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GCSE Higher Maths Revision Notes

Here's a list of topics and question types to help you revise for the Higher GCSE Maths exam. It looks short . . . but that's because they are only additional topics; you also need to know all the foundation topics! You will have learnt a LOT of topics, so make sure you re-visit the foundation skills to make sure nothing has been forgotten.

Click here to download the list below as a PDF
  • Use fractional and negative indices
  • Work with surds (irrational numbers)
  • Use the Sine and Cosine rules and the rule for area of a triangle
  • Use all of the circle theorems – check our revision sheet for these
  • Solve simultaneous equations - try our revision sheet
  • Factorise quadratic equations (i.e. changing an equation like 2x² + 6x + 4 into (x + 2)(x + 2))
  • Solve quadratic equations (e.g. x² + 6x + 5 = 0) by factorising
  • Solve quadratic equations using the formula
  • Use the “difference of 2 squares”, e.g. x² - 9
  • Work out cumulative frequency, draw the graph and find the median and quartiles
  • Read and draw a box plot
  • Create histograms
  • Create frequency polygons
  • Understand stretches and shifts of graphs (this is when you have f(x) )
  • Construct a bisector of an angle and a perpendicular bisector of a line using a pair of compasses
  • Use a scale factor to find out the missing lengths on similar shapes
  • Understand that, with similar shapes, you multiply by the scale factor twice when finding area and three times when finding volume
  • Complete a probability tree
  • Find the probability of events: know when to multiply the fractions and when to add them
  • Change the subject of a formula
  • Use standard form
  • Use direct proportion and indirect proportion (using the α symbol)
  • Understand and use vectors
  • Find the equation of a perpendicular line
  • Use compound interest
  • Simplify algebraic fractions
  • Write recurring decimals as fractions
  • Use the equations for surface area and volume of spheres and cones
  • Substitute values into an equation so you can draw the graph
  • Use upper and lower bounds

If you don't have a GCSE workbook to use for practice, you might find the CGP workbook handy.

Foundation GCSE Maths Revision Notes
Progress And Advance In Maths Revision & Practice for Ages 11 too 13

Online SATs Test

11 Plus Revision Pack
Perfect for 11 Plus & SATs Revision

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