IB Maths AA HL Paper 3 practice

Current AA HL Paper 3 has two compulsory extended problems, 55 marks and 75 minutes of working time, with a graphic display calculator. It contributes 20% of the subject grade. Practise extracting the givens, using earlier results and turning a conjecture into a justified argument.

Five minutes of reading time precede working time.

This is for AA HL only. AA SL has no Paper 3: try the SL sample instead. AI and the 2029 course are separate (check your course).

The current Paper 3 format

55marks
75minutes, plus 5 reading
20%of the HL grade
2compulsory questions

A graphic display calculator is needed; symbolic (CAS) features are not allowed. Older specimen papers print 60 minutes: that timing is historical. Current sessions are 75 minutes.

Read the problem before choosing a method

Three decisions from the start of an original investigation: for integers n ≥ 0, I_n is the integral of xⁿe^x from 0 to 1.

1 · What is given?

Pick everything the question gives you. Leave out anything you would have to prove.

2 · How can you find $I_1$ ?

3 · Does a table prove the limit?

A calculator gives $nI_n \approx 2.28, 2.67, 2.71$ for $n = 10, 100, 1000$ . Does this prove that $nI_n \to e$ ?

Conjecture, then justify

The whole investigation is free to try with working: 24 marks from one original question, not a full 55-mark paper. No sign-up.

Try the original HL investigation

Method and accuracy marks are decided from your working. Reasoning marks, and any method the marker does not recognise, are shown as uncertain for you to compare with the scheme; they are never confirmed by machine.

Try a different investigation

Sums of reciprocals of three consecutive integers: 21 marks, from conjecture to induction, a telescoping proof and a generalisation. The full scheme, with both proof methods, opens after each part.

Open the 21-mark investigationFree

Turn the missed step into your next practice

After your attempt, where did it go wrong?

All Paper 3 practice Practise using the AA booklet Find my next AA task

Choose a complete timed paper

HL Paper 3 (problem solving), set 1

75 minutes, 55 marks, calculator. Part of IB Maths Genius Pro.

Open HL Paper 3 All papers

The full course has one complete HL set: Papers 1, 2 and 3.

The full AA course, HL

AA Maths covers analysis and approaches at SL and HL. The full course is US$149 today, charged in USD. One payment, tax included, with access until 31 December 2028. AI and the 2029 syllabus are not included.

See the full AA course · US$149

Questions about AA HL Paper 3

Are both questions compulsory?

Yes. There is no choice: answer both extended problems.

If I have a calculator, do I still need proof?

Yes. The calculator helps you find values and spot a pattern. Marks for reasoning need an argument that holds for every case, which a table of values cannot give.

Do SL, AI or the 2029 course have this paper?

AA SL has no Paper 3. AI is a different course with its own papers. The course first assessed in 2029 is a separate syllabus; this page covers the current course, examined through November 2028.