Mathematics – Further

unit icon 9 Units
unit icon 111 Lessons
unit icon 1 Year
This course develops and extends a set of transferable skills. These include the skill of working with mathematical information, as well as the ability to think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings.
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Please note, that all courses offered are subject to receiving a minimum enrolment number. Your Pamoja point of contact will be in touch as we approach the start date if we are unable to take a course forward.

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Course Structure

The course covers the following topics:

Minimum entry requirements

The Cambridge International A Level Mathematics Further (9231) syllabus require students to have already studied mathematics to an advanced level. To successfully study for Cambridge International AS and A Level with us, students need to have attained a strong pass in Cambridge International A Level Mathematics (9709) – taking the following papers:
  • Pure Mathematics 1
  • Pure Mathematics 3
  • Mechanics
  • Probability and Statistics 1
A student may have taken an alternative qualification or papers, and it will be the school’s responsibility to check that any qualifications cover the expected prior knowledge. It is the school’s responsibility to ensure that the student has met the minimum entry requirements of that the student will be able to undertake additional study alongside their Further Mathematics course. Pamoja Taught courses and Pamoja teachers assume that these minimum entry requirements have been met and the student therefore has the necessary foundational knowledge and ability to work at the pace required by the course.  

Benefits for students

Taking International AS and A Level Mathematics – Further will enable students to:
  • become experienced in a wide range of technical and social tools
  • develop skills like time management, communication and digital literacy

Cambridge International calculator guidance

International AS and A Level Mathematics students will require a scientific calculator when studying the course and for examinations. As stated below, Cambridge International allows for a wide range of calculators to be used in examinations. Pamoja teachers have suggested the Casio ClassWiz models as suitable for this course, such as the fx-991 EX. Candidates can use programmable calculators [in examinations]. However, calculators with any of the following facilities are not allowed, unless stated otherwise in the syllabus:
  • graphic display
  • data banks
  • dictionaries
  • language translators
  • retrieval or manipulation of text or formulae
  • QWERTY keyboards
  • built-in symbolic algebraic manipulations (output must be numeric not algebraic)
  • symbolic differentiation or integration (output must be numeric not algebraic)
  • capability of any remote communication


*Course available from September 2020, for first exams in June 2022. 

Course structure

This course is available as a single year course only. Consequently Pamoja does not currently offer Further Mathematics at AS Level. The course covers the following topics:
  • Mechanics 1 – including projectile motion, moments, equilibrium, centre of mass, circular motion
  • Matrices and Vectors
  • Calculus – including hyperbolic and inverse trigonometric functions, second derivatives, differential equations, and applications
  • Complex numbers – de Moivre’s theorem
  • Statistics 1 – including discrete and continuous random variables, statistical distributions, sampling and hypothesis testing
  • Statistics 2 – including expectation and variance, goodness of fit and non-parametric tests
  • Series & sequences
  • Proof by induction
  • Polynomials (cubic and quartic)
  • Polar coordinates
  • Mechanics 2 – including Hooke’s Law, work, momentum, Newton’s Laws
In each year there is also time for revision and trial examinations.  

Activities and assessments

The course includes the following activities: readings and practice questions on each topic, quizzes, self-assessments and marked assignments. Teachers will review and grade assignments during the course. There are also unit discussions to support students with each topic. The final examination consists of  four externally-assessed papers:
  • Paper 1—2 hours, 30% AL, structured questions on Further Pure Mathematics 1
  • Paper 2—2 hours, 30% AL, structured questions on Further Pure Mathematics 2
  • Paper 3—1 hour 30 minutes, 20% AL, structured questions on Further Mechanics
  • Paper 4—1 hour 30 minutes, 20% AL, structured questions on Further Probability and Statistics

Advice from our teachers

This course is twice the pace of a standard two-year A Level course. In order to succeed in International A Level Further Mathematics in a single year, we recommend students set aside twenty to thirty hours a week to study. It is important that students regularly keep up with the readings and the course activities in a timely manner. And that they contact their Pamoja teacher if they fall behind or need help with assignments.

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