FMPRFurther Maths, Maths & Physics Revision
Pearson Edexcel A level · 9MA0

Mathematics

Every topic Edexcel 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

Topics 1 to 10, Papers 1 and 2.

1ProofProving statements are always true (by deduction, exhaustion or contradiction) and disproving them with a counter-example.1 point
  1. 1.1Proof by deduction, exhaustion and counter-example (Year 12); proof by contradiction (Year 13)Y12–13
Practise this topic 1 question
2Algebra and functionsThe algebra toolkit: indices, surds, quadratics, simultaneous equations, inequalities, polynomials, graph sketching, functions, transformations and partial fractions.11 points
  1. 2.1Laws of indices for all rational exponentsY12
  2. 2.2Surds and rationalising the denominatorY12
  3. 2.3Quadratic functions: discriminant, completing the square, solvingY12
  4. 2.4Simultaneous equations, one linear and one quadraticY12
  5. 2.5Linear and quadratic inequalities; set notation; graphical interpretationY12
  6. 2.6Polynomials: algebraic division, factor theorem; simplifying rational expressionsY12–13
  7. 2.7Graphs of cubics, quartics and reciprocals (Year 12); modulus graphs (Year 13); proportionY12–13
  8. 2.8Composite and inverse functions; domain and rangeY13
  9. 2.9Transformations of y = f(x) (Year 12); combinations and modulus (Year 13)Y12–13
  10. 2.10Partial fractionsY13
  11. 2.11Functions in modellingY13
Practise this topic 1 question
3Coordinate geometry in the (x, y) planeEquations of straight lines and circles, and curves given by parametric equations.4 points
  1. 3.1Straight lines; parallel and perpendicular gradientsY12
  2. 3.2CirclesY12
  3. 3.3Parametric equationsY13
  4. 3.4Parametric equations in modellingY13
4Sequences and seriesBinomial expansions, sequences, arithmetic and geometric series, and sigma notation.6 points
  1. 4.1Binomial expansion: positive integer n (Year 12); rational n (Year 13)Y12–13
  2. 4.2Sequences: nth term, recurrence relations; increasing, decreasing, periodicY13
  3. 4.3Sigma notationY13
  4. 4.4Arithmetic sequences and seriesY13
  5. 4.5Geometric sequences and series; sum to infinityY13
  6. 4.6Sequences and series in modellingY13
Practise this topic 1 question
5TrigonometrySine and cosine rules, radians, trigonometric graphs, identities, the addition and double angle formulae, and solving trigonometric equations.9 points
  1. 5.1sin, cos, tan; sine and cosine rules; area (Year 12); radians, arc length, sector area (Year 13)Y12–13
  2. 5.2Small angle approximationsY13
  3. 5.3Graphs, symmetries and periodicity of sin, cos and tanY12–13
  4. 5.4sec, cosec and cot; inverse trigonometric functionsY13
  5. 5.5tan θ = sin θ / cos θ and sin²θ + cos²θ = 1 (Year 12); sec²θ and cosec²θ identities (Year 13)Y12–13
  6. 5.6Double angle and compound angle formulae; R formY13
  7. 5.7Solve trigonometric equations in a given intervalY12–13
  8. 5.8Proofs involving trigonometric identitiesY13
  9. 5.9Trigonometric functions in contextY13
Practise this topic 1 question
6Exponentials and logarithmsExponential functions such as eˣ, logarithms and their laws, and modelling growth and decay.7 points
  1. 6.1Functions aˣ and eˣ and their graphsY12
  2. 6.2Gradient of e^(kx); exponential modelsY12
  3. 6.3Logarithms; ln xY12
  4. 6.4Laws of logarithmsY12
  5. 6.5Solve aˣ = bY12
  6. 6.6Logarithmic graphs to estimate parametersY12
  7. 6.7Exponential growth and decay modelsY12
Practise this topic 1 question
7DifferentiationFinding 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. 7.1Gradient, rate of change, first principles, second derivatives (Year 12); convexity and inflection (Year 13)Y12–13
  2. 7.2Differentiate xⁿ (Year 12); eˣ, aˣ, trigonometric functions and ln x (Year 13)Y12–13
  3. 7.3Tangents, normals, stationary points; increasing and decreasing functionsY12–13
  4. 7.4Product, quotient and chain rules; connected rates of changeY13
  5. 7.5Implicit and parametric differentiationY13
  6. 7.6Construct simple differential equationsY13
Practise this topic 2 questions
8IntegrationReversing differentiation to find areas and solve problems: standard integrals, substitution, integration by parts, partial fractions and differential equations.8 points
  1. 8.1Fundamental Theorem of CalculusY12
  2. 8.2Integrate xⁿ (Year 12); eˣ, 1/x and trigonometric functions (Year 13)Y12–13
  3. 8.3Definite integrals and areas (Year 12); including parametric curves (Year 13)Y12–13
  4. 8.4Integration as the limit of a sumY13
  5. 8.5Integration by substitution and by partsY13
  6. 8.6Integration using partial fractionsY13
  7. 8.7Separable differential equationsY13
  8. 8.8Interpret solutions of differential equationsY13
Practise this topic 1 question
9Numerical methodsFinding approximate answers when exact ones are not possible: sign changes, iteration, Newton–Raphson and the trapezium rule.5 points
  1. 9.1Locate roots by change of signY13
  2. 9.2Iteration; cobweb and staircase diagramsY13
  3. 9.3Newton–Raphson methodY13
  4. 9.4Trapezium ruleY13
  5. 9.5Numerical methods in contextY13
10VectorsVectors in two and three dimensions: magnitude, direction, position vectors and geometric problems.5 points
  1. 10.1Vectors in 2D (Year 12) and 3D (Year 13)Y12–13
  2. 10.2Magnitude and direction; unit vectorsY12–13
  3. 10.3Add vectors; multiply by scalars; parallel vectorsY12–13
  4. 10.4Position vectors; distance between pointsY12–13
  5. 10.5Vectors in pure mathematics and in contextY12–13

Statistics

Topics 1 to 5, Paper 3 Section A.

1Statistical samplingHow data is collected: populations, samples and the different sampling methods.1 point
  1. 1.1Populations and samples; sampling methodsY12
2Data presentation and interpretationShowing and summarising data: diagrams, averages, spread, correlation and regression, outliers and cleaning data.4 points
  1. 2.1Histograms, frequency polygons, box plots, cumulative frequencyY12
  2. 2.2Scatter diagrams and regression lines (Year 12); change of variable and PMCC (Year 13)Y12–13
  3. 2.3Measures of location and spread; standard deviationY12
  4. 2.4Outliers; cleaning dataY12
3ProbabilityProbability with Venn diagrams, tree diagrams and conditional probability.3 points
  1. 3.1Mutually exclusive and independent eventsY12
  2. 3.2Conditional probabilityY13
  3. 3.3Modelling with probabilityY13
4Statistical distributionsThe binomial and normal distributions and when each is a sensible model.3 points
  1. 4.1Discrete distributions, including the binomialY12
  2. 4.2The Normal distribution; Normal approximation to the binomialY13
  3. 4.3Choose an appropriate distributionY13
Practise this topic 1 question
5Statistical hypothesis testingHypothesis testing: deciding whether data gives evidence against a claim, for proportions, means and correlation.3 points
  1. 5.1Language of hypothesis testing (Year 12); correlation coefficient tests (Year 13)Y12–13
  2. 5.2Hypothesis test for a binomial proportionY12
  3. 5.3Hypothesis test for the mean of a Normal distributionY13
Practise this topic 1 question

Mechanics

Topics 6 to 9, Paper 3 Section B.

6Quantities and units in mechanicsSI units for mechanics and converting between them.1 point
  1. 6.1SI quantities and unitsY12
7KinematicsDescribing motion: displacement, velocity and acceleration, motion graphs, the suvat equations, calculus and projectiles.5 points
  1. 7.1Language of kinematicsY12
  2. 7.2Displacement–time and velocity–time graphsY12
  3. 7.3Constant acceleration formulae (Year 12); in 2D with vectors (Year 13)Y12–13
  4. 7.4Calculus in kinematics (Year 12); in 2D with vectors (Year 13)Y12–13
  5. 7.5ProjectilesY13
Practise this topic 1 question
8Forces and Newton's lawsForces and Newton's laws: resolving forces, inclined planes, connected particles, pulleys and friction.6 points
  1. 8.1Force; Newton's first lawY12
  2. 8.2Newton's second law (Year 12); resolving forces (Year 13)Y12–13
  3. 8.3Weight and motion under gravityY12
  4. 8.4Newton's third law; equilibrium; connected particlesY12–13
  5. 8.5Resultant forces; dynamics in a planeY13
  6. 8.6Friction, F ≤ μRY13
Practise this topic 1 question
9MomentsMoments: the turning effect of a force, and rigid bodies in equilibrium.1 point
  1. 9.1Moments; equilibrium of rigid bodiesY13

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
LDSThe large data setA real data set provided by the exam board. Questions assume you have explored it in lessons.1 point
  1. LDSFamiliarity with the Pearson large data setY12–13
App 1Formulae you must recall (not in the formulae booklet)Formulae that are not in the exam formulae booklet, 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 GCSE Maths, and any of the pure content can appear in the applied paper.1 point
  1. AKGCSE Mathematics and the pure contentY12–13

The exam papers

Paper 1: Pure Mathematics 12 hours · 100 marks · 33⅓%9MA0/01
Paper 2: Pure Mathematics 22 hours · 100 marks · 33⅓%9MA0/02
Paper 3: Statistics and Mechanics2 hours · 100 marks · 33⅓%9MA0/03