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.

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

Perfect for 11 Plus & SATs Revision

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