Advanced Mathematics · University & competition
An extra-deep three-term British Further Mathematics programme with 15 units, 75 complete lessons across Further Pure, Statistics, Mechanics and Discrete Mathematics.
Every topic, lesson by lesson.
Term 1 · Unit 1
Extend the number system and interpret arithmetic geometrically.
Term 1 · Unit 2
Use matrix algebra to solve systems and represent linear transformations.
Term 1 · Unit 3
Connect coefficients, roots and transformations of polynomial equations.
Term 1 · Unit 4
Prove identities, divisibility and matrix statements recursively.
Term 1 · Unit 5
Manipulate finite sums and derive closed forms for standard powers.
Term 2 · Unit 6
Represent curves by radius and angle and analyse polar geometry.
Term 2 · Unit 7
Develop hyperbolic identities, inverses and calculus.
Term 2 · Unit 8
Solve and interpret first- and second-order differential models.
Term 2 · Unit 9
Use advanced substitutions, reduction and multistep calculus reasoning.
Term 2 · Unit 10
Analyse lines, planes, products and distances in space.
Term 3 · Unit 11
Model multivariable and continuous uncertainty with deeper inference.
Term 3 · Unit 12
Extend force and motion models to momentum, energy and circular motion.
Term 3 · Unit 13
Optimise networks and algorithms using exact finite structures.
Term 3 · Unit 14
Analyse iterative methods, stability and computational efficiency.
Term 3 · Unit 15
Connect pure, statistical, mechanical and discrete ideas in rigorous problems.
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.
This course satisfies the following education systems.
