AQA · GCSE · Mathematics
AQA GCSE Mathematics Syllabus
The complete AQA GCSE Mathematics specification mapped to 72 topics. Click any topic for free revision notes and practice questions.
Algebraic fractions
simplifying, adding, subtracting, multiplying and dividing
Angles
at a point, on a straight line, parallel lines and transversals
Basic probability
calculating, listing outcomes and sample space diagrams
Circle theorems
angles, tangents, chords and cyclic quadrilaterals
Circles
circumference, area and parts of a circle (arc, sector, segment)
Fractions
operations, converting between fractions, decimals and percentages
Linear inequalities
solving and representing on a number line
Percentages
percentage of amounts, percentage change, reverse percentages
Properties of 2D shapes
angles, triangles, quadrilaterals and polygons
Quadratic graphs
plotting, recognising features and interpreting
Ratio
simplifying, dividing quantities, solving problems
Real-life graphs
distance–time, speed–time, conversion and other contexts
Representing and interpreting data
bar charts, pie charts, pictograms, line graphs and stem-and-leaf diagrams
Scatter graphs
plotting, drawing and interpreting lines of best fit, correlation
Similarity
identifying similar shapes and using scale factors for lengths, areas and volumes
Statistical measures
mean, median, mode and range for discrete and grouped data
Straight-line graphs
plotting, equation y = mx + c, gradient and intercept
Surds
simplifying, rationalising the denominator and basic calculations
Transformations
translation, rotation, reflection and enlargement including fractional and negative scale factors
Types of number
integers, fractions, decimals, primes, factors and multiples
Units
converting between metric and imperial, compound measures (speed, density, pressure)
Vectors
notation, addition, subtraction and scalar multiplication
All topics
Bearings
Combined events, possibility spaces and mutually exclusive and exhaustive events
Comparing distributions using statistical measures and diagrams
Composite and inverse functions
Congruence and congruency criteria (SSS, SAS, ASA, RHS)
Constructions, loci and scale drawings
Cumulative frequency graphs and box plots
Direct and inverse proportion
Exact trigonometric values for 0°, 30°, 45°, 60°, 90°
Expanding single and double brackets
Factorising quadratic expressions
Frequency polygons and histograms with equal class widths
Gradients of curves and area under graphs including kinematics interpretation
Graphs of circles and other implicit curves
Highest common factor (HCF) and lowest common multiple (LCM)
Histograms with unequal class widths and frequency density
Interior and exterior angles of polygons
Iteration and iterative methods to solve equations
Laws of indices (including negative and fractional indices)
Maps, scale drawings and scale factors
Order of operations (BIDMAS/BODMAS)
Perimeter and area of 2D shapes including trapezium and compound shapes
Plans and elevations
Plotting and interpreting quadratic, cubic, reciprocal and other non-linear graphs
Pythagoras' theorem in 2D and 3D
Quadratic and other non-linear inequalities
Quadratic and other non-linear sequences including nth term
Rearranging formulae (changing the subject)
Relative frequency and experimental probability
Rounding, estimation and limits of accuracy
Sampling methods and questionnaire design
Sequences including arithmetic and geometric sequences, nth term
Simplifying and manipulating algebraic expressions
Simultaneous equations (linear)
Simultaneous equations involving one linear and one quadratic
Sine rule, cosine rule and area of a triangle using ½ab sinC
Solving equations graphically including finding intersections
Solving linear equations
Solving quadratic equations by completing the square and the quadratic formula
Solving quadratic equations by factorising
Standard form
Substitution into formulae and expressions
Time calculations and timetables
Transformations of graphs and functions
Tree diagrams including conditional probability
Trigonometry in 3D problems
Trigonometry in right-angled triangles (SOH CAH TOA)
Upper and lower bounds and error intervals
Venn diagrams and set notation in probability
Volume and surface area of prisms, cylinders, pyramids, cones and spheres
Practise the whole syllabus.
Free, instantly-marked AQA GCSE Mathematics questions across every topic above.
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