Further Mathematics

This course expands on the material covered in A Level Mathematics, delving deeper into advanced concepts and introducing new areas of study. Students develop advanced problem-solving skills, logical reasoning, and the ability to apply mathematical models to real-world situations. Several exam boards offer Further Mathematics qualifications, each with its own syllabus. The key concepts across all boards generally include problem-solving, communication using mathematical language and notation, and mathematical modelling. Further Mathematics is often studied alongside A Level Mathematics and is highly regarded by universities, particularly for mathematics-related courses.

Exam Boards and Syllabi

Several exam boards offer Further Mathematics qualifications in the UK. These include:

• Cambridge International Examinations (CIE): Offers the Cambridge International AS & A Level Mathematics - Further (9231). This syllabus is designed for high-ability learners and covers a range of topics including further pure mathematics, further mechanics, and further probability & statistics.
• Edexcel: The Edexcel A Level Further Mathematics syllabus covers core pure mathematics, further pure mathematics, further statistics, further mechanics, and decision mathematics.
• AQA: The AQA A Level Further Mathematics syllabus includes further pure mathematics, further mechanics, and further statistics.
• OCR: The OCR A Level Further Mathematics A (H245) specification includes a mandatory pure core and allows students to choose two additional areas from statistics, mechanics, discrete mathematics, and additional pure mathematics.

Syllabus Content Example (CIE 9231)

The CIE 9231 syllabus is structured into four papers:

• Paper 1: Further Pure Mathematics 1: Covers topics such as roots of polynomial equations, rational functions and graphs, summation of series, matrices, polar coordinates, vectors, and proof by induction.
• Paper 2: Further Pure Mathematics 2: Builds on Paper 1 and includes hyperbolic functions, matrices (including eigenvalues and eigenvectors), differentiation, integration, complex numbers, and differential equations.
• Paper 3: Further Mechanics: Expands on mechanics concepts from A Level Mathematics, covering projectile motion, equilibrium of a rigid body, circular motion, Hooke's law, linear motion under a variable force, and momentum.
• Paper 4: Further Probability & Statistics: Develops further the probability and statistics content from A Level Mathematics, including continuous random variables, inference using normal and t-distributions, χ² tests, non-parametric tests, and probability generating functions.

Assessment

Assessment for Further Mathematics typically involves written examinations. The specific format and weighting of papers vary depending on the exam board. It's essential to consult the relevant syllabus for detailed assessment information. Calculators are permitted in exams, but they must not have symbolic algebraic manipulation, symbolic differentiation, or symbolic integration capabilities.

This information provides a general overview of Further Mathematics. For specific details, it's crucial to refer to the syllabus published by the relevant exam board.