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Mathematics (Syllabus A) (Mauritius) — Yes — Mauritius only — CIE 4024 Mathematics (Syllabus D) Yes Yes Yes Cannot be combined with syllabuses 0580 & 0581 , 4021, 4026 & 4029 (O Level) link: CIE 4026 Mathematics (Syllabus E) (Brunei) — Yes — Brunei only; last exam in 2010 — CIE 4029 Mathematics (Syllabus D) (Mauritius) No Yes Yes
Most IGCSE subjects offer a choice of tiered examinations: Core or Extended papers (in Cambridge International), and Foundation or Higher papers (in Edexcel). This is designed to make IGCSE suitable for students with varying levels of ability. In some subjects, IGCSE can be taken with or without coursework.
Further Mathematics, as studied within the International Baccalaureate Diploma Programme, was a Higher Level (HL) course that could be taken in conjunction with Mathematics HL or on its own. It consisted of studying all four of the options in Mathematics HL, plus two additional topics. Topics studied in Further Mathematics included: [9]
The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.