Further Mathematics

Further Mathematics is the title given to a number of advanced secondary mathematics courses. Higher and Further Mathematics may also refer to any of several advanced mathematics courses at many institutions.

In the United Kingdom Further Mathematics describes a course studied in addition to the standard mathematics AS-Level and A-Level courses. In Victoria, Australia it describes a course delivered as part of the Victorian Certificate of Education. See the section on Victoria for a more detailed explanation. Globally, it describes a course delivered as part of the International Baccalaureate Diploma.

UK

Background

A qualification in Further Mathematics involves studying both pure and applied modules. Whilst the pure modules - formerly known as Pure 4-6 (or Core 4-6), now known as Further Pure 1-3 (4 exists for the AQA board [http://www.aqa.org.uk/qual/pdf/AQA-5361-6371-W-SP-08.PDF] ) - are of a higher standard than those in the standard course, the applied modules need not be. The topics covered by Further Mathematics are more sophisticated and conceptually advanced compared to the single A-level Mathematics.

Some schools and colleges in places such as Hong Kong and India take examinations set by British boards and consequently the subject is offered internationally.

Because smaller schools and colleges may not be able to offer Further Mathematics (as it is a very low-intake course requiring well-trained teachers), universities do not require the course, and may offer "catch-up" classes covering the additional content. An exception is the University of Cambridge, where you must have Further Mathematics to at least AS level to study for a degree in mathematics at all colleges except Emmanuel, which accepts physics as an alternative [http://www.cam.ac.uk/admissions/undergraduate/courses/maths/requirements.html] .

Further Maths is currently the fastest-growing subject at A level, with the number of students increasing by 23% in 2006, and a network has been set up to offer the subject to pupils at schools which cannot provide it. [http://www.economist.com/world/britain/displaystory.cfm?story_id=7950110] Further Maths is commonly expressed as the most difficult A-level currently offered in the U.K., this is mainly because it is the only subject to further the study (as an extra AS or full A-level) of one particular subject. Although the subject has quite a high proportion of students achieving top grade results, students taking the subject tend to be highly intelligent, those less likely to achieve top grades are usually discouraged from the course as it can disrupt their performance in other studies.

List of the areas of study on the syllabus

*Inequalities
*Series
*Complex numbers
*Numerical solutions to equations
*First and second order differential equations
*Hyperbolic functions
*Further calculus
*Coordinate systems, including polar coordinates and intrinsic equations.
*Maclaurin series and Taylor series
*Matrix algebra
*Vectors
*Numerical methods
*Proof

Australia (Victoria)

In contrast with other Further Mathematics courses, Further Maths as part of the VCE is the easiest level of mathematics. Any student wishing to undertake tertiary studies in areas such as Science, Engineering, Commerce, Economics, and some Information Technology courses, must undertake one or both of the other two VCE maths subjects- Mathematical Methods or Specialist Mathematics. The Further Mathematics syllabus in VCE consists of three core modules, which all students undertake, plus three modules chosen by the student (or usually by the school or teacher) from a list of six. The core modules are Univariate Data, Bivariate Data and Time Series. The optional modules are Number Patterns, Geometry and Trigonometry, Graphs and Relations, Business-Related Mathematics, Networks and Decision Mathematics, or Matrices.

International Baccalaureate

Further Mathematics, as studied within the International Baccalaureate Diploma is a Standard Level course that can only be taken in conjunction with Higher Level (HL) Mathematics. It assumes knowledge of the core syllabus of the HL course, and consists of studying all four of the options studied at Higher Level, plus an extra geometry unit.

The syllabus consists of:
*Topic 1 - Geometry
*Topic 2 - Statistics and Probability
*Topic 3 - Sets, Relations, and Groups
*Topic 4 - Series and Differential Equations
*Topic 5 - Discrete Mathematics

External links

* [http://www.vcaa.vic.edu.au/vce/studies/mathematics/further/furthermathindex.html/ VCAA - Further Mathematics]
* [http://www.fmnetwork.org.uk/ The Further Mathematics Network]
* [http://www.edexcel.org.uk/qualifications/QualificationAward.aspx?id=83442 Edexcel Further Mathematics Material]
* [http://www.ocr.org.uk/OCR/WebSite/docroot/qualifications/qualificationhome/showQualification.do?qual_oid=14896&site=OCR&oid=14896&server=PRODUKTION OCR Further Mathematics Material]