IB Mathematics: Analysis and Approaches exam guide (SL and HL)
Every topic of the current IB Mathematics: analysis and approaches course for May 2027, at SL and HL, mapped to a free lesson and a book chapter, with the papers, the exploration, technology rules, how answers are marked and a 10-week revision plan.
The exam at a glance
May 2027 candidates are assessed on the current course (the guide first assessed in 2021). A new course starts teaching in August 2027 and is first assessed in May 2029, so it does not affect you if you sit in May 2027 or May 2028. At both levels the exams are 80% of the grade and the internal assessment is 20%.
Standard Level 150 teaching hours
| Component | Technology | Time | Marks | Weighting |
|---|---|---|---|---|
| Paper 1 | No technology allowed | 1 hour 30 minutes | 80 | 40% |
| Paper 2 | Technology required (GDC) | 1 hour 30 minutes | 80 | 40% |
| Internal assessment | The exploration | 10–15 hours of class time | 20 | 20% |
Higher Level 240 teaching hours
| Component | Technology | Time | Marks | Weighting |
|---|---|---|---|---|
| Paper 1 | No technology allowed | 2 hours | 110 | 30% |
| Paper 2 | Technology required (GDC) | 2 hours | 110 | 30% |
| Paper 3 | Technology required | Check the May 2027 timetable | 55 | 20% |
| Internal assessment | The exploration | 10–15 hours of class time | 20 | 20% |
Papers 1 and 2 each have Section A (compulsory short-response questions) and Section B (compulsory extended-response questions); at HL each section is worth approximately 55 marks. HL Paper 3 has two compulsory extended-response problem-solving questions. The exploration is a written mathematical report of approximately 12–20 pages long with double line spacing.
What changes from May 2029 (not for May 2027)The new course trims the papers: SL Papers 1 and 2 go from 80 to 75 marks, HL Papers 1 and 2 from 110 to 100 marks, and HL Paper 3 to 50 marks in one hour. Financial applications and bivariate data leave both levels, and HL also loses proof by counterexample and Euler’s method. If you sit in May 2027, revise everything below; the 80/20 split between exams and the exploration stays the same.
What is on the exam, topic by topic
The IB does not publish a weighting for each topic, so each heading shows the recommended teaching hours at SL and HL, which is a fair guide to how much of the course it fills. Rows marked HL are additional higher level content. Each row links to a free step of our Mathematics guide and to the matching chapter of Mathematics Made Simple.
Topic 1: Number and algebra SL 19 hours, HL 39 hours
| Level | What you must know | Learn it here | Chapter in the book |
|---|---|---|---|
| SL | Arithmetic and geometric sequences and series; sigma notation | Sequences, Series and the Binomial Theorem | Chapter 6 |
| SL | Infinite geometric series | Sequences, Series and the Binomial Theorem | Chapter 6 |
| SL | Laws of exponents and logarithms; solving exponential equations | Indices, Surds and Polynomials, Exponentials and Logarithms | Chapters 1 and 5 |
| SL | The binomial theorem for natural n | Sequences, Series and the Binomial Theorem | Chapter 6 |
| HL | Binomial expansion for fractional and negative indices | Sequences, Series and the Binomial Theorem | Chapter 6 |
| HL | Partial fractions | Integration by Parts and Partial Fractions | Chapter 14 |
| HL | Complex numbers: Cartesian, polar and exponential forms | Complex Numbers | Chapter 19 |
| HL | De Moivre’s theorem and roots of complex numbers | Complex Numbers | Chapter 19 |
Topic 2: Functions SL 21 hours, HL 32 hours
| Level | What you must know | Learn it here | Chapter in the book |
|---|---|---|---|
| SL | Equations of straight lines; parallel and perpendicular lines | Lines and Circles | Chapter 4 |
| SL | Functions: domain, range, composite and inverse functions | Functions and Inverses | Chapter 3 |
| SL | Graphs, key features and transformations | Functions and Inverses | Chapter 3 |
| SL | Quadratic functions, the discriminant and inequalities | Quadratics and Inequalities | Chapter 2 |
| SL | Rational functions and asymptotes | Functions and Inverses | Chapter 3 |
| SL | Exponential and logarithmic functions and equations | Exponentials and Logarithms | Chapter 5 |
| HL | Polynomials: factor and remainder theorems, roots | Indices, Surds and Polynomials | Chapter 1 |
| HL | Modulus functions and further inequalities | Quadratics and Inequalities, Functions and Inverses | Chapters 2 and 3 |
Topic 3: Geometry and trigonometry SL 25 hours, HL 51 hours
| Level | What you must know | Learn it here | Chapter in the book |
|---|---|---|---|
| SL | Radians, arc length and sector area | Trigonometry: Radians, Graphs and Equations | Chapter 7 |
| SL | Unit circle, exact values and trigonometric graphs | Trigonometry: Radians, Graphs and Equations | Chapter 7 |
| SL | Pythagorean identity and double-angle identities | Trigonometry: Radians, Graphs and Equations, Trigonometric Identities and the Harmonic Form | Chapters 7 and 8 |
| SL | Solving trigonometric equations in an interval | Trigonometry: Radians, Graphs and Equations | Chapter 7 |
| HL | Reciprocal and inverse trig functions; compound angles | Trigonometric Identities and the Harmonic Form | Chapter 8 |
| HL | Vectors: scalar and vector products, lines and planes | Vectors and Lines in 3D | Chapter 18 |
Topic 4: Statistics and probability SL 27 hours, HL 33 hours
Statistics and probability is covered by our separate Statistics guide, which takes you from describing data through probability, the binomial and normal distributions to regression.
Topic 5: Calculus SL 28 hours, HL 55 hours
Not covered by the Mathematics guideA few parts of topics 1 and 3 are not in our lessons: financial applications, approximation and error, proof (including proof by induction at HL), counting principles, systems of linear equations, 3D solids and the sine and cosine rules. Use your class notes and past papers for these. The remaining 30 hours of the course are for the investigation, problem-solving and modelling skills behind the exploration.
How answers are marked
- Method marks come first. IB mark schemes award marks for a correct method as well as for the correct answer, so show every step you take. A correct answer with no working may not earn full marks, and a wrong answer with a clear method can still score.
- Accuracy marks follow the method. Carry full calculator accuracy through your working and round only at the end, to the accuracy the paper’s instructions ask for.
- Paper 1 is all by hand. No technology is allowed, so practise exact values, surds, fractions and logarithms until they are quick.
- On Paper 2, write down what the GDC did. Technology is required, so use it, but record the equation you solved, the function you graphed or the integral you evaluated before the result. An answer that appears from nowhere is hard to give method marks to.
- Section B questions build. Later parts often use earlier answers. If you are stuck on part (a), use the value given in a “show that” or make a clear assumption and carry on.
- HL Paper 3 rewards reasoning. Its two problem-solving questions lead you through an unfamiliar idea. Explain each step and look for the pattern the early parts are setting up.
Calculators (GDC)
- Paper 1: no technology at either level. Every calculation is by hand.
- Paper 2: technology required at both levels. Bring a graphing display calculator (GDC). Check with your school which models are allowed in May 2027.
- HL Paper 3: technology required. Treat it like Paper 2 for calculator use.
- Know your GDC. Practise solving equations, finding intersections, maxima and minima, numerical derivatives and definite integrals, and switching between degrees and radians.
10-week revision plan
| Week | Focus | Do this |
|---|---|---|
| 1 | Topic 1 | Sequences, series, exponents, logs and the binomial theorem. HL: complex numbers. |
| 2 | Topic 2 | Functions, transformations, quadratics and rational functions. HL: polynomials and modulus. |
| 3 | Topic 3 | Radians, trigonometric graphs, identities and equations. HL: vectors, lines and planes. |
| 4 | Topic 4 | Probability and distributions with the Statistics guide; normal distribution on the GDC. |
| 5 | Topic 5, SL | Limits, derivative rules, tangents and normals, stationary points. |
| 6 | Topic 5, SL | Optimisation, kinematics, integration and area between curves. |
| 7 | Topic 5, HL | First principles, L’Hôpital, implicit differentiation and related rates. |
| 8 | Topic 5, HL | Substitution and parts, volumes, differential equations and Maclaurin series. |
| 9 | Paper 1 | Timed Paper 1s with no calculator, marked against the mark scheme. |
| 10 | Papers 2 and 3 | Timed Paper 2s with the GDC; HL students add a Paper 3 every other day. |
Common mistakes that cost marks
Common mistakeWriting only a GDC answer on Paper 2, with no indication of the equation or integral used.
Common mistakeLeaving the calculator in degrees for a calculus question in radians.
Common mistakeDropping \( +C \), or forgetting to use the initial condition, in an indefinite integral or differential equation.
Common mistakeRounding early, so the final answer is outside the accepted range.
Common mistakeNot checking an answer against the domain, for example a negative length or a logarithm of a negative number.
Ready to practise at exam level?
Mathematics Made Simple covers algebra, functions and calculus for AP, Cambridge and IB in 20 chapters, with worked examples and full worked answers. The practice book adds exam-style questions for every chapter.
Further reading
More free material for this exam: