BetterMath Notes & resources

Notes & resources

The complete notes, the answers, and other resources for IB Mathematics AA HL.

Cover of BetterMath: Mathematics, Analysis & Approaches, Higher Level. Fourth edition · October 2026.

The notes

Every chapter is free to read or download. The book and the workbook come after one short form.

All 17 chapters are out now. Higher Level content is marked throughout.

Syllabus mapEvery AA HL syllabus point, and the chapter that teaches it

BetterMath Notes Online

All 17 chapters to read online, or download each one
Start hereHow to read these notes · contents · symbols and notationRead

Number & Algebra3 chapters

1Exponents & Logarithms1.1, 1.5, 1.7 · 37 ppWhat an exponent counts, standard form, logarithms as exponents reversed, the laws of logarithms, and solving exponential equations.Open
2Sequences & Series1.2–1.4, 1.8–1.10 · 57 ppArithmetic and geometric sequences and series, sigma notation, infinite geometric series, financial applications, counting principles and the binomial theorem.Open
3Proofs1.6, 1.15 · 36 ppDeductive proof, disproof by counterexample, proof by contradiction and proof by induction.Open

Functions3 chapters

4Lines & Quadratics1.16, 2.1–2.4, 2.6, 2.7 · 53 ppFunctions, linear functions and simultaneous linear equations, quadratic functions, equations and inequalities, and the discriminant.Open
5Functions & Graphs2.5, 2.8–2.11, 2.13–2.16 · 73 ppComposite and inverse functions, transformations and symmetry of graphs, reciprocal and rational functions, and exponential and logarithmic functions.Open
6Polynomials1.11, 2.12 · 38 ppPolynomial graphs and division, the remainder and factor theorems, solving polynomial equations, the sum and product of roots, and partial fractions.Open

Geometry & Trigonometry3 chapters

7Shapes & Measures3.1–3.4 · 40 ppThree-dimensional geometry, volumes and surface areas, the sine and cosine rules, elevation, depression and bearings, and radians, arc length and sector area.Open
8Trigonometry3.5–3.11 · 50 ppThe unit circle, trigonometric identities and graphs, reciprocal and inverse trigonometric functions, and solving trigonometric equations.Open
9Vectors3.12–3.18 · 53 ppMagnitude and direction, position vectors, the scalar and vector products, vector equations of lines and planes, and distances in three dimensions.Open

Statistics & Probability3 chapters

10Statistics4.1–4.4, 4.10 · 49 ppSampling and data, measures of central tendency and dispersion, visualising distributions, correlation and linear regression.Open
11Probability4.5, 4.6, 4.11, 4.13 · 44 ppThe language of probability, counting outcomes, combined events, conditional probability and independence, tree diagrams and Bayes' theorem.Open
12Probability Distributions4.7–4.9, 4.12, 4.14 · 43 ppDiscrete and continuous random variables, expected value and variance, the binomial and normal distributions, standardisation and the inverse normal.Open

Calculus4 chapters

13Limits & Derivatives5.1–5.4, 5.6–5.8, 5.12, 5.13, 5.15 · 48 ppLimits, the derivative, differentiating powers and the standard functions, the rules of differentiation, tangents and normals, higher derivatives and L'Hôpital's rule.Open
14Derivative Applications5.8, 5.9, 5.14 · 44 ppStationary points and points of inflexion, optimisation, kinematics, implicit differentiation and related rates.Open
15Integral Calculus5.5, 5.9–5.11, 5.15–5.17 · 61 ppAntiderivatives and definite integrals, standard integrals, substitution and integration by parts, areas between curves, volumes of revolution and kinematics.Open
16Differential Equations5.18, 5.19 · 39 ppSeparable and homogeneous equations, the integrating factor, Maclaurin series and Euler's method.Open

Number & Algebra1 chapter

17Complex Numbers1.12–1.14 · 42 ppCartesian and modulus–argument form, roots of complex numbers, and trigonometric identities from De Moivre's theorem.Open
BetterMath: the complete book, with answersAll 17 chapters with the answers bound in · 842 pp · 3.7 MB · download for freeWorkbookEvery question in the notes, with room to work · 712 pp · 1.8 MB · free to download

Practice worksheets

For teachers only, on request

These sheets are for teachers to use in class. If you would like them, send me your details and I will do my best to share them with you. I share them where I can, so I cannot promise to meet every request.

  • The complete practice worksheets, all 17 chaptersTo use in class, with answers at the end of each sheet

Prefer email? Write to ibxhasan@gmail.com.

Request the worksheets

I will do my best to reply by email. Your details are never shared or sold.

What the worksheets cover

Open a chapter to see its sheets
1Exponents & Logarithms5 sheets
  • 1.1Exponents and Surds31 questions · 2 pp
  • 1.2Standard Form29 questions · 2 pp
  • 1.3The Logarithm29 questions · 2 pp
  • 1.4The Laws of Logarithms26 questions · 2 pp
  • 1.5Solving Exponential Equations23 questions · 2 pp
2Sequences & Series10 sheets
  • 2.1Arithmetic Sequences24 questions · 2 pp
  • 2.2Arithmetic Series21 questions · 2 pp
  • 2.3Geometric Sequences25 questions · 2 pp
  • 2.4Geometric Series19 questions · 2 pp
  • 2.5Sigma Notation21 questions · 2 pp
  • 2.6Infinite Geometric Series20 questions · 2 pp
  • 2.7Financial Applications11 questions · 2 pp
  • 2.8Counting Principles23 questions · 2 pp
  • 2.9The Binomial Theorem23 questions · 2 pp
  • 2.10The Binomial Series18 questions · 2 pp
3Proofs4 sheets
  • 3.1Deductive Proof20 questions · 2 pp
  • 3.2Disproof by Counterexample20 questions · 2 pp
  • 3.3Proof by Contradiction16 questions · 2 pp
  • 3.4Proof by Induction16 questions · 2 pp
4Lines & Quadratics6 sheets
  • 4.1Functions23 questions · 2 pp
  • 4.2Linear Functions21 questions · 2 pp
  • 4.3Systems of Linear Equations20 questions · 2 pp
  • 4.4Quadratic Functions and Equations50 questions · 4 pp
  • 4.5Quadratic Inequalities20 questions · 2 pp
  • 4.6The Discriminant24 questions · 2 pp
5Functions & Graphs5 sheets
  • 5.1Composite Functions23 questions · 2 pp
  • 5.2Transformations of Graphs23 questions · 2 pp
  • 5.3Symmetry and Related Graphs22 questions · 2 pp
  • 5.4Reciprocal and Rational Functions21 questions · 2 pp
  • 5.5Exponential and Logarithmic Functions23 questions · 2 pp
6Polynomials6 sheets
  • 6.1Polynomial Functions and their Graphs23 questions · 2 pp
  • 6.2Polynomial Division24 questions · 2 pp
  • 6.3The Remainder and Factor Theorems24 questions · 2 pp
  • 6.4Solving Polynomial Equations23 questions · 2 pp
  • 6.5Sum and Product of Roots24 questions · 2 pp
  • 6.6Partial Fractions24 questions · 2 pp
7Shapes & Measures5 sheets
  • 7.1Three-Dimensional Geometry34 questions · 4 pp
  • 7.2Volumes and Surface Areas of Solids36 questions · 4 pp
  • 7.3The Sine and Cosine Rules39 questions · 4 pp
  • 7.4Elevation, Depression and Bearings36 questions · 4 pp
  • 7.5Radians, Arc Length, and Sector Area43 questions · 4 pp
8Trigonometry6 sheets
  • 8.1The Unit Circle47 questions · 4 pp
  • 8.2Trigonometric Identities43 questions · 4 pp
  • 8.3Graphs of Trigonometric Functions36 questions · 4 pp
  • 8.4Reciprocal Trigonometric Functions22 questions · 2 pp
  • 8.5Inverse Trigonometric Functions23 questions · 2 pp
  • 8.6Solving Trigonometric Equations37 questions · 4 pp
9Vectors7 sheets
  • 9.1Vectors: Magnitude and Direction21 questions · 2 pp
  • 9.2Position Vectors and Geometry18 questions · 2 pp
  • 9.3The Scalar Product19 questions · 2 pp
  • 9.4The Vector Equation of a Line35 questions · 4 pp
  • 9.5The Vector Product19 questions · 2 pp
  • 9.6Planes34 questions · 4 pp
  • 9.7Distances33 questions · 4 pp
10Statistics6 sheets
  • 10.1Sampling and Data21 questions · 2 pp
  • 10.2Measures of Central Tendency18 questions · 2 pp
  • 10.3Measures of Dispersion22 questions · 2 pp
  • 10.4Visualising Distributions33 questions · 4 pp
  • 10.5Correlation36 questions · 4 pp
  • 10.6Linear Regression19 questions · 2 pp
11Probability6 sheets
  • 11.1The Language of Probability18 questions · 2 pp
  • 11.2Counting the Outcomes21 questions · 2 pp
  • 11.3Combining Events40 questions · 4 pp
  • 11.4Conditional Probability and Independence18 questions · 2 pp
  • 11.5Tree Diagrams34 questions · 4 pp
  • 11.6Bayes’ Theorem32 questions · 4 pp
12Probability Distributions6 sheets
  • 12.1Discrete Random Variables19 questions · 2 pp
  • 12.2Expected Value and Variance21 questions · 2 pp
  • 12.3The Binomial Distribution19 questions · 2 pp
  • 12.4Continuous Random Variables34 questions · 4 pp
  • 12.5The Normal Distribution35 questions · 4 pp
  • 12.6Standardisation and the Inverse Normal36 questions · 4 pp
13Limits & Derivatives8 sheets
  • 13.1Limits22 questions · 2 pp
  • 13.2The Derivative16 questions · 2 pp
  • 13.3Differentiating Powers26 questions · 2 pp
  • 13.4Tangents and Normals20 questions · 2 pp
  • 13.5The Standard Derivatives27 questions · 2 pp
  • 13.6The Rules of Differentiation27 questions · 2 pp
  • 13.7Higher Derivatives22 questions · 2 pp
  • 13.8L’Hôpital’s Rule22 questions · 2 pp
14Derivative Applications6 sheets
  • 14.1Stationary Points and Their Nature19 questions · 2 pp
  • 14.2Points of Inflexion19 questions · 2 pp
  • 14.3Optimisation15 questions · 2 pp
  • 14.4Kinematics20 questions · 2 pp
  • 14.5Implicit Differentiation18 questions · 2 pp
  • 14.6Related Rates16 questions · 2 pp
15Integral Calculus9 sheets
  • 15.1Definite Integrals39 questions · 4 pp
  • 15.1Antiderivatives24 questions · 2 pp
  • 15.2Standard Integrals25 questions · 2 pp
  • 15.3Rewriting Before Integrating20 questions · 2 pp
  • 15.4Integration by Substitution19 questions · 2 pp
  • 15.5Integration by Parts12 questions · 2 pp
  • 15.6Areas37 questions · 4 pp
  • 15.7Volumes of Revolution36 questions · 4 pp
  • 15.8Kinematics by Integration17 questions · 2 pp
16Differential Equations5 sheets
  • 16.1Separable Variables20 questions · 2 pp
  • 16.2Homogeneous Differential Equations19 questions · 2 pp
  • 16.3The Integrating Factor19 questions · 2 pp
  • 16.4Maclaurin Series39 questions · 4 pp
  • 16.5Euler’s Method35 questions · 4 pp
17Complex Numbers5 sheets
  • 17.1Cartesian Form21 questions · 2 pp
  • 17.2Modulus and Argument47 questions · 4 pp
  • 17.3Products, Quotients and22 questions · 2 pp
  • 17.4Roots of Complex Numbers41 questions · 4 pp
  • 17.5Trigonometric Identities from De Moivre17 questions · 2 pp

How each chapter works

  • Notes that explain whyEach idea starts from why it is true, with a fully worked example.
  • Formula booklet markedResults printed in the IB formula booklet are flagged.
  • Your Turn, every sectionPractice straight after each idea, while it is fresh.
  • Tips and cautionsExam craft, and mistakes worth avoiding.
  • Exam-style problemsPaper 1 and Paper 2 style questions to end each chapter.
  • Challenge QuestionsPaper 3 style; good starting points for the Internal Assessment.
  • ReflectionsTheory of Knowledge, history, real-world uses and enrichment.
  • Without compromiseFull Higher Level depth, with nothing simplified away.

Coming later

Still in progress, and tried in class first. Each will be shared once it is ready.

  • Practice worksheets
  • Markschemes
  • Lesson slides
  • Paper 3 practice investigations
  • Exploration starter guide
  • Worked exploration ideas

The book and the workbook

One form for both

Please fill out this form to get the book and the workbook.

  • BetterMath, fourth editionAll 17 chapters with the answers bound in · 842 pages · 3.7 MB
  • BetterMath WorkbookEvery question in the notes, with room to work · 712 pages · 1.8 MB

Before you download

Your details are never shared or sold.