Mathematics revision notes

One chapter for each section of the YMA01 syllabus, with worked examples. Read a chapter, then practise it with real past-paper questions.

1. 1QuadraticsCompleting the square, the discriminant, quadratic equations and inequalities, simultaneous equations with one linear and one quadratic, and equations that are quadratic in a function of x.7 min readDownload PDF
2. 2FunctionsDomain and range, composite functions, one-one functions and their inverses, and transformations of the graph of y = f(x).6 min readDownload PDF
3. 3Coordinate geometryStraight lines in all their forms, parallel and perpendicular lines, the equation of a circle, tangents, and where lines and curves meet.5 min readDownload PDF
4. 4Circular measureRadians, converting to and from degrees, arc length, sector area, and how to find the area of a segment.4 min readDownload PDF
5. 5TrigonometryGraphs of sine, cosine and tangent, exact values, inverse notation and principal values, the two basic identities, and solving trigonometric equations in an interval.6 min readDownload PDF
6. 6SeriesThe binomial expansion for a positive integer power, arithmetic and geometric progressions, their sums, and the sum to infinity of a convergent geometric progression.5 min readDownload PDF
7. 7DifferentiationThe gradient as a limit, the power rule and chain rule, tangents and normals, increasing and decreasing functions, rates of change, and stationary points.5 min readDownload PDF
8. 8IntegrationIntegration as reverse differentiation, finding the constant, definite integrals, areas under and between curves, and volumes of revolution.4 min readDownload PDF
9. 9AlgebraThe modulus function, polynomial division, the factor and remainder theorems. partial fractions and the binomial expansion for any rational power.8 min readDownload PDF
10. 10Logarithms and exponentialsLogarithms and indices, the laws of logarithms, e to the x and ln x, equations with the unknown in a power, and turning a relationship into a straight line.5 min readDownload PDF
11. 11Further trigonometrySecant, cosecant and cotangent, the identities that use them, the addition and double angle formulae, and writing a sin x + b cos x as a single wave.5 min readDownload PDF
12. 12Further differentiationDerivatives of exponentials, logarithms and trigonometric functions, the product and quotient rules, and curves defined parametrically or implicitly. It also adds the inverse tangent.4 min readDownload PDF
13. 13Further integrationStandard integrals, using trigonometric identities, and the trapezium rule. It also adds partial fractions, integrals of f'(x)/f(x), integration by parts and substitution.5 min readDownload PDF
14. 14Numerical solution of equationsLocating a root with a graph or a sign change, and using an iterative formula to find a root to a required accuracy.4 min readDownload PDF
15. 15VectorsVector notation and operations, magnitude and unit vectors, the equation of a line, whether lines meet, and the scalar product.5 min readDownload PDF
16. 16Differential equationsWriting a rate of change as a differential equation, separating the variables, using an initial condition, and interpreting the solution in context.4 min readDownload PDF
17. 17Forces and equilibriumIdentifying forces, components and resultants, equilibrium of a particle, the normal contact force and friction, limiting equilibrium, and Newton's third law.6 min readDownload PDF
18. 18KinematicsDistance, speed, displacement, velocity and acceleration, motion graphs, the constant acceleration formulae, and using calculus when the acceleration varies.6 min readDownload PDF
19. 19MomentumLinear momentum as a vector, conservation of momentum in a direct impact, particles that coalesce or rebound, and collisions in a chain.4 min readDownload PDF
20. 20Newton's laws of motionNewton's second law, mass and weight, motion on slopes and in lifts, and connected particles joined by strings and rods.6 min readDownload PDF
21. 21Representation of dataStem-and-leaf diagrams, box-and-whisker plots, histograms, cumulative frequency graphs, measures of centre and spread, and the mean and standard deviation from totals, including coded totals.6 min readDownload PDF
22. 22ProbabilityProbability by counting, the addition and multiplication rules, exclusive and independent events, tree diagrams, and conditional probability.4 min readDownload PDF
23. 23Discrete random variablesProbability distribution tables, expectation and variance, the binomial distribution, and the geometric distribution.5 min readDownload PDF
24. 24The normal distributionModelling continuous data with a normal distribution, using tables, finding probabilities, working back to the mean or standard deviation, and approximating the binomial with a continuity correction.4 min readDownload PDF
25. 25ProofWhat a proof must do, proof by exhaustion, disproof by counter-example, proof by contradiction, and proof by mathematical induction.7 min readDownload PDF
26. 26Parametric equationsCurves given by x and y in terms of a parameter, converting between parametric and Cartesian forms, and finding points on a parametric curve.4 min readDownload PDF
27. 27Models, vectors and moments in mechanicsMathematical modelling and the standard modelling words in mechanics, vectors for displacement, velocity, acceleration and force in a plane, and the moment of a force.7 min readDownload PDF
28. 28Models in probability and statisticsWhat a statistical model is, how to describe a model's assumptions, and how to comment on whether a model is suitable.4 min readDownload PDF
29. 29Correlation and regressionScatter diagrams, explanatory and response variables, the least squares regression line, interpreting its gradient and intercept, and the product moment correlation coefficient.5 min readDownload PDF