IB Math AA HL Paper 3: What It Tests and How to Prepare

By Michael Thompson · Education Specialist; 10 years teaching the IB at Bromsgrove School · Published 4 October 2026 · Updated 6 October 2026

IB Math AA HL Paper 3 is the exam that only Analysis and Approaches HL students sit. It is HL-only, allows a graphic display calculator, runs for 1 hour 15 minutes, and counts for 20% of your final HL grade. Unlike Papers 1 and 2, which test a broad range of syllabus topics through many shorter questions, Paper 3 gives you just two long, structured problems built around unfamiliar situations that you must investigate as you go. This guide explains exactly what the paper demands, why it feels different from the rest of your IB Math AA HL exams, and the preparation habits that matter most. The current AA HL course is examined up to and including November 2028, so this page is for students sitting any session through that date.

Key Takeaways

• HL only, 1 hour 15 minutes, 20% of your grade: Paper 3 does not exist at SL; it sits alongside Papers 1 and 2, which each carry 30% of the HL grade, and the exploration, which carries the remaining 20%.
• Two compulsory extended-response questions: There are no short questions and no optional questions - you answer both problems in full, no matter how uncomfortable the opening looks.
• Technology is allowed: Unlike Paper 1, which is technology-free, Paper 3 lets you use your GDC - and you should use it actively for graphing, computing and checking numerical results.
• Problems build from accessible parts toward a generalisation: Early sub-parts are designed to be manageable; the results you prove or compute in them feed directly into the harder parts later in the same question.
• Assessment objectives include reasoning and inquiry approaches: Paper 3's problem-solving questions put these to work - investigating unfamiliar situations and making or testing conjectures, not just recalling the syllabus.
• Read the whole question before you write anything: Seeing where a question ends tells you what the early parts are leading toward, which changes how you frame your working from the start.

In This Article

1. What Is IB Math AA HL Paper 3
2. Why Paper 3 Feels Different from Papers 1 and 2
3. What the IB Math AA HL Syllabus Covers in Paper 3
4. How a Paper 3 Question Is Structured: An Annotated Example
5. How to Prepare for IB Math AA HL Paper 3
6. IB Math Unseen Problem Approaches: Building the Right Mindset
7. Common Mistakes to Avoid in Paper 3
8. What to Do Next

1. What Is IB Math AA HL Paper 3

IB Math AA HL Paper 3 is an HL-only component of the IB Diploma Programme Mathematics: Analysis and Approaches course. SL students do not sit it at all. Per the IB subject brief, a graphic display calculator (GDC) is permitted throughout and the paper carries 20% of the total HL grade. The IB's page on the updated course adds that the current Paper 3 is worth 55 marks and lasts one hour and 15 minutes; the IB's May 2027 examination schedule gives the same 1 hour 15 minutes. The new course first assessed in May 2029 cuts it to one hour and 50 marks.

To put that weighting in context, Papers 1 and 2 each carry 30%, and the internal assessment exploration carries the remaining 20%. Paper 3 is therefore equal in weight to the exploration, despite being just 75 minutes long.

The structure is deliberately spare. The subject brief confirms there are exactly two compulsory extended-response problem-solving questions, no short-response questions, and no optional questions. You answer both, in full.

That format is the non-obvious thing about this paper. Most exam components reward breadth: answer ten questions, move on. Paper 3 does the opposite. Each of the two questions is a sustained investigation that builds through connected sub-parts toward a generalisation or proof. Missing an early part does not automatically end your run through a question, but the structure means later parts often depend on results you established earlier.

The current AA course is examined up to and including November 2028. A new IB mathematics course is first assessed in May 2029. This guide is written for students preparing under the current specification.

2. Why Paper 3 Feels Different from Papers 1 and 2

Papers 1 and 2 at HL each last 2 hours and each contribute 30% to your final grade, per the IB Mathematics: analysis and approaches subject brief. Their format is familiar: a spread of questions testing different areas of the syllabus, where a weak answer on one question rarely derails the whole paper.

Paper 3 replaces that breadth with depth. It lasts 1 hour 15 minutes, counts for 20% of your HL grade, and contains exactly two compulsory extended-response problems. There are no short questions, no optional questions, and no fresh start between topics.

The structure is deliberately unfamiliar. Each problem opens with a scenario you have not seen before, then guides you through a sequence of sub-parts that build on one another. Early parts often look straightforward, and that is the trap: the result you produce in part (a) is usually the tool you need in part (e). Students who treat each sub-part as self-contained miss the thread entirely.

The IB subject brief lists six assessment objectives for the course, including problem solving, reasoning and inquiry approaches, and those three are the ones Paper 3's long, unfamiliar problems stretch most: investigating a situation you have not met before and making or testing conjectures. These are not the objectives rewarded by rapid-fire recall. A student who has memorised every formula but cannot spot a pattern across four connected sub-parts will find Paper 3 harder than Papers 1 and 2, not easier.

The practical takeaway: before writing anything, read both questions in full. The final sub-part tells you where the problem is heading, which makes the earlier steps easier to interpret.

3. What the IB Math AA HL Syllabus Covers in Paper 3

The IB Mathematics: analysis and approaches subject brief sets the HL AA course at 240 teaching hours: 210 across five topic areas, plus 30 for investigational, problem-solving and modelling skills and the exploration:

Paper 3 draws on HL content from across all five areas. No single topic is guaranteed to dominate a given session, and the unfamiliar-situation format means a single question can pull threads from several topic areas at once. Predicting "it will be calculus this year" is not a useful revision strategy.

The 30 hours for investigational, problem-solving and modelling skills build the habits Paper 3 tests. Those hours also cover the exploration and are the same at SL, but they are not a vague soft-skills add-on. The subject brief lists the course's assessment objectives: knowledge and understanding, problem solving, communication and interpretation, technology, reasoning, and inquiry approaches. Paper 3's unfamiliar problems lean especially hard on that last one. The question guides you into unfamiliar territory; your job is to follow the logic, not recognise a template.

So treat every topic area as live, and give investigative problem-solving the same attention you give calculus.

4. How a Paper 3 Question Is Structured: An Annotated Example

A single Paper 3 question is nothing like a standard exam question. It usually runs to a long chain of sub-parts that takes you from specific cases towards a general result or proof, with most parts building on the ones before.

To see the arc, take a classic investigation that suits the format: the functions f_n(x) = cos(n arccos x) on -1 ≤ x ≤ 1, which turn out to be polynomials. (The outline below was written for this guide to show the shape of such a question; it is not taken from an IB paper.)

The arc is the important thing to notice:

• Early sub-parts have you work out and sketch the first few cases, such as f1(x) = x and f2(x) = 2x² - 1, and notice what kind of function each one is.
• Middle sub-parts take one feature you met in those first cases, such as where each graph turns, and ask you to describe it for any n.
• Later sub-parts ask for a result that holds for every n. Writing θ = arccos x and adding the compound-angle expansions of cos((n + 1)θ) and cos((n - 1)θ) gives f{n+1}(x) + f{n-1}(x) = 2x fn(x). Combined with f1 and f2 from the early parts, that recurrence shows every fn(x) is a polynomial in x.

This is a common pattern in IB Math AA HL Paper 3: the question builds up results through its early parts, then asks you to prove or generalise. A student who starts writing without reading the full question can miss that the groundwork has already been laid for them.

5. How to Prepare for IB Math AA HL Paper 3

The biggest preparation mistake is treating IB Math AA HL Paper 3 like a longer version of Papers 1 and 2. The IB subject brief lists "inquiry approaches" among the course's assessment objectives and describes Paper 3 as two problem-solving questions, so the skill being tested is mathematical investigation, not recognition of familiar question types. Drilling past Paper 1 questions builds fluency; it does not build the investigative instinct Paper 3 rewards.

Read the whole question before writing anything. The final sub-part reveals where the problem is heading, and that destination reframes what the early sub-parts are actually asking you to build. A part that looks like routine differentiation often turns out to be constructing a component you will need three sub-parts later.

Once you start, use your results actively. Paper 3 questions are designed so each answer feeds forward: an expression you derive in part (b) is almost certainly the tool you need in part (d). If your part (d) answer does not connect to what came before, that is a signal to check your earlier working, not to push on blindly.

Use your GDC as an investigative instrument, not just a calculator:

• Graph a function to observe its behaviour before attempting a proof.
• Compute numerical cases to test a conjecture before committing to a general argument.
• Verify a symbolic answer numerically as a quick plausibility check.

Time management across the paper matters. With 75 minutes and two compulsory extended-response questions, neither question should be abandoned. If you are stuck on a sub-part after a few minutes, write down what you know, try a specific numerical case, and move to the next sub-part. Partial working that shows correct reasoning can still earn credit, so a blank page is always the worst outcome.

6. IB Math Unseen Problem Approaches: Building the Right Mindset

Encountering a scenario you have never seen before is not a sign something has gone wrong. It is the intended experience. The IB subject brief lists inquiry approaches as one of the course's assessment objectives. In practice that means investigating an unfamiliar situation, forming conjectures, testing them with specific cases, and then proving or disproving them. Recognising that structure turns a bewildering question into a familiar process.

The specific mindset shifts that help:

• Conjecture first, prove second. When a question asks you to "find a pattern" or "suggest a general result", try small values of n first, write down what you notice, then formalise it. Proof by induction fits naturally here. It recurs throughout HL content and aligns with the generalisation arc that Paper 3 questions are built around. If your induction technique is not fluent under timed conditions, that is the one thing worth drilling before the exam.

• Use the GDC to see before you sketch. Plot the function on your graphic display calculator first to understand its shape, then annotate the sketch with only what the question explicitly asks for. Adding unrequested intercepts or stationary point coordinates costs time without earning marks.

• Keep your working chain visible. Mathematical communication is assessed. The logical link from one sub-part to the next must be legible, not just the final answer.

• Check backwards before you start from scratch. If you are stuck on part (e), spend thirty seconds checking whether a result from part (b) or (c) applies before attacking it independently, because Paper 3 questions are deliberately scaffolded so that earlier answers feed later ones.

7. Common Mistakes to Avoid in Paper 3

The errors below are structural, not mathematical. Fixing them costs nothing except habit.

• Reading only the first sub-part before starting. The final sub-part reveals where the whole question is going. Read all parts first. Thirty seconds of scanning changes every decision you make in the opening parts.

• Ignoring earlier results. Paper 3 questions are designed so each answer is a stepping stone. If sub-part (c) gives you a recurrence relation and sub-part (e) asks for a proof, that relation is your starting point, not a coincidence. Restarting from first principles wastes time and usually misses the intended method.

• Working purely symbolically when the GDC would help. Technology is allowed for a reason. Plotting a function to confirm the number of stationary points, or evaluating a term numerically to test a conjecture, takes seconds and can stop you pursuing a false path for several minutes.

• Spending too long on one question. Both questions carry substantial weight. An uneven split that leaves the second question barely attempted is one of the costliest Paper 3 errors you can make.

• Writing a conjecture without testing it first. Check your conjecture on at least one specific case before attempting a proof. A "proof" of a false conjecture can look rigorous on the page, and it earns nothing.

• Omitting domain conditions. If the problem states n ∈ Z⁺, that condition must appear in your answer wherever it is relevant. Dropping it, particularly in proof by induction questions, leaves the argument incomplete.

8. What to Do Next

Your next move is specific: ask your teacher for a specimen or past Paper 3 with its markscheme. Close your notes, set a 1 hour 15 minute timer, and attempt it. Check the markscheme only after time is up. Keep the IB Mathematics: Analysis and Approaches subject brief to hand too; it sets out the paper's format and weighting.

The exam structure, weightings, and assessment objectives referenced throughout this article come from that subject brief; the mark total and the date of the new course come from the IB's page on the updated course. For the complete subject guide and any updates, access the IBO's Programme Resource Centre through your school.

One practical point worth repeating: reading all parts of a problem before writing anything is a habit, not an instinct. It takes deliberate repetition to stick. Find one extended unfamiliar problem this week and practise that read-first pass before you touch your pen.

The AA HL course keeps its current format through November 2028, so this advice holds whichever session you sit before then. Ask for that practice paper now, and sit it timed before your next lesson.

FAQ

Is a calculator allowed in IB Math AA HL Paper 3?

Yes - technology, in practice your graphic display calculator (GDC), is allowed in Paper 3; it is one of two technology-permitted papers at HL, the other being Paper 2, per the IB subject brief.

How long is IB Math AA HL Paper 3?

Paper 3 lasts 1 hour 15 minutes and is worth 55 marks, per the IB's May 2027 examination schedule and its analysis and approaches updates page; only the new course first assessed in May 2029 cuts it to one hour and 50 marks.

What is IB Math AA HL Paper 3?

It is an HL-only exam paper containing two compulsory extended-response problem-solving questions, worth 20% of the total HL grade, in which students investigate unfamiliar mathematical situations using technology.

How hard is IB Math AA HL?

IB Mathematics: analysis and approaches HL is widely considered one of the most demanding IB Diploma subjects; like every HL course it has 240 teaching hours, and its assessment objectives include reasoning and inquiry approaches, which Paper 3 tests through unfamiliar problems.

How should I prepare for IB Math AA HL Paper 3?

The most effective preparation is practising unseen extended problems: read each question fully before starting, use early sub-part results in later parts, and use your GDC to graph or compute cases before writing proofs.

Does Paper 3 cover the whole IB Math AA HL syllabus?

Paper 3 draws on HL content from across the syllabus - the five topic areas total 210 guided hours at HL - so no single topic is guaranteed; the investigational format means questions routinely cross topic boundaries.

References

• Diploma Programme Subject Brief - Mathematics: analysis and approaches, first assessments for SL and HL 2021 (International Baccalaureate Organization) - https://www.ibo.org/contentassets/5895a05412144fe890312bad52b17044/subject-brief-dp-math-analysis-and-approaches-en.pdf
• Mathematics: analysis and approaches updates - International Baccalaureate - https://www.ibo.org/university-admission/latest-curriculum-updates/dp-mathematics-analysis-and-approaches-updates/