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Compulsory content10 topics
AProof1 sub-topic
- A1Proof by induction for sums, divisibility and matrix powersNo lesson for this sub-topic yet.Y12
BComplex numbers11 sub-topics
- B1Solving polynomial equations with complex rootsNo lesson for this sub-topic yet.Y12
- B2Arithmetic with complex numbers in the form x + iyNo lesson for this sub-topic yet.Y12
- B3Complex conjugates and conjugate pairs of rootsNo lesson for this sub-topic yet.Y12
- B4Use and interpret Argand diagramsNo lesson for this sub-topic yet.Y12
- B5Convert between Cartesian and modulus–argument formNo lesson for this sub-topic yet.Y12
- B6Multiply and divide complex numbers in modulus–argument formNo lesson for this sub-topic yet.Y12
- B7Loci in the Argand diagram, such as |z − a| > r and arg(z − a) = θNo lesson for this sub-topic yet.Y12
- B8De Moivre's theorem: multiple angle formulae and sums of seriesNo lesson for this sub-topic yet.Y13
- B9Exponential form: e^(iθ) = cos θ + i sin θ and z = re^(iθ)No lesson for this sub-topic yet.Y13
- B10The nth roots of a complex number and regular polygonsNo lesson for this sub-topic yet.Y13
- B11Complex roots of unity to solve geometric problemsNo lesson for this sub-topic yet.Y13
CMatrices11 sub-topics
- C1Adding, subtracting and multiplying matricesNo lesson for this sub-topic yet.Y12
- C2Zero and identity matricesNo lesson for this sub-topic yet.Y12
- C3Matrices as linear transformations in 2D and 3DNo lesson for this sub-topic yet.Y12
- C4Invariant points and invariant linesNo lesson for this sub-topic yet.Y12
- C5Determinants as area and volume scale factorsNo lesson for this sub-topic yet.Y12–13
- C6Singular matrices and inverse matricesNo lesson for this sub-topic yet.Y12–13
- C7Solve three linear simultaneous equations using the inverse matrixNo lesson for this sub-topic yet.Y13
- C8The geometry of three simultaneous equationsNo lesson for this sub-topic yet.Y13
- C9Factorise determinants using row and column operationsNo lesson for this sub-topic yet.Y13
- C10Eigenvalues, eigenvectors and the characteristic equationNo lesson for this sub-topic yet.Y13
- C11Diagonalising a matrix and finding its powersNo lesson for this sub-topic yet.Y13
DFurther algebra and functions16 sub-topics
- D1Roots and coefficients of polynomials up to quarticsNo lesson for this sub-topic yet.Y12
- D2Polynomials with transformed rootsNo lesson for this sub-topic yet.Y12
- D3Standard results for sums of integers, squares and cubesNo lesson for this sub-topic yet.Y12
- D4Method of differences, including with partial fractionsNo lesson for this sub-topic yet.Y12
- D5Find the Maclaurin series of a function, including the general termNo lesson for this sub-topic yet.Y13
- D6Standard Maclaurin series and their ranges of validityNo lesson for this sub-topic yet.Y12
- D7Evaluate limits using Maclaurin series or l'Hôpital's ruleNo lesson for this sub-topic yet.Y13
- D8Solve cubic and quartic polynomial inequalitiesNo lesson for this sub-topic yet.Y12
- D9Solve inequalities of the form (ax + b)/(cx + d) < (ex + f)/(gx + h)No lesson for this sub-topic yet.Y12
- D10Modulus functions and related inequalitiesNo lesson for this sub-topic yet.Y13
- D11Sketch y = 1/f(x) given the graph of y = f(x)No lesson for this sub-topic yet.Y13
- D12Graphs of rational functions (ax + b)/(cx + d)No lesson for this sub-topic yet.Y12
- D13Rational functions with a quadratic numerator or denominatorNo lesson for this sub-topic yet.Y12–13
- D14Ranges and stationary points of rational functions without calculusNo lesson for this sub-topic yet.Y12
- D15Sketch the parabola, ellipse, hyperbola and rectangular hyperbolaNo lesson for this sub-topic yet.Y12
- D16Transformations of curvesNo lesson for this sub-topic yet.Y12–13
EFurther calculus9 sub-topics
- E1Improper integralsNo lesson for this sub-topic yet.Y13
- E2Derive and use formulae for volumes of revolutionNo lesson for this sub-topic yet.Y12
- E3Mean value of a functionNo lesson for this sub-topic yet.Y12
- E4Integrate using partial fractions, including quadratic factorsNo lesson for this sub-topic yet.Y13
- E5Differentiate inverse trigonometric functionsNo lesson for this sub-topic yet.Y13
- E6Integrals leading to inverse trigonometric functionsNo lesson for this sub-topic yet.Y13
- E7Arc length and area of surface of revolution, Cartesian and parametricNo lesson for this sub-topic yet.Y13
- E8Derive and use reduction formulaeNo lesson for this sub-topic yet.Y13
- E9Limits of xᵏeˣ and xᵏ ln x for improper integralsNo lesson for this sub-topic yet.Y13
FFurther vectors6 sub-topics
- F1Vector and Cartesian forms of the equation of a straight line in 3DNo lesson for this sub-topic yet.Y12
- F2Vector and Cartesian forms of the equation of a planeNo lesson for this sub-topic yet.Y13
- F3Scalar product: angles between lines, planes, and a line and a planeNo lesson for this sub-topic yet.Y12–13
- F4Check whether vectors are perpendicular using the scalar productNo lesson for this sub-topic yet.Y12
- F5The vector product and areas of trianglesNo lesson for this sub-topic yet.Y13
- F6Intersections of lines and planes, and perpendicular distancesNo lesson for this sub-topic yet.Y12–13
GPolar coordinates3 sub-topics
- G1Converting between polar and Cartesian coordinatesNo lesson for this sub-topic yet.Y12
- G2Sketch curves with r given as a function of θNo lesson for this sub-topic yet.Y12
- G3Areas enclosed by polar curvesNo lesson for this sub-topic yet.Y13
HHyperbolic functions7 sub-topics
- H1Hyperbolic functions and their graphsNo lesson for this sub-topic yet.Y12
- H2Differentiate and integrate hyperbolic functionsNo lesson for this sub-topic yet.Y13
- H3Inverse hyperbolic functions: definitions, domains and rangesNo lesson for this sub-topic yet.Y12
- H4Derive and use logarithmic forms of the inverse hyperbolic functionsNo lesson for this sub-topic yet.Y12
- H5Integrals leading to inverse hyperbolic functionsNo lesson for this sub-topic yet.Y13
- H6Hyperbolic identities, including tanh x = sinh x / cosh xNo lesson for this sub-topic yet.Y12
- H7Construct proofs involving hyperbolic functions and identitiesNo lesson for this sub-topic yet.Y13
IDifferential equations11 sub-topics
- I1Integrating factor for dy/dx + P(x)y = Q(x)No lesson for this sub-topic yet.Y13
- I2General and particular solutionsNo lesson for this sub-topic yet.Y13
- I3Differential equations in kinematics and other modelling contextsNo lesson for this sub-topic yet.Y13
- I4Second order homogeneous equations using the auxiliary equationNo lesson for this sub-topic yet.Y13
- I5Second-order non-homogeneous differential equationsNo lesson for this sub-topic yet.Y13
- I6Sign of the discriminant and the form of the solutionNo lesson for this sub-topic yet.Y13
- I7Simple harmonic motion, ẍ = −ω²xNo lesson for this sub-topic yet.Y13
- I8Damped oscillations: light, critical and heavy dampingNo lesson for this sub-topic yet.Y13
- I9Coupled first order simultaneous differential equationsNo lesson for this sub-topic yet.Y13
- I10Hooke's law to form the equation of simple harmonic motionNo lesson for this sub-topic yet.Y13
- I11Damped motion with damping force proportional to velocityNo lesson for this sub-topic yet.Y13
JNumerical methods3 sub-topics
- J1Mid-ordinate rule and Simpson's ruleNo lesson for this sub-topic yet.Y13
- J2Euler's step by step method for first order differential equationsNo lesson for this sub-topic yet.Y13
- J3Improved Euler methodNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Optional application 1: mechanics5 topics
MADimensional analysis2 sub-topics
- MA1Dimensions of quantities and dimensional consistencyNo lesson for this sub-topic yet.Y12
- MA2Predicting formulae using dimensionsNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
MBMomentum and collisions4 sub-topics
- MB1Conservation of momentum, including velocities as vectorsNo lesson for this sub-topic yet.Y12–13
- MB2The coefficient of restitution and Newton's experimental lawNo lesson for this sub-topic yet.Y12–13
- MB3Impulse and momentum, Ft = mv − muNo lesson for this sub-topic yet.Y12–13
- MB4Impulse of a variable force, I = ∫F dtNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
MCWork, energy and power7 sub-topics
- MC1Work done by a force, WD = Fd cos θNo lesson for this sub-topic yet.Y12
- MC2Gravitational potential energyNo lesson for this sub-topic yet.Y12
- MC3Kinetic energyNo lesson for this sub-topic yet.Y12
- MC4Hooke's law and modulus of elasticityNo lesson for this sub-topic yet.Y12
- MC5Work done by a variable force, WD = ∫F dxNo lesson for this sub-topic yet.Y12
- MC6Elastic potential energyNo lesson for this sub-topic yet.Y12
- MC7Power, P = FvNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
MDCircular motion6 sub-topics
- MD1Motion of a particle in a circle at constant speedNo lesson for this sub-topic yet.Y12
- MD2Angular speedNo lesson for this sub-topic yet.Y12
- MD3Relationships between speed, angular speed, radius and accelerationNo lesson for this sub-topic yet.Y12
- MD4Position, velocity and acceleration vectors in circular motionNo lesson for this sub-topic yet.Y13
- MD5Conical pendulum, with one or two stringsNo lesson for this sub-topic yet.Y13
- MD6Motion in a vertical circleNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
MECentres of mass and moments6 sub-topics
- ME1Centre of mass of a system of particlesNo lesson for this sub-topic yet.Y13
- ME2Centre of mass of a composite bodyNo lesson for this sub-topic yet.Y13
- ME3Centre of mass of a lamina by integrationNo lesson for this sub-topic yet.Y13
- ME4Centres of mass of solids of revolutionNo lesson for this sub-topic yet.Y13
- ME5Sliding and toppling, including suspended bodies and inclined planesNo lesson for this sub-topic yet.Y13
- ME6Rigid bodies in equilibrium: moments and couplesNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Optional application 2: statistics8 topics
SADiscrete random variables (DRVs) and expectation7 sub-topics
- SA1Discrete random variables as tables or functionsNo lesson for this sub-topic yet.Y12
- SA2Probabilities for a DRVNo lesson for this sub-topic yet.Y12
- SA3Mean, variance, standard deviation, mode and median of a DRVNo lesson for this sub-topic yet.Y12
- SA4E(X), E(X²) and Var(X)No lesson for this sub-topic yet.Y12
- SA5Expectation and variance of functions of a DRVNo lesson for this sub-topic yet.Y12
- SA6Discrete uniform distributionNo lesson for this sub-topic yet.Y12
- SA7Proofs of the mean and variance of the discrete uniform distributionNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
SBPoisson distribution5 sub-topics
- SB1The Poisson distribution and when to use itNo lesson for this sub-topic yet.Y12
- SB2Poisson probabilitiesNo lesson for this sub-topic yet.Y12
- SB3Mean, variance and standard deviationNo lesson for this sub-topic yet.Y12
- SB4Sums of independent Poisson variablesNo lesson for this sub-topic yet.Y12
- SB5Hypothesis test for the mean of a Poisson distributionNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
SCType I and Type II errors2 sub-topics
- SC1Type I and Type II errorsNo lesson for this sub-topic yet.Y12–13
- SC2The power of a testNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
SDContinuous random variables (CRVs)8 sub-topics
- SD1Probability density functionsNo lesson for this sub-topic yet.Y12
- SD2Probability over an intervalNo lesson for this sub-topic yet.Y12
- SD3Median and quartilesNo lesson for this sub-topic yet.Y12
- SD4Mean, variance and standard deviationNo lesson for this sub-topic yet.Y12
- SD5Expectation and variance of functions of a CRVNo lesson for this sub-topic yet.Y12
- SD6Cumulative distribution functionsNo lesson for this sub-topic yet.Y13
- SD7The rectangular distribution, its mean and varianceNo lesson for this sub-topic yet.Y13
- SD8Expectation and variance of sums of independent random variablesNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
SEChi-squared tests for association5 sub-topics
- SE1n × m contingency tablesNo lesson for this sub-topic yet.Y12
- SE2The χ² statistic and degrees of freedomNo lesson for this sub-topic yet.Y12
- SE3Convention that expected frequencies exceed 5No lesson for this sub-topic yet.Y12
- SE4Sources of association in contextNo lesson for this sub-topic yet.Y12
- SE5Yates' correctionNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
SFExponential distribution4 sub-topics
- SF1The exponential distribution and when to use itNo lesson for this sub-topic yet.Y13
- SF2Probabilities from the exponential distributionNo lesson for this sub-topic yet.Y13
- SF3Proofs of the mean, variance and standard deviationNo lesson for this sub-topic yet.Y13
- SF4Time between Poisson events is exponentially distributedNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
SGInference – one sample t-distribution1 sub-topic
- SG1t-test for the mean of a normal distribution with unknown varianceNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
SHConfidence intervals4 sub-topics
- SH1Confidence interval for a normal mean with known varianceNo lesson for this sub-topic yet.Y12
- SH2Large-sample confidence interval with unknown varianceNo lesson for this sub-topic yet.Y12
- SH3Inferences from confidence intervalsNo lesson for this sub-topic yet.Y12
- SH4Confidence intervals using the t-distributionNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Optional application 3: discrete mathematics7 topics
DAGraphs7 sub-topics
- DA1Language of graphs: vertex, edge, trail, cycle, degree, subgraphNo lesson for this sub-topic yet.Y12
- DA2Eulerian, semi-Eulerian and Hamiltonian graphsNo lesson for this sub-topic yet.Y12
- DA3Euler's formula for connected planar graphsNo lesson for this sub-topic yet.Y12
- DA4Kuratowski's theoremNo lesson for this sub-topic yet.Y13
- DA5Complete and bipartite graphs, adjacency matrices and complementsNo lesson for this sub-topic yet.Y12
- DA6Simple graphs, connected graphs and treesNo lesson for this sub-topic yet.Y12
- DA7Isomorphism between graphsNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
DBNetworks5 sub-topics
- DB1Language of networks: node, arc, weightNo lesson for this sub-topic yet.Y12
- DB2Minimum spanning treesNo lesson for this sub-topic yet.Y12
- DB3Route inspectionNo lesson for this sub-topic yet.Y12
- DB4Travelling salesperson: upper and lower boundsNo lesson for this sub-topic yet.Y12
- DB5Evaluate and refine network modelsNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
DCNetwork flows7 sub-topics
- DC1Flows in directed networksNo lesson for this sub-topic yet.Y12
- DC2Cuts and their valuesNo lesson for this sub-topic yet.Y12
- DC3Maximum flow–minimum cut theoremNo lesson for this sub-topic yet.Y12
- DC4Supersources and supersinksNo lesson for this sub-topic yet.Y12
- DC5Augment flows to find the maximum flowNo lesson for this sub-topic yet.Y13
- DC6Arcs with upper and lower capacitiesNo lesson for this sub-topic yet.Y13
- DC7Nodes of restricted capacityNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
DDLinear programming4 sub-topics
- DD1Formulate constrained optimisation problemsNo lesson for this sub-topic yet.Y12
- DD2Graphical solutionNo lesson for this sub-topic yet.Y12
- DD3Simplex algorithm with slack variablesNo lesson for this sub-topic yet.Y13
- DD4Interpret a Simplex tableauNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
DECritical path analysis6 sub-topics
- DE1Activity-on-node precedence networksNo lesson for this sub-topic yet.Y12
- DE2Earliest and latest start and finish timesNo lesson for this sub-topic yet.Y12
- DE3Critical activities, critical paths and floatNo lesson for this sub-topic yet.Y12
- DE4Refine models and assess changesNo lesson for this sub-topic yet.Y12
- DE5Gantt (cascade) charts and resource histogramsNo lesson for this sub-topic yet.Y13
- DE6Resource levellingNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
DFGame theory for zero-sum games6 sub-topics
- DF1Pay-off matricesNo lesson for this sub-topic yet.Y12
- DF2Play-safe strategies and the value of a gameNo lesson for this sub-topic yet.Y12
- DF3Stable solutionsNo lesson for this sub-topic yet.Y12
- DF4Dominated strategiesNo lesson for this sub-topic yet.Y12
- DF5Optimal mixed strategies, including graphical methodsNo lesson for this sub-topic yet.Y12
- DF6Convert larger games to linear programming problemsNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
DGBinary operations12 sub-topics
- DG1Binary operations, including modular arithmeticNo lesson for this sub-topic yet.Y12
- DG2CommutativityNo lesson for this sub-topic yet.Y12
- DG3AssociativityNo lesson for this sub-topic yet.Y12
- DG4Cayley tablesNo lesson for this sub-topic yet.Y12
- DG5Identity elementsNo lesson for this sub-topic yet.Y12
- DG6InversesNo lesson for this sub-topic yet.Y12
- DG7Language of groups: order, period, subgroupNo lesson for this sub-topic yet.Y13
- DG8Group axiomsNo lesson for this sub-topic yet.Y13
- DG9Finite, infinite, cyclic and abelian groupsNo lesson for this sub-topic yet.Y13
- DG10Lagrange's theoremNo lesson for this sub-topic yet.Y13
- DG11GeneratorsNo lesson for this sub-topic yet.Y13
- DG12Isomorphism between finite groupsNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Across the whole course4 topics
OT1Mathematical argument, language and proof5 sub-topics
- OT1.1Construct and present mathematical argumentsNo lesson for this sub-topic yet.Y12–13
- OT1.2Mathematical language and syntaxNo lesson for this sub-topic yet.Y12–13
- OT1.3Set notationNo lesson for this sub-topic yet.Y12–13
- OT1.4FunctionsNo lesson for this sub-topic yet.Y12–13
- OT1.5Critique arguments and proofsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
OT2Mathematical problem solving5 sub-topics
- OT2.1Recognise the underlying structure of a problemNo lesson for this sub-topic yet.Y12–13
- OT2.2Extended arguments for unstructured problemsNo lesson for this sub-topic yet.Y12–13
- OT2.3Interpret solutions in contextNo lesson for this sub-topic yet.Y12–13
- OT2.6The problem-solving cycleNo lesson for this sub-topic yet.Y12–13
- OT2.7Diagrams in problem solvingNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
OT3Mathematical modelling5 sub-topics
- OT3.1Build a modelNo lesson for this sub-topic yet.Y12–13
- OT3.2Use a modelNo lesson for this sub-topic yet.Y12–13
- OT3.3Interpret a model's outputsNo lesson for this sub-topic yet.Y12–13
- OT3.4Refine and evaluate a modelNo lesson for this sub-topic yet.Y12–13
- OT3.5Modelling assumptionsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
AKAssumed knowledge1 sub-topic
- AKGCSE and A level Mathematics contentNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
Core Pure Mathematics9 topics
1Proof1 sub-topic
- 1.1Proof by mathematical inductionY12
2Complex numbers11 sub-topics
- 2.1Solving polynomial equations with complex rootsY12
- 2.2Arithmetic in Cartesian formY12
- 2.3Complex conjugatesY12
- 2.4Argand diagramsY12
- 2.5Modulus–argument formY12
- 2.6Multiplying and dividing in modulus–argument formY12
- 2.7Loci and regions in the Argand diagramY12
- 2.8De Moivre's theoremY13
- 2.9Exponential (Euler) formY13
- 2.10nth roots of a complex numberY13
- 2.11Roots of unity and geometryY13
3Matrices8 sub-topics
- 3.1Matrix operationsY12
- 3.2Zero and identity matricesY12
- 3.3Linear transformationsY12
- 3.4Invariant points and invariant linesY12
- 3.5DeterminantsY12
- 3.6Inverse matricesY12
- 3.7Solving three linear equationsY12
- 3.8Geometry of three planesY12
4Further algebra and functions6 sub-topics
- 4.1Roots and coefficients of polynomialsY12
- 4.2Transforming rootsY12
- 4.3Standard results for sumsY12
- 4.4Method of differencesY13
- 4.5Maclaurin seriesY13
- 4.6Standard Maclaurin seriesY13
5Further calculus7 sub-topics
- 5.1Volumes of revolution (Cartesian)Y12
- 5.1Volumes of revolution (parametric and modelling)Y13
- 5.2Improper integralsY13
- 5.3Mean value of a functionY13
- 5.4Integration using partial fractionsY13
- 5.5Differentiating inverse trigonometric functionsY13
- 5.6Integrals leading to inverse trig functionsY13
6Further vectors5 sub-topics
- 6.1Equations of lines in 3DY12
- 6.2Equations of planesY12
- 6.3Scalar product, planes and anglesY12
- 6.4Perpendicular vectorsY12
- 6.5Intersections and perpendicular distancesY12
7Polar coordinates3 sub-topics
- 7.1Polar and Cartesian conversionY13
- 7.2Sketching polar curvesY13
- 7.3Areas and tangentsY13
8Hyperbolic functions5 sub-topics
- 8.1Definitions and graphsY13
- 8.2Differentiating and integrating hyperbolic functionsY13
- 8.3Inverse hyperbolic functionsY13
- 8.4Logarithmic formsY13
- 8.5Integrals leading to inverse hyperbolic functionsY13
9Differential equations9 sub-topics
- 9.1Integrating factor methodY13
- 9.2General and particular solutionsY13
- 9.3Modelling with first-order equationsY13
- 9.4Second-order homogeneous equationsY13
- 9.5Second-order non-homogeneous equationsY13
- 9.6Auxiliary equation casesY13
- 9.7Simple harmonic motionY13
- 9.8Damped and forced oscillationsY13
- 9.9Coupled first-order systemsY13
Further Pure Mathematics 1 (FP1)7 topics
1Further trigonometry3 sub-topics
- 1.1The t-formulaeY12
- 1.2Proving identities with t-formulaeY12
- 1.3Solving equations with t-formulaeY12
No practice questions for this topic yet.Specification points
2Further calculus5 sub-topics
- 2.1Taylor seriesY13
- 2.2Series expansions to evaluate limitsY13
- 2.3Leibnitz's theoremY13
- 2.4L'Hôpital's ruleY13
- 2.5Weierstrass substitutionY13
No practice questions for this topic yet.Specification points
3Further differential equations2 sub-topics
- 3.1Taylor series solutions of differential equationsY13
- 3.2Reducible differential equationsY13
No practice questions for this topic yet.Specification points
4Coordinate systems6 sub-topics
- 4.1Conics: parabola and rectangular hyperbolaY12
- 4.1Conics: ellipse and hyperbolaY13
- 4.2Focus–directrix propertiesY12
- 4.2Eccentricity, foci and directrices of ellipse and hyperbolaY13
- 4.3Tangents and normals to conicsY12
- 4.4Loci problemsY12
No practice questions for this topic yet.Specification points
5Further vectors3 sub-topics
- 5.1Vector productY12
- 5.2Scalar triple productY12
- 5.3Vector geometry with the vector productY13
No practice questions for this topic yet.Specification points
6Further numerical methods2 sub-topics
- 6.1Numerical solution of differential equationsY12
- 6.2Simpson's ruleY13
No practice questions for this topic yet.Specification points
7Inequalities1 sub-topic
- 7.1InequalitiesY12
No practice questions for this topic yet.Specification points
Further Statistics 1 (FS1)8 topics
1Discrete probability distributions1 sub-topic
- 1.1Discrete probability distributionsY12
No practice questions for this topic yet.Specification points
2Poisson and binomial distributions3 sub-topics
- 2.1The Poisson distributionY12
- 2.2Mean and variance of binomial and PoissonY12
- 2.3Poisson approximation to the binomialY12
No practice questions for this topic yet.Specification points
3Geometric and negative binomial distributions3 sub-topics
- 3.1Geometric and negative binomial modelsY13
- 3.2Mean and variance of the geometric distributionY13
- 3.3Mean and variance of the negative binomialY13
No practice questions for this topic yet.Specification points
4Hypothesis testing2 sub-topics
- 4.1Hypothesis tests for the mean of a Poisson distributionY12
- 4.2Hypothesis tests for the parameter of a geometric distributionY13
No practice questions for this topic yet.Specification points
5The Central Limit Theorem1 sub-topic
- 5.1The Central Limit TheoremY13
No practice questions for this topic yet.Specification points
6Chi-squared tests2 sub-topics
- 6.1Chi-squared tests (discrete uniform, binomial, Poisson)Y12
- 6.1Chi-squared tests for geometric distributionsY13
No practice questions for this topic yet.Specification points
7Probability generating functions3 sub-topics
- 7.1Probability generating functionsY13
- 7.2Mean and variance from PGFsY13
- 7.3PGF of a sum of independent variablesY13
No practice questions for this topic yet.Specification points
8Quality of tests1 sub-topic
- 8.1Quality of testsY13
No practice questions for this topic yet.Specification points
Further Mechanics 1 (FM1)5 topics
1Momentum and impulse2 sub-topics
- 1.1Momentum and impulseY12
- 1.2Momentum as a vectorY13
No practice questions for this topic yet.Specification points
2Work, energy and power1 sub-topic
- 2.1Work, energy and powerY12
No practice questions for this topic yet.Specification points
3Elastic strings and springs and elastic energy2 sub-topics
- 3.1Hooke's lawY13
- 3.2Elastic potential energyY13
No practice questions for this topic yet.Specification points
4Elastic collisions in one dimension2 sub-topics
- 4.1Direct impact and Newton's law of restitutionY12
- 4.2Successive direct impactsY12
No practice questions for this topic yet.Specification points
5Elastic collisions in two dimensions2 sub-topics
- 5.1Oblique impact of smooth elastic spheresY13
- 5.2Successive oblique impactsY13
No practice questions for this topic yet.Specification points
Decision Mathematics 1 (D1)5 topics
1Algorithms and graph theory4 sub-topics
- 1.1Algorithms and orderY12
- 1.2Bin packing and sortingY12
- 1.3Graph theoryY12
- 1.4Planarity algorithm and Hamiltonian cyclesY13
No practice questions for this topic yet.Specification points
2Algorithms on graphs3 sub-topics
- 2.1Minimum spanning treesY12
- 2.2Dijkstra's algorithmY12
- 2.2Floyd's algorithmY13
No practice questions for this topic yet.Specification points
3Algorithms on graphs II2 sub-topics
- 3.1Route inspection (Chinese postman)Y12
- 3.2Travelling salesman problemY13
No practice questions for this topic yet.Specification points
4Critical path analysis6 sub-topics
- 4.1Activity networksY12
- 4.2Precedence tablesY12
- 4.3Critical path analysisY12
- 4.4Float and Gantt chartsY12
- 4.5Resource histograms and levellingY13
- 4.6SchedulingY13
No practice questions for this topic yet.Specification points
5Linear programming5 sub-topics
- 5.1Formulating linear programming problemsY12
- 5.1Slack, surplus and artificial variablesY13
- 5.2Graphical solution of LP problemsY12
- 5.3The Simplex algorithmY13
- 5.4Two-stage Simplex and big-MY13
No practice questions for this topic yet.Specification points
Further Pure Mathematics 2 (FP2)6 topics
1Groups5 sub-topics
- 1.1Group axiomsY13
- 1.2Examples of groups and Cayley tablesY13
- 1.3Order and subgroupsY13
- 1.4Lagrange's theoremY13
- 1.5IsomorphismY13
No practice questions for this topic yet.Specification points
2Further calculus2 sub-topics
- 2.1Reduction formulaeY13
- 2.2Arc length and area of surface of revolutionY13
No practice questions for this topic yet.Specification points
3Further matrix algebra3 sub-topics
- 3.1Eigenvalues and eigenvectorsY13
- 3.2DiagonalisationY13
- 3.3Cayley–Hamilton theoremY13
No practice questions for this topic yet.Specification points
4Further complex numbers2 sub-topics
- 4.1Further loci and regionsY13
- 4.2Transformations of the complex planeY13
No practice questions for this topic yet.Specification points
5Number theory7 sub-topics
- 5.1Division algorithm and Euclidean algorithmY13
- 5.2Bézout's identityY13
- 5.3Modular arithmeticY13
- 5.4Fermat's little theoremY13
- 5.5Divisibility testsY13
- 5.6Solving congruence equationsY13
- 5.7CombinatoricsY13
No practice questions for this topic yet.Specification points
6Further sequences and series3 sub-topics
- 6.1Recurrence relationsY13
- 6.2Solving recurrence relationsY13
- 6.3Proving closed forms by inductionY13
No practice questions for this topic yet.Specification points
Further Statistics 2 (FS2)7 topics
1Linear regression2 sub-topics
- 1.1Least squares linear regressionY13
- 1.2ResidualsY13
No practice questions for this topic yet.Specification points
2Continuous probability distributions4 sub-topics
- 2.1Continuous random variablesY13
- 2.2Relationship between pdf and cdfY13
- 2.3Summary measuresY13
- 2.4Continuous uniform distributionY13
No practice questions for this topic yet.Specification points
3Correlation3 sub-topics
- 3.1Product moment correlation coefficientY13
- 3.2Spearman's rank correlationY13
- 3.3Testing for zero correlationY13
No practice questions for this topic yet.Specification points
4Combinations of random variables1 sub-topic
- 4.1Combinations of random variablesY13
No practice questions for this topic yet.Specification points
5Estimation, confidence intervals and tests using a normal distribution5 sub-topics
- 5.1Estimators and biasY13
- 5.2Confidence intervalsY13
- 5.3Confidence limits for a normal mean (variance known)Y13
- 5.4Test for the difference of two normal means (variances known)Y13
- 5.5Large-sample methodsY13
No practice questions for this topic yet.Specification points
6Other hypothesis tests and confidence intervals2 sub-topics
- 6.1Tests and intervals for a normal varianceY13
- 6.2F-test for equality of variancesY13
No practice questions for this topic yet.Specification points
7Confidence intervals and tests using the t-distribution3 sub-topics
- 7.1t-tests and intervals for a normal mean (variance unknown)Y13
- 7.2Paired t-testY13
- 7.3Two-sample t-test (equal unknown variances)Y13
No practice questions for this topic yet.Specification points
Further Mechanics 2 (FM2)5 topics
1Motion in a circle2 sub-topics
- 1.1Horizontal circular motionY13
- 1.2Motion in a vertical circleY13
No practice questions for this topic yet.Specification points
2Centres of mass of plane figures2 sub-topics
- 2.1Moments and discrete centres of massY13
- 2.2Centres of mass of plane figures and frameworksY13
No practice questions for this topic yet.Specification points
3Further centres of mass3 sub-topics
- 3.1Centres of mass by integrationY13
- 3.2Equilibrium of rigid bodiesY13
- 3.3Toppling and slidingY13
No practice questions for this topic yet.Specification points
4Further dynamics2 sub-topics
- 4.1Variable force in one dimensionY13
- 4.2Simple harmonic motionY13
No practice questions for this topic yet.Specification points
5Further kinematics1 sub-topic
- 5.1Further kinematicsY13
No practice questions for this topic yet.Specification points
Decision Mathematics 2 (D2)7 topics
1Transportation problems3 sub-topics
- 1.1Transportation: initial solutionY13
- 1.2Transportation: improving the solutionY13
- 1.3Transportation as a linear programY13
No practice questions for this topic yet.Specification points
2Allocation (assignment) problems2 sub-topics
- 2.1Allocation and the Hungarian algorithmY13
- 2.2Allocation as a linear programY13
No practice questions for this topic yet.Specification points
3Flows in networks5 sub-topics
- 3.1CutsY13
- 3.2Labelling procedureY13
- 3.3Max-flow min-cut theoremY13
- 3.4Supersources, supersinks and vertex capacitiesY13
- 3.5Upper and lower capacitiesY13
No practice questions for this topic yet.Specification points
4Dynamic programming1 sub-topic
- 4.1Dynamic programmingY13
No practice questions for this topic yet.Specification points
5Game theory5 sub-topics
- 5.1Two-person zero-sum gamesY13
- 5.2Play-safe strategies and stable solutionsY13
- 5.3DominanceY13
- 5.4Mixed strategies: graphical methodY13
- 5.5Mixed strategies via linear programmingY13
No practice questions for this topic yet.Specification points
6Recurrence relations2 sub-topics
- 6.1Recurrence relations: modellingY13
- 6.2Solving recurrence relationsY13
No practice questions for this topic yet.Specification points
7Decision analysis2 sub-topics
- 7.1Decision treesY13
- 7.2Expected monetary value and utilityY13
No practice questions for this topic yet.Specification points
Across the whole course5 topics
OT1Mathematical argument, language and proof5 sub-topics
- OT1.1Construct and present mathematical argumentsY12–13
- OT1.2Mathematical language and syntaxY12–13
- OT1.3Set notationY12–13
- OT1.4FunctionsY12–13
- OT1.5Critique arguments and proofsY12–13
No practice questions for this topic yet.Specification points
OT2Mathematical problem solving5 sub-topics
- OT2.1Recognise the underlying structure of a problemY12–13
- OT2.2Extended arguments for unstructured problemsY12–13
- OT2.3Interpret solutions in contextY12–13
- OT2.6The problem-solving cycleY12–13
- OT2.7Diagrams in problem solvingY12–13
No practice questions for this topic yet.Specification points
OT3Mathematical modelling5 sub-topics
- OT3.1Build a modelY12–13
- OT3.2Use a modelY12–13
- OT3.3Interpret a model's outputsY12–13
- OT3.4Refine and evaluate a modelY12–13
- OT3.5Modelling assumptionsY12–13
No practice questions for this topic yet.Specification points
A1Formulae you must recall (not in the formulae booklet)6 sub-topics
- PPure formulae from A level MathematicsY12–13
- CPFurther pure formulaeY12–13
- CCalculusY12–13
- VVectorsY12–13
- SStatisticsY12–13
- MMechanicsY12–13
No practice questions for this topic yet.Specification points
AKAssumed knowledge1 sub-topic
- AKA level Mathematics contentY12–13
No practice questions for this topic yet.Specification points
Pure mathematics10 topics
AProof1 sub-topic
- A1Proof by deduction, exhaustion, counter-example and contradictionNo lesson for this sub-topic yet.Y12–13
BAlgebra and functions11 sub-topics
- B1Laws of indices for all rational exponentsNo lesson for this sub-topic yet.Y12
- B2Surds, including rationalising the denominatorNo lesson for this sub-topic yet.Y12
- B3Quadratic functions, the discriminant and completing the squareNo lesson for this sub-topic yet.Y12
- B4Simultaneous equations, one linear and one quadraticNo lesson for this sub-topic yet.Y12
- B5Linear and quadratic inequalitiesNo lesson for this sub-topic yet.Y12
- B6Polynomials, the factor theorem and algebraic divisionNo lesson for this sub-topic yet.Y12
- B7Graphs of functions, including modulus graphs and asymptotesNo lesson for this sub-topic yet.Y12–13
- B8Composite and inverse functionsNo lesson for this sub-topic yet.Y13
- B9Transformations of y = f(x), including combinationsNo lesson for this sub-topic yet.Y12–13
- B10Partial fractionsNo lesson for this sub-topic yet.Y13
- B11Functions in modellingNo lesson for this sub-topic yet.Y13
CCoordinate geometry in the (x, y) plane4 sub-topics
- C1Straight lines, including parallel and perpendicular linesNo lesson for this sub-topic yet.Y12
- C2Coordinate geometry of the circleNo lesson for this sub-topic yet.Y12
- C3Parametric equationsNo lesson for this sub-topic yet.Y13
- C4Parametric equations in modellingNo lesson for this sub-topic yet.Y13
DSequences and series6 sub-topics
- D1Binomial expansionNo lesson for this sub-topic yet.Y12–13
- D2Sequences and recurrence relationsNo lesson for this sub-topic yet.Y13
- D3Sigma notationNo lesson for this sub-topic yet.Y13
- D4Arithmetic sequences and seriesNo lesson for this sub-topic yet.Y13
- D5Geometric sequences and seriesNo lesson for this sub-topic yet.Y13
- D6Sequences and series in modellingNo lesson for this sub-topic yet.Y13
ETrigonometry9 sub-topics
- E1Trigonometry, radians, arc length and sector areaNo lesson for this sub-topic yet.Y12–13
- E2Small angle approximationsNo lesson for this sub-topic yet.Y13
- E3Graphs, symmetries and periodicity of sin, cos and tanNo lesson for this sub-topic yet.Y12
- E4Reciprocal and inverse trigonometric functionsNo lesson for this sub-topic yet.Y13
- E5Trigonometric identitiesNo lesson for this sub-topic yet.Y12–13
- E6Double angle and compound angle formulaeNo lesson for this sub-topic yet.Y13
- E7Solve trigonometric equations in a given intervalNo lesson for this sub-topic yet.Y12–13
- E8Proofs involving trigonometric functionsNo lesson for this sub-topic yet.Y13
- E9Trigonometric functions in contextNo lesson for this sub-topic yet.Y13
FExponentials and logarithms7 sub-topics
- F1Functions aˣ and eˣ and their graphsNo lesson for this sub-topic yet.Y12
- F2The gradient of e^(kx) and exponential modelsNo lesson for this sub-topic yet.Y12
- F3Logarithms and ln xNo lesson for this sub-topic yet.Y12
- F4Laws of logarithmsNo lesson for this sub-topic yet.Y12
- F5Solve equations of the form aˣ = bNo lesson for this sub-topic yet.Y12
- F6Logarithmic graphs to estimate parameters in y = axⁿ and y = kbˣNo lesson for this sub-topic yet.Y12
- F7Exponential growth and decay in modellingNo lesson for this sub-topic yet.Y12
GDifferentiation6 sub-topics
- G1Gradients, first principles and second derivativesNo lesson for this sub-topic yet.Y12–13
- G2Differentiating standard functionsNo lesson for this sub-topic yet.Y12–13
- G3Tangents, normals and stationary pointsNo lesson for this sub-topic yet.Y12
- G4The product, quotient and chain rulesNo lesson for this sub-topic yet.Y13
- G5Implicit and parametric differentiationNo lesson for this sub-topic yet.Y13
- G6Construct simple differential equationsNo lesson for this sub-topic yet.Y13
HIntegration8 sub-topics
- H1Fundamental theorem of calculusNo lesson for this sub-topic yet.Y12
- H2Integrating standard functionsNo lesson for this sub-topic yet.Y12–13
- H3Definite integrals and areas between curvesNo lesson for this sub-topic yet.Y12–13
- H4Integration as the limit of a sumNo lesson for this sub-topic yet.Y13
- H5Integration by substitution and by partsNo lesson for this sub-topic yet.Y13
- H6Integration using partial fractionsNo lesson for this sub-topic yet.Y13
- H7First order separable differential equationsNo lesson for this sub-topic yet.Y13
- H8Interpret solutions of differential equations in contextNo lesson for this sub-topic yet.Y13
INumerical methods4 sub-topics
- I1Locate roots by change of signNo lesson for this sub-topic yet.Y13
- I2Iteration and the Newton–Raphson methodNo lesson for this sub-topic yet.Y13
- I3Trapezium ruleNo lesson for this sub-topic yet.Y13
- I4Numerical methods in contextNo lesson for this sub-topic yet.Y13
JVectors5 sub-topics
- J1Vectors in two and three dimensionsNo lesson for this sub-topic yet.Y12–13
- J2Magnitude, direction and component formNo lesson for this sub-topic yet.Y12
- J3Adding vectors and multiplying by scalarsNo lesson for this sub-topic yet.Y12
- J4Position vectors and distancesNo lesson for this sub-topic yet.Y12–13
- J5Vectors in pure mathematics and in contextNo lesson for this sub-topic yet.Y12–13
Mechanics4 topics
PQuantities and units in mechanics1 sub-topic
- P1Fundamental and derived quantities and SI unitsNo lesson for this sub-topic yet.Y12
QKinematics5 sub-topics
- Q1Language of kinematicsNo lesson for this sub-topic yet.Y12
- Q2Displacement–time and velocity–time graphsNo lesson for this sub-topic yet.Y12
- Q3Constant acceleration formulae, including in 2DNo lesson for this sub-topic yet.Y12–13
- Q4Calculus in kinematics, including in 2DNo lesson for this sub-topic yet.Y12–13
- Q5ProjectilesNo lesson for this sub-topic yet.Y13
RForces and Newton's laws6 sub-topics
- R1Forces and Newton's first lawNo lesson for this sub-topic yet.Y12
- R2Newton's second law and resolving forcesNo lesson for this sub-topic yet.Y12–13
- R3Weight and motion in a straight line under gravityNo lesson for this sub-topic yet.Y12–13
- R4Newton's third law, pulleys and connected particlesNo lesson for this sub-topic yet.Y12–13
- R5Resultant forces and dynamics in a planeNo lesson for this sub-topic yet.Y13
- R6Friction, F ≤ μRNo lesson for this sub-topic yet.Y13
SMoments1 sub-topic
- S1Moments in simple static contextsNo lesson for this sub-topic yet.Y13
Statistics6 topics
KStatistical sampling1 sub-topic
- K1Populations, samples and sampling techniquesNo lesson for this sub-topic yet.Y12
LData presentation and interpretation4 sub-topics
- L1Diagrams for single-variable data, including histogramsNo lesson for this sub-topic yet.Y12
- L2Scatter diagrams, regression and correlationNo lesson for this sub-topic yet.Y12
- L3Averages, spread and standard deviationNo lesson for this sub-topic yet.Y12
- L4Outliers and cleaning dataNo lesson for this sub-topic yet.Y12
MProbability3 sub-topics
- M1Mutually exclusive and independent eventsNo lesson for this sub-topic yet.Y12
- M2Conditional probabilityNo lesson for this sub-topic yet.Y13
- M3Modelling with probabilityNo lesson for this sub-topic yet.Y13
NStatistical distributions3 sub-topics
- N1Discrete distributions, including the binomial distributionNo lesson for this sub-topic yet.Y12–13
- N2The normal distributionNo lesson for this sub-topic yet.Y13
- N3Choose an appropriate distributionNo lesson for this sub-topic yet.Y13
OStatistical hypothesis testing3 sub-topics
- O1The language of hypothesis testingNo lesson for this sub-topic yet.Y12–13
- O2Hypothesis test for a binomial proportionNo lesson for this sub-topic yet.Y12
- O3Hypothesis test for the mean of a normal distributionNo lesson for this sub-topic yet.Y13
LDSThe large data set1 sub-topic
- LDSFamiliarity with the AQA large data setNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
Across the whole course5 topics
OT1Mathematical argument, language and proof5 sub-topics
- OT1.1Construct and present mathematical argumentsNo lesson for this sub-topic yet.Y12–13
- OT1.2Mathematical language and syntaxNo lesson for this sub-topic yet.Y12–13
- OT1.3Set notationNo lesson for this sub-topic yet.Y12–13
- OT1.4FunctionsNo lesson for this sub-topic yet.Y12–13
- OT1.5Critique arguments and proofsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
OT2Mathematical problem solving7 sub-topics
- OT2.1Recognise the underlying structure of a problemNo lesson for this sub-topic yet.Y12–13
- OT2.2Extended arguments for unstructured problemsNo lesson for this sub-topic yet.Y12–13
- OT2.3Interpret solutions in contextNo lesson for this sub-topic yet.Y12–13
- OT2.4Numerical methods to a required accuracyNo lesson for this sub-topic yet.Y12–13
- OT2.5Accuracy and limitations of solutionsNo lesson for this sub-topic yet.Y12–13
- OT2.6The problem-solving cycleNo lesson for this sub-topic yet.Y12–13
- OT2.7Diagrams in problem solvingNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
OT3Mathematical modelling5 sub-topics
- OT3.1Build a modelNo lesson for this sub-topic yet.Y12–13
- OT3.2Use a modelNo lesson for this sub-topic yet.Y12–13
- OT3.3Interpret a model's outputsNo lesson for this sub-topic yet.Y12–13
- OT3.4Refine and evaluate a modelNo lesson for this sub-topic yet.Y12–13
- OT3.5Modelling assumptionsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
ABFormulae you must recall (not given in the exam)5 sub-topics
- PPureNo lesson for this sub-topic yet.Y12–13
- CCalculusNo lesson for this sub-topic yet.Y12–13
- VVectorsNo lesson for this sub-topic yet.Y12–13
- SStatisticsNo lesson for this sub-topic yet.Y12–13
- MMechanicsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
AKAssumed knowledge1 sub-topic
- AKGCSE MathematicsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
Pure mathematics10 topics
1Proof1 sub-topic
- 1.1Proof by deduction, exhaustion, counter-example and contradictionNo lesson for this sub-topic yet.Y12–13
2Algebra and functions11 sub-topics
- 2.1Laws of indices for all rational exponentsNo lesson for this sub-topic yet.Y12
- 2.2Surds and rationalising the denominatorNo lesson for this sub-topic yet.Y12
- 2.3Quadratic functions: discriminant, completing the square, solvingNo lesson for this sub-topic yet.Y12
- 2.4Simultaneous equations, one linear and one quadraticNo lesson for this sub-topic yet.Y12
- 2.5Linear and quadratic inequalitiesNo lesson for this sub-topic yet.Y12
- 2.6Polynomials, the factor theorem and algebraic divisionNo lesson for this sub-topic yet.Y12–13
- 2.7Graphs of cubics, quartics, reciprocals and modulus functionsNo lesson for this sub-topic yet.Y12–13
- 2.8Composite and inverse functionsNo lesson for this sub-topic yet.Y13
- 2.9Transformations of y = f(x)No lesson for this sub-topic yet.Y12–13
- 2.10Partial fractionsNo lesson for this sub-topic yet.Y13
- 2.11Functions in modellingNo lesson for this sub-topic yet.Y13
3Coordinate geometry in the (x, y) plane4 sub-topics
- 3.1Straight lines and their gradientsNo lesson for this sub-topic yet.Y12
- 3.2CirclesNo lesson for this sub-topic yet.Y12
- 3.3Parametric equationsNo lesson for this sub-topic yet.Y13
- 3.4Parametric equations in modellingNo lesson for this sub-topic yet.Y13
4Sequences and series6 sub-topics
- 4.1Binomial expansionNo lesson for this sub-topic yet.Y12–13
- 4.2Sequences and recurrence relationsNo lesson for this sub-topic yet.Y13
- 4.3Sigma notationNo lesson for this sub-topic yet.Y13
- 4.4Arithmetic sequences and seriesNo lesson for this sub-topic yet.Y13
- 4.5Geometric sequences and seriesNo lesson for this sub-topic yet.Y13
- 4.6Sequences and series in modellingNo lesson for this sub-topic yet.Y13
5Trigonometry9 sub-topics
- 5.1Trigonometry, radians, arc length and sector areaNo lesson for this sub-topic yet.Y12–13
- 5.2Small angle approximationsNo lesson for this sub-topic yet.Y13
- 5.3Graphs, symmetries and periodicity of sin, cos and tanNo lesson for this sub-topic yet.Y12–13
- 5.4Reciprocal and inverse trigonometric functionsNo lesson for this sub-topic yet.Y13
- 5.5Trigonometric identitiesNo lesson for this sub-topic yet.Y12–13
- 5.6Double angle and compound angle formulaeNo lesson for this sub-topic yet.Y13
- 5.7Solve trigonometric equations in a given intervalNo lesson for this sub-topic yet.Y12–13
- 5.8Proofs involving trigonometric identitiesNo lesson for this sub-topic yet.Y13
- 5.9Trigonometric functions in contextNo lesson for this sub-topic yet.Y13
6Exponentials and logarithms7 sub-topics
- 6.1Functions aˣ and eˣ and their graphsNo lesson for this sub-topic yet.Y12
- 6.2The gradient of e^(kx) and exponential modelsNo lesson for this sub-topic yet.Y12
- 6.3Logarithms and ln xNo lesson for this sub-topic yet.Y12
- 6.4Laws of logarithmsNo lesson for this sub-topic yet.Y12
- 6.5Solve aˣ = bNo lesson for this sub-topic yet.Y12
- 6.6Logarithmic graphs to estimate parametersNo lesson for this sub-topic yet.Y12
- 6.7Exponential growth and decay modelsNo lesson for this sub-topic yet.Y12
7Differentiation6 sub-topics
- 7.1Gradients, first principles and second derivativesY12–13
- 7.2Differentiating standard functionsY12–13
- 7.3Tangents, normals and stationary pointsY12–13
- 7.4The product, quotient and chain rulesY13
- 7.5Implicit and parametric differentiationY13
- 7.6Construct simple differential equationsY13
8Integration8 sub-topics
- 8.1Fundamental theorem of calculusNo lesson for this sub-topic yet.Y12
- 8.2Integrating standard functionsNo lesson for this sub-topic yet.Y12–13
- 8.3Definite integrals and areasNo lesson for this sub-topic yet.Y12–13
- 8.4Integration as the limit of a sumNo lesson for this sub-topic yet.Y13
- 8.5Integration by substitution and by partsNo lesson for this sub-topic yet.Y13
- 8.6Integration using partial fractionsNo lesson for this sub-topic yet.Y13
- 8.7Separable differential equationsNo lesson for this sub-topic yet.Y13
- 8.8Interpret solutions of differential equationsNo lesson for this sub-topic yet.Y13
9Numerical methods5 sub-topics
- 9.1Locate roots by change of signNo lesson for this sub-topic yet.Y13
- 9.2Iteration, cobweb and staircase diagramsNo lesson for this sub-topic yet.Y13
- 9.3Newton–Raphson methodNo lesson for this sub-topic yet.Y13
- 9.4Trapezium ruleNo lesson for this sub-topic yet.Y13
- 9.5Numerical methods in contextNo lesson for this sub-topic yet.Y13
10Vectors5 sub-topics
- 10.1Vectors in two and three dimensionsNo lesson for this sub-topic yet.Y12–13
- 10.2Magnitude, direction and unit vectorsNo lesson for this sub-topic yet.Y12–13
- 10.3Adding vectors, scalar multiples and parallel vectorsNo lesson for this sub-topic yet.Y12–13
- 10.4Position vectors and distancesNo lesson for this sub-topic yet.Y12–13
- 10.5Vectors in pure mathematics and in contextNo lesson for this sub-topic yet.Y12–13
Statistics5 topics
1Statistical sampling1 sub-topic
- 1.1Populations, samples and sampling methodsNo lesson for this sub-topic yet.Y12
2Data presentation and interpretation4 sub-topics
- 2.1Histograms, frequency polygons, box plots, cumulative frequencyNo lesson for this sub-topic yet.Y12
- 2.2Scatter diagrams, regression lines and correlationNo lesson for this sub-topic yet.Y12–13
- 2.3Measures of location and spreadNo lesson for this sub-topic yet.Y12
- 2.4Outliers and cleaning dataNo lesson for this sub-topic yet.Y12
3Probability3 sub-topics
- 3.1Mutually exclusive and independent eventsNo lesson for this sub-topic yet.Y12
- 3.2Conditional probabilityNo lesson for this sub-topic yet.Y13
- 3.3Modelling with probabilityNo lesson for this sub-topic yet.Y13
4Statistical distributions3 sub-topics
- 4.1Discrete distributions, including the binomialNo lesson for this sub-topic yet.Y12
- 4.2The normal distribution and the normal approximation to the binomialNo lesson for this sub-topic yet.Y13
- 4.3Choose an appropriate distributionNo lesson for this sub-topic yet.Y13
5Statistical hypothesis testing3 sub-topics
- 5.1Hypothesis testing, including tests for correlationNo lesson for this sub-topic yet.Y12–13
- 5.2Hypothesis test for a binomial proportionNo lesson for this sub-topic yet.Y12
- 5.3Hypothesis test for the mean of a normal distributionNo lesson for this sub-topic yet.Y13
Mechanics4 topics
6Quantities and units in mechanics1 sub-topic
- 6.1SI quantities and unitsNo lesson for this sub-topic yet.Y12
7Kinematics5 sub-topics
- 7.1Language of kinematicsNo lesson for this sub-topic yet.Y12
- 7.2Displacement–time and velocity–time graphsNo lesson for this sub-topic yet.Y12
- 7.3Constant acceleration formulae, including in 2DNo lesson for this sub-topic yet.Y12–13
- 7.4Calculus in kinematics, including in 2DNo lesson for this sub-topic yet.Y12–13
- 7.5ProjectilesNo lesson for this sub-topic yet.Y13
8Forces and Newton's laws6 sub-topics
- 8.1Forces and Newton's first lawNo lesson for this sub-topic yet.Y12
- 8.2Newton's second law and resolving forcesNo lesson for this sub-topic yet.Y12–13
- 8.3Weight and motion under gravityNo lesson for this sub-topic yet.Y12
- 8.4Newton's third law, equilibrium and connected particlesNo lesson for this sub-topic yet.Y12–13
- 8.5Resultant forces and dynamics in a planeNo lesson for this sub-topic yet.Y13
- 8.6Friction, F ≤ μRNo lesson for this sub-topic yet.Y13
9Moments1 sub-topic
- 9.1Moments and equilibrium of rigid bodiesNo lesson for this sub-topic yet.Y13
Across the whole course6 topics
OT1Mathematical argument, language and proof5 sub-topics
- OT1.1Construct and present mathematical argumentsNo lesson for this sub-topic yet.Y12–13
- OT1.2Mathematical language and syntaxNo lesson for this sub-topic yet.Y12–13
- OT1.3Set notationNo lesson for this sub-topic yet.Y12–13
- OT1.4FunctionsNo lesson for this sub-topic yet.Y12–13
- OT1.5Critique arguments and proofsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
OT2Mathematical problem solving7 sub-topics
- OT2.1Recognise the underlying structure of a problemNo lesson for this sub-topic yet.Y12–13
- OT2.2Extended arguments for unstructured problemsNo lesson for this sub-topic yet.Y12–13
- OT2.3Interpret solutions in contextNo lesson for this sub-topic yet.Y12–13
- OT2.4Numerical methods to a required accuracyNo lesson for this sub-topic yet.Y12–13
- OT2.5Accuracy and limitations of solutionsNo lesson for this sub-topic yet.Y12–13
- OT2.6The problem-solving cycleNo lesson for this sub-topic yet.Y12–13
- OT2.7Diagrams in problem solvingNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
OT3Mathematical modelling5 sub-topics
- OT3.1Build a modelNo lesson for this sub-topic yet.Y12–13
- OT3.2Use a modelNo lesson for this sub-topic yet.Y12–13
- OT3.3Interpret a model's outputsNo lesson for this sub-topic yet.Y12–13
- OT3.4Refine and evaluate a modelNo lesson for this sub-topic yet.Y12–13
- OT3.5Modelling assumptionsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
LDSThe large data set1 sub-topic
- LDSFamiliarity with the Pearson large data setNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
A1Formulae you must recall (not in the formulae booklet)5 sub-topics
- PPureNo lesson for this sub-topic yet.Y12–13
- CCalculusNo lesson for this sub-topic yet.Y12–13
- VVectorsNo lesson for this sub-topic yet.Y12–13
- SStatisticsNo lesson for this sub-topic yet.Y12–13
- MMechanicsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
AKAssumed knowledge1 sub-topic
- AKGCSE Mathematics and the pure contentNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
Core content8 topics
3.1Measurements and their errors3 sub-topics
- 3.1.1Use of SI units and their prefixesNo lesson for this sub-topic yet.Y12
- 3.1.2Limitation of physical measurementsNo lesson for this sub-topic yet.Y12
- 3.1.3Estimation of physical quantitiesNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
3.2Particles and radiation11 sub-topics
- 3.2.1 Particles
- 3.2.1.1Constituents of the atomNo lesson for this sub-topic yet.Y12
- 3.2.1.2Stable and unstable nucleiNo lesson for this sub-topic yet.Y12
- 3.2.1.3Particles, antiparticles and photonsNo lesson for this sub-topic yet.Y12
- 3.2.1.4Particle interactionsNo lesson for this sub-topic yet.Y12
- 3.2.1.5Classification of particlesNo lesson for this sub-topic yet.Y12
- 3.2.1.6Quarks and antiquarksNo lesson for this sub-topic yet.Y12
- 3.2.1.7Applications of conservation lawsNo lesson for this sub-topic yet.Y12
- 3.2.2 Electromagnetic radiation and quantum phenomena
- 3.2.2.1The photoelectric effectNo lesson for this sub-topic yet.Y12
- 3.2.2.2Collisions of electrons with atomsNo lesson for this sub-topic yet.Y12
- 3.2.2.3Energy levels and photon emissionNo lesson for this sub-topic yet.Y12
- 3.2.2.4Wave-particle dualityNo lesson for this sub-topic yet.Y12
3.3Waves6 sub-topics
- 3.3.1 Progressive and stationary waves
- 3.3.1.1Progressive wavesNo lesson for this sub-topic yet.Y12
- 3.3.1.2Longitudinal and transverse wavesNo lesson for this sub-topic yet.Y12
- 3.3.1.3Principle of superposition of waves and formation of stationary wavesNo lesson for this sub-topic yet.Y12
- 3.3.2 Refraction, diffraction and interference
- 3.3.2.1InterferenceNo lesson for this sub-topic yet.Y12
- 3.3.2.2DiffractionNo lesson for this sub-topic yet.Y12
- 3.3.2.3Refraction at a plane surfaceNo lesson for this sub-topic yet.Y12
3.4Mechanics and materials10 sub-topics
- 3.4.1 Force, energy and momentum
- 3.4.1.1Scalars and vectorsNo lesson for this sub-topic yet.Y12
- 3.4.1.2MomentsNo lesson for this sub-topic yet.Y12
- 3.4.1.3Motion along a straight lineNo lesson for this sub-topic yet.Y12
- 3.4.1.4Projectile motionNo lesson for this sub-topic yet.Y12
- 3.4.1.5Newton's laws of motionNo lesson for this sub-topic yet.Y12
- 3.4.1.6MomentumNo lesson for this sub-topic yet.Y12
- 3.4.1.7Work, energy and powerNo lesson for this sub-topic yet.Y12
- 3.4.1.8Conservation of energyNo lesson for this sub-topic yet.Y12
- 3.4.2 Materials
- 3.4.2.1Bulk properties of solidsNo lesson for this sub-topic yet.Y12
- 3.4.2.2The Young modulusNo lesson for this sub-topic yet.Y12
3.5Electricity6 sub-topics
- 3.5.1 Current electricity
- 3.5.1.1Basics of electricityNo lesson for this sub-topic yet.Y12
- 3.5.1.2Current–voltage characteristicsNo lesson for this sub-topic yet.Y12
- 3.5.1.3ResistivityNo lesson for this sub-topic yet.Y12
- 3.5.1.4CircuitsNo lesson for this sub-topic yet.Y12
- 3.5.1.5Potential dividerNo lesson for this sub-topic yet.Y12
- 3.5.1.6Electromotive force and internal resistanceNo lesson for this sub-topic yet.Y12
3.6Further mechanics and thermal physics7 sub-topics
- 3.6.1 Periodic motion
- 3.6.1.1Circular motionNo lesson for this sub-topic yet.Y13
- 3.6.1.2Simple harmonic motion (SHM)No lesson for this sub-topic yet.Y13
- 3.6.1.3Simple harmonic systemsNo lesson for this sub-topic yet.Y13
- 3.6.1.4Forced vibrations and resonanceNo lesson for this sub-topic yet.Y13
- 3.6.2 Thermal physics
- 3.6.2.1Thermal energy transferNo lesson for this sub-topic yet.Y13
- 3.6.2.2Ideal gasesNo lesson for this sub-topic yet.Y13
- 3.6.2.3Molecular kinetic theory modelNo lesson for this sub-topic yet.Y13
3.7Fields and their consequences18 sub-topics
- 3.7.1 Fields
- 3.7.1FieldsNo lesson for this sub-topic yet.Y13
- 3.7.2 Gravitational fields
- 3.7.2.1Newton's lawNo lesson for this sub-topic yet.Y13
- 3.7.2.2Gravitational field strengthNo lesson for this sub-topic yet.Y13
- 3.7.2.3Gravitational potentialNo lesson for this sub-topic yet.Y13
- 3.7.2.4Orbits of planets and satellitesNo lesson for this sub-topic yet.Y13
- 3.7.3 Electric fields
- 3.7.3.1Coulomb's lawNo lesson for this sub-topic yet.Y13
- 3.7.3.2Electric field strengthNo lesson for this sub-topic yet.Y13
- 3.7.3.3Electric potentialNo lesson for this sub-topic yet.Y13
- 3.7.4 Capacitance
- 3.7.4.1CapacitanceNo lesson for this sub-topic yet.Y13
- 3.7.4.2Parallel plate capacitorNo lesson for this sub-topic yet.Y13
- 3.7.4.3Energy stored by a capacitorNo lesson for this sub-topic yet.Y13
- 3.7.4.4Capacitor charge and dischargeNo lesson for this sub-topic yet.Y13
- 3.7.5 Magnetic fields
- 3.7.5.1Magnetic flux densityNo lesson for this sub-topic yet.Y13
- 3.7.5.2Moving charges in a magnetic fieldNo lesson for this sub-topic yet.Y13
- 3.7.5.3Magnetic flux and flux linkageNo lesson for this sub-topic yet.Y13
- 3.7.5.4Electromagnetic inductionNo lesson for this sub-topic yet.Y13
- 3.7.5.5Alternating currentsNo lesson for this sub-topic yet.Y13
- 3.7.5.6The operation of a transformerNo lesson for this sub-topic yet.Y13
3.8Nuclear physics8 sub-topics
- 3.8.1 Radioactivity
- 3.8.1.1Rutherford scatteringNo lesson for this sub-topic yet.Y13
- 3.8.1.2α, β and γ radiationNo lesson for this sub-topic yet.Y13
- 3.8.1.3Radioactive decayNo lesson for this sub-topic yet.Y13
- 3.8.1.4Nuclear instabilityNo lesson for this sub-topic yet.Y13
- 3.8.1.5Nuclear radiusNo lesson for this sub-topic yet.Y13
- 3.8.1.6Mass and energyNo lesson for this sub-topic yet.Y13
- 3.8.1.7Induced fissionNo lesson for this sub-topic yet.Y13
- 3.8.1.8Safety aspectsNo lesson for this sub-topic yet.Y13
Option A: Astrophysics1 topic
3.9Astrophysics14 sub-topics
- 3.9.1 Telescopes
- 3.9.1.1Astronomical telescope consisting of two converging lensesNo lesson for this sub-topic yet.Y13
- 3.9.1.2Reflecting telescopesNo lesson for this sub-topic yet.Y13
- 3.9.1.3Single dish radio telescopes, I-R, U-V and X-ray telescopesNo lesson for this sub-topic yet.Y13
- 3.9.1.4Advantages of large diameter telescopesNo lesson for this sub-topic yet.Y13
- 3.9.2 Classification of stars
- 3.9.2.1Classification by luminosityNo lesson for this sub-topic yet.Y13
- 3.9.2.2Absolute magnitude, MNo lesson for this sub-topic yet.Y13
- 3.9.2.3Classification by temperature, black-body radiationNo lesson for this sub-topic yet.Y13
- 3.9.2.4Principles of the use of stellar spectral classesNo lesson for this sub-topic yet.Y13
- 3.9.2.5The Hertzsprung-Russell (HR) diagramNo lesson for this sub-topic yet.Y13
- 3.9.2.6Supernovae, neutron stars and black holesNo lesson for this sub-topic yet.Y13
- 3.9.3 Cosmology
- 3.9.3.1Doppler effectNo lesson for this sub-topic yet.Y13
- 3.9.3.2Hubble's lawNo lesson for this sub-topic yet.Y13
- 3.9.3.3QuasarsNo lesson for this sub-topic yet.Y13
- 3.9.3.4Detection of exoplanetsNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Option B: Medical physics1 topic
3.10Medical physics19 sub-topics
- 3.10.1 Physics of the eye
- 3.10.1.1Physics of visionNo lesson for this sub-topic yet.Y13
- 3.10.1.2Defects of vision and their correction using lensesNo lesson for this sub-topic yet.Y13
- 3.10.2 Physics of the ear
- 3.10.2.1Ear as a sound detection systemNo lesson for this sub-topic yet.Y13
- 3.10.2.2Sensitivity and frequency responseNo lesson for this sub-topic yet.Y13
- 3.10.2.3Defects of hearingNo lesson for this sub-topic yet.Y13
- 3.10.3 Biological measurement
- 3.10.3.1Simple ECG machines and the normal ECG waveformNo lesson for this sub-topic yet.Y13
- 3.10.4 Non-ionising imaging
- 3.10.4.1Ultrasound imagingNo lesson for this sub-topic yet.Y13
- 3.10.4.2Fibre optics and endoscopyNo lesson for this sub-topic yet.Y13
- 3.10.4.3Magnetic resonance (MR) scannerNo lesson for this sub-topic yet.Y13
- 3.10.5 X-ray imaging
- 3.10.5.1The physics of diagnostic X-raysNo lesson for this sub-topic yet.Y13
- 3.10.5.2Image detection and enhancementNo lesson for this sub-topic yet.Y13
- 3.10.5.3Absorption of X-raysNo lesson for this sub-topic yet.Y13
- 3.10.5.4CT scannerNo lesson for this sub-topic yet.Y13
- 3.10.6 Radionuclide imaging and therapy
- 3.10.6.1Imaging techniquesNo lesson for this sub-topic yet.Y13
- 3.10.6.2Half-lifeNo lesson for this sub-topic yet.Y13
- 3.10.6.3Gamma cameraNo lesson for this sub-topic yet.Y13
- 3.10.6.4Use of high-energy X-raysNo lesson for this sub-topic yet.Y13
- 3.10.6.5Use of radioactive implantsNo lesson for this sub-topic yet.Y13
- 3.10.6.6Imaging comparisonsNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Option C: Engineering physics1 topic
3.11Engineering physics12 sub-topics
- 3.11.1 Rotational dynamics
- 3.11.1.1Concept of moment of inertiaNo lesson for this sub-topic yet.Y13
- 3.11.1.2Rotational kinetic energyNo lesson for this sub-topic yet.Y13
- 3.11.1.3Rotational motionNo lesson for this sub-topic yet.Y13
- 3.11.1.4Torque and angular accelerationNo lesson for this sub-topic yet.Y13
- 3.11.1.5Angular momentumNo lesson for this sub-topic yet.Y13
- 3.11.1.6Work and powerNo lesson for this sub-topic yet.Y13
- 3.11.2 Thermodynamics and engines
- 3.11.2.1First law of thermodynamicsNo lesson for this sub-topic yet.Y13
- 3.11.2.2Non-flow processesNo lesson for this sub-topic yet.Y13
- 3.11.2.3The p–V diagramNo lesson for this sub-topic yet.Y13
- 3.11.2.4Engine cyclesNo lesson for this sub-topic yet.Y13
- 3.11.2.5Second law and enginesNo lesson for this sub-topic yet.Y13
- 3.11.2.6Reversed heat enginesNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Option D: Turning points in physics1 topic
3.12Turning points in physics15 sub-topics
- 3.12.1 The discovery of the electron
- 3.12.1.1Cathode raysNo lesson for this sub-topic yet.Y13
- 3.12.1.2Thermionic emission of electronsNo lesson for this sub-topic yet.Y13
- 3.12.1.3Specific charge of the electronNo lesson for this sub-topic yet.Y13
- 3.12.1.4Principle of Millikan's determination of the electronic charge, eNo lesson for this sub-topic yet.Y13
- 3.12.2 Wave-particle duality
- 3.12.2.1Newton's corpuscular theory of lightNo lesson for this sub-topic yet.Y13
- 3.12.2.2Significance of Young's double slits experimentNo lesson for this sub-topic yet.Y13
- 3.12.2.3Electromagnetic wavesNo lesson for this sub-topic yet.Y13
- 3.12.2.4The discovery of photoelectricityNo lesson for this sub-topic yet.Y13
- 3.12.2.5Wave–particle dualityNo lesson for this sub-topic yet.Y13
- 3.12.2.6Electron microscopesNo lesson for this sub-topic yet.Y13
- 3.12.3 Special relativity
- 3.12.3.1The Michelson-Morley experimentNo lesson for this sub-topic yet.Y13
- 3.12.3.2Einstein's theory of special relativityNo lesson for this sub-topic yet.Y13
- 3.12.3.3Time dilationNo lesson for this sub-topic yet.Y13
- 3.12.3.4Length contractionNo lesson for this sub-topic yet.Y13
- 3.12.3.5Mass and energyNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Option E: Electronics1 topic
3.13Electronics18 sub-topics
- 3.13.1 Discrete semiconductor devices
- 3.13.1.1MOSFET (metal-oxide semiconducting field-effect transistor)No lesson for this sub-topic yet.Y13
- 3.13.1.2Zener diodeNo lesson for this sub-topic yet.Y13
- 3.13.1.3PhotodiodeNo lesson for this sub-topic yet.Y13
- 3.13.1.4Hall effect sensorNo lesson for this sub-topic yet.Y13
- 3.13.2 Analogue and digital signals
- 3.13.2.1Difference between analogue and digital signalsNo lesson for this sub-topic yet.Y13
- 3.13.3 Analogue signal processing
- 3.13.3.1LC resonance filtersNo lesson for this sub-topic yet.Y13
- 3.13.3.2The ideal operational amplifierNo lesson for this sub-topic yet.Y13
- 3.13.4 Operational amplifier in:
- 3.13.4.1Inverting amplifier configurationNo lesson for this sub-topic yet.Y13
- 3.13.4.2Non-inverting amplifier configurationNo lesson for this sub-topic yet.Y13
- 3.13.4.3Summing amplifier configurationNo lesson for this sub-topic yet.Y13
- 3.13.4.4Real operational amplifiersNo lesson for this sub-topic yet.Y13
- 3.13.5 Digital signal processing
- 3.13.5.1Combinational logicNo lesson for this sub-topic yet.Y13
- 3.13.5.2Sequential logicNo lesson for this sub-topic yet.Y13
- 3.13.5.3AstablesNo lesson for this sub-topic yet.Y13
- 3.13.6 Data communication systems
- 3.13.6.1Principles of communication systemsNo lesson for this sub-topic yet.Y13
- 3.13.6.2Transmission mediaNo lesson for this sub-topic yet.Y13
- 3.13.6.3Time-division multiplexingNo lesson for this sub-topic yet.Y13
- 3.13.6.4Amplitude (AM) and frequency modulation (FM) techniquesNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
Across the whole course3 topics
MSMathematical skills35 sub-topics
- MS 0.1Units and prefixesNo lesson for this sub-topic yet.Y12–13
- MS 0.2Decimal and standard formNo lesson for this sub-topic yet.Y12–13
- MS 0.3Ratios, fractions and percentagesNo lesson for this sub-topic yet.Y12–13
- MS 0.4Estimating effects of changing parametersNo lesson for this sub-topic yet.Y12–13
- MS 0.5Calculator: powers, exponentials and logsNo lesson for this sub-topic yet.Y12–13
- MS 0.6Calculator: sin, cos and tanNo lesson for this sub-topic yet.Y12–13
- MS 1.1Significant figuresNo lesson for this sub-topic yet.Y12–13
- MS 1.2Means of repeated readingsNo lesson for this sub-topic yet.Y12–13
- MS 1.3Simple probabilityNo lesson for this sub-topic yet.Y12–13
- MS 1.4Order-of-magnitude calculationsNo lesson for this sub-topic yet.Y12–13
- MS 1.5Combining uncertaintiesNo lesson for this sub-topic yet.Y12–13
- MS 2.1Symbols =, <, ≪, ≫, >, ∝, ≈, ΔNo lesson for this sub-topic yet.Y12–13
- MS 2.2Changing the subjectNo lesson for this sub-topic yet.Y12–13
- MS 2.3Substituting values with unitsNo lesson for this sub-topic yet.Y12–13
- MS 2.4Solving equationsNo lesson for this sub-topic yet.Y12–13
- MS 2.5LogarithmsNo lesson for this sub-topic yet.Y12–13
- MS 3.1Graphical, numerical and algebraic formsNo lesson for this sub-topic yet.Y12–13
- MS 3.2Plotting dataNo lesson for this sub-topic yet.Y12–13
- MS 3.3y = mx + cNo lesson for this sub-topic yet.Y12–13
- MS 3.4Gradient and interceptNo lesson for this sub-topic yet.Y12–13
- MS 3.5Rate of change from a straight lineNo lesson for this sub-topic yet.Y12–13
- MS 3.6Tangents to curvesNo lesson for this sub-topic yet.Y12–13
- MS 3.7Instantaneous and average ratesNo lesson for this sub-topic yet.Y12–13
- MS 3.8Area under a graphNo lesson for this sub-topic yet.Y12–13
- MS 3.9Calculus ideas without calculusNo lesson for this sub-topic yet.Y12–13
- MS 3.10Logarithmic plotsNo lesson for this sub-topic yet.Y12–13
- MS 3.11Testing exponential and power laws with log plotsNo lesson for this sub-topic yet.Y12–13
- MS 3.12Sketching k/x, kx², kx, sin x, cos x, e^(±x), sin²x, cos²xNo lesson for this sub-topic yet.Y12–13
- MS 4.1Angles in 2D and 3D structuresNo lesson for this sub-topic yet.Y12–13
- MS 4.22D and 3D formsNo lesson for this sub-topic yet.Y12–13
- MS 4.3Areas and volumesNo lesson for this sub-topic yet.Y12–13
- MS 4.4Pythagoras and angle sum of a triangleNo lesson for this sub-topic yet.Y12–13
- MS 4.5Sin, cos and tan in physical problemsNo lesson for this sub-topic yet.Y12–13
- MS 4.6Small-angle approximationsNo lesson for this sub-topic yet.Y12–13
- MS 4.7Degrees and radiansNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
PSPractical skills10 sub-topics
- PS1.1Solve problems set in practical contextsNo lesson for this sub-topic yet.Y12–13
- PS1.2Apply knowledge to practical contextsNo lesson for this sub-topic yet.Y12–13
- PS2.1Comment on experimental design and evaluate methodsNo lesson for this sub-topic yet.Y12–13
- PS2.2Present data appropriatelyNo lesson for this sub-topic yet.Y12–13
- PS2.3Evaluate results and conclusions using uncertaintiesNo lesson for this sub-topic yet.Y12–13
- PS2.4Identify variables, including control variablesNo lesson for this sub-topic yet.Y12–13
- PS3.1Plot and interpret graphsNo lesson for this sub-topic yet.Y12–13
- PS3.2Process and analyse data with the maths skillsNo lesson for this sub-topic yet.Y12–13
- PS3.3Margins of error, accuracy and precisionNo lesson for this sub-topic yet.Y12–13
- PS4.1Use a wide range of instruments and techniquesNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
ATApparatus and techniques12 sub-topics
- ATaAnalogue instrumentsNo lesson for this sub-topic yet.Y12–13
- ATbDigital instrumentsNo lesson for this sub-topic yet.Y12–13
- ATcImproving accuracyNo lesson for this sub-topic yet.Y12–13
- ATdStopwatches and light gatesNo lesson for this sub-topic yet.Y12–13
- ATeCalipers and micrometersNo lesson for this sub-topic yet.Y12–13
- ATfBuilding circuits from diagramsNo lesson for this sub-topic yet.Y12–13
- ATgDesigning and checking circuitsNo lesson for this sub-topic yet.Y12–13
- AThSignal generators and oscilloscopesNo lesson for this sub-topic yet.Y12–13
- ATiGenerating and measuring wavesNo lesson for this sub-topic yet.Y12–13
- ATjLasers and light sourcesNo lesson for this sub-topic yet.Y12–13
- ATkICT and data loggersNo lesson for this sub-topic yet.Y12–13
- ATlIonising radiation and detectorsNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points
Topics 1 to 1313 topics
1Working as a physicist8 sub-topics
- 1Base and derived quantities and SI unitsNo lesson for this sub-topic yet.Y12
- 2Practical skills and techniquesNo lesson for this sub-topic yet.Y12
- 3Estimating physical quantitiesNo lesson for this sub-topic yet.Y12
- 4Limitations of physical measurementNo lesson for this sub-topic yet.Y12
- 5Communicating information with appropriate terminologyNo lesson for this sub-topic yet.Y12
- 6Applications and implications of scienceNo lesson for this sub-topic yet.Y12
- 7The scientific community and validating knowledgeNo lesson for this sub-topic yet.Y12
- 8How society uses science in decision makingNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
2Mechanics22 sub-topics
- 9Equations for uniformly accelerated motionNo lesson for this sub-topic yet.Y12
- 10Displacement–time, velocity–time and acceleration–time graphsNo lesson for this sub-topic yet.Y12
- 11Quantities from gradients and areas of graphsNo lesson for this sub-topic yet.Y12
- 12Scalar and vector quantitiesNo lesson for this sub-topic yet.Y12
- 13Resolving a vector into perpendicular componentsNo lesson for this sub-topic yet.Y12
- 14Resultant of coplanar vectorsNo lesson for this sub-topic yet.Y12
- 15Independence of vertical and horizontal motion of a projectileNo lesson for this sub-topic yet.Y12
- 16Free-body force diagramsNo lesson for this sub-topic yet.Y12
- 17Newton's first and second laws and terminal velocityNo lesson for this sub-topic yet.Y12
- 18Gravitational field strength and weight, W = mgNo lesson for this sub-topic yet.Y12
- 19CP1: Determine the acceleration of a freely-falling objectNo lesson for this sub-topic yet.Y12
- 20Newton's third lawNo lesson for this sub-topic yet.Y12
- 21Momentum, p = mvNo lesson for this sub-topic yet.Y12
- 22Conservation of linear momentum in one dimensionNo lesson for this sub-topic yet.Y12
- 23Moment of a forceNo lesson for this sub-topic yet.Y12
- 24Centre of gravity and the principle of momentsNo lesson for this sub-topic yet.Y12
- 25Work doneNo lesson for this sub-topic yet.Y12
- 26Kinetic energyNo lesson for this sub-topic yet.Y12
- 27Gravitational potential energyNo lesson for this sub-topic yet.Y12
- 28Conservation of energyNo lesson for this sub-topic yet.Y12
- 29PowerNo lesson for this sub-topic yet.Y12
- 30EfficiencyNo lesson for this sub-topic yet.Y12
3Electric circuits18 sub-topics
- 31Electric current as rate of flow of chargeNo lesson for this sub-topic yet.Y12
- 32Potential difference as work done per unit chargeNo lesson for this sub-topic yet.Y12
- 33Resistance and Ohm's lawNo lesson for this sub-topic yet.Y12
- 34Current and conservation of chargeNo lesson for this sub-topic yet.Y12
- 35Potential difference and conservation of energyNo lesson for this sub-topic yet.Y12
- 36Resistors in series and parallelNo lesson for this sub-topic yet.Y12
- 37Electrical powerNo lesson for this sub-topic yet.Y12
- 38I–V characteristicsNo lesson for this sub-topic yet.Y12
- 39Resistivity, R = ρl/ANo lesson for this sub-topic yet.Y12
- 40CP2: Determine the electrical resistivity of a materialNo lesson for this sub-topic yet.Y12
- 41I = nqvA and the range of resistivitiesNo lesson for this sub-topic yet.Y12
- 42Potential along a uniform current-carrying wireNo lesson for this sub-topic yet.Y12
- 43Potential dividersNo lesson for this sub-topic yet.Y12
- 44Potential dividers with thermistors and LDRsNo lesson for this sub-topic yet.Y12
- 45E.m.f. and internal resistanceNo lesson for this sub-topic yet.Y12
- 46CP3: Measure the e.m.f. and internal resistance of a cellNo lesson for this sub-topic yet.Y12
- 47Resistance and temperatureNo lesson for this sub-topic yet.Y12
- 48Resistance and illuminationNo lesson for this sub-topic yet.Y12
4Materials10 sub-topics
- 49DensityNo lesson for this sub-topic yet.Y12
- 50UpthrustNo lesson for this sub-topic yet.Y12
- 51Viscosity and Stokes' lawNo lesson for this sub-topic yet.Y12
- 52CP4: Use a falling-ball method to determine the viscosity of a liquidNo lesson for this sub-topic yet.Y12
- 53Hooke's law and stiffnessNo lesson for this sub-topic yet.Y12
- 54Stress, strain and the Young modulusNo lesson for this sub-topic yet.Y12
- 55Force–extension and force–compression graphsNo lesson for this sub-topic yet.Y12
- 56Stress–strain graphs and breaking stressNo lesson for this sub-topic yet.Y12
- 57CP5: Determine the Young modulus of a materialNo lesson for this sub-topic yet.Y12
- 58Elastic strain energyNo lesson for this sub-topic yet.Y12
No practice questions for this topic yet.Specification points
5Waves and the particle nature of light38 sub-topics
- 59Amplitude, frequency, period, speed and wavelengthNo lesson for this sub-topic yet.Y12
- 60The wave equation, v = fλNo lesson for this sub-topic yet.Y12
- 61Longitudinal wavesNo lesson for this sub-topic yet.Y12
- 62Transverse wavesNo lesson for this sub-topic yet.Y12
- 63Graphs of wavesNo lesson for this sub-topic yet.Y12
- 64CP6: Determine the speed of sound in air using a 2-beam oscilloscopeNo lesson for this sub-topic yet.Y12
- 65Superposition, coherence, path difference and phaseNo lesson for this sub-topic yet.Y12
- 66Phase difference and path differenceNo lesson for this sub-topic yet.Y12
- 67Standing waves, nodes and antinodesNo lesson for this sub-topic yet.Y12
- 68Speed of a transverse wave on a stringNo lesson for this sub-topic yet.Y12
- 69CP7: Factors affecting the frequency of a vibrating stringNo lesson for this sub-topic yet.Y12
- 70Intensity, I = P/ANo lesson for this sub-topic yet.Y12
- 71Refraction, Snell's law and refractive indexNo lesson for this sub-topic yet.Y12
- 72Critical angleNo lesson for this sub-topic yet.Y12
- 73Total internal reflectionNo lesson for this sub-topic yet.Y12
- 74Measuring refractive indexNo lesson for this sub-topic yet.Y12
- 75Focal length of converging and diverging lensesNo lesson for this sub-topic yet.Y12
- 76Ray diagramsNo lesson for this sub-topic yet.Y12
- 77Power of a lens, P = 1/fNo lesson for this sub-topic yet.Y12
- 78Thin lenses in combinationNo lesson for this sub-topic yet.Y12
- 79Real and virtual imagesNo lesson for this sub-topic yet.Y12
- 80The thin lens equationNo lesson for this sub-topic yet.Y12
- 81MagnificationNo lesson for this sub-topic yet.Y12
- 82Plane polarisationNo lesson for this sub-topic yet.Y12
- 83Diffraction and Huygens' constructionNo lesson for this sub-topic yet.Y12
- 84Diffraction grating, nλ = d sin θNo lesson for this sub-topic yet.Y12
- 85CP8: Determine the wavelength of light using a diffraction gratingNo lesson for this sub-topic yet.Y12
- 86Electron diffractionNo lesson for this sub-topic yet.Y12
- 87De Broglie wavelengthNo lesson for this sub-topic yet.Y12
- 88Transmission and reflection at interfacesNo lesson for this sub-topic yet.Y12
- 89Pulse–echo techniqueNo lesson for this sub-topic yet.Y12
- 90Wave and photon models of electromagnetic radiationNo lesson for this sub-topic yet.Y12
- 91Photon energy, E = hfNo lesson for this sub-topic yet.Y12
- 92Photoelectric emissionNo lesson for this sub-topic yet.Y12
- 93Threshold frequency, work function and the photoelectric equationNo lesson for this sub-topic yet.Y12
- 94The electronvoltNo lesson for this sub-topic yet.Y12
- 95Photoelectric effect as evidence for the particle nature of lightNo lesson for this sub-topic yet.Y12
- 96Atomic line spectra and energy levelsNo lesson for this sub-topic yet.Y12
6Further mechanics11 sub-topics
- 97Impulse, FΔt = ΔpNo lesson for this sub-topic yet.Y13
- 98CP9: Force exerted on an object and its change of momentumNo lesson for this sub-topic yet.Y13
- 99Conservation of linear momentum in two dimensionsNo lesson for this sub-topic yet.Y13
- 100CP10: Use ICT to analyse collisions between small spheresNo lesson for this sub-topic yet.Y13
- 101Elastic and inelastic collisionsNo lesson for this sub-topic yet.Y13
- 102Kinetic energy, Ek = p²/2mNo lesson for this sub-topic yet.Y13
- 103Radians and degreesNo lesson for this sub-topic yet.Y13
- 104Angular velocity, v = ωrNo lesson for this sub-topic yet.Y13
- 105Centripetal accelerationNo lesson for this sub-topic yet.Y13
- 106Centripetal forceNo lesson for this sub-topic yet.Y13
- 107Equations for centripetal forceNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
7Electric and magnetic fields22 sub-topics
- 108Electric fieldsNo lesson for this sub-topic yet.Y13
- 109Electric field strength, E = F/QNo lesson for this sub-topic yet.Y13
- 110Coulomb's lawNo lesson for this sub-topic yet.Y13
- 111Field due to a point chargeNo lesson for this sub-topic yet.Y13
- 112Electric field and electric potentialNo lesson for this sub-topic yet.Y13
- 113Uniform field between parallel plates, E = V/dNo lesson for this sub-topic yet.Y13
- 114Potential in a radial fieldNo lesson for this sub-topic yet.Y13
- 115Field lines and equipotentialsNo lesson for this sub-topic yet.Y13
- 116Capacitance, C = Q/VNo lesson for this sub-topic yet.Y13
- 117Energy stored by a capacitorNo lesson for this sub-topic yet.Y13
- 118Charging and discharging capacitors and the time constantNo lesson for this sub-topic yet.Y13
- 119CP11: Analyse the p.d. across a charging and discharging capacitorNo lesson for this sub-topic yet.Y13
- 120Exponential discharge equationsNo lesson for this sub-topic yet.Y13
- 121Magnetic flux density, flux and flux linkageNo lesson for this sub-topic yet.Y13
- 122Force on a moving chargeNo lesson for this sub-topic yet.Y13
- 123Force on a current-carrying conductor, F = BIl sin θNo lesson for this sub-topic yet.Y13
- 124Induced e.m.f. from relative motionNo lesson for this sub-topic yet.Y13
- 125Induced e.m.f. from a changing currentNo lesson for this sub-topic yet.Y13
- 126Lenz's lawNo lesson for this sub-topic yet.Y13
- 127Faraday's lawNo lesson for this sub-topic yet.Y13
- 128Alternating current: frequency, period, peak and r.m.s.No lesson for this sub-topic yet.Y13
- 129Peak and r.m.s. valuesNo lesson for this sub-topic yet.Y13
8Nuclear and particle physics14 sub-topics
- 130Nucleon number and proton numberNo lesson for this sub-topic yet.Y13
- 131Alpha particle scatteringNo lesson for this sub-topic yet.Y13
- 132Thermionic emission and accelerating electronsNo lesson for this sub-topic yet.Y13
- 133Linear accelerators, cyclotrons and detectorsNo lesson for this sub-topic yet.Y13
- 134Charged particles in a magnetic field, r = p/BQNo lesson for this sub-topic yet.Y13
- 135Conservation laws in particle interactionsNo lesson for this sub-topic yet.Y13
- 136High energies to probe nucleon structureNo lesson for this sub-topic yet.Y13
- 137Pair creation and annihilationNo lesson for this sub-topic yet.Y13
- 138MeV, GeV and MeV/c²No lesson for this sub-topic yet.Y13
- 139Relativistic increase in particle lifetimeNo lesson for this sub-topic yet.Y13
- 140The standard quark–lepton modelNo lesson for this sub-topic yet.Y13
- 141AntiparticlesNo lesson for this sub-topic yet.Y13
- 142Conservation of charge, baryon number and lepton numberNo lesson for this sub-topic yet.Y13
- 143Particle equationsNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
9Thermodynamics12 sub-topics
- 144Specific heat capacity and specific latent heatNo lesson for this sub-topic yet.Y13
- 145CP12: Calibrate a thermistor in a potential divider as a thermostatNo lesson for this sub-topic yet.Y13
- 146CP13: Determine the specific latent heat of a phase changeNo lesson for this sub-topic yet.Y13
- 147Internal energyNo lesson for this sub-topic yet.Y13
- 148Absolute zeroNo lesson for this sub-topic yet.Y13
- 149Kinetic theory, pV = ⅓Nm⟨c²⟩No lesson for this sub-topic yet.Y13
- 150Ideal gas equation, pV = NkTNo lesson for this sub-topic yet.Y13
- 151CP14: Pressure and volume of a gas at fixed temperatureNo lesson for this sub-topic yet.Y13
- 152Mean kinetic energy, ½m⟨c²⟩ = 3/2 kTNo lesson for this sub-topic yet.Y13
- 153Black body radiationNo lesson for this sub-topic yet.Y13
- 154Stefan–Boltzmann lawNo lesson for this sub-topic yet.Y13
- 155Wien's lawNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
10Space8 sub-topics
- 156Intensity and luminosityNo lesson for this sub-topic yet.Y13
- 157Trigonometric parallaxNo lesson for this sub-topic yet.Y13
- 158Standard candlesNo lesson for this sub-topic yet.Y13
- 159Hertzsprung–Russell diagramNo lesson for this sub-topic yet.Y13
- 160Life cycles of starsNo lesson for this sub-topic yet.Y13
- 161Doppler effectNo lesson for this sub-topic yet.Y13
- 162Redshift and Hubble's law, v = H₀dNo lesson for this sub-topic yet.Y13
- 163The age and fate of the universe and dark matterNo lesson for this sub-topic yet.Y13
No practice questions for this topic yet.Specification points
11Nuclear radiation10 sub-topics
- 164Binding energy and mass deficitNo lesson for this sub-topic yet.Y13
- 165Atomic mass unitNo lesson for this sub-topic yet.Y13
- 166Fission and fusionNo lesson for this sub-topic yet.Y13
- 167Conditions for fusionNo lesson for this sub-topic yet.Y13
- 168Background radiationNo lesson for this sub-topic yet.Y13
- 169Alpha, beta and gamma radiationNo lesson for this sub-topic yet.Y13
- 170Nuclear equationsNo lesson for this sub-topic yet.Y13
- 171CP15: Investigate the absorption of gamma radiation by leadNo lesson for this sub-topic yet.Y13
- 172Random nature of radioactive decayNo lesson for this sub-topic yet.Y13
- 173Half-life and decay equationsNo lesson for this sub-topic yet.Y13
12Gravitational fields7 sub-topics
- 174Gravitational fieldsNo lesson for this sub-topic yet.Y13
- 175Gravitational field strength, g = F/mNo lesson for this sub-topic yet.Y13
- 176Newton's law of universal gravitationNo lesson for this sub-topic yet.Y13
- 177Field due to a point massNo lesson for this sub-topic yet.Y13
- 178Gravitational potentialNo lesson for this sub-topic yet.Y13
- 179Comparing electric and gravitational fieldsNo lesson for this sub-topic yet.Y13
- 180OrbitsNo lesson for this sub-topic yet.Y13
13Oscillations11 sub-topics
- 181Condition for simple harmonic motionNo lesson for this sub-topic yet.Y13
- 182Equations of simple harmonic motionNo lesson for this sub-topic yet.Y13
- 183Mass–spring system and simple pendulumNo lesson for this sub-topic yet.Y13
- 184Velocity from a displacement–time graphNo lesson for this sub-topic yet.Y13
- 185Acceleration from a velocity–time graphNo lesson for this sub-topic yet.Y13
- 186ResonanceNo lesson for this sub-topic yet.Y13
- 187CP16: Determine an unknown mass using resonant frequenciesNo lesson for this sub-topic yet.Y13
- 188Energy in damped and undamped oscillatorsNo lesson for this sub-topic yet.Y13
- 189Free and forced oscillationsNo lesson for this sub-topic yet.Y13
- 190Forced oscillations near the natural frequencyNo lesson for this sub-topic yet.Y13
- 191Damping and plastic deformationNo lesson for this sub-topic yet.Y13
Across the whole course1 topic
MSMathematical skills35 sub-topics
- 0.1Units and prefixesNo lesson for this sub-topic yet.Y12–13
- 0.2Decimal and standard formNo lesson for this sub-topic yet.Y12–13
- 0.3Ratios, fractions and percentagesNo lesson for this sub-topic yet.Y12–13
- 0.4Estimating effects of changing parametersNo lesson for this sub-topic yet.Y12–13
- 0.5Calculator: powers, exponentials and logsNo lesson for this sub-topic yet.Y12–13
- 0.6Calculator: sin, cos and tanNo lesson for this sub-topic yet.Y12–13
- 1.1Significant figuresNo lesson for this sub-topic yet.Y12–13
- 1.2Means of repeated readingsNo lesson for this sub-topic yet.Y12–13
- 1.3Simple probabilityNo lesson for this sub-topic yet.Y12–13
- 1.4Order-of-magnitude calculationsNo lesson for this sub-topic yet.Y12–13
- 1.5Combining uncertaintiesNo lesson for this sub-topic yet.Y12–13
- 2.1Symbols =, <, ≪, ≫, >, ∝, ≈, ΔNo lesson for this sub-topic yet.Y12–13
- 2.2Changing the subjectNo lesson for this sub-topic yet.Y12–13
- 2.3Substituting values with unitsNo lesson for this sub-topic yet.Y12–13
- 2.4Solving equationsNo lesson for this sub-topic yet.Y12–13
- 2.5LogarithmsNo lesson for this sub-topic yet.Y12–13
- 3.1Graphical, numerical and algebraic formsNo lesson for this sub-topic yet.Y12–13
- 3.2Plotting dataNo lesson for this sub-topic yet.Y12–13
- 3.3y = mx + cNo lesson for this sub-topic yet.Y12–13
- 3.4Gradient and interceptNo lesson for this sub-topic yet.Y12–13
- 3.5Rate of change from a straight lineNo lesson for this sub-topic yet.Y12–13
- 3.6Tangents to curvesNo lesson for this sub-topic yet.Y12–13
- 3.7Instantaneous and average ratesNo lesson for this sub-topic yet.Y12–13
- 3.8Area under a graphNo lesson for this sub-topic yet.Y12–13
- 3.9Calculus ideas without calculusNo lesson for this sub-topic yet.Y12–13
- 3.10Logarithmic plotsNo lesson for this sub-topic yet.Y12–13
- 3.11Testing exponential and power laws with log plotsNo lesson for this sub-topic yet.Y12–13
- 3.12Sketching k/x, kx², kx, sin x, cos x, e^(±x), sin²x, cos²xNo lesson for this sub-topic yet.Y12–13
- 4.1Angles in 2D and 3D structuresNo lesson for this sub-topic yet.Y12–13
- 4.22D and 3D formsNo lesson for this sub-topic yet.Y12–13
- 4.3Areas and volumesNo lesson for this sub-topic yet.Y12–13
- 4.4Pythagoras and angle sum of a triangleNo lesson for this sub-topic yet.Y12–13
- 4.5Sin, cos and tan in physical problemsNo lesson for this sub-topic yet.Y12–13
- 4.6Small-angle approximationsNo lesson for this sub-topic yet.Y12–13
- 4.7Degrees and radiansNo lesson for this sub-topic yet.Y12–13
No practice questions for this topic yet.Specification points