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Compulsory content

Proof1 lesson

Proof by mathematical induction: sums of series, divisibility, powers of matricesY12

Complex numbers11 lessons

Solve quadratics with real coefficients; cubics and quartics given a root or quadratic factorY12
Add, subtract, multiply and divide complex numbers in the form x + iy; real and imaginary partsY12
Complex conjugates; non-real roots of real polynomials occur in conjugate pairsY12
Use and interpret Argand diagramsY12
Convert between Cartesian and modulus–argument formY12
Multiply and divide complex numbers in modulus–argument formY12
Construct and interpret simple loci in the Argand diagram, such as |z − a| > r and arg(z − a) = θY12
De Moivre's theorem: multiple angle formulae and sums of seriesY13
Exponential form: e^(iθ) = cos θ + i sin θ and z = re^(iθ)Y13
The n distinct nth roots of re^(iθ); vertices of a regular n-gonY13
Complex roots of unity to solve geometric problemsY13

Matrices11 lessons

Add, subtract and multiply conformable matrices; multiply a matrix by a scalarY12
Zero and identity matricesY12
Matrices as linear transformations in 2D; single reflections and rotations in 3D; successive transformationsY12
Invariant points and invariant linesY12
Determinants as scale factors and effect on orientation (2 × 2 in AS; 3 × 3 at A level)Y12–13
Singular and non-singular matrices; inverses (2 × 2 in AS; 3 × 3 at A level)Y12–13
Solve three linear simultaneous equations using the inverse matrixY13
Interpret geometrically the solution, or failure of solution, of three simultaneous equationsY13
Factorise determinants using row and column operationsY13
Eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices; characteristic equationY13
Diagonalise matrices, M = UDU⁻¹; powers of MY13

Further algebra and functions16 lessons

Relationships between roots and coefficients of polynomials up to quarticsY12
Form a polynomial whose roots are a linear transformation of the roots of anotherY12
Standard results for sums of integers, squares and cubesY12
Method of differences, including with partial fractionsY12
Find the Maclaurin series of a function, including the general termY13
Maclaurin series of eˣ, ln(1 + x), sin x, cos x and (1 + x)ⁿ with ranges of validityY12
Evaluate limits using Maclaurin series or l'Hôpital's ruleY13
Solve cubic and quartic polynomial inequalitiesY12
Solve inequalities of the form (ax + b)/(cx + d) < (ex + f)/(gx + h)Y12
Modulus functions and related inequalitiesY13
Sketch y = 1/f(x) given the graph of y = f(x)Y13
Graphs of rational functions (ax + b)/(cx + d): asymptotes, intercepts, inequalitiesY12
Graphs of rational functions with quadratic numerator or denominator, including oblique asymptotesY12–13
Use quadratic theory (not calculus) to find ranges and stationary points of rational functionsY12
Sketch the parabola, ellipse, hyperbola and rectangular hyperbolaY12
Transformations of curves: translations, stretches, reflections, rotations and enlargementsY12–13

Further calculus9 lessons

Improper integralsY13
Derive and use formulae for volumes of revolutionY12
Mean value of a functionY12
Integrate using partial fractions, including quadratic factorsY13
Differentiate inverse trigonometric functionsY13
Integrate 1/√(a² − x²) and 1/(a² + x²); choose trigonometric substitutionsY13
Arc length and area of surface of revolution, Cartesian and parametricY13
Derive and use reduction formulaeY13
Limits of xᵏeˣ and xᵏ ln x for improper integralsY13

Further vectors6 lessons

Vector and Cartesian forms of the equation of a straight line in 3DY12
Vector and Cartesian forms of the equation of a planeY13
Scalar product: angles between lines, planes, and a line and a planeY12–13
Check whether vectors are perpendicular using the scalar productY12
Vector product; (r − a) × b = 0; area of a triangleY13
Intersections of lines and planes; perpendicular distancesY12–13

Polar coordinates3 lessons

Polar coordinates; convert between polar and Cartesian formsY12
Sketch curves with r given as a function of θY12
Areas enclosed by polar curvesY13

Hyperbolic functions7 lessons

Definitions, domains, ranges and graphs of sinh, cosh, tanh, sech, cosech and cothY12
Differentiate and integrate hyperbolic functionsY13
Inverse hyperbolic functions: definitions, domains and rangesY12
Derive and use logarithmic forms of the inverse hyperbolic functionsY12
Integrate 1/√(x² + a²) and 1/√(x² − a²); choose substitutionsY13
Hyperbolic identities, including tanh x = sinh x / cosh xY12
Construct proofs involving hyperbolic functions and identitiesY13

Differential equations11 lessons

Integrating factor for dy/dx + P(x)y = Q(x)Y13
General and particular solutionsY13
Differential equations in kinematics and other modelling contextsY13
Second order homogeneous equations using the auxiliary equationY13
Second order non-homogeneous equations: complementary function and particular integralY13
Sign of the discriminant and the form of the solutionY13
Simple harmonic motion, ẍ = −ω²xY13
Damped oscillations: light, critical and heavy dampingY13
Coupled first order simultaneous differential equationsY13
Hooke's law to form the equation of simple harmonic motionY13
Damped motion with damping force proportional to velocityY13

Numerical methods3 lessons

Mid-ordinate rule and Simpson's ruleY13
Euler's step by step method for first order differential equationsY13
Improved Euler methodY13

Optional application 1: mechanics

Dimensional analysis2 lessons · Option M

Dimensions of quantities; dimensional consistencyY12
Predict formulae; find powers in a proposed formulaY12

Momentum and collisions4 lessons · Option M

Conservation of momentum, including velocities as vectorsY12–13
Coefficient of restitution and Newton's experimental law, including fixed smooth surfacesY12–13
Impulse and momentum, Ft = mv − muY12–13
Impulse of a variable force, I = ∫F dtY12

Work, energy and power7 lessons · Option M

Work done by a force, WD = Fd cos θY12
Gravitational potential energyY12
Kinetic energyY12
Hooke's law and modulus of elasticityY12
Work done by a variable force, WD = ∫F dxY12
Elastic potential energyY12
Power, P = FvY12–13

Circular motion6 lessons · Option M

Motion of a particle in a circle at constant speedY12
Angular speedY12
Relationships between speed, angular speed, radius and accelerationY12
Position, velocity and acceleration vectors in circular motionY13
Conical pendulum, with one or two stringsY13
Motion in a vertical circleY13

Centres of mass and moments6 lessons · Option M

Centre of mass of a system of particlesY13
Centre of mass of a composite bodyY13
Centre of mass of a lamina by integrationY13
Centres of mass of solids of revolutionY13
Sliding and toppling, including suspended bodies and inclined planesY13
Rigid bodies in equilibrium: moments and couplesY13

Optional application 2: statistics

Discrete random variables (DRVs) and expectation7 lessons · Option S

Discrete random variables as tables or functionsY12
Probabilities for a DRVY12
Mean, variance, standard deviation, mode and median of a DRVY12
E(X), E(X²) and Var(X)Y12
Expectation and variance of functions of a DRVY12
Discrete uniform distributionY12
Proofs of the mean and variance of the discrete uniform distributionY12

Poisson distribution5 lessons · Option S

Conditions for a Poisson model; X ~ Po(λ)Y12
Poisson probabilitiesY12
Mean, variance and standard deviationY12
Sums of independent Poisson variablesY12
Hypothesis test for the mean of a Poisson distributionY12

Type I and Type II errors2 lessons · Option S

Type I and Type II errors; probability of a Type I errorY12–13
Power of a test; probability of a Type II errorY13

Continuous random variables (CRVs)8 lessons · Option S

Probability density functionsY12
Probability over an intervalY12
Median and quartilesY12
Mean, variance and standard deviationY12
Expectation and variance of functions of a CRVY12
Cumulative distribution functionsY13
Rectangular distribution; proofs of its mean and varianceY13
Expectation and variance of sums of independent random variablesY12

Chi-squared tests for association5 lessons · Option S

n × m contingency tablesY12
The χ² statistic and degrees of freedomY12
Convention that expected frequencies exceed 5Y12
Sources of association in contextY12
Yates' correctionY13

Exponential distribution4 lessons · Option S

Conditions for an exponential model; pdf and cdfY13
Probabilities from the exponential distributionY13
Proofs of the mean, variance and standard deviationY13
Time between Poisson events is exponentially distributedY13

Inference – one sample t-distribution1 lesson · Option S

t-test for the mean of a normal distribution with unknown varianceY13

Confidence intervals4 lessons · Option S

Confidence interval for a normal mean with known varianceY12
Large-sample confidence interval with unknown varianceY12
Inferences from confidence intervalsY12
Confidence intervals using the t-distributionY13

Optional application 3: discrete mathematics

Graphs7 lessons · Option D

Language of graphs: vertex, edge, trail, cycle, degree, subgraphY12
Eulerian, semi-Eulerian and Hamiltonian graphsY12
Euler's formula for connected planar graphsY12
Kuratowski's theoremY13
Complete and bipartite graphs; adjacency matrices; complementsY12
Simple graphs, connected graphs and treesY12
Isomorphism between graphsY13

Networks5 lessons · Option D

Language of networks: node, arc, weightY12
Minimum spanning treesY12
Route inspectionY12
Travelling salesperson: upper and lower boundsY12
Evaluate and refine network modelsY12

Network flows7 lessons · Option D

Flows in directed networksY12
Cuts and their valuesY12
Maximum flow–minimum cut theoremY12
Supersources and supersinksY12
Augment flows to find the maximum flowY13
Arcs with upper and lower capacitiesY13
Nodes of restricted capacityY13

Linear programming4 lessons · Option D

Formulate constrained optimisation problemsY12
Graphical solutionY12
Simplex algorithm with slack variablesY13
Interpret a Simplex tableauY13

Critical path analysis6 lessons · Option D

Activity-on-node precedence networksY12
Earliest and latest start and finish timesY12
Critical activities, critical paths and floatY12
Refine models and assess changesY12
Gantt (cascade) charts and resource histogramsY13
Resource levellingY13

Game theory for zero-sum games6 lessons · Option D

Pay-off matricesY12
Play-safe strategies and the value of a gameY12
Stable solutionsY12
Dominated strategiesY12
Optimal mixed strategies, including graphical methodsY12
Convert larger games to linear programming problemsY13

Binary operations12 lessons · Option D

Binary operations, including modular arithmetic and matrix multiplicationY12
CommutativityY12
AssociativityY12
Cayley tablesY12
Identity elementsY12
InversesY12
Language of groups: order, period, subgroupY13
Group axiomsY13
Finite and infinite groups; cyclic and abelian groups; symmetry groupsY13
Lagrange's theoremY13
GeneratorsY13
Isomorphism between finite groupsY13

Across the whole course

Mathematical argument, language and proof5 lessons

Construct and present mathematical argumentsY12–13
Mathematical language and syntaxY12–13
Set notationY12–13
FunctionsY12–13
Critique arguments and proofsY12–13

Mathematical problem solving5 lessons

Recognise the underlying structure of a problemY12–13
Extended arguments for unstructured problemsY12–13
Interpret solutions in contextY12–13
The problem-solving cycleY12–13
Diagrams in problem solvingY12–13

Mathematical modelling5 lessons

Build a modelY12–13
Use a modelY12–13
Interpret a model's outputsY12–13
Refine and evaluate a modelY12–13
Modelling assumptionsY12–13

Assumed knowledge1 lesson

GCSE and A level Mathematics contentY12–13

Core Pure Mathematics

Proof1 lesson

Proof by mathematical inductionY12

Complex numbers11 lessons

Solving polynomial equations with complex rootsY12
Arithmetic in Cartesian formY12
Complex conjugatesY12
Argand diagramsY12
Modulus–argument formY12
Multiplying and dividing in modulus–argument formY12
Loci and regions in the Argand diagramY12
De Moivre's theoremY13
Exponential (Euler) formY13
nth roots of a complex numberY13
Roots of unity and geometryY13

Matrices8 lessons

Matrix operationsY12
Zero and identity matricesY12
Linear transformationsY12
Invariant points and invariant linesY12
DeterminantsY12
Inverse matricesY12
Solving three linear equationsY12
Geometry of three planesY12

Further algebra and functions6 lessons

Roots and coefficients of polynomialsY12
Transforming rootsY12
Standard results for sumsY12
Method of differencesY13
Maclaurin seriesY13
Standard Maclaurin seriesY13

Further calculus7 lessons

Volumes of revolution (Cartesian)Y12
Volumes of revolution (parametric and modelling)Y13
Improper integralsY13
Mean value of a functionY13
Integration using partial fractionsY13
Differentiating inverse trigonometric functionsY13
Integrals leading to inverse trig functionsY13

Further vectors5 lessons

Equations of lines in 3DY12
Equations of planesY12
Scalar product, planes and anglesY12
Perpendicular vectorsY12
Intersections and perpendicular distancesY12

Polar coordinates3 lessons

Polar and Cartesian conversionY13
Sketching polar curvesY13
Areas and tangentsY13

Hyperbolic functions5 lessons

Definitions and graphsY13
Differentiating and integrating hyperbolic functionsY13
Inverse hyperbolic functionsY13
Logarithmic formsY13
Integrals leading to inverse hyperbolic functionsY13

Differential equations9 lessons

Integrating factor methodY13
General and particular solutionsY13
Modelling with first-order equationsY13
Second-order homogeneous equationsY13
Second-order non-homogeneous equationsY13
Auxiliary equation casesY13
Simple harmonic motionY13
Damped and forced oscillationsY13
Coupled first-order systemsY13

Further Pure Mathematics 1 (FP1)

Further Trigonometry3 lessons · Option FP1

The t-formulaeY12
Proving identities with t-formulaeY12
Solving equations with t-formulaeY12

Further calculus5 lessons · Option FP1

Taylor seriesY13
Series expansions to evaluate limitsY13
Leibnitz's theoremY13
L'Hôpital's ruleY13
Weierstrass substitutionY13

Further differential equations2 lessons · Option FP1

Taylor series solutions of differential equationsY13
Reducible differential equationsY13

Coordinate systems6 lessons · Option FP1

Conics: parabola and rectangular hyperbolaY12
Conics: ellipse and hyperbolaY13
Focus–directrix propertiesY12
Eccentricity, foci and directrices of ellipse and hyperbolaY13
Tangents and normals to conicsY12
Loci problemsY12

Further Vectors3 lessons · Option FP1

Vector productY12
Scalar triple productY12
Vector geometry with the vector productY13

Further numerical methods2 lessons · Option FP1

Numerical solution of differential equationsY12
Simpson's ruleY13

Inequalities1 lesson · Option FP1

InequalitiesY12

Further Statistics 1 (FS1)

Discrete probability distributions1 lesson · Option FS1

Discrete probability distributionsY12

Poisson & binomial distributions3 lessons · Option FS1

The Poisson distributionY12
Mean and variance of binomial and PoissonY12
Poisson approximation to the binomialY12

Geometric and negative binomial distributions3 lessons · Option FS1

Geometric and negative binomial modelsY13
Mean and variance of the geometric distributionY13
Mean and variance of the negative binomialY13

Hypothesis Testing2 lessons · Option FS1

Hypothesis tests for the mean of a Poisson distributionY12
Hypothesis tests for the parameter of a geometric distributionY13

Central Limit Theorem1 lesson · Option FS1

Central Limit TheoremY13

Chi Squared Tests2 lessons · Option FS1

Chi-squared tests (discrete uniform, binomial, Poisson)Y12
Chi-squared tests for geometric distributionsY13

Probability generating functions3 lessons · Option FS1

Probability generating functionsY13
Mean and variance from PGFsY13
PGF of a sum of independent variablesY13

Quality of tests1 lesson · Option FS1

Quality of testsY13

Further Mechanics 1 (FM1)

Momentum and impulse2 lessons · Option FM1

Momentum and impulseY12
Momentum as a vectorY13

Work, energy and power1 lesson · Option FM1

Work, energy and powerY12

Elastic strings and springs and elastic energy2 lessons · Option FM1

Hooke's lawY13
Elastic potential energyY13

Elastic collisions in one dimension2 lessons · Option FM1

Direct impact and Newton's law of restitutionY12
Successive direct impactsY12

Elastic collisions in two dimensions2 lessons · Option FM1

Oblique impact of smooth elastic spheresY13
Successive oblique impactsY13

Decision Mathematics 1 (D1)

Algorithms and graph theory4 lessons · Option D1

Algorithms and orderY12
Bin packing and sortingY12
Graph theoryY12
Planarity algorithm and Hamiltonian cyclesY13

Algorithms on graphs3 lessons · Option D1

Minimum spanning treesY12
Dijkstra's algorithmY12
Floyd's algorithmY13

Algorithms on graphs II2 lessons · Option D1

Route inspection (Chinese postman)Y12
Travelling salesman problemY13

Critical path analysis6 lessons · Option D1

Activity networksY12
Precedence tablesY12
Critical path analysisY12
Float and Gantt chartsY12
Resource histograms and levellingY13
SchedulingY13

Linear programming5 lessons · Option D1

Formulating linear programming problemsY12
Slack, surplus and artificial variablesY13
Graphical solution of LP problemsY12
The Simplex algorithmY13
Two-stage Simplex and big-MY13

Further Pure Mathematics 2 (FP2)

Groups5 lessons · Option FP2

Group axiomsY13
Examples of groups and Cayley tablesY13
Order and subgroupsY13
Lagrange's theoremY13
IsomorphismY13

Further Calculus2 lessons · Option FP2

Reduction formulaeY13
Arc length and area of surface of revolutionY13

Further matrix algebra3 lessons · Option FP2

Eigenvalues and eigenvectorsY13
DiagonalisationY13
Cayley–Hamilton theoremY13

Further complex numbers2 lessons · Option FP2

Further loci and regionsY13
Transformations of the complex planeY13

Number theory7 lessons · Option FP2

Division algorithm and Euclidean algorithmY13
Bézout's identityY13
Modular arithmeticY13
Fermat's little theoremY13
Divisibility testsY13
Solving congruence equationsY13
CombinatoricsY13

Further sequences and series3 lessons · Option FP2

Recurrence relationsY13
Solving recurrence relationsY13
Proving closed forms by inductionY13

Further Statistics 2 (FS2)

Linear Regression2 lessons · Option FS2

Least squares linear regressionY13
ResidualsY13

Continuous probability distributions4 lessons · Option FS2

Continuous random variablesY13
Relationship between pdf and cdfY13
Summary measuresY13
Continuous uniform distributionY13

Correlation3 lessons · Option FS2

Product moment correlation coefficientY13
Spearman's rank correlationY13
Testing for zero correlationY13

Combinations of random variables1 lesson · Option FS2

Combinations of random variablesY13

Estimation, confidence intervals and tests using a normal distribution5 lessons · Option FS2

Estimators and biasY13
Confidence intervalsY13
Confidence limits for a normal mean (variance known)Y13
Test for the difference of two normal means (variances known)Y13
Large-sample methodsY13

Other Hypothesis Tests and confidence intervals2 lessons · Option FS2

Tests and intervals for a normal varianceY13
F-test for equality of variancesY13

Confidence intervals and tests using the t – distribution3 lessons · Option FS2

t-tests and intervals for a normal mean (variance unknown)Y13
Paired t-testY13
Two-sample t-test (equal unknown variances)Y13

Further Mechanics 2 (FM2)

Motion in a circle2 lessons · Option FM2

Horizontal circular motionY13
Motion in a vertical circleY13

Centres of mass of plane figures2 lessons · Option FM2

Moments and discrete centres of massY13
Centres of mass of plane figures and frameworksY13

Further centres of mass3 lessons · Option FM2

Centres of mass by integrationY13
Equilibrium of rigid bodiesY13
Toppling and slidingY13

Further dynamics2 lessons · Option FM2

Variable force in one dimensionY13
Simple harmonic motionY13

Further kinematics1 lesson · Option FM2

Further kinematicsY13

Decision Mathematics 2 (D2)

Transportation problems3 lessons · Option D2

Transportation: initial solutionY13
Transportation: improving the solutionY13
Transportation as a linear programY13

Allocation (assignment) problems2 lessons · Option D2

Allocation and the Hungarian algorithmY13
Allocation as a linear programY13

Flows in networks5 lessons · Option D2

CutsY13
Labelling procedureY13
Max-flow min-cut theoremY13
Supersources, supersinks and vertex capacitiesY13
Upper and lower capacitiesY13

Dynamic programming1 lesson · Option D2

Dynamic programmingY13

Game theory5 lessons · Option D2

Two-person zero-sum gamesY13
Play-safe strategies and stable solutionsY13
DominanceY13
Mixed strategies: graphical methodY13
Mixed strategies via linear programmingY13

Recurrence relations2 lessons · Option D2

Recurrence relations: modellingY13
Solving recurrence relationsY13

Decision analysis2 lessons · Option D2

Decision treesY13
Expected monetary value and utilityY13

Across the whole course

Mathematical argument, language and proof5 lessons

Construct and present mathematical argumentsY12–13
Mathematical language and syntaxY12–13
Set notationY12–13
FunctionsY12–13
Critique arguments and proofsY12–13

Mathematical problem solving5 lessons

Recognise the underlying structure of a problemY12–13
Extended arguments for unstructured problemsY12–13
Interpret solutions in contextY12–13
The problem-solving cycleY12–13
Diagrams in problem solvingY12–13

Mathematical modelling5 lessons

Build a modelY12–13
Use a modelY12–13
Interpret a model's outputsY12–13
Refine and evaluate a modelY12–13
Modelling assumptionsY12–13

Formulae you must recall (not in the formulae booklet)6 lessons

Pure formulae from A level MathematicsY12–13
Further pure formulaeY12–13
CalculusY12–13
VectorsY12–13
StatisticsY12–13
MechanicsY12–13

Assumed knowledge1 lesson

A level Mathematics contentY12–13

Pure mathematics

Proof1 lesson

Structure of mathematical proof: deduction, exhaustion, counter-example; proof by contradictionY12–13

Algebra and functions11 lessons

Laws of indices for all rational exponentsY12
Surds, including rationalising the denominatorY12
Quadratic functions: discriminant, completing the square, solving quadraticsY12
Simultaneous equations, one linear and one quadraticY12
Linear and quadratic inequalities; graphical interpretationY12
Polynomials: expanding, factorising, algebraic division, factor theorem; simplifying rational expressionsY12
Graphs of functions, including modulus graphs; asymptotes; proportionY12–13
Composite and inverse functionsY13
Transformations of y = f(x), including combinationsY12–13
Partial fractionsY13
Functions in modellingY13

Coordinate geometry in the (x, y) plane4 lessons

Equation of a straight line; parallel and perpendicular linesY12
Coordinate geometry of the circleY12
Parametric equations; conversion to Cartesian formY13
Parametric equations in modellingY13

Sequences and series6 lessons

Binomial expansion: positive integer n (Year 12) and rational n (Year 13)Y12–13
Sequences: nth term and recurrence relations; increasing, decreasing and periodicY13
Sigma notationY13
Arithmetic sequences and seriesY13
Geometric sequences and series; sum to infinityY13
Sequences and series in modellingY13

Trigonometry9 lessons

sin, cos and tan; sine and cosine rules; area of a triangle; radians, arc length and sector areaY12–13
Small angle approximationsY13
Graphs, symmetries and periodicity of sin, cos and tanY12
sec, cosec and cot; arcsin, arccos and arctanY13
Identities tan θ = sin θ / cos θ and sin²θ + cos²θ = 1; sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θY12–13
Double angle and compound angle formulae; R cos(θ ± α) formY13
Solve trigonometric equations in a given intervalY12–13
Proofs involving trigonometric functionsY13
Trigonometric functions in contextY13

Exponentials and logarithms7 lessons

Functions aˣ and eˣ and their graphsY12
Gradient of e^(kx); exponential modelsY12
Logarithms; ln x as the inverse of eˣY12
Laws of logarithmsY12
Solve equations of the form aˣ = bY12
Logarithmic graphs to estimate parameters in y = axⁿ and y = kbˣY12
Exponential growth and decay in modellingY12

Differentiation6 lessons

Derivative as gradient and rate of change; first principles; second derivatives; convex and concave curvesY12–13
Differentiate xⁿ (Year 12); e^(kx), a^(kx), sin kx, cos kx, tan kx and ln x (Year 13)Y12–13
Tangents, normals, stationary points; increasing and decreasing functionsY12
Product, quotient and chain rules; connected rates of change; inverse functionsY13
Implicit and parametric differentiationY13
Construct simple differential equationsY13

Integration8 lessons

Fundamental Theorem of CalculusY12
Integrate xⁿ (Year 12); e^(kx), 1/x, sin kx and cos kx (Year 13)Y12–13
Definite integrals; areas under and between curvesY12–13
Integration as the limit of a sumY13
Integration by substitution and by partsY13
Integration using partial fractionsY13
First order separable differential equationsY13
Interpret solutions of differential equations in contextY13

Numerical methods4 lessons

Locate roots by change of signY13
Iteration, cobweb and staircase diagrams; Newton–RaphsonY13
Trapezium ruleY13
Numerical methods in contextY13

Vectors5 lessons

Vectors in two dimensions (Year 12) and three dimensions (Year 13)Y12–13
Magnitude and direction; component formY12
Add vectors; multiply by scalarsY12
Position vectors; distance between two pointsY12–13
Vectors in pure mathematics and in contextY12–13

Mechanics

Quantities and units in mechanics1 lesson

Fundamental and derived quantities and SI unitsY12

Kinematics5 lessons

Language of kinematicsY12
Displacement–time and velocity–time graphsY12
Constant acceleration formulae; extension to 2D using vectorsY12–13
Calculus in kinematics; extension to 2D using vectorsY12–13
Motion under gravity in a vertical plane; projectilesY13

Forces and Newton's laws6 lessons

Force; Newton's first lawY12
Newton's second law; resolving forces (Year 13)Y12–13
Weight and motion in a straight line under gravityY12–13
Newton's third law; equilibrium; pulleys and connected particlesY12–13
Resultant forces; dynamics in a planeY13
Friction, F ≤ μRY13

Moments1 lesson

Moments in simple static contextsY13

Statistics

Statistical sampling1 lesson

Populations and samples; sampling techniques; critique samplingY12

Data presentation and interpretation4 lessons

Diagrams for single-variable data, including histogramsY12
Scatter diagrams and regression lines; correlationY12
Measures of central tendency and variation, including standard deviationY12
Outliers; cleaning dataY12

Probability3 lessons

Mutually exclusive and independent eventsY12
Conditional probabilityY13
Modelling with probabilityY13

Statistical distributions3 lessons

Discrete distributions, including the binomial distributionY12–13
The Normal distributionY13
Choose an appropriate distributionY13

Statistical hypothesis testing3 lessons

Language of hypothesis testing; correlation coefficient testsY12–13
Hypothesis test for a binomial proportionY12
Hypothesis test for the mean of a Normal distributionY13

The large data set1 lesson

Familiarity with the AQA large data setY12–13

Across the whole course

Mathematical argument, language and proof5 lessons

Construct and present mathematical argumentsY12–13
Mathematical language and syntaxY12–13
Set notationY12–13
FunctionsY12–13
Critique arguments and proofsY12–13

Mathematical problem solving7 lessons

Recognise the underlying structure of a problemY12–13
Extended arguments for unstructured problemsY12–13
Interpret solutions in contextY12–13
Numerical methods to a required accuracyY12–13
Accuracy and limitations of solutionsY12–13
The problem-solving cycleY12–13
Diagrams in problem solvingY12–13

Mathematical modelling5 lessons

Build a modelY12–13
Use a modelY12–13
Interpret a model's outputsY12–13
Refine and evaluate a modelY12–13
Modelling assumptionsY12–13

Formulae you must recall (not given in the exam)5 lessons

PureY12–13
CalculusY12–13
VectorsY12–13
StatisticsY12–13
MechanicsY12–13

Assumed knowledge1 lesson

GCSE MathematicsY12–13

Pure Mathematics

Proof1 lesson

Proof by deduction, exhaustion and counter-example (Year 12); proof by contradiction (Year 13)Y12–13

Algebra and functions11 lessons

Laws of indices for all rational exponentsY12
Surds and rationalising the denominatorY12
Quadratic functions: discriminant, completing the square, solvingY12
Simultaneous equations, one linear and one quadraticY12
Linear and quadratic inequalities; set notation; graphical interpretationY12
Polynomials: algebraic division, factor theorem; simplifying rational expressionsY12–13
Graphs of cubics, quartics and reciprocals (Year 12); modulus graphs (Year 13); proportionY12–13
Composite and inverse functions; domain and rangeY13
Transformations of y = f(x) (Year 12); combinations and modulus (Year 13)Y12–13
Partial fractionsY13
Functions in modellingY13

Coordinate geometry in the (x, y) plane4 lessons

Straight lines; parallel and perpendicular gradientsY12
CirclesY12
Parametric equationsY13
Parametric equations in modellingY13

Sequences and series6 lessons

Binomial expansion: positive integer n (Year 12); rational n (Year 13)Y12–13
Sequences: nth term, recurrence relations; increasing, decreasing, periodicY13
Sigma notationY13
Arithmetic sequences and seriesY13
Geometric sequences and series; sum to infinityY13
Sequences and series in modellingY13

Trigonometry9 lessons

sin, cos, tan; sine and cosine rules; area (Year 12); radians, arc length, sector area (Year 13)Y12–13
Small angle approximationsY13
Graphs, symmetries and periodicity of sin, cos and tanY12–13
sec, cosec and cot; inverse trigonometric functionsY13
tan θ = sin θ / cos θ and sin²θ + cos²θ = 1 (Year 12); sec²θ and cosec²θ identities (Year 13)Y12–13
Double angle and compound angle formulae; R formY13
Solve trigonometric equations in a given intervalY12–13
Proofs involving trigonometric identitiesY13
Trigonometric functions in contextY13

Exponentials and logarithms7 lessons

Functions aˣ and eˣ and their graphsY12
Gradient of e^(kx); exponential modelsY12
Logarithms; ln xY12
Laws of logarithmsY12
Solve aˣ = bY12
Logarithmic graphs to estimate parametersY12
Exponential growth and decay modelsY12

Differentiation6 lessons

Gradient, rate of change, first principles, second derivatives (Year 12); convexity and inflection (Year 13)Y12–13
Differentiate xⁿ (Year 12); eˣ, aˣ, trigonometric functions and ln x (Year 13)Y12–13
Tangents, normals, stationary points; increasing and decreasing functionsY12–13
Product, quotient and chain rules; connected rates of changeY13
Implicit and parametric differentiationY13
Construct simple differential equationsY13

Integration8 lessons

Fundamental Theorem of CalculusY12
Integrate xⁿ (Year 12); eˣ, 1/x and trigonometric functions (Year 13)Y12–13
Definite integrals and areas (Year 12); including parametric curves (Year 13)Y12–13
Integration as the limit of a sumY13
Integration by substitution and by partsY13
Integration using partial fractionsY13
Separable differential equationsY13
Interpret solutions of differential equationsY13

Numerical methods5 lessons

Locate roots by change of signY13
Iteration; cobweb and staircase diagramsY13
Newton–Raphson methodY13
Trapezium ruleY13
Numerical methods in contextY13

Vectors5 lessons

Vectors in 2D (Year 12) and 3D (Year 13)Y12–13
Magnitude and direction; unit vectorsY12–13
Add vectors; multiply by scalars; parallel vectorsY12–13
Position vectors; distance between pointsY12–13
Vectors in pure mathematics and in contextY12–13

Statistics

Statistical sampling1 lesson

Populations and samples; sampling methodsY12

Data presentation and interpretation4 lessons

Histograms, frequency polygons, box plots, cumulative frequencyY12
Scatter diagrams and regression lines (Year 12); change of variable and PMCC (Year 13)Y12–13
Measures of location and spread; standard deviationY12
Outliers; cleaning dataY12

Probability3 lessons

Mutually exclusive and independent eventsY12
Conditional probabilityY13
Modelling with probabilityY13

Statistical distributions3 lessons

Discrete distributions, including the binomialY12
The Normal distribution; Normal approximation to the binomialY13
Choose an appropriate distributionY13

Statistical hypothesis testing3 lessons

Language of hypothesis testing (Year 12); correlation coefficient tests (Year 13)Y12–13
Hypothesis test for a binomial proportionY12
Hypothesis test for the mean of a Normal distributionY13

Mechanics

Quantities and units in mechanics1 lesson

SI quantities and unitsY12

Kinematics5 lessons

Language of kinematicsY12
Displacement–time and velocity–time graphsY12
Constant acceleration formulae (Year 12); in 2D with vectors (Year 13)Y12–13
Calculus in kinematics (Year 12); in 2D with vectors (Year 13)Y12–13
ProjectilesY13

Forces and Newton's laws6 lessons

Force; Newton's first lawY12
Newton's second law (Year 12); resolving forces (Year 13)Y12–13
Weight and motion under gravityY12
Newton's third law; equilibrium; connected particlesY12–13
Resultant forces; dynamics in a planeY13
Friction, F ≤ μRY13

Moments1 lesson

Moments; equilibrium of rigid bodiesY13

Across the whole course

Mathematical argument, language and proof5 lessons

Construct and present mathematical argumentsY12–13
Mathematical language and syntaxY12–13
Set notationY12–13
FunctionsY12–13
Critique arguments and proofsY12–13

Mathematical problem solving7 lessons

Recognise the underlying structure of a problemY12–13
Extended arguments for unstructured problemsY12–13
Interpret solutions in contextY12–13
Numerical methods to a required accuracyY12–13
Accuracy and limitations of solutionsY12–13
The problem-solving cycleY12–13
Diagrams in problem solvingY12–13

Mathematical modelling5 lessons

Build a modelY12–13
Use a modelY12–13
Interpret a model's outputsY12–13
Refine and evaluate a modelY12–13
Modelling assumptionsY12–13

The large data set1 lesson

Familiarity with the Pearson large data setY12–13

Formulae you must recall (not in the formulae booklet)5 lessons

PureY12–13
CalculusY12–13
VectorsY12–13
StatisticsY12–13
MechanicsY12–13

Assumed knowledge1 lesson

GCSE Mathematics and the pure contentY12–13

Core content

Measurements and their errors3 lessons

Use of SI units and their prefixesY12
Limitation of physical measurementsY12
Estimation of physical quantitiesY12

Particles and radiation11 lessons

3.2.1 Particles
Constituents of the atomY12
Stable and unstable nucleiY12
Particles, antiparticles and photonsY12
Particle interactionsY12
Classification of particlesY12
Quarks and antiquarksY12
Applications of conservation lawsY12
3.2.2 Electromagnetic radiation and quantum phenomena
The photoelectric effectY12
Collisions of electrons with atomsY12
Energy levels and photon emissionY12
Wave-particle dualityY12

Waves6 lessons

3.3.1 Progressive and stationary waves
Progressive wavesY12
Longitudinal and transverse wavesY12
Principle of superposition of waves and formation of stationary wavesY12
3.3.2 Refraction, diffraction and interference
InterferenceY12
DiffractionY12
Refraction at a plane surfaceY12

Mechanics and materials10 lessons

3.4.1 Force, energy and momentum
Scalars and vectorsY12
MomentsY12
Motion along a straight lineY12
Projectile motionY12
Newton's laws of motionY12
MomentumY12
Work, energy and powerY12
Conservation of energyY12
3.4.2 Materials
Bulk properties of solidsY12
The Young modulusY12

Electricity6 lessons

3.5.1 Current electricity
Basics of electricityY12
Current–voltage characteristicsY12
ResistivityY12
CircuitsY12
Potential dividerY12
Electromotive force and internal resistanceY12

Further mechanics and thermal physics7 lessons

3.6.1 Periodic motion
Circular motionY13
Simple harmonic motion (SHM)Y13
Simple harmonic systemsY13
Forced vibrations and resonanceY13
3.6.2 Thermal physics
Thermal energy transferY13
Ideal gasesY13
Molecular kinetic theory modelY13

Fields and their consequences18 lessons

3.7.1 Fields
FieldsY13
3.7.2 Gravitational fields
Newton's lawY13
Gravitational field strengthY13
Gravitational potentialY13
Orbits of planets and satellitesY13
3.7.3 Electric fields
Coulomb's lawY13
Electric field strengthY13
Electric potentialY13
3.7.4 Capacitance
CapacitanceY13
Parallel plate capacitorY13
Energy stored by a capacitorY13
Capacitor charge and dischargeY13
3.7.5 Magnetic fields
Magnetic flux densityY13
Moving charges in a magnetic fieldY13
Magnetic flux and flux linkageY13
Electromagnetic inductionY13
Alternating currentsY13
The operation of a transformerY13

Nuclear physics8 lessons

3.8.1 Radioactivity
Rutherford scatteringY13
α, β and γ radiationY13
Radioactive decayY13
Nuclear instabilityY13
Nuclear radiusY13
Mass and energyY13
Induced fissionY13
Safety aspectsY13

Option A: Astrophysics

Astrophysics14 lessons · Option A

3.9.1 Telescopes
Astronomical telescope consisting of two converging lensesY13
Reflecting telescopesY13
Single dish radio telescopes, I-R, U-V and X-ray telescopesY13
Advantages of large diameter telescopesY13
3.9.2 Classification of stars
Classification by luminosityY13
Absolute magnitude, MY13
Classification by temperature, black-body radiationY13
Principles of the use of stellar spectral classesY13
The Hertzsprung-Russell (HR) diagramY13
Supernovae, neutron stars and black holesY13
3.9.3 Cosmology
Doppler effectY13
Hubble's lawY13
QuasarsY13
Detection of exoplanetsY13

Option B: Medical physics

Medical physics19 lessons · Option B

3.10.1 Physics of the eye
Physics of visionY13
Defects of vision and their correction using lensesY13
3.10.2 Physics of the ear
Ear as a sound detection systemY13
Sensitivity and frequency responseY13
Defects of hearingY13
3.10.3 Biological measurement
Simple ECG machines and the normal ECG waveformY13
3.10.4 Non-ionising imaging
Ultrasound imagingY13
Fibre optics and endoscopyY13
Magnetic resonance (MR) scannerY13
3.10.5 X-ray imaging
The physics of diagnostic X-raysY13
Image detection and enhancementY13
Absorption of X-raysY13
CT scannerY13
3.10.6 Radionuclide imaging and therapy
Imaging techniquesY13
Half-lifeY13
Gamma cameraY13
Use of high-energy X-raysY13
Use of radioactive implantsY13
Imaging comparisonsY13

Option C: Engineering physics

Engineering physics12 lessons · Option C

3.11.1 Rotational dynamics
Concept of moment of inertiaY13
Rotational kinetic energyY13
Rotational motionY13
Torque and angular accelerationY13
Angular momentumY13
Work and powerY13
3.11.2 Thermodynamics and engines
First law of thermodynamicsY13
Non-flow processesY13
The p–V diagramY13
Engine cyclesY13
Second Law and enginesY13
Reversed heat enginesY13

Option D: Turning points in physics

Turning points in physics15 lessons · Option D

3.12.1 The discovery of the electron
Cathode raysY13
Thermionic emission of electronsY13
Specific charge of the electronY13
Principle of Millikan's determination of the electronic charge, eY13
3.12.2 Wave-particle duality
Newton's corpuscular theory of lightY13
Significance of Young's double slits experimentY13
Electromagnetic wavesY13
The discovery of photoelectricityY13
Wave–particle dualityY13
Electron microscopesY13
3.12.3 Special relativity
The Michelson-Morley experimentY13
Einstein's theory of special relativityY13
Time dilationY13
Length contractionY13
Mass and energyY13

Option E: Electronics

Electronics18 lessons · Option E

3.13.1 Discrete semiconductor devices
MOSFET (metal-oxide semiconducting field-effect transistor)Y13
Zener diodeY13
PhotodiodeY13
Hall effect sensorY13
3.13.2 Analogue and digital signals
Difference between analogue and digital signalsY13
3.13.3 Analogue signal processing
LC resonance filtersY13
The ideal operational amplifierY13
3.13.4 Operational amplifier in:
inverting amplifier configurationY13
non-inverting amplifier configurationY13
summing amplifier configurationY13
Real operational amplifiersY13
3.13.5 Digital signal processing
Combinational logicY13
Sequential logicY13
AstablesY13
3.13.6 Data communication systems
Principles of communication systemsY13
Transmission mediaY13
Time-division multiplexingY13
Amplitude (AM) and frequency modulation (FM) techniquesY13

Across the whole course

Mathematical skills35 lessons

Units and prefixesY12–13
Decimal and standard formY12–13
Ratios, fractions and percentagesY12–13
Estimating effects of changing parametersY12–13
Calculator: powers, exponentials and logsY12–13
Calculator: sin, cos and tanY12–13
Significant figuresY12–13
Means of repeated readingsY12–13
Simple probabilityY12–13
Order-of-magnitude calculationsY12–13
Combining uncertaintiesY12–13
Symbols =, <, ≪, ≫, >, ∝, ≈, ΔY12–13
Changing the subjectY12–13
Substituting values with unitsY12–13
Solving equationsY12–13
LogarithmsY12–13
Graphical, numerical and algebraic formsY12–13
Plotting dataY12–13
y = mx + cY12–13
Gradient and interceptY12–13
Rate of change from a straight lineY12–13
Tangents to curvesY12–13
Instantaneous and average ratesY12–13
Area under a graphY12–13
Calculus ideas without calculusY12–13
Logarithmic plotsY12–13
Testing exponential and power laws with log plotsY12–13
Sketching k/x, kx², kx, sin x, cos x, e^(±x), sin²x, cos²xY12–13
Angles in 2D and 3D structuresY12–13
2D and 3D formsY12–13
Areas and volumesY12–13
Pythagoras and angle sum of a triangleY12–13
sin, cos and tan in physical problemsY12–13
Small-angle approximationsY12–13
Degrees and radiansY12–13

Practical skills10 lessons

Solve problems set in practical contextsY12–13
Apply knowledge to practical contextsY12–13
Comment on experimental design and evaluate methodsY12–13
Present data appropriatelyY12–13
Evaluate results and conclusions using uncertaintiesY12–13
Identify variables, including control variablesY12–13
Plot and interpret graphsY12–13
Process and analyse data with the maths skillsY12–13
Margins of error, accuracy and precisionY12–13
Use a wide range of instruments and techniquesY12–13

Apparatus and techniques12 lessons

Analogue instrumentsY12–13
Digital instrumentsY12–13
Improving accuracyY12–13
Stopwatches and light gatesY12–13
Calipers and micrometersY12–13
Building circuits from diagramsY12–13
Designing and checking circuitsY12–13
Signal generators and oscilloscopesY12–13
Generating and measuring wavesY12–13
Lasers and light sourcesY12–13
ICT and data loggersY12–13
Ionising radiation and detectorsY12–13

Topics 1 to 13

Working as a Physicist8 lessons

Base and derived quantities; SI unitsY12
Practical skills and techniquesY12
Estimating physical quantitiesY12
Limitations of physical measurementY12
Communicating information with appropriate terminologyY12
Applications and implications of scienceY12
The scientific community and validating knowledgeY12
How society uses science in decision makingY12

Mechanics22 lessons

Equations for uniformly accelerated motionY12
Displacement–time, velocity–time and acceleration–time graphsY12
Quantities from gradients and areas of graphsY12
Scalar and vector quantitiesY12
Resolving a vector into perpendicular componentsY12
Resultant of coplanar vectorsY12
Independence of vertical and horizontal motion of a projectileY12
Free-body force diagramsY12
Newton's first and second laws; terminal velocityY12
Gravitational field strength and weight, W = mgY12
CP1: Determine the acceleration of a freely-falling objectY12
Newton's third lawY12
Momentum, p = mvY12
Conservation of linear momentum in one dimensionY12
Moment of a forceY12
Centre of gravity; principle of momentsY12
Work doneY12
Kinetic energyY12
Gravitational potential energyY12
Conservation of energyY12
PowerY12
EfficiencyY12

Electric Circuits18 lessons

Electric current as rate of flow of chargeY12
Potential difference as work done per unit chargeY12
Resistance; Ohm's lawY12
Current and conservation of chargeY12
Potential difference and conservation of energyY12
Resistors in series and parallelY12
Electrical powerY12
I–V characteristicsY12
Resistivity, R = ρl/AY12
CP2: Determine the electrical resistivity of a materialY12
I = nqvA and the range of resistivitiesY12
Potential along a uniform current-carrying wireY12
Potential dividersY12
Potential dividers with thermistors and LDRsY12
e.m.f. and internal resistanceY12
CP3: Determine the e.m.f. and internal resistance of an electrical cellY12
Resistance and temperatureY12
Resistance and illuminationY12

Materials10 lessons

DensityY12
UpthrustY12
Stokes' law; viscosityY12
CP4: Use a falling-ball method to determine the viscosity of a liquidY12
Hooke's law; stiffnessY12
Stress, strain and the Young modulusY12
Force–extension and force–compression graphsY12
Stress–strain graphs; breaking stressY12
CP5: Determine the Young modulus of a materialY12
Elastic strain energyY12

Waves and Particle Nature of Light38 lessons

Amplitude, frequency, period, speed and wavelengthY12
The wave equation, v = fλY12
Longitudinal wavesY12
Transverse wavesY12
Graphs of wavesY12
CP6: Determine the speed of sound in air using a 2-beam oscilloscopeY12
Superposition, coherence, path difference and phaseY12
Phase difference and path differenceY12
Standing waves; nodes and antinodesY12
Speed of a transverse wave on a stringY12
CP7: Effect of length, tension and mass per unit length on the frequency of a vibrating stringY12
Intensity, I = P/AY12
Refraction; Snell's law; refractive indexY12
Critical angleY12
Total internal reflectionY12
Measuring refractive indexY12
Focal length of converging and diverging lensesY12
Ray diagramsY12
Power of a lens, P = 1/fY12
Thin lenses in combinationY12
Real and virtual imagesY12
The thin lens equationY12
MagnificationY12
Plane polarisationY12
Diffraction; Huygens' constructionY12
Diffraction grating, nλ = d sin θY12
CP8: Determine the wavelength of light using a diffraction gratingY12
Electron diffractionY12
de Broglie wavelengthY12
Transmission and reflection at interfacesY12
Pulse–echo techniqueY12
Wave and photon models of electromagnetic radiationY12
Photon energy, E = hfY12
Photoelectric emissionY12
Threshold frequency, work function and the photoelectric equationY12
The electronvoltY12
Photoelectric effect as evidence for the particle nature of lightY12
Atomic line spectra and energy levelsY12

Further Mechanics11 lessons

Impulse, FΔt = ΔpY13
CP9: Force exerted on an object and its change of momentumY13
Conservation of linear momentum in two dimensionsY13
CP10: Use ICT to analyse collisions between small spheresY13
Elastic and inelastic collisionsY13
Kinetic energy, Ek = p²/2mY13
Radians and degreesY13
Angular velocity, v = ωrY13
Centripetal accelerationY13
Centripetal forceY13
Equations for centripetal forceY13

Electric and Magnetic Fields22 lessons

Electric fieldsY13
Electric field strength, E = F/QY13
Coulomb's lawY13
Field due to a point chargeY13
Electric field and electric potentialY13
Uniform field between parallel plates, E = V/dY13
Potential in a radial fieldY13
Field lines and equipotentialsY13
Capacitance, C = Q/VY13
Energy stored by a capacitorY13
Charging and discharging; time constant RCY13
CP11: Display and analyse the p.d. across a charging and discharging capacitorY13
Exponential discharge equationsY13
Magnetic flux density, flux and flux linkageY13
Force on a moving chargeY13
Force on a current-carrying conductor, F = BIl sin θY13
Induced e.m.f. from relative motionY13
Induced e.m.f. from a changing currentY13
Lenz's lawY13
Faraday's lawY13
Alternating current: frequency, period, peak and r.m.s.Y13
Peak and r.m.s. valuesY13

Nuclear and Particle Physics14 lessons

Nucleon number and proton numberY13
Alpha particle scatteringY13
Thermionic emission; accelerating electronsY13
Linear accelerators, cyclotrons and detectorsY13
Charged particles in a magnetic field, r = p/BQY13
Conservation laws in particle interactionsY13
High energies to probe nucleon structureY13
Pair creation and annihilationY13
MeV, GeV and MeV/c²Y13
Relativistic increase in particle lifetimeY13
The standard quark–lepton modelY13
AntiparticlesY13
Conservation of charge, baryon number and lepton numberY13
Particle equationsY13

Thermodynamics12 lessons

Specific heat capacity and specific latent heatY13
CP12: Calibrate a thermistor in a potential divider as a thermostatY13
CP13: Determine the specific latent heat of a phase changeY13
Internal energyY13
Absolute zeroY13
Kinetic theory, pV = ⅓Nm⟨c²⟩Y13
Ideal gas equation, pV = NkTY13
CP14: Pressure and volume of a gas at fixed temperatureY13
Mean kinetic energy, ½m⟨c²⟩ = 3/2 kTY13
Black body radiationY13
Stefan–Boltzmann lawY13
Wien's lawY13

Space8 lessons

Intensity and luminosityY13
Trigonometric parallaxY13
Standard candlesY13
Hertzsprung–Russell diagramY13
Life cycles of starsY13
Doppler effectY13
Redshift; Hubble's law, v = H₀dY13
Age and fate of the universe; dark matterY13

Nuclear Radiation10 lessons

Binding energy and mass deficitY13
Atomic mass unitY13
Fission and fusionY13
Conditions for fusionY13
Background radiationY13
Alpha, beta and gamma radiationY13
Nuclear equationsY13
CP15: Investigate the absorption of gamma radiation by leadY13
Random nature of radioactive decayY13
Half-life and decay equationsY13

Gravitational Fields7 lessons

Gravitational fieldsY13
Gravitational field strength, g = F/mY13
Newton's law of universal gravitationY13
Field due to a point massY13
Gravitational potentialY13
Comparing electric and gravitational fieldsY13
OrbitsY13

Oscillations11 lessons

Condition for simple harmonic motionY13
Equations of simple harmonic motionY13
Mass–spring system and simple pendulumY13
Velocity from a displacement–time graphY13
Acceleration from a velocity–time graphY13
ResonanceY13
CP16: Determine an unknown mass using resonant frequenciesY13
Energy in damped and undamped oscillatorsY13
Free and forced oscillationsY13
Forced oscillations near the natural frequencyY13
Damping and plastic deformationY13

Across the whole course

Mathematical skills35 lessons

Units and prefixesY12–13
Decimal and standard formY12–13
Ratios, fractions and percentagesY12–13
Estimating effects of changing parametersY12–13
Calculator: powers, exponentials and logsY12–13
Calculator: sin, cos and tanY12–13
Significant figuresY12–13
Means of repeated readingsY12–13
Simple probabilityY12–13
Order-of-magnitude calculationsY12–13
Combining uncertaintiesY12–13
Symbols =, <, ≪, ≫, >, ∝, ≈, ΔY12–13
Changing the subjectY12–13
Substituting values with unitsY12–13
Solving equationsY12–13
LogarithmsY12–13
Graphical, numerical and algebraic formsY12–13
Plotting dataY12–13
y = mx + cY12–13
Gradient and interceptY12–13
Rate of change from a straight lineY12–13
Tangents to curvesY12–13
Instantaneous and average ratesY12–13
Area under a graphY12–13
Calculus ideas without calculusY12–13
Logarithmic plotsY12–13
Testing exponential and power laws with log plotsY12–13
Sketching k/x, kx², kx, sin x, cos x, e^(±x), sin²x, cos²xY12–13
Angles in 2D and 3D structuresY12–13
2D and 3D formsY12–13
Areas and volumesY12–13
Pythagoras and angle sum of a triangleY12–13
sin, cos and tan in physical problemsY12–13
Small-angle approximationsY12–13
Degrees and radiansY12–13