IB Mathematics: Analysis and Approaches

Course notes for SL and HL

These notes follow the IB Diploma Programme course Mathematics: Analysis and Approaches (SL and HL). Each section explains one idea, works through examples step by step, and ends with about ten practice questions. Every solution is hidden until you click it — try the question first.

How to read the labels

• SL 1.5 — content for both SL and HL students
• AHL 1.10 — HL only (Additional Higher Level)
• Extension — beyond the syllabus; read it if you are curious

Units in teaching order

Grade 11 — Term 1

• Unit 1 — Exponents and Logarithms
• Unit 2 — Sequences and Series
• Unit 3 — Partial Fractions HL only
• Unit 4 — The Binomial Theorem
• Unit 5 — Counting Principles HL only
• Unit 6 — Mathematical Proofs

Grade 11 — Term 2

• Unit 7 — Linear Functions
• Unit 8 — Quadratic Functions
• Unit 9 — Functions
• Unit 10 — Further Functions
• Unit 11 — Polynomials and Inequalities HL only
• Unit 12 — Graph Transformations

Grade 11 — Term 3

• Unit 14 — Trigonometric Functions
• Unit 15 — Statistics
• Unit 17 — Correlation and Regression

Grade 11 — Term 4

• Unit 24 — Differentiation Techniques
• Unit 25 — Applications of Differentiation

Grade 12 — Term 1

• Unit 27 — Integration Techniques
• Unit 28 — Applications of Integration
• Unit 29 — Kinematics
• Unit 26 — Limits HL only
• Unit 30 — Maclaurin Series HL only
• Unit 31 — Differential Equations HL only

Grade 12 — Term 2

• Unit 16 — Probability
• Unit 18 — Discrete Random Variables and the Binomial Distribution
• Unit 19 — Continuous Random Variables and the Normal Distribution
• Unit 23 — Complex Numbers HL only
• Unit 20 — Vectors I HL only
• Unit 21 — Vectors II HL only
• Unit 22 — Vectors III HL only
• Unit 32 — Systems of Linear Equations HL only