Year 13 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
- Proof, partial fractions and functionsProof by contradiction, partial fractions, the modulus function, composite and inverse functions, and transformations of graphs including modulus graphs.100 questionsLesson video
- Binomial expansion and seriesThe binomial expansion for rational powers and its validity, arithmetic and geometric series, sigma notation, and sequences defined recursively.100 questionsLesson video
- Further trigonometryRadians, arc length and sector area, small angle approximations, secant, cosecant and cotangent, inverse trigonometric functions, addition formulae, double angle and R sin(x plus alpha) forms.100 questionsLesson video
Spring term
- Parametric equations and vectorsParametric equations and converting to Cartesian form, modelling with parametric equations, and vectors in two and three dimensions including magnitude, direction, position vectors and unit vectors.100 questionsLesson video
- Further differentiationThe chain, product and quotient rules, differentiating exponential, logarithmic and trigonometric functions, implicit and parametric differentiation, and rates of change.100 questionsLesson video
- Further integrationIntegration by substitution, by parts and using partial fractions, integrating trigonometric and exponential functions, areas, and the trapezium rule.100 questionsLesson video
Summer term
- Differential equations and numerical methodsForming and solving first-order differential equations by separating variables, location of roots, iteration, the Newton-Raphson method and when it fails.100 questionsLesson video
- Statistical distributions and hypothesis testsThe normal distribution and its use as an approximation, hypothesis tests on the binomial and normal mean, tests for correlation, and conditional probability with Venn and tree diagrams.100 questionsLesson video
- Projectiles, moments and variable accelerationProjectile motion, variable acceleration with calculus, moments and equilibrium of rigid bodies, friction, and connected particles.100 questionsLesson video
Terms are approximate: schools order these units differently.