**Course Description and Aims:** The Mathematics: analysis and approaches course is broken into the following sections:â€¯ Number and Algebra; Functions; Geometry and Trigonometry; Statistics and Probability; Calculus.â€¯â€¯â€¯

This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL.

The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of choice of course. However, Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

**Higher Level Distinction**â€¯

The Higher Level course covers all of the same core material as the Standard Level course plus additional Higher Level content.

The HL course extends this is several key areas including:â€¯

- Number and Algebra â€“ mathematical proof, complex numbers, permutations, and combinations.
- Functions â€“ polynomial, rational and absolute value functions.
- Geometry and Trigonometry â€“ reciprocal trigonometric functions and vectors.
- Statistics and Probability â€“ continuous random variables
- Calculus â€“ differentiation by first principles, limits, integration techniques and Maclaurin series.

**Assessment:**â€¯

**External Assessment (**80% SL, 80% HL)â€¯

Examination Paper 1 (40% SL, 30% HL): A combination of short answer and extended response questions on course content. Paper 1 is completed without the use of a graphics calculator.

Examination Paper 2 (40% SL, 30% HL): A combination of short answer and extended response questions on course content. Paper 2 is completed with access to a graphics calculator.

Examination Paper 3 (HL only, 20%): Two extended response problem-solving questions. Paper 3 is completed with access to a graphics calculator. â€¯â€¯

**Internal Assessment (**20% SL, 20% HL)â€¯

The internal assessment (IA) is an exploration task into a mathematical topic chosen by the student. The task is submitted as a report and is 12 â€“ 20 pages in length (with double line spacing).