IB Math AA HL Notes

Mathematics: Analysis and Approaches

Aimnova provides free IB Math AA HL revision notes aligned to the current syllabus, covering all five units plus the HL-only extensions — complex numbers and De Moivre’s theorem, vectors, proof by induction and contradiction, and further calculus including Maclaurin series, L’Hôpital’s rule and differential equations.

Math AA HL extends the SL course with greater algebraic rigour, a heavier calculus load, and a dedicated Paper 3 problem-solving investigation. Paper 1 remains non-calculator, so exact methods and proof technique are essential.

Use the structured unit list below to revise systematically and ensure every HL-only topic is covered before Papers 1, 2 and 3.

What's included

Unit-by-unit Math AA notes mapped to the IB syllabus
Worked examples that show full method for the non-calculator Paper 1
Linked flashcards for spaced revision of key formulas and definitions
Exam Vault practice aligned to command terms and mark-scheme logic
SL and HL coverage with level toggle
Free to access — no account required for notes

How to use Math AA HL notes

1Start with a unit overview. Click any Unit heading to see every topic and the key methods it covers.
2Read micro-topic notes. Read one micro-topic at a time and follow the full worked method, not just the result.
3Test with flashcards. Use Math AA flashcards to keep formulas, exact values and proof steps fresh.
4Practise exam questions. Practise in Exam Vault and check where method marks are lost before the final line.

Unit 1

1.1Standard form

1.2Arithmetic sequences & series

1.3Geometric sequences & series

1.4Financial applications

1.7Exponent & log laws

1.8Infinite geometric series

1.9Binomial theorem

1.10Counting & binomial (HL only)

1.11Partial fractions (HL only)

1.12Complex numbers: Cartesian (HL only)

1.13Complex numbers: polar (HL only)

1.14De Moivre & roots (HL only)

1.15Proof by induction (HL only)

1.16Systems of equations (HL only)

Unit 2

2.1Straight lines

2.2Functions, domain & range

2.4Key features of graphs

2.5Composite & inverse functions

2.6Quadratic functions

2.7Quadratic equations & discriminant

2.8Rational functions & asymptotes

2.9Exponential & log functions

2.10Solving equations

2.11Transformations

2.12Factor & remainder (HL only)

2.13Rational functions (HL only)

2.14Odd, even & self-inverse (HL only)

2.15Inequalities (HL only)

2.16Modulus functions (HL only)

Unit 3

3.2Sine & cosine rules

3.3Bearings & elevation

3.4Radians, arcs & sectors

3.5Unit circle & exact values

3.6Identities & double angles

3.7Trig graphs & transformations

3.8Trig equations

3.9Reciprocal & inverse trig (HL only)

3.10Compound angles (HL only)

3.11Trig relationships (HL only)

3.12Vectors (HL only)

3.13Scalar product (HL only)

3.14Vector lines (HL only)

3.15Classifying lines (HL only)

3.16Vector product (HL only)

3.17Vector planes (HL only)

3.18Lines & planes (HL only)

Unit 4

4.1Sampling & reliability

4.2Data presentation

4.3Central tendency & spread

4.4Correlation & regression

4.5Probability basics

4.6Combined & conditional events

4.7Discrete random variables

4.8Binomial distribution

4.9Normal distribution

4.10Regression & prediction

4.11Conditional probability

4.12z-values & inverse normal

4.13Bayes' theorem (HL only)

4.14Continuous random variables (HL only)

Unit 5

5.1Introduction to derivatives

5.2Increasing & decreasing

5.3Differentiating polynomials

5.4Tangents & normals

5.5Introduction to integration

5.6Chain, product & quotient

5.7Second derivative

5.8Optimisation & inflexion

5.10Integration by substitution

5.11Definite integrals & areas

5.12First principles (HL only)

5.13Limits & l'Hopital (HL only)

5.14Implicit & related rates (HL only)

5.15Further calculus (HL only)

5.16Integration by parts (HL only)

5.17Volumes of revolution (HL only)

5.18Differential equations (HL only)

5.19Maclaurin series (HL only)

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