UK · Subject guide
Mathematics
A-Level Mathematics (AQA 7357), against the DfE/Ofqual subject content.
01 · Overview
Mathematics
A-Level Mathematics (AQA 7357), against the DfE/Ofqual subject content.
- Subject guide
- A-Levels
- Topics mapped
- 20
02 · Complete topic map
Complete topic map
Every topic recorded for this subject in the curriculum is reproduced below in its full hierarchy. The descriptions reflect the mapped scope without implying additional exam rules.
- 01
Overarching themes
Cross-cutting competencies in mathematical argument, language and proof; problem solving; and mathematical modelling that run through the whole qualification.
- 02
Proof
Methods of mathematical proof including deduction, exhaustion, disproof by counter-example and proof by contradiction.
- 03
Algebra and functions
Indices, surds, quadratics, simultaneous and inequality solving, polynomials, the modulus function, composite and inverse functions, graph transformations and partial fractions.
- 04
Coordinate geometry in the (x, y) plane
Straight lines, circles and parametric equations of curves, including conversion between parametric and Cartesian forms.
- 05
Sequences and series
Arithmetic and geometric sequences and series, sigma notation, binomial expansion, and recurrence relations including increasing, decreasing and periodic sequences.
- 06
Trigonometry
Radian measure, trigonometric ratios, identities, reciprocal and inverse functions, addition and double-angle formulae, and solving trigonometric equations.
- 07
Exponentials and logarithms
Exponential functions, the number e, laws of logarithms, exponential growth and decay models and the use of logarithmic graphs to estimate parameters.
- 08
Differentiation
Differentiation from first principles, rules for products, quotients and composite functions, implicit and parametric differentiation, and applications such as rates of change, stationary points and connected rates.
- 09
Integration
Indefinite and definite integration, integration as the reverse of differentiation, by substitution and by parts, areas under curves and solving differential equations.
- 10
Numerical methods
Locating roots by sign change, iterative methods including the Newton-Raphson method, and numerical integration using the trapezium rule.
- 11
Vectors
Two- and three-dimensional vectors, magnitude and direction, vector arithmetic, position vectors and their use in geometric and kinematic problems.
- 12
Statistical sampling
Populations and samples, sampling methods including random and non-random techniques, and the limitations of sampling.
- 13
Data presentation and interpretation
Interpreting single- and bivariate data, measures of central tendency and spread, outliers, correlation and regression, and use of the large data set.
- 14
Probability
Probability of events, mutually exclusive and independent events, conditional probability, Venn diagrams, tree diagrams and probability formulae.
- 15
Statistical distributions
Discrete and continuous distributions, the binomial distribution and the normal distribution as models for real-world situations.
- 16
Statistical hypothesis testing
Formulating hypotheses and conducting tests using the binomial distribution, correlation coefficients and the normal distribution.
- 17
Quantities and units in mechanics
Use of SI and related units for quantities such as length, time, mass, velocity, acceleration and force in mechanics.
- 18
Kinematics
Motion in a straight line and in two dimensions, displacement-velocity-acceleration relationships, motion graphs, the constant-acceleration equations and the use of calculus for variable acceleration including projectiles.
- 19
Forces and Newton's laws
Newton's laws of motion, forces as vectors, weight, friction, connected particles and motion under gravity.
- 20
Moments
Moments of forces about a point and the equilibrium of rigid bodies.
03 · Where this subject applies
Where this subject applies
These pathways and regions are explicitly connected to the subject in the curriculum.
Pathways and specifications
AS-Level
Advanced Subsidiary — the first year of A-Level study (standalone or first half of the full A-Level).
A-Level (A2)
The full Advanced Level — AS content plus the second-year A2 content.
Nations and regions
All registered regions
04 · Official sources
Official sources
The public sources below are referenced directly by this subject or by one of its topics.
This editorial selection points to the relevant official bodies. Always confirm current requirements, dates and amendments with your school or college and the appropriate awarding organisation.
2
Public references
UK · EuraStudy Guides
Place this subject inside the complete curriculum.
Open the curriculum guide to see every subject and topic, or continue to EuraStudy Summa to begin working with the material.