Maths › Revision posters

A-level Maths revision posters

One page per topic, with the key diagrams, results and points to remember. Print them for your wall or save them to your phone. Select a poster to open it full size.

Proof

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

Algebra and functions

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

Coordinate geometry

• 
  Straight linesDownload
• 
  CirclesDownload
• 
  Parametric equationsDownload

Sequences and series

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

Trigonometry

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

Exponentials and logarithms

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

Differentiation

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

Integration

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

Numerical methods

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

Vectors

• 
  Vectors in two dimensionsDownload
• 
  Vectors in three dimensionsDownload

Statistics

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

Mechanics

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

Further proof

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

Complex numbers

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

Matrices

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

Further algebra and series

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

Further vectors

• 
  Lines and planes in three dimensionsDownload
• 
  Intersections, angles and distancesDownload

Further calculus

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

Hyperbolic functions

• 
  Hyperbolic functions and identitiesDownload
• 
  Calculus with hyperbolic functionsDownload

Polar coordinates

• 
  Polar curvesDownload
• 
  Areas with polar coordinatesDownload

Differential equations

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

Further Pure 1

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

Further Statistics 1

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

Further Pure 2

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

Further Statistics 2

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

Further Mechanics 1

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

Further Mechanics 2

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

Decision Mathematics 1

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

Decision Mathematics 2

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

Posters are © Ink Learning Ltd, all rights reserved: print them, pin them and share them, and please link here rather than re-publishing copies. The diagrams inside them are published separately and on their own terms, which are set out in using our diagrams.