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    OCR A-Level Further Mathematics

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    Course overview

    The OCR A-Level Further Mathematics specification covers 40 topics with 313 learning objectives (H245). Use the topic browser below to explore subtopics, exam tips, common mistakes, and key terminology for each area of the course.

    • 40 topics
    • 1 study page
    • 313 learning objectives
    Course H245
    40
    topics
    1
    audio lessons

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    Your exams

    • Pure Core 1 (AL):Written PaperTuesday, 18 May 2027, PM
    • Pure Core 2 (AL):Written PaperThursday, 20 May 2027, PM
    • Statistics (AL):Written PaperTuesday, 25 May 2027, PM
    • Mechanics (AL):Written PaperThursday, 10 June 2027, PM
    • Discrete Mathematics (AL):Written PaperTuesday, 15 June 2027, PM
    • Additional Pure Mathematics (AL):Written PaperFriday, 18 June 2027, PM
    Official timetable (opens in a new tab)

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    40 topics

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    About this course

    About OCR A-Level Further Mathematics

    OCR A-Level Further Mathematics (H245) is a challenging and rewarding course that builds directly on the knowledge and skills developed in A-Level Mathematics. It is designed for students who enjoy problem-solving and want to explore more advanced pure mathematical concepts alongside specialist applied topics. The course deepens your understanding of algebra, geometry, and calculus, while also introducing entirely new areas such as complex numbers, matrices, and hyperbolic functions. You will learn to construct rigorous proofs, model real-world systems with differential equations, and work with abstract structures that underpin higher-level mathematics, making it an excellent foundation for university courses in mathematics, physics, engineering, or computer science.

    The specification is structured into two distinct parts: mandatory Core Pure content and optional applied modules. All students study the same Core Pure topics, which cover advanced pure mathematics including proof by induction, further vectors, polar coordinates, and further calculus. You then personalize your qualification by choosing two optional papers from a range including Further Mechanics, Further Statistics, Decision Mathematics, and the unique Further Pure with Technology (FPT) option. This flexibility allows you to tailor your studies to your interests and career aspirations, whether you are drawn to the mathematical modelling of physical systems, the data-driven world of statistics, the algorithmic thinking of decision maths, or the exploration of pure mathematics using technology.

    OCR’s linear approach means all examinations are taken at the end of the two-year course, encouraging a deep, connected understanding of the subject. The course is demanding but highly respected, equipping you with analytical and logical thinking skills that are prized by universities and employers alike. To succeed, you should have a strong grasp of A-Level Mathematics, as many topics are extensions of concepts met in that course. Regular practice, careful attention to proof, and the ability to apply mathematics in unfamiliar contexts are essential. For those who love a mathematical challenge, OCR Further Mathematics offers a rich and stimulating journey into the heart of the discipline.

    Assessment Structure

    The OCR A-Level Further Mathematics qualification is assessed entirely by written examination, with no coursework. Students sit four papers, each lasting 1 hour 30 minutes and worth 75 marks, contributing 25% of the final grade. Papers 1 and 2 (Core Pure 1 and Core Pure 2) cover the mandatory pure content. For Papers 3 and 4, students choose two options from: Further Pure with Technology, Further Statistics, Further Mechanics, or Decision Mathematics. This structure provides 300 total marks, and all papers are taken in the summer of the second year, testing the full two-year linear course.

    Why Choose OCR?

    • Unique optional module: OCR is the only major board to offer 'Further Pure with Technology', where you use software such as GeoGebra to investigate pure mathematics, blending traditional rigour with modern computational tools – ideal for students interested in the intersection of maths and computing.
    • Greater applied choice: With four distinct option areas, OCR allows you to specialise in the fields most relevant to your future plans. Whether you want to deepen mechanics for engineering, focus on statistics for data science, or tackle decision maths for operational research, OCR’s range is broader than many other boards.
    • Clear and well-structured specification: OCR’s resources and past papers are highly regarded for their clarity and challenge. The questions are designed to test true mathematical understanding and problem-solving ability, which develops resilient, independent thinkers well-prepared for university admission tests and interviews.

    Frequently Asked Questions

    What is the difference between OCR Further Mathematics and other exam boards like AQA or Edexcel?
    The main differences lie in the optional modules and assessment style. OCR uniquely offers 'Further Pure with Technology', a paper that integrates software use, which is not available from AQA or Edexcel. Edexcel tends to have a larger choice of applied modules (including Further Pure 1 and 2 separately), while AQA’s structure is more fixed. OCR’s papers are known for their emphasis on problem-solving and proof, often with multi-step, unstructured questions that test deep understanding. All boards cover similar core pure content, but the flavour of questions and exact topic weighting can vary, so using past papers to check your comfort with the style is wise.
    Can I take OCR Further Mathematics if I studied AQA or Edexcel for A-Level Maths?
    Yes, it is perfectly possible, and many students do so. The A-Level Mathematics content is broadly the same across all boards, so the foundational skills are identical. However, you should be aware that OCR Further Mathematics assumes familiarity with any board’s A-Level Maths, and there is no requirement to have studied OCR’s own Maths course. You may need to briefly check that your Maths syllabus covered a few specific prerequisites (like radians and some proof techniques), but schools routinely combine different boards. Speak to your teacher to ensure any minimal gaps are addressed quickly.
    How many exams are there in OCR Further Mathematics A Level?
    There are four written examination papers in total, each lasting 1 hour and 30 minutes. Papers 1 and 2 are Core Pure 1 and Core Pure 2, covering all the mandatory pure content. Papers 3 and 4 are your two chosen optional papers from Further Mechanics, Further Statistics, Decision Mathematics, or Further Pure with Technology. All papers carry equal weighting (25% each, 75 marks per paper), and you take them all at the end of the two-year course.
    What is the 'Further Pure with Technology' option and should I choose it?
    Further Pure with Technology (FPT) is a unique OCR paper where you use mathematical software (like GeoGebra) to explore and solve pure mathematics problems. In the exam, you are given access to a laptop with the software, and questions ask you to investigate functions, curves, sequences, and numerical methods interactively. It is ideal if you enjoy using technology to visualise and understand mathematics, and it provides a great bridge to computational maths at university. However, not all schools can offer it due to facilities, so check availability. It is no easier or harder than other options, just different, and it is well-regarded as a modern mathematical skill.
    Is there any coursework in OCR Further Mathematics?
    No, OCR Further Mathematics A-Level is assessed entirely by written examinations. There is no coursework or controlled assessment component. All skills, including the use of technology in the Further Pure with Technology paper, are tested in the final exams under timed conditions. This means your grade depends solely on your performance in the four end-of-course papers, so consistent revision and exam technique are crucial.
    Assessment and exam guidance

    What Gets Top Grades

    A*/Grade 9

    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

    OCR
    State
    1 mark

    Give a single fact or term

    Identify
    1 mark

    Name or select

    Describe
    2-4 marks

    Account of process or features

    Explain
    3-6 marks

    Give reasons with BUSINESS-FACING outcomes

    Analyse
    6-9 marks

    Examine methodically showing cause→effect→outcome

    Evaluate
    9-12 marks

    Judge, weigh up evidence, reach SYNOPTIC conclusion

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