IB Mathematics

Complete revision notes for IB Mathematics, covering the full syllabus with worked examples, common pitfalls, and exam-style problems.

Core Topics

Number and Algebra

• Number and Algebra — Sequences, series, binomial theorem, and proof by induction
• Complex Numbers — Complex arithmetic, polar form, and De Moivre”s theorem
• Complex Numbers (Overview) — Complex arithmetic, polar form, De Moivre’s theorem, and roots of unity

Functions and Equations

• Functions and Equations — Functions, composite functions, inverse functions, transformations, and equations
• Sequences and Series — Arithmetic and geometric sequences and series, sigma notation, and binomial theorem

Geometry and Trigonometry

• Trigonometry — Trigonometric functions, identities, equations, and the unit circle
• Vectors — Vector algebra and geometry in two and three dimensions

Calculus

• Calculus — Limits, differentiation, integration, and their applications
• Differentiation — Differentiation rules, techniques, and applications
• Integration Techniques — Integration techniques, definite integrals, area and volume, and applications
• Integration — Further integration methods and applications
• Differential Equations — First order separable equations, integrating factors, and second order equations
• Sequences and Series (Calculus) — Maclaurin and Taylor series, convergence, and the binomial theorem

Probability and Statistics

• Probability — Probability theory, conditional probability, Bayes’ theorem, and distributions
• Statistics — Descriptive statistics, correlation, regression, and hypothesis testing
• Statistics (Overview) — Descriptive statistics, correlation, regression, conditional probability, and permutations and combinations

Vectors and Matrices

• Vectors in Three Dimensions — Vector operations, dot and cross products, equations of lines and planes, and shortest distances
• Matrices and Linear Transformations — Matrix operations, determinants, inverses, solving systems, and eigenvalues
• Complex Numbers (Advanced) — Cartesian and polar form, De Moivre’s theorem, roots of unity, and Euler’s formula

Proof and Logic

• Proof — Direct proof, contradiction, induction, counterexamples, and proof by exhaustion
• Proof and Logic — Logical reasoning and proof techniques
• Logic — Propositional and predicate logic

Exam Resources

Related Content

• A-Level Maths: A-Level Maths
• DSE Maths: DSE Maths
• University Maths: University Maths

Common Pitfalls

1. Misreading the question, particularly with ‘hence’ vs ‘hence or otherwise’ — the former requires using previous work.

2. Cancelling terms instead of factors — $\frac{ab + ac}{a}$ simplifies to $b + c$, not $bc$.

Overview

This section provides comprehensive Ib Maths content, covering all specification points with detailed explanations, worked examples, and practice questions.

Content Structure

Each page in this section includes:

• Definitions: Clear, precise explanations of key concepts
• Worked Examples: Step-by-step solutions with annotations
• Practice Questions: Examination-style questions with detailed solutions
• Common Pitfalls: Errors to avoid and how to fix them
• Exam Tips: Strategies for maximising marks

How to Use These Notes

1. Read the introductory page to understand the topic overview
2. Work through each sub-topic in order
3. Attempt the practice questions before checking solutions
4. Use the flashcards to revise key terminology
5. Complete the diagnostic test to identify remaining gaps

Key Topics

• Core definitions and principles
• Application to examination-style questions
• Links to related topics across the specification
• Assessment objective alignment

Revision Strategies

• Active Recall: Test yourself regularly rather than re-reading notes
• Spaced Practice: Revisit this topic at increasing intervals
• Interleaving: Mix with other topics during revision sessions
• Elaboration: Explain concepts in your own words

Exam Preparation

Focus on command word interpretation and mark scheme analysis. Practice timing yourself on questions to build speed and accuracy. Review examiner reports for this topic to understand common student errors.