Ask an HL student which IB maths paper scares them and most will say Paper 3. It is short, it counts for a fifth of the grade, and it looks unlike anything in the textbook. The good news: Paper 3 is the most *coachable* paper in the course, because every question is built the same way. Once a student sees the pattern, the fear goes.
The facts (current course, May 2027 and 2028 exams)
- HL only – both AA HL and AI HL.
- 60 minutes, 55 marks, 20% of the final grade.
- Two compulsory extended-response problem-solving questions.
- A graphic display calculator (GDC) is required.
For the new course (first exams May 2029) Paper 3 stays at one hour but drops to 50 marks. Our new syllabus post has the details.
How a Paper 3 question is built
Each question is a guided investigation, usually 25–30 marks. It almost always follows this shape:
- Warm-up parts. Calculate a few specific cases – often with the GDC. These are easy marks that many students rush and get wrong.
- Spot a pattern. "Suggest an expression for…" or "conjecture a result". The earlier answers are the evidence.
- Prove or justify. Show the pattern holds in general – by algebra, induction (AA) or a clear argument.
- Extend. Apply the result to a new situation, or change one condition and see what happens.
Students who treat the parts as separate questions lose marks. Students who see that each part feeds the next – the word "hence" is a strong hint – pick up most of the marks.
A method for the exam
- Read both questions fully first (3–4 minutes). Know where each one is heading before you start.
- Split the time roughly 30/30, and move on if a later part is stuck. Early parts of the second question are easier marks than the last part of the first.
- Use the GDC to explore, not just to calculate. Graph, tabulate, try several values. Patterns appear faster on screen.
- Write the result you are using, even if you could not prove it. If you could not show part (c), you can usually still *use* its result in part (d) and earn the marks there.
- Label clearly which part you are answering, especially when you come back to one.
Common mistakes we see
- Rushing the warm-up parts and carrying a wrong number all the way through.
- Writing a conjecture without testing it on one more case.
- Giving a "proof" that only checks examples.
- Spending 40 minutes on question 1 and leaving easy marks in question 2.
- Not writing any working for GDC results – the markscheme still expects to see what was done.
A practice plan that works
From the start of Year 2: one Paper 3 question every two weeks, untimed, discussed afterwards. The aim is to learn the *shape*, not to finish fast.
From January: full Paper 3s under 60-minute timing, every week or two, marked against the markscheme. Keep an error log: was each lost mark a reading error, a GDC error, a proof gap or time?
Final six weeks: mix Paper 3 practice with Papers 1 and 2. Paper 3 rewards the same algebra and calculus fluency the other papers need.
Use past Paper 3s from 2021 onwards (the first exams of the current course) and the specimen papers. Older "Paper 3" options papers from before 2021 are a different style.
How Maths Bodhi helps HL students with Paper 3
Most students do not need more content for Paper 3 – they need a method and the confidence to use it under time. That is how we teach it:
- A diagnostic Paper 3 in the first or second session, to see whether marks are lost in reading, pattern-finding, proof or timing.
- Guided walk-throughs of real Paper 3 questions: the student leads, the tutor asks the questions an examiner would.
- Timed papers with markscheme feedback from January, with a written note of what to fix next.
- Proof and induction practice for AA HL, and modelling and GDC practice for AI HL.
Ajay Vatsyayan (M.Tech, 14+ years teaching maths) teaches IB DP maths at Maths Bodhi and has taught students from schools across Gurgaon, including Pathways World School, The Shri Ram School (Moulsari), Scottish High International School and Lancers International School. Maths Bodhi is independent and not affiliated with any school. Read Ajay's profile or see the AA HL and AI HL course pages.
Sessions run at home across Gurgaon – Golf Course Road, the DLF phases, Sohna Road and Sectors 43, 54 and 56 – or online. See IB maths home tutor in Gurugram, our IB DP maths revision programme, or book a free demo class.
More IB DP guides: the IB DP maths guide for Gurgaon families, how to get a 7 in IB maths and GDC skills for IB maths.
Paper structure verified against the current IB AA and AI guides by the Maths Bodhi team (October 2026). Exam method reviewed by Ajay Vatsyayan.
Frequently asked questions
- How long is IB maths HL Paper 3?
- In the current course (exams in 2027 and 2028), Paper 3 is 60 minutes, worth 55 marks and 20% of the final HL grade. It has two compulsory extended-response problem-solving questions.
- Is a calculator allowed in IB maths Paper 3?
- Yes. A graphic display calculator is required in Paper 3 for both AA HL and AI HL.
- Do SL students take Paper 3?
- No. Paper 3 is taken only by HL students in AA and AI.
- How should I practise for IB maths Paper 3?
- Start with one untimed question every two weeks in Year 2 to learn the structure, then move to timed full papers from January, marked against the markscheme with an error log.