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:

Number

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

Algebra

• 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

Geometry

• 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