FMPRFurther Maths, Maths & Physics Revision
AQA A-level · 7357

Mathematics

Every topic AQA can examine. Tap a topic to see its specification points; Y12 and Y13 show which year each one is taught.

Official specification (PDF)

Pure mathematics

Sections A to J. Assessed on all three papers.

AProofProving statements are always true (by deduction, exhaustion or contradiction) and disproving them with a counter-example.1 point
  1. A1Structure of mathematical proof: deduction, exhaustion, counter-example; proof by contradictionY12–13
Practise this topic 1 question
BAlgebra and functionsThe algebra toolkit: indices, surds, quadratics, simultaneous equations, inequalities, polynomials, graph sketching, functions, transformations and partial fractions.11 points
  1. B1Laws of indices for all rational exponentsY12
  2. B2Surds, including rationalising the denominatorY12
  3. B3Quadratic functions: discriminant, completing the square, solving quadraticsY12
  4. B4Simultaneous equations, one linear and one quadraticY12
  5. B5Linear and quadratic inequalities; graphical interpretationY12
  6. B6Polynomials: expanding, factorising, algebraic division, factor theorem; simplifying rational expressionsY12
  7. B7Graphs of functions, including modulus graphs; asymptotes; proportionY12–13
  8. B8Composite and inverse functionsY13
  9. B9Transformations of y = f(x), including combinationsY12–13
  10. B10Partial fractionsY13
  11. B11Functions in modellingY13
Practise this topic 1 question
CCoordinate geometry in the (x, y) planeEquations of straight lines and circles, and curves given by parametric equations.4 points
  1. C1Equation of a straight line; parallel and perpendicular linesY12
  2. C2Coordinate geometry of the circleY12
  3. C3Parametric equations; conversion to Cartesian formY13
  4. C4Parametric equations in modellingY13
DSequences and seriesBinomial expansions, sequences, arithmetic and geometric series, and sigma notation.6 points
  1. D1Binomial expansion: positive integer n (Year 12) and rational n (Year 13)Y12–13
  2. D2Sequences: nth term and recurrence relations; increasing, decreasing and periodicY13
  3. D3Sigma notationY13
  4. D4Arithmetic sequences and seriesY13
  5. D5Geometric sequences and series; sum to infinityY13
  6. D6Sequences and series in modellingY13
Practise this topic 1 question
ETrigonometrySine and cosine rules, radians, trigonometric graphs, identities, the addition and double angle formulae, and solving trigonometric equations.9 points
  1. E1sin, cos and tan; sine and cosine rules; area of a triangle; radians, arc length and sector areaY12–13
  2. E2Small angle approximationsY13
  3. E3Graphs, symmetries and periodicity of sin, cos and tanY12
  4. E4sec, cosec and cot; arcsin, arccos and arctanY13
  5. E5Identities tan θ = sin θ / cos θ and sin²θ + cos²θ = 1; sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θY12–13
  6. E6Double angle and compound angle formulae; R cos(θ ± α) formY13
  7. E7Solve trigonometric equations in a given intervalY12–13
  8. E8Proofs involving trigonometric functionsY13
  9. E9Trigonometric functions in contextY13
Practise this topic 1 question
FExponentials and logarithmsExponential functions such as eˣ, logarithms and their laws, and modelling growth and decay.7 points
  1. F1Functions aˣ and eˣ and their graphsY12
  2. F2Gradient of e^(kx); exponential modelsY12
  3. F3Logarithms; ln x as the inverse of eˣY12
  4. F4Laws of logarithmsY12
  5. F5Solve equations of the form aˣ = bY12
  6. F6Logarithmic graphs to estimate parameters in y = axⁿ and y = kbˣY12
  7. F7Exponential growth and decay in modellingY12
Practise this topic 1 question
GDifferentiationFinding gradients and rates of change: the rules for differentiating, tangents, stationary points, the product, quotient and chain rules, and implicit and parametric curves.6 points
  1. G1Derivative as gradient and rate of change; first principles; second derivatives; convex and concave curvesY12–13
  2. G2Differentiate xⁿ (Year 12); e^(kx), a^(kx), sin kx, cos kx, tan kx and ln x (Year 13)Y12–13
  3. G3Tangents, normals, stationary points; increasing and decreasing functionsY12
  4. G4Product, quotient and chain rules; connected rates of change; inverse functionsY13
  5. G5Implicit and parametric differentiationY13
  6. G6Construct simple differential equationsY13
Practise this topic 2 questions
HIntegrationReversing differentiation to find areas and solve problems: standard integrals, substitution, integration by parts, partial fractions and differential equations.8 points
  1. H1Fundamental Theorem of CalculusY12
  2. H2Integrate xⁿ (Year 12); e^(kx), 1/x, sin kx and cos kx (Year 13)Y12–13
  3. H3Definite integrals; areas under and between curvesY12–13
  4. H4Integration as the limit of a sumY13
  5. H5Integration by substitution and by partsY13
  6. H6Integration using partial fractionsY13
  7. H7First order separable differential equationsY13
  8. H8Interpret solutions of differential equations in contextY13
Practise this topic 1 question
INumerical methodsFinding approximate answers when exact ones are not possible: sign changes, iteration, Newton–Raphson and the trapezium rule.4 points
  1. I1Locate roots by change of signY13
  2. I2Iteration, cobweb and staircase diagrams; Newton–RaphsonY13
  3. I3Trapezium ruleY13
  4. I4Numerical methods in contextY13
JVectorsVectors in two and three dimensions: magnitude, direction, position vectors and geometric problems.5 points
  1. J1Vectors in two dimensions (Year 12) and three dimensions (Year 13)Y12–13
  2. J2Magnitude and direction; component formY12
  3. J3Add vectors; multiply by scalarsY12
  4. J4Position vectors; distance between two pointsY12–13
  5. J5Vectors in pure mathematics and in contextY12–13

Mechanics

Sections P to S. Assessed on Paper 2.

PQuantities and units in mechanicsSI units for mechanics and converting between them.1 point
  1. P1Fundamental and derived quantities and SI unitsY12
QKinematicsDescribing motion: displacement, velocity and acceleration, motion graphs, the suvat equations, calculus and projectiles.5 points
  1. Q1Language of kinematicsY12
  2. Q2Displacement–time and velocity–time graphsY12
  3. Q3Constant acceleration formulae; extension to 2D using vectorsY12–13
  4. Q4Calculus in kinematics; extension to 2D using vectorsY12–13
  5. Q5Motion under gravity in a vertical plane; projectilesY13
Practise this topic 1 question
RForces and Newton's lawsForces and Newton's laws: resolving forces, inclined planes, connected particles, pulleys and friction.6 points
  1. R1Force; Newton's first lawY12
  2. R2Newton's second law; resolving forces (Year 13)Y12–13
  3. R3Weight and motion in a straight line under gravityY12–13
  4. R4Newton's third law; equilibrium; pulleys and connected particlesY12–13
  5. R5Resultant forces; dynamics in a planeY13
  6. R6Friction, F ≤ μRY13
Practise this topic 1 question
SMomentsMoments: the turning effect of a force, and rigid bodies in equilibrium.1 point
  1. S1Moments in simple static contextsY13

Statistics

Sections K to O. Assessed on Paper 3, with the large data set.

KStatistical samplingHow data is collected: populations, samples and the different sampling methods.1 point
  1. K1Populations and samples; sampling techniques; critique samplingY12
LData presentation and interpretationShowing and summarising data: diagrams, averages, spread, correlation and regression, outliers and cleaning data.4 points
  1. L1Diagrams for single-variable data, including histogramsY12
  2. L2Scatter diagrams and regression lines; correlationY12
  3. L3Measures of central tendency and variation, including standard deviationY12
  4. L4Outliers; cleaning dataY12
MProbabilityProbability with Venn diagrams, tree diagrams and conditional probability.3 points
  1. M1Mutually exclusive and independent eventsY12
  2. M2Conditional probabilityY13
  3. M3Modelling with probabilityY13
NStatistical distributionsThe binomial and normal distributions and when each is a sensible model.3 points
  1. N1Discrete distributions, including the binomial distributionY12–13
  2. N2The Normal distributionY13
  3. N3Choose an appropriate distributionY13
Practise this topic 1 question
OStatistical hypothesis testingHypothesis testing: deciding whether data gives evidence against a claim, for proportions, means and correlation.3 points
  1. O1Language of hypothesis testing; correlation coefficient testsY12–13
  2. O2Hypothesis test for a binomial proportionY12
  3. O3Hypothesis test for the mean of a Normal distributionY13
Practise this topic 1 question
LDSThe large data setA real data set published by AQA. Statistics questions assume you have explored it in lessons.1 point
  1. LDSFamiliarity with the AQA large data setY12–13

Across the whole course

Not a topic of its own: the specification applies these to every paper.

OT1Mathematical argument, language and proofWriting clear mathematical arguments: correct notation, logic words such as 'implies', set notation and functions. Applies to every paper.5 points
  1. OT1.1Construct and present mathematical argumentsY12–13
  2. OT1.2Mathematical language and syntaxY12–13
  3. OT1.3Set notationY12–13
  4. OT1.4FunctionsY12–13
  5. OT1.5Critique arguments and proofsY12–13
OT2Mathematical problem solvingSolving unfamiliar problems, using numerical methods where needed, judging accuracy and explaining what the answer means. Applies to every paper.7 points
  1. OT2.1Recognise the underlying structure of a problemY12–13
  2. OT2.2Extended arguments for unstructured problemsY12–13
  3. OT2.3Interpret solutions in contextY12–13
  4. OT2.4Numerical methods to a required accuracyY12–13
  5. OT2.5Accuracy and limitations of solutionsY12–13
  6. OT2.6The problem-solving cycleY12–13
  7. OT2.7Diagrams in problem solvingY12–13
OT3Mathematical modellingTurning a real situation into maths, using the model, then judging and improving it. Applies to every paper.5 points
  1. OT3.1Build a modelY12–13
  2. OT3.2Use a modelY12–13
  3. OT3.3Interpret a model's outputsY12–13
  4. OT3.4Refine and evaluate a modelY12–13
  5. OT3.5Modelling assumptionsY12–13
App BFormulae you must recall (not given in the exam)Formulae that are not given in the exam, so you must learn them by heart.5 points
  1. PPureY12–13
  2. CCalculusY12–13
  3. VVectorsY12–13
  4. SStatisticsY12–13
  5. MMechanicsY12–13
AKAssumed knowledgeA level Maths builds on the whole of GCSE Maths.1 point
  1. AKGCSE MathematicsY12–13

The exam papers

Paper 1: pure mathematics (A to I)2 hours · 100 marks · 33⅓%7357/1
Paper 2: pure and mechanics (adds J, P to S)2 hours · 100 marks · 33⅓%7357/2
Paper 3: pure and statistics (adds K to O)2 hours · 100 marks · 33⅓%7357/3