Mathematics: Analysis and Approaches · IB HL
IB Mathematics: Analysis and Approaches HL — papers & markbands
No calculator (Paper 1), calculator allowed (Paper 2) and — at HL — an extended problem-solving paper (Paper 3). Below are the papers you'll sit and how examiners award marks. Practise past papers, learn the markbands, then check your own answers for feedback.
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Mathematics: Analysis and Approaches HL chapters
43 topics · free- 1.1Sequences and series: arithmetic and geometric
- 1.2Exponents and logarithms
- 1.3The binomial theorem
- 1.4Counting principles, permutations and combinations
- 1.5Proof: induction, contradiction and counterexample
- 1.6Complex numbers: Cartesian, polar and Euler form
- 1.7Complex numbers: De Moivre's theorem and roots
- 1.8Systems of linear equations
- 2.1Linear functions and equations of straight lines
- 2.2Functions: domain, range, composite and inverse
- 2.3Quadratic functions and equations
- 2.4Transformations of graphs
- 2.5Rational functions and their graphs
- 2.6Exponential and logarithmic functions
- 2.7Polynomial functions, factor and remainder theorems
- 2.8Solving equations and inequalities; modulus functions
- 3.1Geometry of 3D solids: volume and surface area
- 3.2Trigonometry: sine and cosine rules
- 3.3The unit circle and radian measure
- 3.4Trigonometric functions and their graphs
- 3.5Trigonometric identities and equations
- 3.6Compound and double angle identities; inverse trig
- 3.7Vectors: properties and operations
- 3.8Vector equations of lines
- 3.9Scalar and vector products; planes
- 4.1Descriptive statistics
- 4.2Bivariate data: correlation and linear regression
- 4.3Probability, Venn diagrams and tree diagrams
- 4.4Discrete random variables and expected value
- 4.5The binomial distribution
- 4.6The normal distribution
- 4.7Conditional probability and Bayes' theorem
- 4.8Continuous random variables and probability density functions
- 5.1Limits and differentiation from first principles
- 5.2Differentiation rules: chain, product and quotient
- 5.3Tangents, normals and the second derivative
- 5.4Optimization and kinematics
- 5.5Integration as antidifferentiation
- 5.6Definite integrals: areas and volumes of revolution
- 5.7Further differentiation: implicit, related rates and L'Hopital
- 5.8Integration techniques: substitution, by parts and partial fractions
- 5.9Differential equations and slope fields
- 5.10Maclaurin series
Papers in Mathematics: Analysis and Approaches HL
- Paper 1HL
Practise this paper under timed conditions, then mark against the band descriptors.
- Paper 2HL
Drill the question style, then review the markbands to push into the top band.
- Paper 3HL
Drill the question style, then review the markbands to push into the top band.
How IB marking differs
Unlike point-based A-Level mark schemes, IB uses markbands — examiners place your answer in a level band against descriptors. Knowing the band wording is how you turn a 5 into a 7.
Check your work
Upload a photo of your answer and get structured, criteria-based feedback on where the marks are.
Get feedback →Frequently asked questions
- What papers are in IB Mathematics: Analysis and Approaches HL?
- IB Mathematics: Analysis and Approaches at HL is assessed by Paper 1, Paper 2, Paper 3, plus internal assessment. No calculator (Paper 1), calculator allowed (Paper 2) and — at HL — an extended problem-solving paper (Paper 3).
- How is IB Mathematics: Analysis and Approaches marked?
- IB uses markbands and assessment criteria rather than point-based A-Level marking codes — examiners place your response in a level band against descriptors. Our guides show what separates the top band from the middle on each paper.
- Where can I find IB Maths AA HL past papers?
- Browse every recent Mathematics: Analysis and Approaches HL exam series on our IB Maths AA past-papers page, organised by session and paper, with mark-scheme guidance for each.
- Is there a free IB Mathematics: Analysis and Approaches course?
- Yes — MarkScheme has a free topic-by-topic IB Mathematics: Analysis and Approaches course with worked examples, flashcards, and criterion practice marking on every syllabus point.
Best free IB Mathematics: Analysis and Approaches resources
Hand-picked, fully legal and free — official IB papers plus the best teacher-made notes and solutions.