IB DP Mathematics: Analysis and Approaches (AA) is designed for students who enjoy developing mathematical arguments, proof, and exploring real and abstract applications. It emphasises algebraic methods and calculus.
SL (150 hours): 5 topics — number & algebra, functions, geometry & trigonometry, statistics & probability, calculus. HL (240 hours): extends all 5 topics significantly — complex numbers, proof by induction, further calculus (Maclaurin series, differential equations), vectors, and further statistics. Assessment: Paper 1 (no calculator), Paper 2 (calculator allowed), Paper 3 (HL only — problem-solving). Internal Assessment: mathematical exploration (20%).
Algebra: sequences, series, binomial theorem, logarithms. Functions: domain, range, composite, inverse, transformations. Trigonometry: unit circle, identities, solving equations. Calculus: limits, differentiation (chain, product, quotient rules), integration, applications (optimisation, area, volume). Statistics: probability distributions, binomial, normal, hypothesis testing.
A 12–20 page investigation into a mathematical topic of the student's choice. Assessed on: presentation, mathematical communication, personal engagement, reflection, and use of mathematics. Popular topics: modelling population growth, Fibonacci in nature, optimisation problems, cryptography, fractals.
Choose AA if you enjoy abstract mathematics, proof, and algebra, or plan to study maths, physics, engineering, or computer science at university. Choose AI (Applications and Interpretation) if you prefer data-driven, technology-assisted maths and plan to study business, social sciences, or design. Both SL and HL are available for each course.
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