-step problems involving upper and lower bounds


  • Solve equations including algebraic fractions
  • Solve simultaneous equations where one is linear and one quadratic, using the substitution method
  • Sketch transformations of graphs
  • Solve quadratic equations by completing the square, and find the minimum and maximum points
  • Recognise equations of circles, work with them to solve problems and draw circles
  • Prove statements using algebra


  • Prove statements using vector geometry
  • Find volumes of frustrums of cones
  • Use trigonometry and Pythagoras’s theorem to solve 3D problems
  • Solve trigonometric equations, and find multiple solutions using graphs
  • Sketch graphs of trigonometric functions after transformations
  • Calculate the area of circle segments

To help you plan your studies and revision, download the checklist as a guide to what you need to know in order to get a grade A* at GCSE Mathematics

Grade A* checklist