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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!

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

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.

Perfect for 11 Plus & SATs Revision

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