Cambridge International AS and A Level Mathematics - Further

Cambridge International A Level Further Mathematics 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.

Learners can apply these skills across a wide range of subjects and these skills equip them well for progression to higher education or directly into employment. Some universities prefer applicants for degrees in mathematics and mathematical/scientific subjects to have an AS or A Level Further Mathematics or equivalent qualification.

This syllabus is intended for high ability learners who have achieved, or are likely to achieve, a high grade in the Cambridge International A Level Mathematics examination. Knowledge of the whole content of the Cambridge International A Level Mathematics syllabus is assumed. Learners will find that the additional time spent studying Further Mathematics will support their understanding of A Level Mathematics.

Aims of the Syllabus

The aims describe the purposes of a course based on this syllabus.
The aims are to enable students to-
• Further develop their mathematical knowledge and skills in a way which encourages confidence and provides satisfaction and enjoyment
• Develop a greater understanding of mathematical principles and a further appreciation of mathematics as a logical and coherent subject
• Acquire a greater range of mathematical skills, particularly those which will enable them to use applications of mathematics in the context of everyday situations and of other subjects they may be studying
• Further develop the ability to analyse problems logically
• Recognise when and how a situation may be represented mathematically, identify and interpret relevant factors and select an appropriate mathematical method to solve the problem
• Use mathematics fluently as a means of communication with emphasis on the use of clear expression
• Acquire the mathematical background necessary for further study in mathematics or related subjects.

Syllabus

1 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

2. Paper 2
   2.1 Hyperbolic functions
   2.2 Matrices
   2.3 Differentiation
   2.4 Integration
   2.5 Complex numbers
   2.6 Differential equations

3. 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

4. Further Probability & Statistics
Paper 4
4.1 Continuous random variables
4.2 Inference using normal and t-distributions
4.3 Non-parametric tests
4.4 Probability generating functions

Objectives of the Assessments
The assessment objectives (AOs) are-

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

2. Application and communication
   • Recognise the appropriate mathematical procedure for a given situation
   • Apply appropriate combinations of mathematical skills and techniques in solving problems
   • Present relevant mathematical work, and communicate corresponding conclusions, in a clear and logical way

Assessment

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

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

PAPER 3
Further Mechanics
5 to 7 structured questions based on the Further Mechanics subject content
Answer all questions. Written examination. Externally assessed. Offered as part of AS Level or A Level
40% of the AS Level
20% of the A Level
1 hour 30 minutes
50 marks

PAPER 4
Further Probability & Statistics
5 to 7 structured questions based on the Further Probability & Statistics subject content.
Answer all questions. Written examination. Externally assessed. Offered as part of AS Level or A Level
40% of the AS Level
20% of the A Level
1 hour 30 minutes
50 marks

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