A level · AQA

Mathematics 7357

Every topic AQA can examine you on. Open a topic to see its sub-topics, lessons and practice questions.

  • 3 papers
  • 112 sub-topics
  • Y12Y13When each is usually taught

Official specification (PDF)

Pure mathematics

Compulsory

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 sub-topic
  1. A1Proof by deduction, exhaustion, counter-example and contradictionY13
BAlgebra and functionsThe algebra toolkit: indices, surds, quadratics, simultaneous equations, inequalities, polynomials, graph sketching, functions, transformations and partial fractions.11 sub-topics
  1. B1Laws of indices for all rational exponentsY12
  2. B2Surds, including rationalising the denominatorY12
  3. B3Quadratic functions, the discriminant and completing the squareY12
  4. B4Simultaneous equations, one linear and one quadraticY12
  5. B5Linear and quadratic inequalitiesY12
  6. B6Polynomials, the factor theorem and algebraic divisionY12
  7. B7Graphs of functions, including modulus graphs and asymptotesY13
  8. B8Composite and inverse functionsY13
  9. B9Transformations of y = f(x), including combinationsY13
  10. B10Partial fractionsY13
  11. B11Functions in modellingY13
CCoordinate geometry in the (x, y) planeEquations of straight lines and circles, and curves given by parametric equations.4 sub-topics
  1. C1Straight lines, including parallel and perpendicular linesY12
  2. C2Coordinate geometry of the circleY12
  3. C3Parametric equationsY13
  4. C4Parametric equations in modellingY13
DSequences and seriesBinomial expansions, sequences, arithmetic and geometric series, and sigma notation.6 sub-topics
  1. D1Binomial expansionY13
  2. D2Sequences and recurrence relationsY13
  3. D3Sigma notationY13
  4. D4Arithmetic sequences and seriesY13
  5. D5Geometric sequences and seriesY13
  6. D6Sequences and series in modellingY13
ETrigonometrySine and cosine rules, radians, trigonometric graphs, identities, the addition and double angle formulae, and solving trigonometric equations.9 sub-topics
  1. E1Trigonometry, radians, arc length and sector areaY13
  2. E2Small angle approximationsY13
  3. E3Graphs, symmetries and periodicity of sin, cos and tanY12
  4. E4Reciprocal and inverse trigonometric functionsY13
  5. E5Trigonometric identitiesY13
  6. E6Double angle and compound angle formulaeY13
  7. E7Solve trigonometric equations in a given intervalY13
  8. E8Proofs involving trigonometric functionsY13
  9. E9Trigonometric functions in contextY13
FExponentials and logarithmsExponential functions such as eˣ, logarithms and their laws, and modelling growth and decay.Y127 sub-topics
  1. F1Functions aˣ and eˣ and their graphsY12
  2. F2The gradient of e^(kx) and exponential modelsY12
  3. F3Logarithms and ln xY12
  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
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 sub-topics
  1. G1Gradients, first principles and second derivativesY13
  2. G2Differentiating standard functionsY13
  3. G3Tangents, normals and stationary pointsY12
  4. G4The product, quotient and chain rulesY13
  5. G5Implicit and parametric differentiationY13
  6. G6Construct simple differential equationsY13
HIntegrationReversing differentiation to find areas and solve problems: standard integrals, substitution, integration by parts, partial fractions and differential equations.8 sub-topics
  1. H1Fundamental theorem of calculusY12
  2. H2Integrating standard functionsY13
  3. H3Definite integrals and areas between curvesY13
  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
INumerical methodsFinding approximate answers when exact ones are not possible: sign changes, iteration, Newton–Raphson and the trapezium rule.Y134 sub-topics
  1. I1Locate roots by change of signY13
  2. I2Iteration and the Newton–Raphson methodY13
  3. I3Trapezium ruleY13
  4. I4Numerical methods in contextY13
JVectorsVectors in two and three dimensions: magnitude, direction, position vectors and geometric problems.5 sub-topics
  1. J1Vectors in two and three dimensionsY13
  2. J2Magnitude, direction and component formY12
  3. J3Adding vectors and multiplying by scalarsY12
  4. J4Position vectors and distancesY13
  5. J5Vectors in pure mathematics and in contextY13

Mechanics

Compulsory

Sections P to S. Assessed on Paper 2.

PQuantities and units in mechanicsSI units for mechanics and converting between them.Y121 sub-topic
  1. P1Fundamental and derived quantities and SI unitsY12
QKinematicsDescribing motion: displacement, velocity and acceleration, motion graphs, the suvat equations, calculus and projectiles.5 sub-topics
  1. Q1Language of kinematicsY12
  2. Q2Displacement–time and velocity–time graphsY12
  3. Q3Constant acceleration formulae, including in 2DY13
  4. Q4Calculus in kinematics, including in 2DY13
  5. Q5ProjectilesY13
RForces and Newton's lawsForces and Newton's laws: resolving forces, inclined planes, connected particles, pulleys and friction.6 sub-topics
  1. R1Forces and Newton's first lawY12
  2. R2Newton's second law and resolving forcesY13
  3. R3Weight and motion in a straight line under gravityY13
  4. R4Newton's third law, pulleys and connected particlesY13
  5. R5Resultant forces and dynamics in a planeY13
  6. R6Friction, F ≤ μRY13
SMomentsMoments: the turning effect of a force, and rigid bodies in equilibrium.Y131 sub-topic
  1. S1Moments in simple static contextsY13

Statistics

Compulsory

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.Y121 sub-topic
  1. K1Populations, samples and sampling techniquesY12
LData presentation and interpretationShowing and summarising data: diagrams, averages, spread, correlation and regression, outliers and cleaning data.Y124 sub-topics
  1. L1Diagrams for single-variable data, including histogramsY12
  2. L2Scatter diagrams, regression and correlationY12
  3. L3Averages, spread and standard deviationY12
  4. L4Outliers and cleaning dataY12
MProbabilityProbability with Venn diagrams, tree diagrams and conditional probability.3 sub-topics
  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 sub-topics
  1. N1Discrete distributions, including the binomial distributionY13
  2. N2The normal distributionY13
  3. N3Choose an appropriate distributionY13
OStatistical hypothesis testingHypothesis testing: deciding whether data gives evidence against a claim, for proportions, means and correlation.3 sub-topics
  1. O1The language of hypothesis testingY13
  2. O2Hypothesis test for a binomial proportionY12
  3. O3Hypothesis test for the mean of a normal distributionY13
LDSThe large data setA real data set published by AQA. Statistics questions assume you have explored it in lessons.1 sub-topic
  1. LDSFamiliarity with the AQA large data setY13

Across the whole course

Compulsory

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 sub-topics
  1. OT1.1Construct and present mathematical argumentsY13
  2. OT1.2Mathematical language and syntaxY13
  3. OT1.3Set notationY13
  4. OT1.4FunctionsY13
  5. OT1.5Critique arguments and proofsY13
OT2Mathematical problem solvingSolving unfamiliar problems, using numerical methods where needed, judging accuracy and explaining what the answer means. Applies to every paper.7 sub-topics
  1. OT2.1Recognise the underlying structure of a problemY13
  2. OT2.2Extended arguments for unstructured problemsY13
  3. OT2.3Interpret solutions in contextY13
  4. OT2.4Numerical methods to a required accuracyY13
  5. OT2.5Accuracy and limitations of solutionsY13
  6. OT2.6The problem-solving cycleY13
  7. OT2.7Diagrams in problem solvingY13
OT3Mathematical modellingTurning a real situation into maths, using the model, then judging and improving it. Applies to every paper.5 sub-topics
  1. OT3.1Build a modelY13
  2. OT3.2Use a modelY13
  3. OT3.3Interpret a model's outputsY13
  4. OT3.4Refine and evaluate a modelY13
  5. OT3.5Modelling assumptionsY13
ABFormulae you must recall (not given in the exam)Formulae that are not given in the exam, so you must learn them by heart.5 sub-topics
  1. PPureY13
  2. CCalculusY13
  3. VVectorsY13
  4. SStatisticsY13
  5. MMechanicsY13
AKAssumed knowledgeA level Maths builds on the whole of GCSE Maths.1 sub-topic
  1. AKGCSE MathematicsY13

The exam papers

Paper 1: Pure mathematics (sections A to I)2 h · 100 marks · 33⅓%7357/1
Paper 2: Pure and mechanics (sections A to J and P to S)2 h · 100 marks · 33⅓%7357/2
Paper 3: Pure and statistics (sections A to I and K to O)2 h · 100 marks · 33⅓%7357/3