Further Mathematics

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Further Mathematics is the title given to a number of advanced secondary mathematics courses.

In the United Kingdom it 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, studied either in addition to or instead of the Mathematical Methods course. Globally, it describes a course delivered as part of the International Baccalaureate Diploma.

Contents

[edit] UK

[edit] 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 [1]) - 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.

The subject is often studied by potential Oxbridge candidates for subjects such as Mathematics, Physics, Computer Science, Engineering and Natural Sciences as it is aimed at high calibre students.

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[2].

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. [3]

[edit] List of the areas of study on the syllabus

[edit] Australia (Victoria)

VCE (Victorian Certificate of Education) Further Mathematics 2006–2009

Rationale Mathematics is the study of function and pattern in number, logic, space and structure. It provides both a framework for thinking and a means of symbolic communication that is powerful, logical, concise and precise. It also provides a means by which people can understand and manage their environment. Essential mathematical activities include calculating and computing, abstracting, conjecturing, proving, applying, investigating, modelling, and problem posing and solving. This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the needs and aspirations of a wide range of students. It is also designed to promote students’ awareness of the importance of mathematics in everyday life in a technological society, and confidence in making effecting use of mathematical ideas, techniques and processes.

Structure Units 3 and 4: Further Mathematics Each unit deals with specific content and is designed to enable students to achieve a set of outcomes. Each outcome is described in terms of key knowledge and skills.

Outcomes Outcomes define what students will know and be able to do as a result of undertaking the study. Outcomes include a summary statement and the key knowledge and skills that underpin them. Only the summary statements have been reproduced below and must be read in conjunction with the key knowledge and skills published in the study design.

Entry The assumed knowledge and skills for Further Mathematics Units 3 and 4 are drawn from General Mathematics Units (basic) 1 and 2. Students who have done only Mathematical Methods Units 1 and 2 or only Mathematical Methods Computer Algebra System (CAS) Units 1 and 2 will also have had access to knowledge and skills to undertake Further Mathematics.

Units 3 and 4: Further Mathematics Further Mathematics consists of a compulsory core area of study ‘Data analysis’ and then a selection of three from six modules in the ‘Applications’ area of study. Unit 3 comprises the ‘Data analysis’ area of study which incorporates a statistical application task, and one of the selected modules from the ‘Applications’ area of study. Unit 4 comprises the two other selected modules from the ‘Applications’ area of study. �Assumed knowledge and skills for the ‘Data analysis’ area of study are contained in the topics: Univariate data, Bivariate data, Linear graphs and modelling, and Linear relations and equations from General Mathematics Units 1 and 2. The appropriate use of technology to support and develop the teaching and learning of mathematics is to be incorporated throughout the units. This will include the use of some of the following technologies for various areas of study or topics: graphics calculators, spreadsheets, graphing packages, statistical analysis systems, dynamic geometry systems, and computer algebra systems. In particular, students are encouraged to use graphics calculators, spreadsheets or statistical software in ‘Data analysis’, dynamic geometry systems in ‘Geometry and trigonometry’ and graphics calculators, graphing packages or computer algebra systems in the remaining areas of study, both in the learning of new material and the application of this material in a variety of different contexts. There are two areas of study: 1. Data analysis – core material 2. Applications – module material: Module 1: Number patterns Module 2: Geometry and trigonometry Module 3: Graphs and relations Module 4: Business-related mathematics Module 5: Networks and decision mathematics Module 6: Matrices

Unit 3 Outcomes Outcome 1 On completion of this unit the student should be able to define and explain key terms and concepts as specified in the content from the areas of study, and use this knowledge to apply related mathematical procedures to solve routine application problems. Outcome 2 On completion of this unit the student should be able to use mathematical concepts and skills developed in the ‘Data analysis’ area of study to analyse a practical and extended situation, and interpret and discuss the outcomes of this analysis in relation to key features of that situation. Outcome 3 On completion of this unit the student should be able to select and appropriately use technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches in the area of study ‘Data analysis’ and the selected module from the ‘Applications’ area of study.

Unit 4 Outcomes Outcome 1 On completion of this unit the student should be able to define and explain key terms and concepts as specified in the content from the ‘Applications’ area of study, and use this knowledge to apply related mathematical procedures to solve routine application problems. Outcome 2 On completion of this unit the student should be able to apply mathematical processes in contexts related to the ‘Applications’ area of study, and analyse and discuss these applications of mathematics. Outcome 3 On the completion of this unit the student should be able to select and appropriately use technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches related to the selected modules for this unit from the ‘Applications’ area of study.

Assessment Satisfactory Completion Demonstrated achievement of the set of outcomes specified for the unit.

Levels of Achievement Units 3 and 4 The Victorian Curriculum and Assessment Authority will supervise the assessment of all students undertaking Units 3 and 4. In Mathematics: Further Mathematics the student’s level of achievement will be determined by school-assessed coursework and two end-of-year examinations. Percentage contributions to the study score in Mathematics are as follows: Further Mathematics Unit 3 school-assessed coursework: 20 per cent Unit 4 school-assessed coursework: 14 per cent Units 3 and 4 examination 1: 33 per cent Units 3 and 4 examination 2: 33 per cent

[edit] 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:

[edit] External links

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