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GCSE Foundation Maths Revision Notes

Here's a list of topics and question types to help you revise for the Foundation GCSE Maths exam. It has been updated for the new 9-1 GCSE maths for 2017. 

It doesn't contain every single thing you could ever come across, but it's pretty close! We've split it into 4 levels of difficulty, but everyone's different - something we think is hard might be easy for you!

Click here to download the list as a PDF

More basic topics:
  • Find the highest common factor (HCF), find the lowest common multiple (LCM) and show a number as a product of its prime factors
  • Know what a square number, cube number and prime number are
  • Find the order of rotational symmetry
  • Add, subtract, multiply and divide fractions
  • Convert between fractions, decimals and percentages
  • Do long multiplication
  • Find the percentage of an amount
  • Name 2D and 3D shapes (these are easily forgotten!)
  • Know what congruent means
  • Find parallel lines, acute angles and obtuse angles
  • Round numbers (e.g. to the nearest ten or to 2 d.p.)
  • Write a number to a given amount of significant figures (e.g. write 24.576 to 3 sig.fig.)
  • Write and plot coordinates
  • Draw plans, side elevations and front elevations from a 3D shape
  • Answer proportion questions, e.g. when given a recipe for 12 cakes and asked to work out the ingredients for 18 cakes
  • Convert between different metric units (e.g. how many metres in a kilometre)

Lower Mid-range difficulty:
  • Find the perimeter and area of shapes
  • Find the volume and surface area of 3D shapes
  • Find angles on a straight line, at a point, in a triangle and in a quadrilateral
  • Change between mixed numbers and top heavy fractions
  • Divide a number into a given ratio, e.g. divide £1200 into the ratio 1 : 2 : 3
  • Find and use the nth term of a sequence
  • Collect algebraic terms together to simplify them (e.g. a + a + a + a + a = 5a)
  • Know how to work with negative numbers, i.e. a minus times a minus equals a plus
  • Find the mean, median, mode and range
  • Work out an estimate of a given sum
  • Complete a 2-way table
  • Multiply decimals (particularly with money problems)
  • Solve algebraic equations, like 3x + 4 = 13
  • Click here to download our Quick Fire Algebra Revision Question Sheet

Higher Mid-range difficulty:
  • Work with indices (e.g. a3 x a4, a5 ÷ a2, (a2)3, a-2)
  • Find the area and circumference of a circle, including sectors of circles
  • Expand brackets (e.g. 2(x + 4) ) and factorise (e.g. 2x²+ 4x)
  • Work out speed and use a distance-time graph
  • Describe correlation on a scatter diagram and draw a line of best fit
  • Use inequalities
  • Answer questions involving perimeter or area when the lengths are written as algebraic expressions
  • Solve algebraic equations with unknowns on both sides, like 2x + 4 = x + 8
  • Substitute values into an equation
  • Construct a stem and leaf diagram
  • Draw a line graph when given the equation of the line, e.g. y = 2x + 4
  • Work out the angles for a pie chart and draw it
  • Work out currency conversion questions

Higher level of difficulty:
  • Find the mean and median from grouped frequency tables
  • Use Standard form
  • Use Pythagoras’ theorem
  • Expand a pair of brackets, e.g. (x + 4)(x + 2)
  • Factorise simple quadratic expressions, e.g. x² + 5x + 6
  • Solve linear simultaneous equations
  • Find probability and use probability tree diagrams
  • Use bearings
  • Rotate, reflect and translate shapes on a coordinate grid and describe a single transformation
  • Enlarge a shape by a scale factor, including fractional scale factors
  • Know and use the rules for angles on parallel lines (alternate, corresponding, opposite, co-interior)
  • Use compound interest
  • Find the exterior and interior angles of a polygon
  • Use trigonometry for right-angled triangles (SOH CAH TOA)
  • Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°
  • Work out direct and indirect proportion
  • Construct triangles, perpendicular bisectors and angle bisectors using a pair of compasses
  • Work out density and pressure
  • Understand y = mx + c and use it to find the equation of a line and the equations of parallel lines

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

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

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