AQA Level 2 Further Maths (8365)
AQA Level 2 Further Maths (8365) is a certificate for students aiming for a high GCSE Maths grade, assessed by two papers, one non-calculator and one calculator. Our AQA Level 2 Certificate in Further Maths course follows the 8365 specification and covers number, algebra, coordinate geometry, calculus, matrix transformations, geometry and trigonometry. Level 2 Further Maths is assessed by a non-calculator and a calculator paper, and is ideal preparation for A-Level Maths. Lessons are live and one-to-one with a verified subject tutor, who works through exam-style questions with you, marks your answers against the AQA mark scheme and shows you where marks are won and lost. Suitable for Year 10 and Year 11 students and resit candidates.
Reviewed by M. Wazid, Master's in Mathematics, Jamia Millia IslamiaLast updated
$13 – $27
per hour
Free demo class · pay only if you continue
What you will learn
Learning outcomes
- Develop advanced algebraic manipulation skills
- Solve complex equations and inequalities
- Work with functions and their graphs
- Understand polynomial expressions and factorisation
- Apply the factor theorem
- Work with sequences and advanced algebraic patterns
- Understand matrices and matrix transformations
- Apply coordinate geometry techniques
- Use advanced trigonometric relationships
- Solve trigonometric problems
- Understand differentiation and its applications
- Find gradients and stationary points
- Apply calculus to mathematical problems
- Work with advanced geometry
- Develop mathematical reasoning and proof
- Solve multi-step mathematical problems
- Apply mathematics to unfamiliar situations
- Prepare for AQA Further Maths examinations
Prerequisites
- Strong GCSE Higher Mathematics knowledge
- Confident algebra skills
- Understanding of linear and quadratic equations
- Knowledge of graphs and functions
- Understanding of geometry and trigonometry
- Strong numerical skills
- Ability to solve multi-step mathematical problems
Tags
Course structure
Syllabus(6 modules)
- Simplifying Surds
- Rationalising Denominators
- Counting Principles
What is AQA Level 2 Further Maths (8365)?
In short: this course gives one-to-one online tutoring for the AQA Level 2 Certificate in Further Mathematics (8365), for strong GCSE students preparing for A-level. A verified maths tutor teaches algebra, coordinate geometry, calculus, matrices and trigonometry beyond GCSE, using AQA past papers.
AQA Level 2 Certificate in Further Mathematics (8365) is an extra qualification for strong GCSE maths students, usually taken alongside GCSE Maths Higher. It introduces A-Level topics such as calculus and matrices, is graded 9 to 4, and is assessed by two papers.
This course covers the full 8365 specification one to one with a verified maths tutor, and is excellent preparation for A-Level Maths and Further Maths.
Official specification: AQA Level 2 Certificate in Further Mathematics 8365.
What's on the AQA Further Maths papers?
There are two papers, each 1 hour 45 minutes and worth 80 marks (50% each). Both papers can test any topic.
| Paper | Details |
|---|---|
| Paper 1 | Non-calculator, 80 marks |
| Paper 2 | Calculator, 80 marks |
Content areas covered
| Area | Key topics |
|---|---|
| Number | Surds, rationalising denominators |
| Algebra | Factor theorem, completing the square, inequalities, simultaneous equations |
| Coordinate geometry | Equations of lines and circles, tangents |
| Calculus | Differentiation, gradients, tangents and normals, stationary points |
| Matrix transformations | Multiplication, the identity matrix, transformations |
| Geometry and trigonometry | Sine and cosine rules, 3D trigonometry, identities and equations |
What does a worked Further Maths question look like?
Here are two short examples of content beyond GCSE: a gradient from calculus and a matrix product.
| Question | Working | Answer |
|---|---|---|
| Find the gradient of y = 3x² − 4x at x = 2 | dy/dx = 6x − 4; at x = 2: 12 − 4 | 8 |
| Multiply the matrix (1 2; 3 4) by the column vector (2, 1) | Row 1: 1 × 2 + 2 × 1 = 4; row 2: 3 × 2 + 4 × 1 = 10 | (4, 10) |
Where do students lose marks in Level 2 Further Maths?
Strong students still lose marks by skipping steps in multi-step problems, making algebra slips under time pressure, misusing calculus notation, mixing up matrix order and not giving exact answers when asked.
| Mark-loser | What to do instead |
|---|---|
| Skipped steps | Show each step for method marks |
| Algebra slips | Check each line and use brackets |
| Calculus notation errors | Write dy/dx correctly and state the gradient clearly |
| Matrix order mixed up | Remember AB is usually not BA |
| Decimals instead of exact answers | Leave surds and fractions exact when asked |
Why take Level 2 Further Maths?
Level 2 Further Maths stretches the most able GCSE students and bridges the gap to A-Level. Students who take it usually find the start of A-Level Maths much easier, especially algebra, coordinate geometry and calculus. Next step: our A-Level Mathematics course.
Exam technique and past papers
Tutors use AQA past papers and mark schemes, teach you to set out algebraic proofs and calculus clearly, and practise the multi-step problems that carry the most marks.
How the lessons work
Lessons are live and one to one on video with a shared whiteboard. Your tutor covers new A-Level-style content carefully, then practises exam questions with you. See also our Mathematics subject page and AQA GCSE Maths Higher.
Further maths tutor online: who this Level 2 course is for, prerequisites and study plan
A further maths tutor online gives you live 1-to-1 lessons on the AQA Level 2 8365 content, including calculus and matrices, and is especially useful if your school does not teach it in class.
This course suits strong GCSE Higher students, and students preparing to move on to A-Level Maths.
Prerequisites: confident GCSE Higher algebra, graphs, geometry and trigonometry.
Course length: 32 lessons across 6 topic areas.
| Stage | Topics | What you can do afterwards |
|---|---|---|
| 1 | Number; algebra and functions | Work with surds, functions and algebraic proof |
| 2 | Coordinate geometry | Use circles, gradients and equations of lines |
| 3 | Calculus | Differentiate and find stationary points |
| 4 | Matrix transformations; geometry | Multiply matrices and apply transformations |
Where it leads: continue to A-Level Maths with our A-Level Mathematics course.
AQA Level 2 Further Maths (8365): frequently asked questions
What is the AQA Further Maths specification code?
The AQA Level 2 Certificate in Further Mathematics code is 8365.
Is Level 2 Further Maths a GCSE?
No. It is a Level 2 certificate taken alongside GCSE Maths, at a similar level but with extra, harder content.
What grades are available in Level 2 Further Maths?
Grades 9 to 4.
How many papers are there?
Two papers, each 1 hour 45 minutes and worth 80 marks: one non-calculator and one calculator.
What calculus is in Level 2 Further Maths?
Differentiation of polynomials, gradients, tangents and normals, and stationary points.
Is Level 2 Further Maths hard?
It's designed for strong mathematicians and includes A-Level-style topics, but it's very manageable with good teaching.
Does Further Maths help with A-Level?
Yes. It introduces calculus, coordinate geometry and harder algebra, which makes the start of A-Level Maths easier.
Can I take Further Maths without GCSE Maths Higher?
It's usually taken by students on GCSE Higher tier. Check with your school.
How much does a Further Maths tutor cost?
The price depends on the tutor and session length. You see the hourly rate before booking, with no subscription.
Do you use AQA past papers?
Yes. Tutors use AQA past papers and mark schemes.
What are the AQA Level 2 Further Maths grade boundaries?
AQA publishes grade boundaries for Level 2 Further Maths (8365) after each June series, and they vary from year to year with paper difficulty. They show the raw marks needed for each grade. Your tutor marks full past papers and compares your scores with recent boundaries to predict your grade and target weak topics.
Is a formulae sheet provided?
AQA has provided a formulae sheet for recent exams; check the arrangements for your exam year.
When do students usually sit Level 2 Further Maths?
Most students sit it in Year 11, in the same June exam series as GCSE Maths Higher. Schools usually offer it to students aiming for grades 7 to 9 who plan to take A-Level Maths. If your school does not run it, you can enter privately through an exam centre, and a tutor can cover the whole course.
How do I find a gradient using calculus?
Differentiate to find dy/dx, then substitute the x-value. For y = 3x² − 4x at x = 2, the gradient is 8.
How do I multiply matrices?
Multiply each row of the first matrix by each column of the second and add the products.
Who should take Level 2 Further Maths?
Students who are secure at the top of GCSE Maths Higher and want extra challenge.
Can a tutor help if my school doesn't teach it?
Yes. Tutors can cover the full content one to one; ask your school about entering you for the exam.
Do you offer lessons in my time zone?
Yes. Lessons are online, so you can book times that suit your time zone.
How often should I have lessons?
Weekly lessons suit most students; add extra sessions before mocks and final exams.
Can I book a single lesson first?
Yes. You can book one session to see if the tutor suits you, with no subscription.
Can I get a further maths tutor online?
Yes. You can learn with a 1-to-1 further maths tutor online through live video lessons. Your tutor teaches the AQA 8365 topics step by step, including those your school may not cover, such as calculus and matrices, and practises past papers so you can apply the methods under exam conditions.
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