# A Level Further Mathematics (9231) tutoring online

> Our A Level Further Mathematics tutors teach Cambridge International 9231 alongside the UK specifications AQA 7367, Pearson Edexcel 9FM0 and OCR A H245. Live 1:1 or small-group online classes cover further pure topics such as complex numbers, matrices and polar coordinates, plus the mechanics and statistics options, with proof-heavy past-paper practice.

Source: https://www.gradeupinternational.com/a-level/further-mathematics
Last updated: 2026-10-01
Publisher: GradeUp International (https://www.gradeupinternational.com/)

Taught by: our most qualified teachers for the subject.

Further Mathematics is usually taken by students aiming for mathematics, physics, engineering, computer science or economics at highly selective universities, some of which list it as preferred or required. It assumes the whole of single A Level Mathematics, so it suits students who find standard calculus comfortable and want harder problems. Many schools teach both qualifications in parallel, which means Further Maths classes regularly use techniques that have only just been introduced in the main Maths course.

Cambridge 9231 has four papers. Further Pure Mathematics 1 with either Further Mechanics or Further Probability & Statistics makes the AS Level, while the A Level requires all four, including Further Pure Mathematics 2. In the UK, AQA sets three two-hour papers, and Edexcel and OCR each use two compulsory core pure papers plus two optional papers of ninety minutes. All three UK specifications are linear, with every paper sat in one May/June series.

The topics are not just harder versions of single Maths. Students meet hyperbolic functions, proof by induction, polar curves, eigenvalues and probability generating functions for the first time, and questions often combine two of these in an unfamiliar setting. The usual sticking points are rigorous proof layout, complex-number loci and algebra-heavy matrix work. Tutoring focuses on building a library of standard methods first, then on reading longer questions so the right method is spotted quickly.

## How is A Level Further Mathematics examined?

### Cambridge International AS & A Level Further Mathematics (9231), Cambridge International Education

| Paper | Duration | Marks | Weighting |
| --- | --- | --- | --- |
| Paper 1: Further Pure Mathematics 1 | 2 hours | 75 | 60% of AS Level / 30% of A Level |
| Paper 2: Further Pure Mathematics 2 | 2 hours | 75 | 30% of A Level |
| Paper 3: Further Mechanics | 1 hour 30 minutes | 50 | 40% of AS Level / 20% of A Level |
| Paper 4: Further Probability & Statistics | 1 hour 30 minutes | 50 | 40% of AS Level / 20% of A Level |

2026–2027 syllabus. AS Level: Paper 1 plus Paper 3 or Paper 4. A Level: all four papers. Assumes knowledge of Cambridge 9709 content. Series: May/June and October/November.

Official syllabus: https://www.cambridgeinternational.org/programmes-and-qualifications/cambridge-international-as-and-a-level-mathematics-further-9231/

### AQA A-level Further Mathematics (7367), AQA

| Paper | Duration | Marks | Weighting |
| --- | --- | --- | --- |
| Paper 1 | 2 hours | 100 | 33⅓% of A Level |
| Paper 2 | 2 hours | 100 | 33⅓% of A Level |
| Paper 3 | 2 hours | 100 | 33⅓% of A Level |

Linear: all papers sat in the same series.

Official syllabus: https://www.aqa.org.uk/subjects/mathematics/a-level/mathematics-7367/specification

### Pearson Edexcel A Level Further Mathematics (9FM0), Pearson Edexcel

| Paper | Duration | Marks | Weighting |
| --- | --- | --- | --- |
| Paper 1: Core Pure Mathematics 1 | 1 hour 30 minutes | 75 | 25% of A Level |
| Paper 2: Core Pure Mathematics 2 | 1 hour 30 minutes | 75 | 25% of A Level |
| Paper 3: Further Mathematics option | 1 hour 30 minutes | 75 | 25% of A Level |
| Paper 4: Further Mathematics option | 1 hour 30 minutes | 75 | 25% of A Level |

Optional papers are chosen from further pure, further statistics, further mechanics and decision mathematics.

Official syllabus: https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html

### OCR A Level Further Mathematics A (H245), OCR

| Paper | Duration | Marks | Weighting |
| --- | --- | --- | --- |
| Pure Core 1 (Y540) | 1 hour 30 minutes | 75 | 25% of A Level |
| Pure Core 2 (Y541) | 1 hour 30 minutes | 75 | 25% of A Level |
| Two optional papers | 1 hour 30 minutes each | 75 | 25% of A Level each |

Official syllabus: https://www.ocr.org.uk/qualifications/as-and-a-level/further-mathematics-a-h235-h245-from-2017/

## What topics are in A Level Further Mathematics?

- Roots of polynomial equations: Forgetting that the sum of squares of roots needs (Σα)² − 2Σαβ, not just squaring each root.
- Rational functions and graphs: Sketching without labelling asymptotes and axis intercepts, which carry separate marks.
- Summation of series and proof by induction: Omitting the formal concluding statement that links the base case and inductive step.
- Matrices and transformations: Multiplying transformation matrices in the wrong order for a combined transformation.
- Polar coordinates: Using the wrong limits when finding an area enclosed by a polar curve.
- Hyperbolic functions and further calculus: Mixing up the sign in Osborn's rule when converting trigonometric identities to hyperbolic ones.
- Complex numbers and de Moivre's theorem: Giving an argument outside the principal range or in degrees.
- Further differential equations: Finding the complementary function but choosing the wrong form of particular integral.
- Further mechanics: projectiles, circular motion and rigid bodies: Taking moments about a point that leaves two unknown forces in the equation.
- Further probability and statistics: t-tests, chi-squared and non-parametric tests: Using the wrong degrees of freedom after combining small expected frequencies.

## How do you get top marks?

- Learn the standard proof layouts (induction, contradiction, method of differences) so the structure is automatic and your attention stays on the algebra.
- Write the result you are using, such as de Moivre's theorem or an eigenvector equation, before applying it; method marks often depend on it.
- Sketch polar curves and complex loci before calculating, because a quick diagram catches wrong limits and regions.
- Use the formula booklet actively in practice so you know exactly which results are given and which must be memorised.
- Budget roughly a mark per minute and move on from a stuck part, since later parts of multi-step questions are often still accessible.

## Fees

1:1: PKR 3,500 / AED 140 / GBP 28 per 60-minute class. Small group: PKR 12,500 per month. [All currencies](https://www.gradeupinternational.com/pricing).

## Frequently asked questions

### Is A Level Further Maths worth taking?

A Level Further Maths is worth taking if you plan to study mathematics, physics, engineering or computer science, because it covers material those degrees use from the first term. Some competitive courses list it as preferred or required. It also strengthens your single Maths grade through extra practice. If your target course does not mention it, weigh the extra workload against the benefit of a different fourth subject.

### How hard is A Level Further Maths compared with A Level Maths?

Further Maths is noticeably harder than A Level Maths because it introduces new abstract topics and expects longer, more rigorous chains of reasoning. Complex numbers, matrices, hyperbolic functions and proof by induction are all new territory. Students who are comfortable with single Maths and enjoy problem-solving usually cope well, especially if they practise regularly rather than relying on understanding alone.

### Can I take Further Maths without A Level Maths?

No, Further Maths cannot sensibly be taken without A Level Maths, because every specification assumes the full single Maths content. The Cambridge 9231 syllabus states that it builds on 9709, and the UK boards make the same assumption. Most students study both at the same time, often finishing single Maths content first so that Further Maths topics have the necessary foundations.

### What options can I choose in Further Maths?

In Cambridge 9231 the options are Further Mechanics and Further Probability & Statistics, and A Level candidates take both alongside two further pure papers. Edexcel and OCR let students choose two optional papers from areas such as further pure, statistics, mechanics and discrete or decision mathematics. AQA sets a third paper with optional application content. Your school usually chooses the options it can teach.

### Do universities require Further Maths for engineering?

Most engineering degrees require A Level Maths but treat Further Maths as helpful rather than essential, although a few selective courses do prefer it. Requirements differ between universities and change over time, so check each course's published entry requirements. If Further Maths is not offered at your school, online tuition can cover it, provided you can register as a candidate at an exam centre.