Year 13 · Ages 17–18

British Year 13 Mathematics

An extra-deep three-term British Year 13 programme with 15 units, 75 complete lessons, advanced calculus, statistics, mechanics and full A-level synthesis.

Complete A Level Mathematics programme

15 topics

75 lessons

3 terms

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What you will be able to do

Manipulate advanced functions, series and trigonometric identities
Apply parametric, implicit and numerical calculus methods
Use vectors and normal models with rigorous reasoning
Model moments, projectiles and variable acceleration
Sustain complete A-level arguments across connected topics

Course contents

Every topic, lesson by lesson.

Term 1 · Unit 1

Advanced algebra and functions

Control rational, composite and modulus structures with full domain awareness.

Term 1 · Unit 2

Partial fractions

Decompose rational functions for algebraic and calculus applications.

Term 1 · Unit 3

Sequences and series

Analyse finite and infinite series, recurrence and general binomial forms.

Term 1 · Unit 4

Advanced trigonometry

Transform identities and solve equations using compound-angle structure.

Term 1 · Unit 5

Parametric equations

Represent curves parametrically and connect parameter change to geometry.

Term 2 · Unit 6

Advanced differentiation

Differentiate composite, implicit and parametric relationships.

Term 2 · Unit 7

Advanced integration

Select substitution, parts and structural methods for difficult integrals.

Term 2 · Unit 8

Numerical methods

Locate and approximate roots while justifying convergence and error.

Term 2 · Unit 9

Vectors in two and three dimensions

Use vector equations to analyse lines, intersections and geometry.

Term 2 · Unit 10

The normal distribution

Standardise continuous data and use normal models critically.

Term 3 · Unit 11

Regression and hypothesis testing

Analyse association and test statistical parameters in context.

Term 3 · Unit 12

Moments and equilibrium

Model rigid bodies using turning effects and force balance.

Term 3 · Unit 13

Projectiles

Resolve two-dimensional motion into independent components.

Term 3 · Unit 14

Variable acceleration

Use calculus to connect displacement, velocity and acceleration.

Term 3 · Unit 15

A Level synthesis

Solve unfamiliar problems spanning Pure Mathematics, Statistics and Mechanics.

Concepts to practise again

Built from your saved practice attempts in this course, weakest question types first.

Complete a practice set in any lesson to see which question types to practise again.

Curriculum alignment

This course satisfies the following education systems.

British Curriculum

A Levels

Cambridge

Edexcel

International Baccalaureate