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### Cambridge A-Level Further Mathematics 9231

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**WHY CHOOSE THIS SYLLABUS? **

Cambridge International AS & A Level Further Mathematics develops 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. Learners can apply these skills across a wide range of subjects and the skills equip them well for progression to higher education or directly into employment. Learners will find that the additional time spent studying this subject will support their understanding of A Level Mathematics.

**ASSESSMENT OVERVIEW**

Paper 1:

- Further Pure Mathematics 1
- 2 hours
- 75 marks
- 6 to 8 structured questions based on the Further Pure Mathematics 1 subject content
- Answer all questions
- Written examination
- Externally assessed
- 60% of the AS Level
- 30% of the A Level
- Compulsory for AS Level and A Level

Paper 2:

- Further Pure Mathematics 2
- 2 hours
- 75 marks
- 7 to 9 structured questions based on the Further Pure Mathematics 2 subject content
- Answer all questions
- Written examination
- Externally assessed
- 30% of the A Level only
- Compulsory for A Level

Paper 3:

- Further Mechanics
- 1 hour 30 minutes
- 50 marks
- 5 to 7 structured questions based on the Further Mechanics subject content
- Answer all questions
- Written examination
- Externally assessed
- 40% of the AS Level
- 20% of the A Level
- Offered as part of AS Level or A Level

Paper 4:

- Further Probability & Statistics
- 1 hour 30 minutes
- 50 marks
- 5 to 7 structured questions based on the Further Probability & Statistics subject content
- Answer all questions
- Written examination
- Externally assessed
- 40% of the AS Level
- 20% of the A Level
- Offered as part of AS Level or A Level

**DETAILS OF THE ASSESSMENT**

**Planning for assessment of AS & A Level Further Mathematics (9231)**

AS & A Level Further Mathematics (9231) can be studied with AS & A Level Mathematics (9709). However, learners may have completed their course in AS & A Level Mathematics before starting the Further Mathematics course.

The AS Level syllabuses are not designed for taking AS Mathematics (9709) and AS Further Mathematics (9231) in parallel after only one year of study. This is because AS Further Mathematics (9231) topics may depend on assumed prior knowledge from A Level Mathematics (9709), such as the Paper 3: Pure Mathematics 3 subject content. Therefore you must plan your teaching carefully if you intend to enter candidates for AS Level Further Mathematics after one year.

**SUBJECT CONTENT**

Further Pure Mathematics 1: Paper 1

- 1.1 Roots of polynomial equations
- 1.2 Rational functions and graphs
- 1.3 Summation of series
- 1.4 Matrices
- 1.5 Polar coordinates
- 1.6 Vectors
- 1.7 Proof by induction

Further Pure Mathematics 2: Paper 2

- 2.1 Hyperbolic functions
- 2.2 Matrices
- 2.3 Differentiation
- 2.4 Integration
- 2.5 Complex numbers
- 2.6 Differential equations

Further Mechanics: Paper 3

- 3.1 Motion of a projectile
- 3.2 Equilibrium of a rigid body
- 3.3 Circular motion
- 3.4 Hooke’s law
- 3.5 Linear motion under a variable force
- 3.6 Momentum

Further Probability & Statistics: Paper 4

- 4.1 Continuous random variables
- 4.2 Inference using normal and t-distributions
- 4.3 x
^{2}-tests - 4.4 Non-parametric tests
- 4.5 Probability generating functions

**SOURCE**

www.cambridgeinternational.org