A level · OCR

Mathematics H240

Every topic OCR 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

Section 1. Assessed on all three papers.

1.01ProofProving statements are always true (by deduction, exhaustion or contradiction) and disproving them with a counter-example.1 sub-topic
  1. 1.01a-dProofY13
1.02Algebra and functionsThe algebra toolkit: indices, surds, quadratics, simultaneous equations, inequalities, polynomials, graph sketching, functions, transformations and partial fractions.11 sub-topics
  1. 1.02aIndicesY12
  2. 1.02bSurdsY12
  3. 1.02cSimultaneous equationsY12
  4. 1.02d-fQuadratic functionsY12
  5. 1.02g-iInequalitiesY12
  6. 1.02j-kPolynomialsY13
  7. 1.02l-tThe modulus function and curve sketchingY13
  8. 1.02u-vFunctionsY13
  9. 1.02w-xGraph transformationsY13
  10. 1.02yPartial fractionsY13
  11. 1.02zModels in contextY13
1.03Coordinate geometry in the x-y planeEquations of straight lines and circles, and curves given by parametric equations.4 sub-topics
  1. 1.03a-cStraight linesY12
  2. 1.03d-fCirclesY12
  3. 1.03gParametric equations of curvesY13
  4. 1.03hParametric equations in contextY13
1.04Sequences and seriesBinomial expansions, sequences, arithmetic and geometric series, and sigma notation.6 sub-topics
  1. 1.04a-dBinomial expansionY13
  2. 1.04e-fSequencesY13
  3. 1.04gSigma notationY13
  4. 1.04hArithmetic sequencesY13
  5. 1.04i-jGeometric sequencesY13
  6. 1.04kModelling with sequences and seriesY13
1.05TrigonometrySine and cosine rules, radians, trigonometric graphs, identities, the addition and double angle formulae, and solving trigonometric equations.9 sub-topics
  1. 1.05a-dSin, cos and tan, the sine and cosine rules, and radiansY13
  2. 1.05eSmall angle approximationsY13
  3. 1.05f-gGraphs and exact values of the trigonometric functionsY13
  4. 1.05h-iInverse and reciprocal trigonometric ratiosY13
  5. 1.05j-kTrigonometric identitiesY13
  6. 1.05l-nFurther trigonometric identitiesY13
  7. 1.05oTrigonometric equationsY13
  8. 1.05pProof involving trigonometric functionsY13
  9. 1.05qTrigonometric functions in contextY13
1.06Exponentials and logarithmsExponential functions such as eˣ, logarithms and their laws, and modelling growth and decay.Y127 sub-topics
  1. 1.06aProperties of the exponential functionY12
  2. 1.06bGradient of e^(kx)Y12
  3. 1.06c-eProperties of the logarithmY12
  4. 1.06fLaws of logarithmsY12
  5. 1.06gEquations involving exponentialsY12
  6. 1.06hReduction to linear formY12
  7. 1.06iModelling using exponential functionsY12
1.07DifferentiationFinding 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. 1.07a-hGradients and differentiation from first principlesY13
  2. 1.07i-lDifferentiation of standard functionsY13
  3. 1.07m-pTangents, normals, stationary points, increasing and decreasing functionsY13
  4. 1.07q-rTechniques of differentiationY13
  5. 1.07sParametric and implicit differentiationY13
  6. 1.07tConstructing differential equationsY13
1.08IntegrationReversing differentiation to find areas and solve problems: standard integrals, substitution, integration by parts, partial fractions and differential equations.8 sub-topics
  1. 1.08aFundamental theorem of calculusY12
  2. 1.08b-cIndefinite integralsY13
  3. 1.08d-fDefinite integrals and areasY13
  4. 1.08gIntegration as the limit of a sumY13
  5. 1.08h-iIntegration by substitution and by partsY13
  6. 1.08jUse of partial fractions in integrationY13
  7. 1.08kDifferential equations with separable variablesY13
  8. 1.08lInterpreting the solution of a differential equationY13
1.09Numerical methodsFinding approximate answers when exact ones are not possible: sign changes, iteration, Newton–Raphson and the trapezium rule.Y135 sub-topics
  1. 1.09a-bSign change methodsY13
  2. 1.09c-eFormal iterative methods: iteration, cobweb and staircase diagramsY13
  3. 1.09c-eFormal iterative methods: the Newton-Raphson methodY13
  4. 1.09fNumerical integrationY13
  5. 1.09gUse numerical methods in contextY13
1.10VectorsVectors in two and three dimensions: magnitude, direction, position vectors and geometric problems.5 sub-topics
  1. 1.10a-bVectorsY13
  2. 1.10cMagnitude and direction of vectorsY13
  3. 1.10dBasic operations on vectorsY13
  4. 1.10e-fPosition vectors and distance between pointsY13
  5. 1.10g-hProblem solving using vectorsY13

Statistics

Compulsory

Section 2. Assessed on Paper 2.

2.01Statistical samplingHow data is collected: populations, samples and the different sampling methods.Y121 sub-topic
  1. 2.01a-dStatistical samplingY12
2.02Data presentation and interpretationShowing and summarising data: diagrams, averages, spread, correlation and regression, outliers and cleaning data.4 sub-topics
  1. 2.02a-bSingle variable dataY12
  2. 2.02c-eBivariate dataY13
  3. 2.02f-gMeasures of average and spreadY12
  4. 2.02h-jOutliers and cleaning dataY12
2.03ProbabilityProbability with Venn diagrams, tree diagrams and conditional probability.3 sub-topics
  1. 2.03aMutually exclusive and independent eventsY12
  2. 2.03b-dProbability, including conditional probabilityY13
  3. 2.03eModelling with probabilityY13
2.04Statistical distributionsThe binomial and normal distributions and when each is a sensible model.3 sub-topics
  1. 2.04a-dDiscrete probability distributionsY12
  2. 2.04e-gThe normal distributionY13
  3. 2.04hSelecting an appropriate distributionY13
2.05Statistical hypothesis testingHypothesis testing: deciding whether data gives evidence against a claim, for proportions, means and correlation.3 sub-topics
  1. 2.05aThe language of hypothesis testing, and tests using Pearson's correlation coefficient (2.05f-g)Y13
  2. 2.05b-cHypothesis test for the proportion in a binomial distributionY12
  3. 2.05d-eHypothesis test for the mean of a normal distributionY13

Mechanics

Compulsory

Section 3. Assessed on Paper 3.

3.01Quantities and units in mechanicsSI units for mechanics and converting between them.Y121 sub-topic
  1. 3.01a-cSI unitsY12
3.02KinematicsDescribing motion: displacement, velocity and acceleration, motion graphs, the suvat equations, calculus and projectiles.5 sub-topics
  1. 3.02aLanguage of kinematicsY12
  2. 3.02b-cGraphical representationY12
  3. 3.02d-eConstant accelerationY13
  4. 3.02f-gNon-uniform accelerationY13
  5. 3.02h-iGravity and projectilesY13
3.03Forces and Newton's lawsForces and Newton's laws: resolving forces, inclined planes, connected particles, pulleys and friction.6 sub-topics
  1. 3.03a-bNewton's first lawY12
  2. 3.03c-eNewton's second lawY13
  3. 3.03f-gWeightY12
  4. 3.03h-oNewton's third lawY13
  5. 3.03p-qApplications of vectors in a planeY13
  6. 3.03rFrictional forcesY13
3.04MomentsMoments: the turning effect of a force, and rigid bodies in equilibrium.Y131 sub-topic
  1. 3.04a-cMomentsY13

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 OCR 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 Mathematics2 h · 100 marks · 33⅓%H240/01
Paper 2: Pure Mathematics and Statistics2 h · 100 marks · 33⅓%H240/02
Paper 3: Pure Mathematics and Mechanics2 h · 100 marks · 33⅓%H240/03