Year 12 maths
Every topic for the year is below, arranged by the term it is taught. Choose a term to show only that term: each topic has a lesson video, worked questions and practice at three levels.
Autumn term
- Algebra, indices and surdsLaws of indices, surds and rationalising denominators, quadratic equations and the discriminant, simultaneous equations, inequalities, polynomial division and the factor theorem.100 questionsLesson video
- Graphs and transformationsSketching polynomial, reciprocal and modulus graphs, finding intersections, graph transformations and proportion.100 questionsLesson video
- Coordinate geometry: lines and circlesEquations of straight lines, parallel and perpendicular gradients, the equation of a circle, tangents and chords and circle geometry.100 questionsLesson video
- Sequences, series and the binomial expansionArithmetic and geometric sequences and series, sigma notation, recurrence relations, and the binomial expansion.100 questionsLesson video
- VectorsVectors in two and three dimensions, magnitude and direction, position vectors, the vector equation of a line and problems in geometry.100 questionsLesson video
Spring term
- Trigonometry for A levelRadians, arc length and sector area, the graphs of sine, cosine and tangent, trigonometric identities and solving trigonometric equations.100 questionsLesson video
- Exponentials and logarithmsExponential functions and growth and decay, the laws of logarithms, solving equations using logarithms and modelling with logarithmic graphs.100 questionsLesson video
- DifferentiationDifferentiating from first principles, the derivative of powers of x, gradients, tangents and normals, increasing and decreasing functions, stationary points and optimisation.100 questionsLesson video
- Statistics: data, probability and hypothesis testingSampling, large data sets, measures of location and spread, probability and the binomial distribution, and one-tailed and two-tailed hypothesis tests.100 questionsLesson video
Summer term
- IntegrationIntegrating powers of x, finding functions from their derivatives, definite integrals and the area under a curve.100 questionsLesson video
- Mechanics: motion and forcesThe constant acceleration equations, vertical motion under gravity, Newton laws, connected particles and pulleys, and resolving forces.100 questionsLesson video
Terms are approximate: schools order these units differently.