IB Maths Paper 3 Problem Solving (HL): The Complete FAQ

Paper 3 is a one-hour, HL-only exam worth 20% of your final Maths grade. According to the IB Mathematics: analysis and approaches guide (first assessed 2021), it consists of two compulsory extended-response questions totalling 55 marks, testing sustained reasoning across several syllabus topics at once — not one isolated skill.

Paper 3 runs for one hour and counts for 20% of your final HL Maths grade — the same weighting as the Internal Assessment. Papers 1 and 2 each run two hours and carry 30% apiece. With only two questions on the whole paper, one poor answer costs proportionally far more than a single question on Paper 1 or 2.

Paper 3 questions are synoptic — each one blends several syllabus topics inside a single extended problem rather than testing one chapter alone. Analysis & Approaches HL tends to combine calculus, proof, complex numbers and sequences; Applications & Interpretation HL tends to combine modelling, statistics and technology-driven, real-world contexts using your GDC.

Yes — Paper 3 exists only for HL Mathematics, in both Analysis & Approaches and Applications & Interpretation. SL students sit just Paper 1 and Paper 2, each worth 40%, with no equivalent extended problem-solving paper. That's one of the clearest structural differences between SL and HL Maths beyond content depth.

Start with past papers, not the textbook — Paper 3 rewards exam technique as much as content knowledge. Work through official past and specimen Paper 3s under strict timed conditions, then read the examiner report for that exact session to see precisely where students lose method marks year after year.

Expect 'show that', 'hence', 'find', 'determine' and 'justify' to dominate Paper 3 far more than Papers 1 and 2. A 'hence' question specifically requires you to build on the previous part's result — using a different, equally valid method instead still loses the method marks tied to that command term.

Read the entire question, all parts, before you write anything — Paper 3 questions build progressively, so part (a) is almost always a clue for part (d). Identify which syllabus topics are being combined, write down every given value, and attempt the easiest sub-part first to bank marks before the harder reasoning.

Most HL teachers, myself included, rank Paper 3 as the toughest of the three papers — not because the content is more advanced, but because it demands sustained reasoning through one long question with no fresh start if you misread part (b). A single early error can cascade through everything that follows.

The biggest mistake is skipping the working for 'show that' steps because you already know the answer — examiners can't award method marks for reasoning they can't see on the page. The second is freezing when a question links unexpected topics, like sequences meeting complex numbers, instead of just working through it step by step.

There's no fixed percentage, because grade boundaries shift slightly each session. HL grade 7 boundaries across all three papers combined have typically sat somewhere in the high-60s to mid-70s percent range in recent sessions. Because Paper 3 has only two questions, losing one entirely is harder to recover from than a similar loss on Paper 1 or 2.

Paper 3 shouldn't decide the choice — both routes share the same one-hour, 20%-weighted format. The real decision is content: Analysis & Approaches HL suits a student heading toward engineering or physics, with heavier calculus and proof; Applications & Interpretation HL suits one leaning toward technology-driven modelling and statistics.

SL Maths is assessed only on Paper 1 and Paper 2 because the course doesn't cover the extra HL-only content or require the same depth of extended, multi-topic reasoning. Paper 3 was built specifically to test that additional HL material and the sustained problem-solving skill that separates HL Mathematics from SL.

Yes — the IB publishes past Paper 3s and specimen papers for both AA and AI HL, and these remain the single most useful free resource for this exam. Working through several sessions' worth, alongside the mark schemes and examiner reports, shows exactly how marks are distributed across a 55-mark, two-question paper.

It can be, provided the resource shows worked solutions with examiner-style mark allocation rather than just final answers — that's usually where students lose the most on Paper 3. Look for topical worksheets that mix syllabus areas the way real Paper 3 questions do, plus full timed mock papers, not a stack of unmarked questions.