Cambridge International AS and A levels – Further Mathematics


Cambridge Assessment International Education(CAIE) offers programs/qualifications broadly divided into four categories

  • Cambridge Primary (5 to 11 years)
  • Cambridge Lower Secondary (11 to 14 years)
  • Cambridge Upper Secondary (14 to 16 years)
  • Cambridge Advanced (16 to 19 years)

The Cambridge Upper Secondary course prepares the students for the advanced levels more specifically AS and A levels; It is not mandatory that students be qualified for Upper secondary to pursue the AS/A levels. Any recognized school certificate equivalent to the Cambridge Upper secondary is acceptable.

Cambridge International AS and A levels are internationally benchmarked qualifications providing an excellent foundation for university education. They are part of the Cambridge Advanced category.

Thousands of students worldwide gain admission into the leading universities yearly with the Cambridge AS and A levels. The syllabuses are designed to provide a deep understanding of the subjects and independent thinking skills.


Assessment Options

Students can choose from a range of assessment options to gain Cambridge AS and A – level qualifications.

  • Take the Cambridge International AS level only. The syllabus content is half a Cambridge International A level.
  • Take a staged assessment route – Cambridge International AS level is one examination series and completes the final Cambridge International A level as a subsequent series. The AS level marks obtained can be carried forward to the full A level twice within a 13-month period. (Not possible though for all subjects)
  • Take all the papers of the Cambridge International A level in the same examination series usually at the end of the course.

Assessments are held twice a year – June and November and the results are out in August and January.



Cambridge AS and A levels curriculum offers a choice of 55 subjects and schools can offer them almost in any combination. This flexibility enables the schools to build an individualized curriculum and the students can choose to specialize in a specific subject area or study a range of subjects.

The A level is typically a two-year course, and the AS level is typically a one-year course.


Further Mathematics AS and A level

Cambridge AS and A level – further mathematics develops and extends a set of skills that can be applied to a range of subjects. These skills equip the students well for progression to higher education or directly into employment. In fact, some universities prefer applicants for degrees in mathematics and mathematical/scientific subjects to have an AS or A level Further mathematics or equivalent qualification.

The key concepts of Cambridge AS and A-level further mathematics are:

  • Problem Solving
  • Communication
  • Mathematical Modeling


Aims of the Further Mathematics Course

The aims describe the purpose of the course based on the syllabus. The aims enable the students to:

  • Further develop their mathematical knowledge and skills, enabling confidence, and providing satisfaction and enjoyment
  • Develop a greater understanding of mathematical principles
  • Enable skills to use the applications of mathematics in everyday situations and of other subjects they might be studying
  • Enhance the ability to analyze a problem logically
  • Recognize when and how a situation may be represented mathematically, and select an appropriate mathematical tool to solve the problem
  • Use mathematics fluently as a means of communication
  • Acquire the mathematical background necessary for further study in mathematics or other subjects


Content Overview

Content Section Assessment component Topics
Further Pure Mathematics 1 Paper 1 Root of polynomial equations, Rational Functions and Graphs, Summation of series, Matrices, Polar Coordinates, Vectors, Proof by Induction
Further Pure Mathematics 2 Paper 2 Hyperbolic Functions, Matrices, Differentiation, Integration, Complex Numbers, Differential Equations
Further Mechanics Paper 3 Motion of a projectile, Equilibrium of a rigid body, Circular motion, Hooke’s Law, Linear motion under a variable force, Momentum
Further Probability and Statistics Paper 4 Continuous random variables, Inference using normal and t-distributions, X^2 tests, Non-parametric tests, Probability generating functions


Assessment Overview


Paper 1

  • Further Pure Mathematics 1 – 2 hours paper
  • 75 marks
  • 6 to 8 structured questions – to attempt all the questions
  • Written examination
  • Externally assessed
  • Weightage – 60% of the AS level and 30% of the A level
  • Compulsory for AS and A levels


Paper 2

  • Further Pure Mathematics 2 – 2 hours paper
  • 75 marks
  • 7 to 9 structured questions – to attempt all questions
  • Written examination
  • Externally assessed
  • Weightage – 30% of A level only
  • Compulsory for A level


Paper 3

  • Further Mechanics – 1 hour 30 minutes paper
  • 50 marks
  • 5 to 7 structured questions – to attempt all questions
  • Written examination
  • Externally assessed
  • Weightage – 40% of the AS level and 20% of the A level
  • Offered as a part of AS level or A level


Paper 4

  • Further probability and statistics – 1 hour 30 minutes paper
  • 50 marks
  • 5 to 7 structured questions – to attempt all questions
  • Written examination
  • Externally assessed
  • Weightage – 40% of the AS level and 20% of the A level
  • Offered as a part of AS level or A level


Assessment Objectives (AO)


AO1 – Knowledge and Understanding

  • Show understanding of mathematical concepts, terminology, and notation.
  • Recall accurately, and use appropriate mathematical manipulative techniques.


AO2 –Application and Communication

  • Recognize the correct mathematical procedure for a given situation.
  • Apply appropriate combinations of mathematical skills and techniques in problem solving.
  • Present relevant mathematical work, and communicate corresponding conclusions in a clear and logical way.


Prior Knowledge

It is expected that the students would have studied the majority if Cambridge AS and A level mathematics subject content before studying Cambridge AS and A level Further Mathematics.


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What is Cambridge International A and AS level mathematics?

Cambridge International AS & A Level math helps develop various adaptable abilities. This includes the ability to work with mathematical data, as well as the capacity to reason deductively and independently, take correctness into account, model problems numerically, analyze outcomes, and reflect on discoveries.

What is the difference between an A level and an AS level?

While A level and AS level are taught similarly, A level is more difficult and requires longer to accomplish. The first year of an A-level program is comparable to an AS level. Your ultimate A-level score is determined by your AS-level performance.

Is A level further maths worth it?

An effective way to get ready for a degree in mathematics is to study A-level Further Mathematics. As it covers a larger spectrum of pure and practical material, including matrices and complex numbers, Advanced Mathematics is highly recommended by many university math departments.

How many universities accept A levels?

More than 850 American colleges legally accept the Cambridge International AS and A Levels. These universities include the ivy league, Harvard, MIT, Stanford, and Yale.

What topics are covered in Cambridge International AS and A levels in Further Mathematics?

The topics covered in Cambridge International AS and A levels in Further Mathematics include complex numbers, matrices, proof by mathematical induction, differential equations, numerical methods, and further calculus. In addition, students may have the opportunity to study topics such as group theory, differential geometry, and topology, depending on their interests and the resources available at their school.

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