---
title: "Edexcel A Level Further Maths 9FM0 Help: Option Routes"
description: "Edexcel A level Further Maths 9FM0 help: the two Core Pure papers, all ten option pairs, how extra options are graded, the calculator rules, and live online classes."
canonical: https://learn.modernagecoders.com/edexcel-a-level-further-maths-9fm0-help
source: src/pages/edexcel-a-level-further-maths-9fm0-help.html
---
> Edexcel A level Further Maths 9FM0 help: the two Core Pure papers, all ten option pairs, how extra options are graded, the calculator rules, and live online classes.

What 9FM0 is

Pearson Edexcel A level Further Mathematics (9FM0) is a linear A level of four 90-minute papers worth 75 marks each: Core Pure Mathematics 1 and 2, which every student sits, plus two optional papers chosen from Further Pure, Further Statistics, Further Mechanics and Decision Mathematics, in ten permitted pairs. Grades A* to E come from the 300-mark total. Modern Age Coders teaches 9FM0 live online in its A Level Further Maths course; students join a 15 to 20 strong batch or learn 1-on-1, after an opening lesson at no cost.

Start here

## Courses a 9FM0 student tends to take

The Further Maths course carries Core Pure and every option. The A level Maths course runs alongside it; statistics adds depth for the FS routes.

[![A Level Further Maths course thumbnail](/images/a-level-further-maths.webp)  EF / 01 A Level Further Maths Core Pure 1 and 2 plus whichever pair of options the student is entered for. Open the syllabus →](/courses/a-level-further-maths-course)[![A-Level Maths course thumbnail](/images/a-level-maths.webp)  EF / 02 A Level Maths The 9MA0 content that Further Maths builds on. Open the syllabus →](/courses/a-level-maths-course-pure-mechanics-statistics)[![Statistics & Probability course thumbnail](/images/statistics-probability-maths.webp)  EF / 03 Statistics and Probability Background for Further Statistics 1 and 2. Open the syllabus →](/courses/statistics-probability-maths-course)

Four papers

## What are the four Edexcel Further Maths papers?

Four, all 1 hour 30 minutes and 75 marks. Papers 1 and 2 are compulsory Core Pure; Papers 3 and 4 are the options.

The specification states that 9FM0 "consists of four externally-examined papers. Students must take Paper 1 and Paper 2, the two mandatory Core Pure papers, and two optional papers." It also says "Students must complete all assessments in May/June in any single year", so all four papers are sat in the same summer. "Calculators can be used in the assessment" on every paper, and the booklet Mathematical Formulae and Statistical Tables is provided.

| Paper | Title | Time | Marks | Weight |
| --- | --- | --- | --- | --- |
| 9FM0/01 | Core Pure Mathematics 1 | 1 hour 30 minutes | 75 | 25% |
| 9FM0/02 | Core Pure Mathematics 2 | 1 hour 30 minutes | 75 | 25% |
| 9FM0/3A to 3D | Option 1: Further Pure 1, Further Statistics 1, Further Mechanics 1 or Decision Mathematics 1 | 1 hour 30 minutes | 75 | 25% |
| 9FM0/4A to 4D | Option 2: Further Pure 2, Further Statistics 2, Further Mechanics 2 or Decision Mathematics 2 | 1 hour 30 minutes | 75 | 25% |

Source: Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0) specification, Issue 4, June 2023, Qualification at a glance, from the [Pearson mathematics 2017 page](https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html).

### Core Pure is not split by topic

The Core Pure content is proof, complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar coordinates, hyperbolic functions and differential equations. Pearson says "Paper 1 and Paper 2 may contain questions on any topics from the Pure Mathematics content."

So there is no "Paper 1 topics" list to revise from. Either paper can ask anything in Core Pure.

### Options carry half the marks

Papers 3 and 4 together are 150 of the 300 marks. Which two a student sits is therefore not a detail: it decides half the A level.

The Department for Education's subject content sets this shape for every board, with a prescribed core of about half and options for the rest. Edexcel delivers the options as separate papers.

Ten routes

## Which Edexcel Further Maths options can be taken together?

Either any two Option 1 papers, or an Option 1 paper with its matching Option 2 paper. Pearson counts ten pairs in all.

Pearson's rule is short: "Students choose a pair of options, either: any two Option 1 papers, or a matching pair of Option 1 and Option 2 papers. This makes a total of ten different option pairs." There are four Option 1 papers, so six ways to pick two of them, and four matching pairs, which gives the ten. Further Statistics 1, Further Mechanics 1 and Decision Mathematics 1 can each be sat as Paper 3 or as Paper 4, which Pearson explains with the note that, for example, Further Statistics 1 "is also the Paper 4 option 4B paper".

| # | Pair | Kind | What it suits |
| --- | --- | --- | --- |
| 1 | Further Pure 1 + Further Pure 2 | Matching pair | Students heading for pure maths or physics |
| 2 | Further Statistics 1 + Further Statistics 2 | Matching pair | Deep statistics, economics, data degrees |
| 3 | Further Mechanics 1 + Further Mechanics 2 | Matching pair | Engineering and physics |
| 4 | Decision Mathematics 1 + Decision Mathematics 2 | Matching pair | Computing and operational research interests |
| 5 | Further Pure 1 + Further Statistics 1 | Two Option 1 papers | A broad pure and data mix |
| 6 | Further Pure 1 + Further Mechanics 1 | Two Option 1 papers | A broad pure and physics mix |
| 7 | Further Pure 1 + Decision Mathematics 1 | Two Option 1 papers | Pure with algorithms and networks |
| 8 | Further Statistics 1 + Further Mechanics 1 | Two Option 1 papers | Two applied areas at first level |
| 9 | Further Statistics 1 + Decision Mathematics 1 | Two Option 1 papers | Applied work without mechanics |
| 10 | Further Mechanics 1 + Decision Mathematics 1 | Two Option 1 papers | Applied work without statistics |

Pairs listed by us from the rule in the 9FM0 specification, Issue 4, page 5 and Appendix 9. The "What it suits" column is our opinion, not Pearson's. Entry codes for each route are in Pearson's UK Information Manual.

1. Ask the school which route it teaches. Many teach one route for the whole class.
2. Check the route against the degree the student is aiming for. Engineering applicants often want mechanics; computing applicants often like decision mathematics.
3. If the student wants a different option, ask whether the school can enter them for it while they are taught elsewhere. Entry is by route code, so the exams officer must know early.
4. Plan teaching time: each option paper is a quarter of the A level, the same as a Core Pure paper.
5. Confirm the final entry, 9FM0 plus the route code, before the entry deadline.

Grading

## How is Edexcel A level Further Maths graded, and what if you take extra options?

On the 300-mark total of four papers, with thresholds that can differ by route. If a student sits more than two options, Pearson grades the combination giving the highest grade.

Pearson writes that 9FM0 "will be graded and certificated on a six-grade scale from A* to E using the total combined marks (out of 300) for the two compulsory papers and the two optional papers chosen. The different routes within the qualification may have different grade thresholds." A student below E receives U.

Taking more than two options is allowed: "Students are permitted to take more than the two optional papers if they want to extend their course of study." Then "the combination of papers that result in the best grade will be used. The combination of papers that is graded may not be the combination that gives the highest number of marks." That last sentence surprises people, but it follows from the previous one: if routes have different thresholds, a lower raw total on one route can still clear a higher grade than a larger total on another.

| Rule | Pearson's wording or a close restatement |
| --- | --- |
| Prior learning | "There are no prior learning or other requirements for this qualification." Pearson adds that students who would benefit most are likely to have a Level 3 GCE in Mathematics |
| Timing | All assessments in May and June of a single year |
| First certification | 2019 |
| Formulae | The booklet Mathematical Formulae and Statistical Tables is provided; some formulae must be recalled |
| Calculator | Must have an iterative function, matrix calculations up to at least 3 × 3, and statistics; no symbolic algebra, differentiation or integration; an exam mode is acceptable if it makes the calculator compliant |

The matrix requirement is particular to Further Maths. A calculator that handles 3 × 3 determinants and inverses saves time on Core Pure, but, as on every A level, working that shows the method still earns the method marks.

Worked examples, ours

## Core Pure and option examples we wrote

Two short Core Pure problems, an induction outline and a Further Mechanics 1 collision. None is a Pearson question.

**Our Core Pure problem on complex numbers.** Solve z2 − 4z + 13 = 0 and describe the roots on an Argand diagram.

### Solving

The discriminant is 16 − 52 = −36, so z = (4 ± 6i) ÷ 2 = 2 ± 3i.

Real-coefficient quadratics always give conjugate pairs, which is a quick check.

### Interpreting

The roots are reflections of each other in the real axis, at (2, 3) and (2, −3). Each has modulus √13.

Their sum 4 and product 13 match the coefficients, a second check worth one line.

**Our Core Pure problem on matrices.** For M = (2 1; 5 3), the determinant is 2 × 3 − 1 × 5 = 1, so M is invertible and M−1 = (3 −1; −5 2). Since det M = 1, M preserves area: a unit square maps to a parallelogram of area 1.

**Our induction outline.** Prove that the sum of r(r + 1) for r = 1 to n equals n(n + 1)(n + 2)/3. Base case n = 1: both sides are 2. Assume it for n = k. Adding (k + 1)(k + 2) gives k(k + 1)(k + 2)/3 + (k + 1)(k + 2) = (k + 1)(k + 2)(k + 3)/3, which is the formula for n = k + 1. Conclude in a sentence that the result holds for all positive integers n. Checked by us for n = 10: both sides are 440.

**Our Further Mechanics 1 problem.** A 3 kg sphere moving at 4 m s−1 hits a 1 kg sphere at rest, directly, with coefficient of restitution e = 0.5. Momentum: 3 × 4 = 3v1 + v2. Restitution: v2 − v1 = 0.5 × 4 = 2. Solving, v1 = 2.5 m s−1 and v2 = 4.5 m s−1, both in the original direction.

| # | Our question | Paper | Answer |
| --- | --- | --- | --- |
| 1 | Find cosh(ln 3) exactly. | Core Pure | 5/3 |
| 2 | Find the Maclaurin series of ex sin x up to the x3 term. | Core Pure | x + x2 + x3/3 |
| 3 | The region under y = √x from x = 0 to 4 is rotated fully about the x-axis. Find the volume. | Core Pure | 8π |
| 4 | Find the area enclosed by the polar curve r = 2 cos θ. | Core Pure | π |
| 5 | X ~ Po(3). Find P(X = 2). | Further Statistics 1 | 0.224 |
| 6 | Apply one pass of quick sort to 9, 4, 7, 1, 8, choosing the middle item as pivot, as the specification directs. | Decision Mathematics 1 | Pivot 7; list becomes 4, 1, 7, 9, 8 |

All examples and practice questions were written by us on 31 October 2026. Pearson publishes past papers, mark schemes and examiners' reports for 9FM0 on its [qualification page](https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html).

When the school's route does not fit

## What if my school does not teach the 9FM0 option I need?

Talk to the exams officer first; an option is entered as part of a route, so the entry has to be planned. Teaching the option can then happen outside school.

Because Pearson enters students for 9FM0 "along with the entry code for the optional route that they wish to take", a student who wants, say, Further Mechanics while the class sits Decision Mathematics needs a different route code, not just extra lessons. Some schools can accommodate that; others cannot. Asking in Year 12 gives everyone time.

Where a school agrees, we teach the missing option as a 1-on-1 course alongside the school's Core Pure lessons, and we teach Core Pure too for students whose school does not offer Further Maths at all. We never enter students ourselves, and we cannot promise a school will change an entry. Our [Further Maths tuition page](/further-maths-tuition-online) covers the subject more broadly.

Progression

## How Core Pure and the options fit across two years

Core Pure grows alongside A level Maths; options are added once the matching A level Maths content is in place.

| Stage | Usually | Sign that it is done |
| --- | --- | --- |
| 1. Core Pure first half | Year 12 | Complex numbers, matrices, proof by induction and roots of polynomials fluent |
| 2. First options | Late Year 12 | Option 1 papers started once the related A level Maths topics are secure |
| 3. Core Pure second half | Year 13 | Hyperbolic functions, polar coordinates, further calculus and differential equations |
| 4. Four-paper practice | Final two terms | Timed 90-minute papers in the student's actual route |

### Why options wait a little

Further Statistics leans on A level statistics, and Further Mechanics on A level mechanics.

Starting them too early means teaching two levels at once.

### Why practice uses the real route

A student sitting FS1 and FM1 practises those papers, not FP1.

Ninety minutes is short; familiarity with the actual paper matters.

The catalogue

## Nine courses near Edexcel Further Maths

Arranged by role. The free class helps us recommend one.

I

### The two maths A levels

Years 12 and 13

UK / EF1 / 01

#### A level further maths

Core Pure and every 9FM0 option.

[Open the syllabus](/courses/a-level-further-maths-course)

UK / EF1 / 02

#### A level maths

The 9MA0 foundation under Further Maths.

[Open the syllabus](/courses/a-level-maths-course-pure-mechanics-statistics)

UK / EF1 / 03

#### Statistics and probability

For FS1 and FS2 routes.

[Open the syllabus](/courses/statistics-probability-maths-course)II

### Supporting skills

Algebra and computation

UK / EF2 / 01

#### Algebra foundations

When manipulation is the bottleneck.

[Open the syllabus](/courses/algebra-foundations-masterclass)

UK / EF2 / 02

#### Maths through coding

Algorithms from Decision Mathematics run in Python.

[Open the syllabus](/courses/maths-through-coding)

UK / EF2 / 03

#### GCSE mathematics

For a younger student preparing early.

[Open the syllabus](/courses/gcse-mathematics-mastery)III

### Beyond A level

Admissions and university

UK / EF3 / 01

#### TMUA and STEP

Admissions tests many Further Maths students sit.

[Open the syllabus](/courses/tmua-mat-step-preparation-course)

UK / EF3 / 02

#### College mathematics

Linear algebra and analysis ahead of university.

[Open the syllabus](/courses/college-mathematics-complete-masterclass)

UK / EF3 / 03

#### Competition mathematics

Olympiad problem solving for strong students.

[Open the syllabus](/courses/olympiad-competition-mathematics-mastery)

How classes run

## Taught to the student's actual route

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. All lessons are set in UK time; our teachers are based in India, and we keep the UK slot the same when the clocks change.

After school

The common slot for Core Pure groups.

Evening

Often used for 1-on-1 option teaching.

Weekend morning

Fits two 90-minute papers back to back.

### Route first

We confirm the student's option pair before planning.

### Core Pure as one

Both papers revised as a single body of content.

### Missing options

1-on-1 teaching for an option the school does not offer.

### Matrix calculator

3 by 3 work practised on the student's own model.

### Proof written out

Induction and conclusions in full sentences.

### Batch or 1-on-1

A group of 15 to 20, or individual lessons.

Student work

## Projects made in our classes

Class work for practice, not exam submissions. More sit in [student labs](/student-labs).

![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp)

AI and ML

#### NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app)

![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp)

AI and ML

#### Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · [Open it](https://misti.modernagecoders.com)

![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp)

AI and ML

#### GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app)

![SkyCast weather forecast application screenshot](/images/projects/skycast.webp)

Web app

#### SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

## Fees for Edexcel 9FM0 classes

UK families pay a single monthly fee in US dollars. A first lesson costs nothing, and we only take payment once a course and a regular slot are settled.

Free first class

USD 0

no card required

- A free 9FM0 lesson in Core Pure or an option
- A check of the student's route
- Booked by phone or WhatsApp

Book it

Group batch

USD 100

a month, billed in US dollars

- A batch of 15 to 20 Further Maths students
- Core Pure across both years
- Common option routes taught in groups
- Quieter weeks in exam season

Start here

One to one

USD 150

a month, billed in US dollars

- One teacher, one student
- Ideal for an option the school does not teach
- Planned around the 9MA0 timetable

Enquire

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Google reviews from parents, unedited.

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9FM0 questions

## What students ask about Edexcel A level Further Maths

### How many exams are in Edexcel A level Further Maths?

Four, each 1 hour 30 minutes and 75 marks. Core Pure Mathematics 1 and 2 are compulsory, and the other two are optional papers.

### What are the Edexcel Further Maths options?

Further Pure 1 and 2, Further Statistics 1 and 2, Further Mechanics 1 and 2, and Decision Mathematics 1 and 2. Students take two of the eight, in an allowed pair.

### Can I take Further Pure 2 with Further Statistics 1?

No. Pearson allows any two Option 1 papers or a matching Option 1 and Option 2 pair. Further Pure 2 only pairs with Further Pure 1.

### How many option routes are there in 9FM0?

Ten. Six come from choosing two of the four Option 1 papers, and four are the matching pairs, such as Further Mechanics 1 with Further Mechanics 2.

### Are the grade boundaries the same for every 9FM0 route?

Not necessarily. Pearson says the different routes may have different grade thresholds, so compare a mark with the boundaries for the route actually sat.

### What happens if I sit three option papers?

Pearson grades whichever combination produces the highest grade. That may not be the combination with the highest raw total, because thresholds can differ between routes.

### Do I need A level Maths to take Edexcel Further Maths?

Pearson sets no formal prior learning requirement, but says students who would benefit most are likely to have a Level 3 GCE in Mathematics. In practice it is taken alongside or after A level Maths.

### What calculator do I need for 9FM0?

One with an iterative function, matrix calculations up to at least 3 by 3, and statistical distributions, without symbolic algebra or calculus. An exam mode is fine if it makes the calculator compliant.

### When are your 9FM0 classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Times are in UK time.

### Are you linked with Pearson or Edexcel?

No. Modern Age Coders is independent and has no connection with Pearson. Every example and practice question here was written by us.

Elsewhere on this site

## More for Further Maths students

The A level Maths companion, costs and the bigger question.

### [Edexcel A level Maths 9MA0 help](/edexcel-a-level-maths-9ma0-help)

The Pearson A level Maths that 9FM0 builds on.

### [Further maths tuition online](/further-maths-tuition-online)

Our general Further Maths page.

### [Is A level Further Maths worth it?](/is-a-level-further-maths-worth-it)

A plain look at the commitment.

### [Further maths tutor cost in the UK](/further-maths-tutor-cost-uk)

How families plan for tuition.

### [TMUA preparation](/tmua-preparation)

An admissions test many Further Maths students take.

### [Coding classes in the UK](/coding-classes-in-united-kingdom)

All our UK pages.

## Related pages in this guide

Part of the guide: [UK maths exam boards and specification codes](/uk-maths-exam-boards-and-specification-codes)

### A level maths and further maths

- [AQA A level Maths 7357 help](/aqa-a-level-maths-7357-help)
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- [IGCSE maths for home-educated students](/igcse-maths-for-home-educated-students-uk)
- [Cambridge A Level Maths 9709 help](/cambridge-a-level-maths-9709-help)
- [Cambridge A level Further Maths 9231 help](/cambridge-a-level-further-maths-9231-help)
- [IGCSE maths tuition online](/igcse-maths-tuition-online)

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- [IB maths tuition online](/ib-maths-tuition-online)

More guides: [UK maths year by year, Reception to Year 11](/uk-maths-year-by-year-guide) · [UK selective school maths tests: 7+, 11+, 13+ and 16+](/uk-selective-school-maths-tests-guide) · [UK university admissions: maths tests and computing applications](/uk-university-admissions-maths-and-computing-guide) · [UK maths enrichment, competitions and able pupils](/uk-maths-enrichment-and-competitions-guide)

Start here

## Book a free 9FM0 class

Send a number and we will ring at a UK time that works. We begin by confirming the student's option route, then teach one Core Pure topic so you can judge the lesson.

Want to look first? [Our courses](/courses) each show a syllabus, [how we teach](/how-we-teach) explains the method, and [student labs](/student-labs) shows projects.

[WhatsApp us](https://wa.me/919123366161?text=Hello%20Modern%20Age%20Coders%2C%20I%20would%20like%20a%20free%20first%20class%20for%20Edexcel%20A%20level%20Further%20Maths%209FM0.) · [+91 91233 66161](tel:+919123366161) · [connect@modernagecoders.com](mailto:connect@modernagecoders.com)

A WhatsApp message gets the swiftest response and costs nothing from a UK phone. We answer from India, so the number starts +91.

### Want a class sooner? Book a priority demo

A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.

[Book a priority demo](/book-demo)

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- [Modular Arithmetic: Clock Maths for Olympiads and Code](/blog/modular-arithmetic-explained)
- [How to Solve Maths Word Problems (Without Keywords)](/blog/how-to-solve-maths-word-problems)

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