Independent study guide · Updated 4 October 2026
IB Past Papers & Study Resources
Find your IB Mathematics course, choose the right revision materials, and practise with a clear plan. This hub brings together AA and AI notes, exercises, worked solutions and historical paper links. Start with your course and examination session before using the resource catalogue below.
Choose the right course and resources
IB Diploma Programme Mathematics has two courses, each offered at Standard Level (SL) and Higher Level (HL). Both involve functions, calculus and mathematical reasoning. The emphasis and required content differ.
| Course | Typical emphasis | How to use this hub |
|---|---|---|
| Analysis and approaches (AA) | Algebraic reasoning, mathematical argument and analysis | Use AA resources at your level. Practise symbolic working as well as technology-supported questions. |
| Applications and interpretation (AI) | Modelling, statistics and interpreting mathematics in context | Use AI resources at your level. Explain assumptions, calculator output, units and what the result means. |
SL and HL are not interchangeable. HL includes additional depth and content. In the legacy catalogue, “AHL” means additional higher-level material, “MAA” means Mathematics AA, and “MAI” means Mathematics AI. Topic numbers belong to the resource author’s organisation; they are not a guarantee that every item matches your current syllabus.
Choose a course with your teacher or counsellor and check the exact course, level and grade required by each university you are considering. AI is not universally the easier choice, and a course’s suitability depends on your intended degree and institution.
Calculator rules for the current courses
- AA SL and HL: Paper 1 is without technology. Paper 2 requires a graphic display calculator; HL Paper 3 also uses technology.
- AI SL and HL: a graphic display calculator is required in all external examination papers.
- Confirm the approved model and exam configuration with your school. An online scientific calculator can help you check practice, but is not a replacement for your permitted examination device.
Use the timetable and instructions for your own exam session. Older guides and specimen papers may show outdated durations. In particular, the May 2026 timetable gives 75 minutes for AA and AI HL Paper 3, while the 2029 curriculum updates specify a reduction to 60 minutes.
What changes for first assessment 2029?
Keep the two syllabus versions separate. For example, AA’s revised content removes financial applications and bivariate data; AI SL removes logarithms and the trapezoidal rule. These changes do not apply to current-course examinations through November 2028. These examples are not a complete change list: use the official update pages in Sources & References and your school’s course guide.
A practical revision routine
- Diagnose one topic. Attempt a short set before opening the notes. Choose the course and level first.
- Explain the error. Record whether it came from the concept, algebra, calculator setup, or interpretation. Write the missing step in your own words.
- Rework without the solution. Then solve a different question using the same idea. Reading a solution is not the same as producing it.
- Combine topics. Once the methods are secure, try a mixed set and then a timed paper that matches your course and session.
For AA Paper 1 practice, put the calculator away. On technology papers, record the equation or model, important inputs and a meaningful interpretation of the output. Keep unrounded values through intermediate steps and round the final answer as the question requires.
Use older papers carefully
Former Mathematics SL, Mathematics HL and Mathematical Studies papers can provide selected topic practice, but should not be treated as current AA/AI mock examinations. Older AA/AI questions also need checking against the revised 2029 content. A year on a folder or cover does not establish its subject coverage, completeness or syllabus compatibility.
Start with the official free sample papers, or ask your school about licensed past-paper access. Purchased papers may also be available through the IB’s authorized retailer. The catalogue keeps existing third-party links; access, availability and terms are controlled by their owners. We do not promise that every linked item is free, current, complete or officially endorsed.
Four worked foundational examples
These original refreshers develop selected skills used in IB Mathematics. They are not official IB questions, a complete syllabus, or a predicted exam paper.
1. Arithmetic sequence: count the gaps
An arithmetic sequence has u4 = 17 and u9 = 42. Find its first term, common difference, twelfth term and the sum of its first twelve terms.
Five steps separate the fourth and ninth terms, so 5d = 42 − 17 = 25, giving d = 5. Since u4 = a + 3d, the first term is a = 17 − 15 = 2.
u12 = 2 + 11 × 5 = 57
S12 = 12 × (2 + 57) ÷ 2 = 354
Watch out: the nth term uses n − 1 differences. There are eleven steps from term 1 to term 12.
2. Geometric sequence: term versus sum
The sequence begins 96, 48, 24, … . The common ratio is r = 48 ÷ 96 = 1/2.
u6 = 96 × (1/2)5 = 3
S6 = 96[1 − (1/2)6] ÷ (1 − 1/2) = 189
Check the sum directly: 96 + 48 + 24 + 12 + 6 + 3 = 189. The sixth term is 3; the first-six-terms sum is 189. A finite sum does not require |r| < 1; that condition is needed for the usual infinite geometric sum.
3. A quadratic and its tangent
Let f(x) = x² − 6x + 5. Factoring gives (x − 1)(x − 5), so the roots are 1 and 5. Completing the square gives (x − 3)² − 4, so the minimum is (3, −4).
For the tangent at x = 4, first differentiate: f′(x) = 2x − 6, hence f′(4) = 2. The point on the curve is (4, f(4)) = (4, −3).
y + 3 = 2(x − 4), so y = 2x − 11
Watch out: f′(4) gives the slope, while f(4) gives the y-coordinate. Use both. You can check quadratic roots and straight-line slope calculations with the algebra calculator.
4. Probability without replacement
A bag contains five red and three blue counters. Two counters are selected at random without replacement.
P(two red) = (5/8) × (4/7) = 5/14
Exactly one red can occur in two disjoint orders: red then blue, or blue then red. Add their probabilities:
P(exactly one red) = (5/8)(3/7) + (3/8)(5/7) = 15/28
Watch out: only seven counters remain after the first draw. The second probability depends on the first result; the draws are not independent.
Try six questions, then check the working
Attempt each question on paper before opening its answer. These selected skills are not intended to cover every course or level.
1. For 7, 11, 15, … find u₁₅ and S₁₅
d = 4, so u15 = 7 + 14 × 4 = 63. Then S15 = 15 × (7 + 63) ÷ 2 = 525.
2. For 12, 18, 27, … find u₅ and S₅
r = 3/2. Thus u5 = 12 × (3/2)4 = 243/4 = 60.75. Adding 12 + 18 + 27 + 40.5 + 60.75 gives S5 = 158.25 = 633/4.
3. For f(x) = x² − 4x + 1, find the minimum and roots
Complete the square: f(x) = (x − 2)² − 3. The minimum is (2, −3). Setting f(x) = 0 gives (x − 2)² = 3, so the roots are 2 − √3 and 2 + √3.
4. Find and classify the stationary points of h(x) = x³ − 6x² + 9x + 1
h′(x) = 3x² − 12x + 9 = 3(x − 1)(x − 3). It is zero at x = 1 and x = 3. The derivative changes from positive to negative at 1, giving a local maximum (1, 5); it changes from negative to positive at 3, giving a local minimum (3, 1). These are local extrema, not global extrema over all real x.
5. If P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3, find P(A | B). Are A and B independent?
P(A | B) = 0.3 ÷ 0.5 = 0.6. They are independent because P(A ∩ B) = 0.3 = 0.6 × 0.5 = P(A)P(B). They are not mutually exclusive: their intersection has nonzero probability.
6. Five independent trials have success probability 0.2 each. What is the probability of exactly two successes?
There are C(5,2) = 10 possible positions for two successes. Each has probability (0.2)²(0.8)³. Therefore the answer is 10 × (0.2)² × (0.8)³ = 0.2048, or 20.48%. The binomial model uses a fixed number of independent trials with the same success probability.
Next, use the resource catalogue below for a longer set at your level. Match every paper, formula booklet and markscheme to its course and examination session.
HeLovesMath is an independent resource. It is not affiliated with or endorsed by the International Baccalaureate Organization. Original examples and diagrams on this guide are separate from the third-party materials credited below.
