A Level Further Mathematics is the most challenging and prestigious mathematics qualification available to pre-university students. This advanced course extends far beyond A Level Mathematics, covering sophisticated topics including complex numbers, matrices, differential equations, and advanced mechanics. Further Mathematics is essential for students targeting the most competitive university courses in mathematics, physics, engineering, and economics at institutions like Cambridge, Oxford, and Imperial College.
Only the most mathematically gifted students attempt Further Mathematics, and successful completion demonstrates exceptional mathematical ability to universities and employers. The course develops advanced problem-solving skills, mathematical maturity, and analytical thinking that provide a significant advantage in competitive university admissions and challenging degree programs.
Further Mathematics is extremely demanding and requires concurrent study with A Level Mathematics. Students typically need A*/A grades in GCSE Mathematics and strong performance in AS Mathematics before attempting this course. This qualification is designed for future mathematicians, physicists, and engineers.
Further Mathematics sets you apart from other applicants to top universities. Cambridge, Oxford, and Imperial College strongly prefer or require Further Mathematics for mathematics, physics, and engineering courses. This qualification demonstrates exceptional mathematical ability and commitment.
Core Pure Mathematics 1: Complex numbers, matrices, proof, mathematical induction (75 marks, 1.5 hours)
Core Pure Mathematics 2: Complex numbers, matrices, further calculus, polar coordinates (75 marks, 1.5 hours)
Option Paper 1: Choice from Further Pure, Further Statistics, Further Mechanics, or Decision Mathematics (75 marks, 1.5 hours)
Option Paper 2: Second choice from available options (75 marks, 1.5 hours)
Further Mathematics develops sophisticated mathematical reasoning, proof techniques, and abstract thinking essential for university-level mathematics. We focus on building mathematical maturity and the ability to tackle novel, challenging problems independently.
Access to all sessions for reviewing complex mathematical concepts and advanced techniques
24/7 access to advanced mathematical guidance for the most challenging problems
Development of sophisticated mathematical thinking and proof techniques
Regular testing with the most challenging Further Mathematics questions
Mastery of advanced exam strategies for maximum performance under pressure
Preparation for the most competitive university mathematics programs worldwide
Ready to start your A-Level Further Maths journey?
Book a Free Trial LessonComplex number operations, Argand diagrams, De Moivre's theorem, and geometric applications.
Matrix operations, transformations, eigenvalues, and systems of linear equations.
Rational functions, modulus functions, and advanced algebraic manipulation.
Advanced integration, differential equations, and parametric differentiation.
Vector products, equations of planes, and geometric applications.
Polar coordinate system, curves in polar form, and area calculations.
Hyperbolic trigonometry, inverse hyperbolic functions, and their applications.
Mathematical induction, proof by contradiction, and rigorous mathematical argument.
Further Pure Mathematics, Further Mechanics, Further Statistics, or Decision Mathematics.
Second choice from available option modules to match university requirements.
2.5 hours/week • 175 total hours over 70 weeks
Payment Options: Full payment or 3 installments of $900
3 hours/week • 168 total hours over 56 weeks
Payment Options: Full payment or 3 installments of $1000
Both tracks include: All sessions, recorded materials, advanced problem sets, regular assessments, expert support, and elite university preparation guidance
"Further Mathematics was by far the most challenging course I've ever taken, but also the most rewarding. The abstract concepts like complex numbers and matrices seemed impossible at first, but my tutor's patient explanations and structured approach made everything clear. The rigorous problem-solving practice prepared me not just for the exams, but for the type of thinking required at Cambridge. I achieved an A* in Further Maths and received an offer to study mathematics at Cambridge. The course gave me a huge advantage in my university applications and prepared me perfectly for undergraduate mathematics."
This A-Level Further Maths tutor online programme is for mathematically exceptional students who are taking Further Mathematics alongside A-Level Maths. Further Mathematics is typically taken by students targeting top universities — particularly Oxbridge, Imperial, or Russell Group programmes in Mathematics, Physics, Engineering, or Economics. These sessions provide personalised support through the most demanding topics, from proof by induction and complex numbers to differential equations and further mechanics.
Further Maths builds directly on A-Level Maths — if you're not yet taking Further Maths, start with our standard A-Level Maths tutoring. Students studying Physics alongside Maths may also benefit from our A-Level Physics tutoring.
A Level Further Mathematics represents the pinnacle of pre-university mathematical education. This course is designed exclusively for the most mathematically gifted students who aspire to study at the world's leading universities. Cambridge, Oxford, Imperial College, and other elite institutions strongly prefer applicants with Further Mathematics for their most competitive programs.
Further Mathematics is more than just an A Level - it's a badge of mathematical excellence that sets you apart from thousands of other applicants. Our program ensures you not only master this demanding qualification but develop the advanced mathematical thinking that will distinguish you throughout your academic and professional career.
Yes, all lessons are aligned with the Cambridge International A-Level Further Mathematics syllabus. Every topic — including complex numbers, matrices, advanced calculus, and further mechanics — is covered systematically with past paper practice throughout.
Lessons take place via video call using an interactive digital whiteboard for working through advanced proofs and problems in real time. All sessions are recorded for review. WhatsApp support is available between lessons.
Yes — in fact, most Further Maths students benefit from tutoring in both subjects. Sessions can be structured to cover both A-Level Maths and Further Maths content, or focused exclusively on the Further Maths extension topics depending on where you need the most support.