Highgrove Education

A level Further Mathematics

The International A level in Further Mathematics is your ultimate mathematical challenge. This course covers a double A level, comprising an A level in Mathematics and an additional A level in Further Mathematics. Not only will you master advanced topics in pure mathematics, including algebra, trigonometry, calculus, and proof, but you’ll also dive into advanced mechanics and statistics, and you’ll also study a module in Decision Maths, useful for budding programmers. It’s all about pushing your mathematical boundaries, discovering the profound connections between different areas of mathematics, and learning to apply mathematics to real-world problems. Whether you aspire to become a mathematician, engineer, data scientist, or simply want to conquer the highest peaks of mathematical knowledge, this course propels you into a world of limitless mathematical possibilities.



Further Maths

Key Information

What you’ll study

Entry Requirements

Assessment Information

Access Course Enrolment:
  • Enrolment in our pre-GCSE or pre-A level access course.
  • Access to our self-study materials and platform, live class lessons, and individual teacher support in Office Hours.
  • Weekly teacher-marked homework.
  • Half termly reports.
  • Support from our SENDCo for pupils with special educational needs or disabilities, including assessment for access arrangement entitlement.
  • Support with English for pupils whose first language is not English.
  • A Highgrove Education Office365 account, including Teams, SharePoint and a school email
QualificationInternational AS Mathematics and AS Further Mathematics, International A level Mathematics and A level Further Mathematics. This is a combined course which results in a double qualification.
Exam board Edexcel
Exams availableJanuary, June and October

Online school, full time or individual courses

Course length2 years A level Mathematics and A level Further Mathematics combined
Weekly study time4 x 45-minute live lessons, 10 x 45-minute self-study lessons, 2 x 45-minute teacher-marked homework
Class sizeMaximum 10
Course start September

Individual Tutoring

Recommended For Mathematics and Further Mathematics combined, approximately 200 x 45-minute individual tutoring lessons, 500 x 45-minute self-study lessons, 100 x 45-minute teacher-marked homework. Pace and level of commitment determined by individual needs.
Course start Flexible

Year 12 exams

Pure Mathematics 1 (Mathematics AS)
  • Algebra and functions
  • Coordinate geometry in the (x, y)
  • Trigonometry
  • Differentiation
  • Integration
Pure Mathematics 2 (Mathematics AS)
  • Proof
  • Algebra and functions
  • Coordinate geometry in the (x, y) plane
  • Sequences and series
  • Exponentials and logarithms
  • Trigonometry
  • Differentiation
  • Integration
Mechanics 1 (Mathematics AS)
  • Mathematical models in mechanics
  • Vectors in mechanics
  • Kinematics of a particle moving in a straight line
  • Dynamics of a particle moving in a straight line or plane
  • Statics of a particle
  • Moments
Pure Mathematics 3 (Mathematics A2)
  • Algebra and functions
  • Trigonometry
  • Exponentials and logarithms
  • Differentiation
  • Integration
  • Numerical methods
Statistics 1 (Mathematics A2)
  • Mathematical models in probability and statistics
  • Representation and summary of data
  • Probability
  • Correlation and regression
  • Discrete random variables
  • Discrete distributions
  • The Normal distribution
Further Pure Mathematics 1 (Further Mathematics AS)
  • Complex numbers
  • Roots of quadratic equations
  • Numerical solution of equations
  • Coordinate systems
  • Matrix algebra
  • Transformations using matrices
  • Series
  • Proof

Year 13 Exams

Pure Mathematics 4 (Mathematics A2)
  • Proof
  • Algebra and functions
  • Coordinate geometry in the (x, y) plane
  • Binomial expansion
  • Differentiation
  • Integration
  • Vectors
Further Pure Mathematics 2 (Further Mathematics AS)
  • Inequalities
  • Series
  • Further complex numbers
  • First order differential equations
  • Second order differential equations
  • Maclaurin and Taylor series
  • Polar coordinates
Further Pure Mathematics 3 (Further Mathematics AS)
  • Hyperbolic functions
  • Further coordinate systems
  • Differentiation
  • Integration
  • Vectors
  • Further matrix algebra
Mechanics 2 (Further Mathematics A2)
  • Kinematics of a particle moving in a straight line or plane
  • Centres of mass
  • Work and energy
  • Collisions
  • Statics of rigid bodies
Statistics 2 (Further Mathematics A2)
  • The Binomial and Poisson distributions
  • Continuous random variables
  • Continuous distributions
  • Samples
  • Hypothesis tests
Decision 1 (Further Mathematics A2)
  • Algorithms
  • Algorithms on graphs
  • Algorithms on graphs II
  • Critical path analysis
  • Linear programming

Year 12 AS Mathematics Modules will be cashed in at the end of the year ensuring pupils achieve an AS qualification in Mathematics after year 12. All other modules will in cashed in the following summer, at which point the exam board will select the modules allocated towards A level Mathematics and A level Further Mathematics which provide the best possible grade outcomes across both qualifications. This means the allocation of modules listed above could vary. For more information take a look at the Edexcel International Mathematics A level Specification: click here

Either

  • A pass in the Highgrove Online School admissions test for Mathematics A level

Or

  • A minimum grade 7 in GCSE Maths, and a strong set of GCSE grades, including several at grade 7 or above.

Year 12 International AS Mathematics, and modules towards A level Mathematics and AS level Further Mathematics

6 Exams (90 minutes each exam)
Paper 1Pure Mathematics 1 (33⅓ % of the total of AS Mathematics, 16⅔ % of the total of A level Mathematics)
Paper 2Pure Mathematics 2 (33⅓ % of the total of AS Mathematics, 16⅔ % of the total of A level Mathematics)
Paper 3Mechanics 1 (33⅓ % of the total of AS Mathematics, 16⅔ % of the total of A level Mathematics)
Paper 4Statistics 1 (16⅔ % of the total of A level Mathematics)
Paper 5Pure Mathematics 3 (16⅔ % of the total of A level Mathematics)
Paper 6Further Pure 1 (33⅓ % of the total of AS Further Mathematics, 16⅔ % of the total of A level Further Mathematics)

Year 13 International A level Mathematics and Further Mathematics

6 Exams(90 minutes each exam)
Paper 7Pure Mathematics 4 (16⅔ % of the total of A level Mathematics)
Paper 8 Mechanics 2 (33⅓ % of the total of AS Further Mathematics, 16⅔ % of the total of A level Further Mathematics)
Paper 9 Further Pure 2 (33⅓ % of the total of AS Further Mathematics, 16⅔ % of the total of A level Further Mathematics)
Paper 10 Statistics 2 (16⅔ % of the total of A level Further Mathematics)
Paper 11 Further Pure 3 (16⅔ % of the total of A level Further Mathematics)
Paper 12 Decision 1 (16⅔ % of the total of A level Further Mathematics)

Progression to University

A Further Mathematics A level is indispensable for rigorous university courses in mathematics, engineering, computer science, theoretical physics, and economics, particularly at top-tier universities. It not only serves as a foundational qualification but also provides a deeper and more advanced understanding of mathematical concepts and techniques. Further Mathematics is especially valuable for those aspiring to pursue highly quantitative or research-intensive fields, where a strong mathematical background is essential. It also enhances one’s problem-solving skills, making it useful for careers in finance, data science, and any domain where complex mathematical analysis is paramount.

Pupils applying to university in the US should note that Further Mathematics and Mathematics may sometimes be considered as a single subject rather than a double award. In the UK there can be a preference for candidates holding four A levels rather than three when one of these A levels is Further Mathematics.

We also offer the following A levels

Our core A level subjects are taught in group classes via a combination of interactive self-study lessons and live lessons led by an expert teacher: 

We have an even wider selection of A levels available via our independent learning and tutoring programmes, including: