IB Mathematics: Analysis and Approaches HL

IB Math AA HL Questionbank: Practice Questions by Topic

Updated October 2026

Exam-style IB Math AA HL practice questions, written for this site in the style of IB papers, sorted by unit and topic, each with a full IB-style mark scheme. They are not official IB questions.

17 topics
723 questions
51 worked examples

Try one now

Free · no sign-in

Differential Equations and Maclaurin · Paper 1 · 5 marks · medium

Use the first two non-zero terms of the Maclaurin series for $\sin x$ to calculate an exact rational approximation for the definite integral $\int_{0}^{1} \frac{\sin x}{x} d x$ .

Worked answer

Two non-zero terms of the sine series: $\sin x \approx x - \frac{x^{3}}{6}$ A1
Divide by $x$ : $\frac{\sin x}{x} \approx 1 - \frac{x^{2}}{6}$ M1
Set up the integral: $\int_{0}^{1} (1 - \frac{x^{2}}{6}) d x$
Integrate: ${[x - \frac{x^{3}}{18}]}_{0}^{1}$ M1A1
Evaluate: $1 - \frac{1}{18} = \frac{17}{18}$ A1

More Differential Equations and Maclaurin questions →

Unit 1: Number and Algebra

Complex Numbers 46 questions · 3 worked10 easy · 20 medium · 16 hardPaper 1: 41 · Paper 2: 5
Counting and Binomials 22 questions · 3 worked5 easy · 8 medium · 9 hardPaper 1: 19 · Paper 2: 3
Partial Fractions 20 questions · 3 worked5 easy · 8 medium · 7 hardPaper 1: 19 · Paper 2: 1
Proof 38 questions · 3 worked12 easy · 15 medium · 11 hardPaper 1: 35 · Paper 2: 3
Systems of Equations 30 questions · 3 worked8 easy · 12 medium · 10 hardPaper 1: 21 · Paper 2: 9

Practise all of Unit 1 →

Unit 2: Functions

Odd, Even, Inverse, Inequalities and Modulus 38 questions · 3 worked11 easy · 17 medium · 9 hard · 1 very hardPaper 1: 33 · Paper 2: 5
Polynomials and Rational Functions 79 questions · 3 worked17 easy · 36 medium · 23 hard · 3 very hardPaper 1: 71 · Paper 2: 8
Transformations and Modulus 20 questions · 3 worked7 easy · 7 medium · 6 hardPaper 1: 16 · Paper 2: 4

Practise all of Unit 2 →

Unit 3: Geometry and Trigonometry

Planes 47 questions · 3 worked12 easy · 23 medium · 11 hard · 1 very hardPaper 1: 36 · Paper 2: 11
Reciprocal and Inverse Trig Functions 58 questions · 3 worked16 easy · 25 medium · 14 hard · 3 very hardPaper 1: 51 · Paper 2: 7
Vector Lines 53 questions · 3 worked10 easy · 21 medium · 21 hard · 1 very hardPaper 1: 38 · Paper 2: 15

Practise all of Unit 3 →

Unit 4: Statistics and Probability

Advanced Random Variables 52 questions · 3 worked13 easy · 25 medium · 14 hardPaper 1: 29 · Paper 2: 23
Conditional Probability 33 questions · 3 worked7 easy · 14 medium · 12 hardPaper 1: 17 · Paper 2: 16

Practise all of Unit 4 →

Unit 5: Calculus

Advanced Differentiation 43 questions · 3 worked9 easy · 17 medium · 17 hardPaper 1: 33 · Paper 2: 10
Advanced Integration 52 questions · 3 worked9 easy · 28 medium · 15 hardPaper 1: 46 · Paper 2: 6
Differential Equations and Maclaurin 62 questions · 3 worked12 easy · 31 medium · 19 hardPaper 1: 42 · Paper 2: 20
First Principles 30 questions · 3 worked8 easy · 12 medium · 9 hard · 1 very hardPaper 1: 24 · Paper 2: 6

Practise all of Unit 5 →

Save your progress and get 5 more questions on every topic, checked instantly. Free account, no card. Join free

More AA HL revision

IB Maths AA HL past papers (official IB papers)
AA HL formula booklet
AA HL revision notes
Concept guides for every sub-topic
AA HL knowledge organisers: each topic on one printable page, and the AA HL formulas to memorise (not in the booklet)
AA HL syllabus checklist: every point of topics 1 to 5, linked to practice (printable)
GDC keystrokes for the TI-Nspire and Casio fx-CG50, and the Casio fx-CG50 guide
IB Maths guide for parents: the exams, AA vs AI and SL vs HL in plain English

Other courses: IB Maths AA SL · IB Maths AI SL · IB Maths AI HL

FAQ

Are these official IB AA HL questions?

No. They are original exam-style questions written for this site in the style of IB papers. IB Math Revision is independent and is not affiliated with or endorsed by the IB. For real past papers, use the links to the official copies on our IB Maths AA HL past papers page.

Do the AA HL questions have mark schemes?

Yes. Every question has a full IB-style mark scheme (M, A and R marks), and every topic page has free step-by-step worked examples and the key formulas.

How many AA HL questions are there?

723 questions in 17 topics, sorted by syllabus unit, plus 51 worked examples.

Can I get my own working marked?

Yes. In the practice area you can photograph your written working and have it marked by AI against the mark scheme. AI marking is part of the paid plans, and you can try it free for 7 days with no card.

What is free on these AA HL pages?

Every topic page is free with no sign-in: sample questions, step-by-step worked examples and the key formulas. The question at the top of this page has its full worked answer open to everyone.

What does a free account add?

A free account (no card) adds 5 more practice questions on every topic with instant feedback, full worked answers on free questions, 3 AI-marked answers a week, free, and your streak and progress on any device. The rest of the bank with its mark schemes, and AI marking, are part of the paid plans.

What else is free here

Save your answers and track your progressA free account remembers the questions you have done on every topic and brings you back to this page.

Join free

Already have an account? Sign in