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Further mathematics

Why study Further Mathematics?

Further Mathematics is for students who enjoy thinking hard and want to discover just how deep and exciting maths can really be. It provides enjoyable, more challenging material than regular maths and the chance to explore more sophisticated mathematical ideas.

What our students say about studying further mathematics

“If you're somebody who enjoys maths I couldn't recommend further maths more - it allows you to go into a deeper and more fulfilling breadth of topics and means every day you get the chance to problem solve and ask mathematical questions.” Oscar Graham 2023-25 Further maths student

“The syllabus introduces the most fascinating and unfamiliar descriptions of the fundamental areas of maths we are used to.” Sophie Smith 2023-25 Further maths student

“Despite being very challenging and a lot of hard work, further maths pushes you out of your comfort zone in a way that is rewarding and allows you develop a deeper understanding of the concepts.” Kira Vinuesa 2023-25 Further maths student

“Further Maths gives you the opportunity to work through more challenging and interesting problems, and allows you to acquire a greater understanding of fascinating mathematical concepts over the two years.” Zachary Bacon Darwin 2023-25 Further maths student

If you’re considering taking a degree in maths, or a related degree at a top university, you should strongly consider taking Further Maths. Many universities consider it an essential prerequisite for these courses.

Course overview

In the first year, we cover the entire A Level Mathematics content as well as the Core Pure 1 component of Further Mathematics. In the second year, we teach Core Pure 2 along with Further Statistics and Further Mechanics.

You will also study the syllabus for the MAT (an entrance exam used by many universities including Oxford) as well as early components of the STEP (Cambridge) during your time in Further Maths at Woodhouse.

  • Core Pure Mathematics 1 (CP1)
    Topics: Complex numbers, matrices, proof, series, volumes of revolution, and vectors.
  • Core Pure Mathematics 2 (CP2)
    Topics: Complex numbers, polar coordinates, differential equations, further calculus, and hyperbolic functions.
  • Further Statistics 1 (FS1)
    Topics: Discrete probability distributions, Poisson distribution, geometric and negative binomial distributions, hypothesis testing, the central limit theorem, chi-squared tests, probability generating functions, and quality of tests.
  • Further Mechanics 1 (FM1)
    Topics: Momentum and impulse, work and energy, elastic strings and springs, and elastic collisions in two dimensions.

Beyond the classroom, Further Mathematics students are encouraged to take part in a range of enrichment activities, including the UKMT Senior Maths Challenge, the Senior Kangaroo, the Girls’ Mathematical Olympiad, and the British Mathematical Olympiad.

How is the course assessed?

In addition to your three Mathematics exams, A Level Further Mathematics is assessed through four equally weighted written exam papers. Each paper lasts 1 hour and 30 minutes and contributes 25% to the final grade. All assessments take place at the end of the second year.

What will I do in lessons?

At Woodhouse, further maths lessons are designed to be engaging, collaborative, and challenging. Your teachers will challenge you and hopefully you will love it!

You can expect to work independently and in groups, explaining complex ideas and learning from each other. Lessons often involve solving puzzles, discussing abstract ideas and exploring problems away from your desk using vertical whiteboards around the room. You’ll be solving university entrance exam problems on a weekly basis.

What Independent study will be expected?

You are expected to study around 10 hours each week outside of lessons, with 5 hours for Maths and 5 hours for Further Maths. One of the biggest challenges is staying on top of the workload and keeping up with regular revision. We cover a lot of content quickly, and there isn’t much time in lessons to revisit previous material. Consistent review and independent study using our departmental SharePoint, textbook questions, and resources from the Integral website are essential.

You will also be expected to complete regular flipped learning tasks which are based around the Cambridge STEP foundation course. You can find examples of these here.

Exam Board

Edexcel
Link to specification

GCSE entry requirements

  • 8 in Mathematics required
  • 5 in English Language required
  • Further Mathematics can only be applied for as part of a 4 A level programme at this stage and by definition it is in combination with A level Mathematics

NB. August Enrolment: Students who achieve grade 9 GCSE Mathematics may be permitted to study Further Mathematics as part of a 3 A level programme which includes A level Mathematics.

What A Levels go well with this one?

Mathematics is compulsory for all students taking Further Mathematics. In addition, many students choose subjects that complement the analytical and problem-solving skills developed in the course. Most commonly, students also take either Computer Science or Physics. Other popular combinations include Philosophy, Economics, Chemistry, Biology, Music, and Art.

What can I do beyond A Levels with this subject?

Studying Further Mathematics opens doors to a wide range of fields, including:

Engineering, Technology and Software Development, Data Analysis and Data Science, Scientific Research, Quantitative Finance, Economics, Actuarial Work, and Artificial Intelligence and Machine Learning.

If you are planning to study mathematics at university, taking Further Mathematics is highly recommended and, in many cases, essential.

Frequently asked questions

What extracurricular maths activities are offered?

The Maths Department offers a range of enrichment opportunities, including the Woodhouse Maths Academy, UKMT Senior Mathematical Challenge, Senior Team Maths Challenge, Mathematical Olympiad for Girls, British Mathematical Olympiad, and Maths Inspiration talks. We also host external speakers who present on engaging and advanced mathematical topics. Our Further Maths students are encouraged to take part by signing up for these activities.

What resources are available?

We use SharePoint to provide access to a wide range of learning materials. In addition, we have subscriptions to online platforms such as Integral and ActiveLearn, which support independent study and exam preparation.

I’m not sure if Further Maths is right for me. Should I take it?

If you are on the fence, we strongly advise you sign up to join the course. It’s much harder to join later due to the challenging content and the fact that the course is oversubscribed. Switching from Further Maths to single maths is easy though!

What support is available for students who are underachieving?

Students who are underachieving receive targeted support from their teachers and, when necessary, from progress managers. We offer various forms of academic support, including mentoring, drop-in sessions, and subject-specific tutorials, to help students catch up and achieve their full potential.

Do I need a graphical calculator?

Your GCSE scientific calculator will not be adequate as it lacks certain functions that the exam requires. We recommend you get the Casio FX-991CW.

Graphical calculators can be expensive. Some students do like to have them, but the course does not require them, even further maths. There are no questions you can do on the graphical calculator that you can’t do on the normal calculator and only very occasionally is it more useful (some graph sketching). If you do want to get one, we recommend the Casio fx-CG100.

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