Revision posters

Revision posters

One page per topic: the diagrams, the results and the handful of points worth remembering. Made to be printed, put on a wall, or saved to a phone. Click a poster to open it full size, or download it to keep; the title goes to the lesson it came from.

Proof

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  The structure of proof: deduction and exhaustionDownload
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  Disproof and proof by contradictionDownload

Algebra and functions

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  Indices and surdsDownload
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  Quadratic functionsDownload
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  Simultaneous equations and inequalitiesDownload
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  Polynomials and the factor theoremDownload
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  Graphs, proportion and transformationsDownload
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  Functions, inverses and the modulusDownload
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  Partial fractionsDownload
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  Functions in modellingDownload

Coordinate geometry

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  Straight linesDownload
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  CirclesDownload
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  Parametric equationsDownload

Sequences and series

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  The binomial expansionDownload
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  The general binomial expansionDownload
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  Sequences and sigma notationDownload
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  Arithmetic seriesDownload
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  Geometric seriesDownload

Trigonometry

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  Triangles and the sine and cosine rulesDownload
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  Trigonometric graphs and equationsDownload
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  Radians, arcs and small anglesDownload
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  Reciprocal and inverse trigonometric functionsDownload
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  Compound angles and the harmonic formDownload
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  Trigonometric modellingDownload

Exponentials and logarithms

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  Exponential functions and eDownload
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  Logarithms and their lawsDownload
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  Log graphs and exponential modelsDownload

Differentiation

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  The derivative from first principlesDownload
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  Differentiating powers of xDownload
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  Tangents, turning points and curve behaviourDownload
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  Differentiating trig, exponentials and logsDownload
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  The product, quotient and chain rulesDownload
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  Implicit and parametric differentiationDownload
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  Rates of change and building differential equationsDownload

Integration

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  Integration as antidifferentiationDownload
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  Definite integrals and areasDownload
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  Integrating standard functionsDownload
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  Integration by substitution and by partsDownload
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  Integrating rational functionsDownload
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  Areas, parametric curves and the limit of a sumDownload
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  Solving differential equationsDownload

Numerical methods

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  Locating roots and iterationDownload
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  The Newton-Raphson methodDownload
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  The trapezium ruleDownload

Vectors

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  Vectors in two dimensionsDownload
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  Vectors in three dimensionsDownload

Statistics

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  Sampling and the large data setDownload
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  Measures of location and spreadDownload
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  Representing and interpreting dataDownload
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  Correlation and regressionDownload
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  Probability and Venn diagramsDownload
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  Conditional probabilityDownload
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  The binomial distributionDownload
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  The normal distributionDownload
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  Hypothesis testing with the binomialDownload
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  Hypothesis testing: correlation and the normalDownload

Mechanics

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  Modelling, quantities and unitsDownload
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  Kinematics with constant accelerationDownload
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  Kinematics with variable accelerationDownload
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  Forces and Newton's lawsDownload
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  Connected particles and pulleysDownload
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  ProjectilesDownload
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  Friction and inclined planesDownload
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  Statics of a particleDownload
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  MomentsDownload

Further proof

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  Proof by induction: sums and seriesDownload
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  Induction: divisibility and matricesDownload

Complex numbers

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  Complex arithmetic and the Argand diagramDownload
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  Modulus, argument and lociDownload
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  De Moivre's theorem and trigonometric identitiesDownload
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  Roots of unity and complex rootsDownload

Matrices

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  Matrix algebra and transformationsDownload
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  Determinants and inversesDownload
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  Systems of equations and invarianceDownload

Further algebra and series

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  Roots of polynomialsDownload
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  Summing series and the method of differencesDownload
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  Maclaurin seriesDownload

Further vectors

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  Lines and planes in three dimensionsDownload
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  Intersections, angles and distancesDownload

Further calculus

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  Volumes of revolutionDownload
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  Mean values and improper integralsDownload
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  Calculus with inverse trigonometric functionsDownload

Hyperbolic functions

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  Hyperbolic functions and identitiesDownload
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  Calculus with hyperbolic functionsDownload

Polar coordinates

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  Polar curvesDownload
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  Areas with polar coordinatesDownload

Differential equations

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  First order equations and integrating factorsDownload
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  Second order equationsDownload
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  Modelling with differential equationsDownload

Further Pure 1

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  The t-formulaeDownload
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  Taylor seriesDownload
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  Limits and L'Hôpital's ruleDownload
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  Leibniz's theorem and the Weierstrass substitutionDownload
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  Series solutions of differential equationsDownload
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  Conic sectionsDownload
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  Tangents, normals and loci of conicsDownload
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  The vector product and the scalar triple productDownload
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  Numerical methods for differential equationsDownload
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  Inequalities and inequationsDownload

Further Statistics 1

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  Discrete random variables and expectationDownload
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  The Poisson distributionDownload
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  Geometric and negative binomial distributionsDownload
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  Hypothesis tests for Poisson and geometric modelsDownload
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  The Central Limit TheoremDownload
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  Goodness-of-fit testsDownload
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  Contingency tablesDownload
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  Probability generating functionsDownload
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  Type I and Type II errors, test size and powerDownload

Further Pure 2

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  Groups and their axiomsDownload
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  Subgroups, Lagrange's theorem and isomorphismDownload
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  Reduction formulaeDownload
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  Arc length and surface areaDownload
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  Functions of two variablesDownload
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  Eigenvalues and eigenvectorsDownload
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  Diagonalisation and the Cayley-Hamilton theoremDownload
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  Further loci and regions in the Argand diagramDownload
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  Transformations of the complex planeDownload
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  The Euclidean algorithm and Bézout's identityDownload
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  Modular arithmetic and Fermat's little theoremDownload
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  CombinatoricsDownload
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  Recurrence relationsDownload

Further Statistics 2

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  Least squares regression and residualsDownload
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  Continuous random variables: density and distribution functionsDownload
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  Mean, variance and skewness of continuous variablesDownload
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  The continuous uniform distributionDownload
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  Correlation coefficients: product moment and SpearmanDownload
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  Testing a correlation coefficientDownload
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  Combinations of normal random variablesDownload
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  Estimators, standard error and confidence intervalsDownload
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  Comparing two normal meansDownload
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  Testing variances: chi-squared and the F-distributionDownload
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  Confidence intervals and tests with the t-distributionDownload
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  Non-parametric testsDownload

Further Mechanics 1

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  Momentum and impulseDownload
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  Impulse and momentum as vectorsDownload
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  Work, energy and powerDownload
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  Hooke's law and elastic stringsDownload
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  Elastic potential energyDownload
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  Direct impact and Newton's law of restitutionDownload
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  Successive impacts and impacts with a wallDownload
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  Oblique impact and impact with a smooth surfaceDownload

Further Mechanics 2

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  Angular speed and horizontal circular motionDownload
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  Motion in a vertical circleDownload
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  Centre of mass of a discrete distributionDownload
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  Centres of mass of plane figures and frameworksDownload
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  Centres of mass by integrationDownload
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  Equilibrium, suspension, toppling and slidingDownload
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  Newton's laws with a variable forceDownload
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  Simple harmonic motionDownload
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  Oscillations on strings and springsDownload
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  Further kinematics: acceleration as a function of x, t or vDownload

Decision Mathematics 1

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  Algorithms, sorting and bin packingDownload
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  Graphs: order, Eulerian paths and planarityDownload
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  Minimum spanning trees: Prim and KruskalDownload
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  Shortest paths: Dijkstra and FloydDownload
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  Route inspectionDownload
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  Further packing and the knapsack problemDownload
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  The travelling salesman problemDownload
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  Critical path analysisDownload
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  Float, Gantt charts and schedulingDownload
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  Linear programming: formulation and graphical solutionDownload
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  The Simplex algorithmDownload

Decision Mathematics 2

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  Transportation problems and the north-west corner methodDownload
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  The stepping-stone methodDownload
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  Allocation and the Hungarian algorithmDownload
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  Flows in networks: cuts and capacityDownload
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  Maximum flow and the labelling procedureDownload
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  Dynamic programming and Bellman's principleDownload
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  Game theory: play safe and stable solutionsDownload
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  Mixed strategies in game theoryDownload
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  Decision trees, expected monetary value and utilityDownload

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