A level · Pearson Edexcel

Mathematics 9MA0

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

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

Official specification (PDF)

Pure mathematics

Compulsory

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 sub-topic
  1. 1.1Proof by deduction, exhaustion, counter-example and contradictionY13
2Algebra and functionsThe algebra toolkit: indices, surds, quadratics, simultaneous equations, inequalities, polynomials, graph sketching, functions, transformations and partial fractions.11 sub-topics
  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 inequalitiesY12
  6. 2.6Polynomials, the factor theorem and algebraic divisionY13
  7. 2.7Graphs of cubics, quartics, reciprocals and modulus functionsY13
  8. 2.8Composite and inverse functionsY13
  9. 2.9Transformations of y = f(x)Y13
  10. 2.10Partial fractionsY13
  11. 2.11Functions in modellingY13
3Coordinate geometry in the (x, y) planeEquations of straight lines and circles, and curves given by parametric equations.4 sub-topics
  1. 3.1Straight lines and their 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 sub-topics
  1. 4.1Binomial expansionY13
  2. 4.2Sequences and recurrence relationsY13
  3. 4.3Sigma notationY13
  4. 4.4Arithmetic sequences and seriesY13
  5. 4.5Geometric sequences and seriesY13
  6. 4.6Sequences and series in modellingY13
5TrigonometrySine and cosine rules, radians, trigonometric graphs, identities, the addition and double angle formulae, and solving trigonometric equations.9 sub-topics
  1. 5.1Trigonometry, radians, arc length and sector areaY13
  2. 5.2Small angle approximationsY13
  3. 5.3Graphs, symmetries and periodicity of sin, cos and tanY13
  4. 5.4Reciprocal and inverse trigonometric functionsY13
  5. 5.5Trigonometric identitiesY13
  6. 5.6Double angle and compound angle formulaeY13
  7. 5.7Solve trigonometric equations in a given intervalY13
  8. 5.8Proofs involving trigonometric identitiesY13
  9. 5.9Trigonometric functions in contextY13
6Exponentials and logarithmsExponential functions such as eˣ, logarithms and their laws, and modelling growth and decay.Y127 sub-topics
  1. 6.1Functions aˣ and eˣ and their graphsY12
  2. 6.2The gradient of e^(kx) and exponential modelsY12
  3. 6.3Logarithms and 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
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 sub-topics
  1. 7.1Gradients, first principles and second derivativesY13
  2. 7.2Differentiating standard functionsY13
  3. 7.3Tangents, normals and stationary pointsY13
  4. 7.4The product, quotient and chain rulesY13
  5. 7.5Implicit and parametric differentiationY13
  6. 7.6Construct simple differential equationsY13
8IntegrationReversing differentiation to find areas and solve problems: standard integrals, substitution, integration by parts, partial fractions and differential equations.8 sub-topics
  1. 8.1Fundamental theorem of calculusY12
  2. 8.2Integrating standard functionsY13
  3. 8.3Definite integrals and areasY13
  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
9Numerical methodsFinding approximate answers when exact ones are not possible: sign changes, iteration, Newton–Raphson and the trapezium rule.Y135 sub-topics
  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 sub-topics
  1. 10.1Vectors in two and three dimensionsY13
  2. 10.2Magnitude, direction and unit vectorsY13
  3. 10.3Adding vectors, scalar multiples and parallel vectorsY13
  4. 10.4Position vectors and distancesY13
  5. 10.5Vectors in pure mathematics and in contextY13

Statistics

Compulsory

Topics 1 to 5, Paper 3 Section A.

1Statistical samplingHow data is collected: populations, samples and the different sampling methods.Y121 sub-topic
  1. 1.1Populations, samples and sampling methodsY12
2Data presentation and interpretationShowing and summarising data: diagrams, averages, spread, correlation and regression, outliers and cleaning data.4 sub-topics
  1. 2.1Histograms, frequency polygons, box plots, cumulative frequencyY12
  2. 2.2Scatter diagrams, regression lines and correlationY13
  3. 2.3Measures of location and spreadY12
  4. 2.4Outliers and cleaning dataY12
3ProbabilityProbability with Venn diagrams, tree diagrams and conditional probability.3 sub-topics
  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 sub-topics
  1. 4.1Discrete distributions, including the binomialY12
  2. 4.2The normal distribution and the normal approximation to the binomialY13
  3. 4.3Choose an appropriate distributionY13
5Statistical hypothesis testingHypothesis testing: deciding whether data gives evidence against a claim, for proportions, means and correlation.3 sub-topics
  1. 5.1Hypothesis testing, including tests for correlationY13
  2. 5.2Hypothesis test for a binomial proportionY12
  3. 5.3Hypothesis test for the mean of a normal distributionY13

Mechanics

Compulsory

Topics 6 to 9, Paper 3 Section B.

6Quantities and units in mechanicsSI units for mechanics and converting between them.Y121 sub-topic
  1. 6.1SI quantities and unitsY12
7KinematicsDescribing motion: displacement, velocity and acceleration, motion graphs, the suvat equations, calculus and projectiles.5 sub-topics
  1. 7.1Language of kinematicsY12
  2. 7.2Displacement–time and velocity–time graphsY12
  3. 7.3Constant acceleration formulae, including in 2DY13
  4. 7.4Calculus in kinematics, including in 2DY13
  5. 7.5ProjectilesY13
8Forces and Newton's lawsForces and Newton's laws: resolving forces, inclined planes, connected particles, pulleys and friction.6 sub-topics
  1. 8.1Forces and Newton's first lawY12
  2. 8.2Newton's second law and resolving forcesY13
  3. 8.3Weight and motion under gravityY12
  4. 8.4Newton's third law, equilibrium and connected particlesY13
  5. 8.5Resultant forces and dynamics in a planeY13
  6. 8.6Friction, F ≤ μRY13
9MomentsMoments: the turning effect of a force, and rigid bodies in equilibrium.Y131 sub-topic
  1. 9.1Moments and equilibrium of rigid bodiesY13

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
LDSThe large data setA real data set provided by the exam board. Questions assume you have explored it in lessons.1 sub-topic
  1. LDSFamiliarity with the Pearson large data setY13
A1Formulae 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 sub-topics
  1. PPureY13
  2. CCalculusY13
  3. VVectorsY13
  4. SStatisticsY13
  5. MMechanicsY13
AKAssumed knowledgeA level Maths builds on GCSE Maths, and any of the pure content can appear in the applied paper.1 sub-topic
  1. AKGCSE Mathematics and the pure contentY13

The exam papers

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