IB Diploma Programme (DP) – Mathematics

Complete guide to Analysis & Approaches (AA) and Applications & Interpretation (AI) at SL & HL.
IB DP Mathematics develops reasoning, modelling, communication, and advanced problem-solving skills.

IB DP Mathematics Pathways
  • Mathematics: Analysis & Approaches (AA) – Algebra, calculus, proofs, and abstract reasoning.
  • Mathematics: Applications & Interpretation (AI) – Statistics, modelling, technology-based problem solving.
Choosing the Right Maths Course
  • AA: Engineering, Physics, Mathematics, Computer Science, Economics.
  • AI: Business, Psychology, Social Sciences, Design, Environmental Studies.

Important: Many universities do not accept AI SL for STEM degrees.

Assessment Structure (All DP Maths Courses)
Component Focus Weightage Format
Paper 1 Pure mathematics ≈80% Short & extended response (no calculator for AA)
Paper 2 Applied problem solving Calculator allowed
Paper 3 (HL) Depth & reasoning Complex multi-step questions
Internal Assessment Mathematical Exploration ≈20% Independent investigation (12–20 pages)
Core Assessment Objectives
Skill Description Where Assessed Key Focus
Knowledge Correct use of concepts and methods All papers Accuracy
Problem Solving Applying maths to unfamiliar contexts Papers 2 & 3 Logical structure
Communication Clear explanation and notation All components Clarity
Technology Effective calculator and software use AI & IA Interpretation
Reasoning & Proof Justification and logical flow AA (especially HL) Proof writing
Mathematics: Analysis & Approaches (AA)
Level Key Topics Expectations Preparation Strategy
AA SL – Curriculum Breakdown
  • Number & Algebra
  • Functions
  • Geometry & Trigonometry
  • Statistics & Probability
  • Introductory Calculus
  • Manipulate algebraic expressions accurately
  • Solve equations and inequalities
  • Understand functions graphically and algebraically
  • Apply basic differentiation techniques
  • Communicate solutions clearly using correct notation
  • Master algebraic fluency early
  • Practise non-calculator questions regularly
  • Focus on showing full working and method marks
  • Memorise key identities and formulas
AA HL
  • Proof by induction
  • Complex numbers
  • Advanced functions
  • Differential and integral calculus
  • Series and sequences
  • Vector geometry
  • Probability distributions
  • Demonstrate abstract reasoning
  • Solve complex, multi-step problems
  • Write clear proof-based responses
  • Link multiple topics within a single question
  • Daily practice of mixed-topic questions
  • Learn formal proof language (therefore, hence, let, assume)
  • Solve Paper 3–style problems weekly
  • Focus on precision, structure, and logical flow
Mathematics: Applications & Interpretation (AI)
Level Key Topics Expectations Preparation Strategy
AI SL
  • Statistics and probability
  • Functions and modelling
  • Financial mathematics
  • Geometry in real-world contexts
  • Use of technology (GDC)
  • Interpret data, tables, and graphs accurately
  • Model real-world situations mathematically
  • Use the calculator effectively
  • Communicate conclusions clearly in context
  • Practise data interpretation regularly
  • Learn calculator functions in depth
  • Focus on explaining results in words, not just numbers
  • Connect mathematical concepts to real-life examples
AI HL
  • Statistical distributions
  • Hypothesis testing
  • Differential equations (modelling focus)
  • Advanced financial models
  • Complex data modelling
  • Apply strong statistical reasoning
  • Interpret large and complex datasets
  • Justify assumptions made in models
  • Evaluate limitations and reliability of results
  • Master statistics terminology and command terms
  • Practise writing clear conclusions
  • Evaluate validity and reliability of mathematical models
  • Link mathematics to social, business, and economic contexts
Internal Assessment (IA)
  • Personal engagement and originality
  • Appropriate mathematical depth
  • Clear structure and reflection
  • Correct notation, graphs, and technology use
IA Timeline
Stage Timeline
Topic Selection Early DP Year 1
Draft Exploration Mid DP Year 1
Feedback & Revision End of DP Year 1
Final Submission Early DP Year 2
Exam Technique & Revision Strategy
  • Daily mixed practice (30–45 minutes)
  • Weekly timed exam sections
  • Error log and reflection
  • Past paper and mark scheme analysis
Common Mistakes Students Make
  • Treating Mathematics as memorisation rather than understanding concepts
  • Skipping explanations and losing method marks
  • Ignoring command terms such as show, prove, justify
  • Weak calculator skills, especially in AI courses
  • Starting the Internal Assessment (IA) too late
Skills DP Mathematics Builds (University Readiness)
Skill Where It’s Developed
Logical reasoning Proofs, derivations, and structured arguments
Data literacy Statistics, probability, and mathematical modelling
Academic writing Internal Assessment explanations and reflections
Problem solving Paper 2 and Paper 3 extended-response questions
Time management Long exam papers with multi-step questions
How Parents Can Support
  • Help choose the correct course (AA vs AI)
  • Encourage consistency over cramming
  • Support IA planning early
  • Help manage exam stress