IB Mathematics: Applications and Interpretation HL

IB Math AI HL Questionbank: Practice Questions by Topic

Updated October 2026

Exam-style IB Math AI 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.

21 topics
723 questions
61 worked examples

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Logs and Infinite Geometric Series · Paper 1 · 6 marks · medium

The sum to infinity of a geometric series is 8. The first term is 6.

(a) Find the common ratio, $r$ .

(b) Given that $r = \log_{x} (\frac{1}{2})$ , find the value of $x$ .

Worked answer

(a)
Substitute into $S_{\infty} = \frac{a}{1 - r}$ : $8 = \frac{6}{1 - r}$ M1
Rearrange: $8 (1 - r) = 6 ⟹ 1 - r = \frac{3}{4}$ M1
$r = \frac{1}{4}$ A1

(b)
Set up the equation: $\log_{x} (\frac{1}{2}) = \frac{1}{4}$ M1
Convert to exponential form: $x^{\frac{1}{4}} = \frac{1}{2}$ M1
Raise both sides to the power 4: $x = {(\frac{1}{2})}^{4} = \frac{1}{16}$ A1

More Logs and Infinite Geometric Series questions →

Unit 1: Number and Algebra

Complex Numbers and Argand Diagrams 31 questions · 3 worked10 easy · 15 medium · 6 hardPaper 1: 31
Eigenvalues, Eigenvectors and Markov Chains 27 questions · 3 worked6 easy · 11 medium · 10 hardPaper 1: 27
Logs and Infinite Geometric Series 51 questions · 3 worked12 easy · 23 medium · 15 hard · 1 very hardPaper 1: 45 · Paper 2: 6
Matrices, Determinants and Inverses 42 questions · 3 worked11 easy · 14 medium · 16 hard · 1 very hardPaper 1: 27 · Paper 2: 15

Practise all of Unit 1 →

Unit 2: Functions

Advanced Modelling 37 questions · 3 worked14 easy · 13 medium · 10 hardPaper 1: 21 · Paper 2: 16
Composite, Inverse and Transformations 50 questions · 3 worked17 easy · 17 medium · 13 hard · 3 very hardPaper 1: 43 · Paper 2: 7
Scaling and Linearising Data 19 questions · 3 worked9 easy · 5 medium · 5 hardPaper 1: 19

Practise all of Unit 2 →

Unit 3: Geometry and Trigonometry

Graph Theory 86 questions · 3 worked23 easy · 34 medium · 25 hard · 4 very hardPaper 1: 56 · Paper 2: 30
Scalar Products and Voronoi 32 questions · 3 worked10 easy · 13 medium · 9 hardPaper 1: 29 · Paper 2: 3
Vectors and Kinematics 44 questions · 3 worked13 easy · 16 medium · 14 hard · 1 very hardPaper 1: 37 · Paper 2: 7

Practise all of Unit 3 →

Unit 4: Statistics and Probability

Chi-Square Goodness of Fit, Independence and Error Types 20 questions · 3 worked9 easy · 6 medium · 5 hardPaper 1: 19 · Paper 2: 1
Confidence Intervals and Hypothesis Testing for Means 25 questions · 3 worked8 easy · 9 medium · 7 hard · 1 very hardPaper 1: 19 · Paper 2: 6
Data Collection and Non-Linear Regression 23 questions · 3 worked9 easy · 7 medium · 6 hard · 1 very hardPaper 1: 20 · Paper 2: 3
Linear Combinations of Random Variables & the Central Limit Theorem 22 questions · 3 worked1 starter · 9 easy · 9 medium · 3 hardPaper 1: 16 · Paper 2: 6
Markov Chains and Transition Matrices 13 questions · 3 worked4 easy · 4 medium · 5 hardPaper 1: 13
Random Variables and Poisson 47 questions · 3 worked13 easy · 19 medium · 15 hardPaper 1: 19 · Paper 2: 28

Practise all of Unit 4 →

Unit 5: Calculus

Advanced Differentiation and Related Rates 40 questions · 2 worked11 easy · 17 medium · 12 hardPaper 1: 36 · Paper 2: 4
Advanced Integration and Kinematics 31 questions · 3 worked7 easy · 13 medium · 10 hard · 1 very hardPaper 1: 27 · Paper 2: 4
Differential Equations and Eulers Method 52 questions · 2 worked12 easy · 20 medium · 18 hard · 2 very hardPaper 1: 38 · Paper 2: 14
Phase Portraits 14 questions · 3 worked4 easy · 8 medium · 2 hardPaper 1: 13 · Paper 2: 1
The Second Derivative and Concavity 17 questions · 3 worked5 easy · 7 medium · 5 hardPaper 1: 17

Practise all of Unit 5 →

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FAQ

Are these official IB AI 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 AI HL past papers page.

Do the AI 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 AI HL questions are there?

723 questions in 21 topics, sorted by syllabus unit, plus 61 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 AI 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.

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