AQA · GCSE · Mathematics
AQA GCSE Mathematics Syllabus
The complete AQA GCSE Mathematics specification mapped to 165 topics. Click any topic for free revision notes and practice questions.
Algebraic fractions
simplifying, adding, subtracting, multiplying and dividing
0 Qs
Angles
at a point, on a straight line, parallel lines and transversals
0 Qs
Area under a curve
estimating and interpreting
0 Qs
Basic probability
calculating, listing outcomes and sample space diagrams
0 Qs
Box plots
drawing, interpreting and comparing distributions
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Circle theorems
angles, tangents, chords and cyclic quadrilaterals
0 Qs
Circles
circumference, area and parts of a circle (arc, sector, segment)
20 Qs⚡ Practice
Combined events
tree diagrams and two-way tables
0 Qs
Conditional probability
Venn diagrams, tree diagrams and formulae
0 Qs
Constructions
triangles, angle bisectors and perpendicular bisectors using ruler and compass
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Cumulative frequency graphs
drawing and interpreting
0 Qs
Direct and inverse proportion
algebraic and graphical representations
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Factorising
common factors and difference of two squares
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Fractions
operations, converting between fractions, decimals and percentages
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operations, mixed numbers and improper fractions
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Gradients of curves
drawing and interpreting tangents
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Linear equations
solving and forming
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Linear inequalities
solving and representing on a number line
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Other non-linear graphs
cubic, reciprocal, exponential, trigonometric
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Percentages
percentage of amounts, percentage change, reverse percentages
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Properties of 2D shapes
angles, triangles, quadrilaterals and polygons
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triangles, quadrilaterals, polygons
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Proportion
direct and inverse proportion problems
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Quadratic equations
solving by completing the square or using the quadratic formula
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solving by factorising
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Quadratic graphs
plotting, recognising features and interpreting
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Ratio
simplifying, dividing quantities, solving problems
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Real-life graphs
distance–time, speed–time, conversion and other contexts
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Representing and interpreting data
bar charts, pie charts, pictograms and line graphs
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bar charts, pie charts, pictograms, line graphs and stem-and-leaf diagrams
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Rounding
to decimal places, significant figures and nearest integer
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Scatter graphs
plotting, drawing and interpreting lines of best fit, correlation
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Sequences
term-to-term and position-to-term rules
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Similarity
identifying similar shapes and using scale factors for lengths, areas and volumes
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Simplifying expressions
collecting like terms, expanding and factorising
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Simultaneous equations
linear–linear (algebraic and graphical)
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linear–quadratic
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Standard form
converting, calculating and interpreting
0 Qs
Statistical measures
mean, median, mode and range for discrete and grouped data
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mean, median, mode and range from lists, tables and grouped data
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Straight-line graphs
plotting, equation y = mx + c, gradient and intercept
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Surds
simplifying, rationalising the denominator and basic calculations
20 Qs⚡ Practice
Transformations
reflection, rotation, translation and enlargement
0 Qs
translation, rotation, reflection and enlargement including fractional and negative scale factors
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Transformations of graphs
translations, reflections, stretches
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Types of number
integers, fractions, decimals, primes, factors and multiples
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integers, primes, factors, multiples
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Units
converting between metric and imperial, compound measures (speed, density, pressure)
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Vector geometry
proofs and problems using vectors
0 Qs
Vectors
notation, addition, subtraction and scalar multiplication
0 Qs
All topics
Algebra
0 Qs
Algebraic fractions
0 Qs
Algebraic notation, terminology and conventions
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Angles in parallel lines and polygons
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Arc lengths and areas of sectors
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Area of a triangle using ½ab sin C
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Arithmetic sequences and finding the nth term
0 Qs
Basic probability including single events and sample spaces
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Bearings
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Bearings and scale drawings
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Circle theorems
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Circumference and area of circles, arcs and sectors
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Combined events, possibility spaces and mutually exclusive and exhaustive events
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Comparing distributions and populations
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Comparing distributions using statistical measures and diagrams
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Completing the square
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Composite and inverse functions
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Compound interest and repeated percentage change
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Conditional probability using two-way tables and formal notation
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Congruence and congruency criteria (SSS, SAS, ASA, RHS)
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Congruence and geometric proof
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Constructions, loci and scale drawings
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Coordinates and linear graphs including gradient and y-intercept
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Coordinates in 2D and 3D
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Cumulative frequency graphs and box plots
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Direct and inverse proportion
Equation of a straight line and parallel and perpendicular lines
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Estimation and approximation
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Exact trigonometric values for 0°, 30°, 45°, 60°, 90°
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Exact values using fractions, surds and pi
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Expanding and factorising expressions including quadratics
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Expanding single and double brackets
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Factorising quadratic expressions
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Fractional and negative scale factor enlargements
0 Qs
Frequency polygons and histograms with equal class widths
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Frequency tables and frequency polygons
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Geometric sequences and other special sequences
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Geometry and Measures
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Gradients of curves and area under graphs including kinematics interpretation
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Graphs of circles and other implicit curves
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Growth and decay including compound and reverse compound problems
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HCF, LCM and prime factor decomposition
0 Qs
Highest common factor (HCF) and lowest common multiple (LCM)
20 Qs⚡ Practice
Histograms and frequency density
0 Qs
Histograms with unequal class widths and frequency density
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Interior and exterior angles of polygons
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Iteration and iterative methods to solve equations
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Laws of indices (including negative and fractional indices)
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Linear inequalities and representing solutions on a number line or graph
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Loci and regions
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Maps, scale drawings and scale factors
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Mean from frequency tables and grouped frequency tables (including estimated mean)
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Mutually exclusive and independent events
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nth term of a quadratic sequence
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Number
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Order of operations (BIDMAS/BODMAS)
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Order of operations and integer arithmetic
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Parallel and perpendicular lines
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Percentages including percentage change, reverse percentage and compound interest
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Perimeter and area of 2D shapes
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Perimeter and area of 2D shapes including trapezium and compound shapes
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Plans and elevations
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Plotting and interpreting quadratic, cubic, reciprocal and other non-linear graphs
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Powers, roots and index laws
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Powers, roots and index notation
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Prime factorisation and product of prime factors
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Probability
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Pythagoras' theorem in 2D and 3D
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Quadratic and other non-linear inequalities
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Quadratic and other non-linear sequences including nth term
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Quadratic inequalities and regions on a graph
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Ratio and proportion
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Ratio, Proportion and Rates of Change
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Real-life graphs and rates of change
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Rearranging formulae (changing the subject)
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Relative frequency and expected outcomes
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Relative frequency and experimental probability
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Rounding, estimation and limits of accuracy
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Sampling methods and questionnaire design
20 Qs⚡ Practice
Scale factors, maps and scale drawings
0 Qs
Scatter graphs, correlation and lines of best fit
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Sequences including arithmetic and geometric sequences, nth term
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Similarity including area and volume scale factors
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Simplifying and manipulating algebraic expressions
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Simultaneous equations (linear)
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Simultaneous equations involving one linear and one quadratic
Sine rule and cosine rule
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Sine rule, cosine rule and area of a triangle using ½ab sinC
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Solving equations graphically including finding intersections
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Solving linear equations
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Solving quadratic equations by completing the square and the quadratic formula
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Solving quadratic equations by factorising
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Speed, density and pressure
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Standard form
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Statistics
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Substitution into formulae and expressions
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Surds and exact calculations
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Time calculations and timetables
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Transformations of graphs and functions
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Tree diagrams including conditional probability
Trigonometric graphs and exact values
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Trigonometry in 3D problems
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Trigonometry in right-angled triangles (sin, cos, tan)
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Trigonometry in right-angled triangles (SOH CAH TOA)
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Units, measures and conversions
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Upper and lower bounds and error intervals
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Upper and lower bounds in calculations
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Vector proofs and geometric arguments using vectors
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Vectors and vector arithmetic
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Venn diagrams and set notation
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Venn diagrams and set notation in probability
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Volume and surface area of composite solids
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Volume and surface area of prisms, cylinders, cones, spheres and pyramids
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Volume and surface area of prisms, cylinders, pyramids, cones and spheres
Writing and using formulae
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