Booking Form Apply
Contact Form Contact
Chat Chat


The Kings Advanced Level Foundation is based on A-level syllabuses, taught by A-level teachers, assessed against A-levels and moderated by an independent Advisory Board of external examiners. As such, it is one of the most highly academic and successful pathways to leading UK universities.

The Further Maths module is a half module, and will be studied in addition to the other 5 modules on the course by those students who the school feels will be able to succeed.

Key Facts

Start Dates:

  • 3 January 2023
  • 3 April 2023 (Extended programme only)
  • 26 June 2023 (Extended programme only)
  • 11 September 2023


  • Bournemouth
  • Brighton
  • London
  • Oxford

Entry level:

  • Academic: Completed 11-12 years of schooling
  • English: IELTS 5.5 or equivalent

Minimum age:

  • 16.5


  • 1 Academic Year (3 terms)
  • Extended programme: 1-2 Academic Years (4-7 terms)


  • Average 21 hours per week (plus homework and private study)

Learning outcomes

  • A deeper understanding of the application of calculus methods to the solution of mechanical and other real-world problems. 
  • Knowledge of, and skills in, a wide range of analytical techniques.
  • An understanding of mathematical methods relating to vectors and matrices, and their applications. 
  • The ability to work confidently with complex numbers and be aware of their application to various systems. 
  • The ability to use approximation and power series methods in the solution of suitable problems. 

Course content and structure

The Advanced Level Foundation programme is highly flexible, and able to adapt to the needs and academic aspirations of each student. It does this through a combination of core modules and a series of elective modules which can be combined in different ways to create main subject streams.

Further Maths is one of the many elective modules offered, and an overview of the syllabus content is shown below.

Term 1

Hyperbolic Functions

  • Definitions 
  • Basic identities 
  • Use in integration 

Differential Equations

  • 1st order variables separable 
  • 1st order linear 
  • 2nd order linear with constant coefficients 

Term 2

Numerical Methods

  • Decimal search 
  • Newton-Raphson method 

Power Series

  • Taylor and Mclaurin series 
  • Use in solving differential equations 


  • Basic algebra of vectors 
  • Scalar product 
  • Vector product 

Term 3


  • Basic concepts 
  • Transformations in 2 and 3 dimensions 
  • Eigenvectors and eigenvalues 

Complex Numbers

  • Basic algebra 
  • Solution of quadratic equations 
  • Modulus and argument; the form reiθ 
  • Transformations of the complex plane 

Sample subject combinations with Further Maths

  • Further Maths, Maths, Physics and Chemistry
  • Further Maths, Maths, Physics and Biology

Sample enrichment activities

  • The Big Bang fair, NEC Birmingham
  • UK Maths Challenge 
  • Bletchley Park visit 
  • Astronomy Club 
  • Science in the News Club
  • Google Science Fair 

Sample academic calendar (2021-2022)

Year 1


  • 6th: term starts
  • Student induction


  • 18 – 22th: half term
  • Progress tests


  • University fairs and talks


  • 10th: term ends
  • End of term exams


  • 3rd: term starts


  • 10th – 11th: half term
  • Progress tests
  • University fairs


  • End of term exams
  • 18th: term ends


  • 4th: term starts


  • Progress tests


  • Exams
  • 10th: term ends

Recommended reading

Below is a list of text books normally used on this course, as well as books which may help you prepare for your studies prior to arrival. In many cases the textbooks will be supplied by the school, and you may borrow them for the duration of your time at school. However, if you already know what three subjects you want to choose you may prefer to purchase one before you arrive.

  • Edexcel AS and A level Further Mathematics, Core Pure Mathematics AS Book 1 
  • Edexcel A level Further Mathematics, Core Pure Mathematics Book 2 
  • Edexcel AS and A level Further Mathematics, Further Pure Mathematics 1 

Thank you for your enquiry.
We'll be in touch soon.
The Kings Admissions Team