Mathematics

GCSE Mathematics

Generic Topics

Number

Integers, decimals, fractions; order of operations
Factors, multiples, primes; HCF & LCM
Indices & roots; standard form
Rounding, estimation, bounds & error intervals
Percentages including reverse; ratio & proportion

Algebra

Simplify, expand, factorise; algebraic manipulation
Linear & quadratic equations; inequalities
Simultaneous equations (linear–linear and lin–quad)
Sequences (arithmetic, geometric, nth term)
Graphs: linear, quadratic, cubic, reciprocal, exponential
Rearranging formulae; algebraic fractions (H)
Surds; iteration; proof (H)

Ratio, Proportion & Rates of Change

Sharing & scaling in a ratio
Direct & inverse proportion; proportional graphs
Compound measures (speed, density, pressure)
Rates of change from graphs; exponential growth/decay

Geometry & Measures

Angle facts; polygons; parallel lines
Constructions & loci; scale drawings; bearings
Pythagoras & trigonometry (right-angled)
Further trigonometry (sine/cosine rule; area) (H)
Transformations; similarity & congruence
Perimeter, area & volume incl. frustums; surface area
Vectors (H); circle theorems; equation of a circle (H)
Units & metric/imperial conversion

Probability

Theoretical & experimental probability; relative frequency
Sample spaces; tree diagrams; Venn diagrams
Mutually exclusive & independent events; conditional probability

Statistics

Data collection & representation (tables, charts, graphs)
Averages (mean/median/mode) & range
Grouped data: estimating the mean; histograms
Cumulative frequency & box plots; correlation & best-fit

Higher/Extension

Algebraic & geometric proof
Surds & algebraic fractions
Iteration & numerical methods
Equation of a circle; further trig identities
Introductory calculus (gradient/area) — common in IGCSE

A Level Mathematics

Generic topics common to AQA, Edexcel (Pearson), OCR, and International A Level specifications.

A LEVEL MATHEMATICS – TOPIC LIST

AQA • OCR • Pearson Edexcel

PURE MATHEMATICS

Proof: deduction, contradiction, exhaustion, algebraic proof
Algebra and functions: quadratics, inequalities, functions, graphs
Coordinate geometry: straight lines, circles
Sequences and series: arithmetic, geometric, sigma notation
Trigonometry: identities, equations, sine & cosine rule
Exponentials and logarithms
Differentiation: rules, tangents, optimisation
Integration: definite/indefinite, area, substitution, parts
Numerical methods
Vectors in 2D and 3D

STATISTICS

Data collection and sampling
Statistical measures
Probability
Binomial and normal distributions
Hypothesis testing

MECHANICS

Scalars and vectors
Kinematics and SUVAT
Forces and Newton's laws
Moments and equilibrium
Work, energy, power
Momentum and collisions

IB Mathematics

Analysis & Approaches (AA) • Applications & Interpretation (AI)

IB MATHEMATICS – TOPIC LIST

Analysis & Approaches (AA) • Applications & Interpretation (AI)
SL & HL

NUMBER & ALGEBRA

Arithmetic and geometric sequences and series
Exponents and logarithms
Financial mathematics (AI focus)
Proof (HL emphasis)

ALGEBRA

Algebraic manipulation
Quadratic functions and equations
Polynomial, rational and radical functions
Equations and inequalities
Systems of equations

FUNCTIONS

Concept of a function
Graphing and transformations
Composite and inverse functions
Exponential and logarithmic functions

GEOMETRY & TRIGONOMETRY

Coordinate geometry
Trigonometric ratios and identities
Radians
Sine and cosine rule
Vectors in 2D and 3D

STATISTICS & PROBABILITY

Data collection and representation
Descriptive statistics
Probability laws
Random variables
Binomial and normal distributions
Correlation and regression

CALCULUS

Limits and continuity (HL focus)
Differentiation and applications
Integration and applications
Differential equations (HL)

INTERNAL ASSESSMENT

Mathematical exploration
Use of technology
Communication and reflection

Primary Mathematics (UK)

Generic topic overview aligned to the National Curriculum for Key Stage 1 (Years 1–2) and Key Stage 2 (Years 3–6).

PRIMARY MATHEMATICS – TOPIC LIST

Aligned with the National Curriculum for England (Years 1–6)

YEAR 1

Counting to 100 forwards and backwards
Place value within 100
Addition and subtraction within 20
Number bonds to 10 and 20
2D and 3D shapes
Measurement: length, mass, volume, time
Simple fractions (half and quarter)

YEAR 2

Place value within 100
Addition and subtraction within 100
Multiplication and division (2, 5, 10)
Fractions: halves, thirds, quarters
Measurement and money
Properties of shapes
Statistics: pictograms and bar charts

YEAR 3

Place value to 1000
Addition and subtraction with exchanges
Multiplication and division (3, 4, 8)
Fractions on a number line
Perimeter
Time and measurement
Statistics: bar charts and tables

YEAR 4

Place value to 10,000
Formal written methods
Times tables up to 12×12
Fractions and decimals
Area and perimeter
Angles and properties of shapes
Statistics: line graphs

YEAR 5

Place value to 1,000,000
Long multiplication and division
Fractions, decimals and percentages
Measurement and conversions
Properties of shapes and angles
Position and direction
Statistics: line graphs and tables

YEAR 6

Place value to 10,000,000
Four operations with large numbers
Ratio and proportion
Algebra basics
Fractions, decimals and percentages
Area, perimeter and volume
Statistics: averages and interpretation
SATs problem solving and reasoning

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Engaging lessons, steady progress, helpful support — and results they’re proud of.

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