Mathematics: Analysis and Approaches (AA) is designed for students who enjoy algebraic manipulation, abstract thinking, and mathematical reasoning. It provides a rigorous foundation in calculus, functions, and proofs, making it an ideal choice for students aiming to study mathematics, engineering, or physical sciences at university. This subject is available at both Standard Level (SL) and Higher Level (HL).
Abstract reasoning and algebraic manipulation
Construction and communication of logical arguments and proofs
Use of calculus in solving theoretical and real-world problems
Mathematical modelling and problem solving
Competence with technology (e.g. GDCs) for investigation and verification
You’ll explore the following topics, with greater depth and complexity at HL:
Number and Algebra – arithmetic sequences, exponents, binomial theorem, logarithms
Functions – function transformations, inverse functions, domain/range, composite functions
Geometry and Trigonometry – radian measure, identities, 3D geometry, circular functions
Statistics and Probability – data analysis, normal distribution, probability
Calculus – limits, derivatives, integration, kinematics
HL students study these topics more rigorously and explore extensions such as advanced calculus, mathematical inductions and proofs.
You’ll also complete an Internal Assessment called the Exploration, a personal mathematical investigation on a topic of your choosing.
Mathematical Exploration (20%)
A written investigation (12–20 pages) where you apply mathematics to a topic that interests you. Assessed on presentation, mathematical reasoning, use of technology, and personal engagement.
Standard Level (SL):
Paper 1 (40%) – No calculator. Short and extended response questions (1 hour 30 mins)
Paper 2 (40%) – Calculator allowed. Similar question types (1 hour 30 mins)
Higher Level (HL):
Paper 1 (30%) – No calculator. Extended questions (2 hours)
Paper 2 (30%) – Calculator allowed. Extended questions (2 hours)
Paper 3 (20%) – Two extended problem-solving questions (1 hour and 15 mins)
This course is recommended for students intending to pursue:
Tertiary Courses: Mathematics, Engineering, Physics, Data Science, Computer Science, Economics
Careers: Engineer, Mathematician, Actuary, Software Developer, Data Analyst, Physicist, Statistician
If you're considering university courses with strong mathematics requirements, especially in the sciences or quantitative fields, AA HL is often preferred or required.