AQA A-Level Further Mathematics
Explore your course, one topic at a time.
Course overview
The AQA A-Level Further Mathematics specification covers 16 topics with 176 learning objectives (7367). Use the topic browser below to explore subtopics, exam tips, common mistakes, and key terminology for each area of the course.
- 16 topics
- 176 learning objectives
- 33
- topics
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Your exams
- Paper 1Thursday, 20 May 2027, PM
- Paper 2Tuesday, 25 May 2027, PM
- Paper 3: DiscreteThursday, 10 June 2027, PM
- Paper 3: MechanicsThursday, 10 June 2027, PM
- Paper 3: StatisticsThursday, 10 June 2027, PM
Always confirm dates and times with your exam centre.
Explore your topics
16 topics
Overarching themes3 topics
- OT1: Mathematical argument, language and proof5 specification points covering Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction;…5 objectives
- OT2: Mathematical problem solving5 specification points covering Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to…5 objectives
- OT3: Mathematical modelling5 specification points covering Translate a situation in context into a mathematical model, making simplifying assumptions., Use a mathematical model with…5 objectives
Compulsory content10 topics
- A: Proof1 objective
- B: Complex numbers8 specification points covering Solve any quadratic equation with real coefficients; solve cubic or quartic equations with real coefficients (given…8 objectives
- C: Matrices11 specification points covering Add, subtract and multiply conformable matrices; multiply a matrix by a scalar., Understand and use zero and identity…11 objectives
- D: Further algebra and functions13 specification points covering Understand and use the relationship between roots and coefficients of polynomial equations up to quartic equations., Form a…13 objectives
- E: Further calculus6 specification points covering Evaluate improper integrals where either the integrand is undefined at a value in the range of integration or the range of…6 objectives
- F: Further vectors6 specification points covering Understand and use the vector and Cartesian forms of an equation of a straight line in 3D., Understand and use the vector…6 objectives
- G: Polar coordinates3 specification points covering Understand and use polar coordinates and be able to convert between polar and Cartesian coordinates., Sketch curves with r…3 objectives
- H: Hyperbolic functions5 specification points covering Understand the definitions of hyperbolic functions sinh x , cosh x and tanh x , including their domains and ranges, and be…5 objectives
- I: Differential equations8 specification points covering Find both general and particular solutions of differential equations., Use differential equations in modelling in kinematics…8 objectives
- J: Numerical methods2 specification points covering Mid-ordinate rule and Simpson’s rule for integration., Euler’s step by step method for solving first order differential…2 objectives
Paper 3 Optional applications3 topics
Mechanics
MA: Dimensional analysis2 specification points covering Finding dimensions of quantities; checking for dimensional consistency., Prediction of formulae; finding powers in potential…2 objectives- MB: Momentum and collisions3 specification points covering Conservation of momentum for linear motion and cases where velocities are given as one or two dimensional vectors (problems…3 objectives
- MC: Work, energy and power5 specification points covering Work done by a force acting in the direction of motion or directly opposing the motion.5 objectives
- MD: Circular motion6 specification points covering Motion of a particle moving in a circle with constant speed (knowledge of radians assumed)., Understand the definition of…6 objectives
- ME: Centres of mass and moments6 specification points covering Centre of mass for a system of particles., Centre of mass for a composite body., Centre of mass of a lamina by integration.6 objectives
Statistics
SA: Discrete random variables (DRVs) and expectation5 specification points covering Understand DRVs with distributions given in the form of a table or function., Evaluate probabilities for a DRV., Evaluate…5 objectives- SB: Poisson distribution5 specification points covering Understand conditions for a Poisson distribution to model a situation.5 objectives
- SC: Type I and Type II errors2 specification points covering Understand Type I and Type II errors and define in context.2 objectives
- SD: Continuous random variables (CRVs)5 specification points covering Understand and use a probability density function, f x , for a continuous distribution and understand the differences…5 objectives
- SE: Chi squared tests for association3 specification points covering Construction of n × m contingency tables., Identification of sources of association in the context of a question., Knowledge…3 objectives
- SF: Exponential distribution4 specification points covering Know the conditions for an exponential distribution to be used as a model.4 objectives
- SG: Inference – one sample t - distribution1 objective
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About this course
About AQA A-Level Further Mathematics
AQA A-Level Further Mathematics is designed for students with a passion for mathematics who want to deepen their understanding beyond the standard A-Level Maths curriculum. It introduces advanced pure topics such as complex numbers, further calculus, and matrices, while also offering a choice of applied modules. This qualification is ideal for those aiming for degrees in mathematics, physics, engineering, or computer science, where strong analytical skills are essential.
The course is structured to develop logical reasoning, problem-solving, and abstract thinking. You will study pure mathematics in greater depth, covering areas like polar coordinates, hyperbolic functions, and differential equations. The applied component allows you to specialise in either Mechanics and Statistics or Discrete and Statistics, depending on your interests and career aspirations. Mechanics is perfect for future engineers and physicists, while Discrete suits those interested in computer science and algorithm design.
AQA’s specification is linear, meaning all exams are taken at the end of the two-year course. The content builds smoothly from A-Level Mathematics, ensuring a coherent learning journey. With a focus on clear, well-structured questions and supportive resources, AQA aims to make advanced mathematics both challenging and rewarding. The qualification is widely respected by universities and employers, opening doors to competitive STEM courses.
Assessment Structure
Assessment is entirely through written examinations, with three papers taken at the end of the course. Paper 1 and Paper 2 both cover pure mathematics and each lasts 2 hours, contributing 100 marks and 33.3% of the A-Level. Paper 3 is a 2-hour applied paper also worth 100 marks and 33.3%; students take either Option A (Mechanics and Statistics) or Option B (Discrete and Statistics). All papers are equally weighted, giving a total of 300 marks for the qualification.
Why Choose AQA?
- AQA offers a Discrete Mathematics option within Further Maths, which is relatively unique among exam boards and highly valued for university courses in computer science, data science, and operational research.
- The specification is known for its clarity and logical progression from A-Level Mathematics, with questions that are well-structured and accessible, reducing unnecessary stress and helping students showcase their true ability.
- AQA provides extensive support materials, including detailed teaching guidance, past papers, and examiner reports, making it easier for both students and teachers to track progress and target areas for improvement.
Frequently Asked Questions
What is the difference between A-Level Mathematics and A-Level Further Mathematics?
Can I study AQA Further Mathematics without having taken GCSE Further Maths?
Which applied option should I choose: Mechanics and Statistics or Discrete and Statistics?
How difficult is AQA A-Level Further Mathematics compared to other exam boards?
What university courses require or prefer A-Level Further Mathematics?
Assessment and exam guidance
What Gets Top Grades
Knowledge & Understanding
Demonstrates comprehensive and accurate knowledge
- Uses correct subject-specific terminology
- Shows detailed understanding of concepts
- Makes accurate connections between topics
- Demonstrates depth beyond surface-level knowledge
Application
Applies knowledge effectively to new contexts
- Selects relevant knowledge for the question
- Adapts understanding to unfamiliar scenarios
- Uses examples appropriately
- Shows awareness of context
Analysis & Evaluation
Develops sophisticated analytical arguments
- Constructs logical chains of reasoning
- Considers multiple perspectives
- Weighs evidence to reach justified conclusions
- Acknowledges limitations and nuances
Key Command Words
Give a single fact or term
Name, select, or recognise
Set out main features briefly
Give an account of what something is like or what happens
Give reasons with developed cause→effect chains
State similarities AND differences (both required)
Examine in detail showing cause→effect→consequence chains
Weigh up BOTH sides, reach JUSTIFIED conclusion
Make judgments about importance with justification
Show formula→substitution→calculation→answer with units
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