IB Mathematics: Applications and Interpretation SL

IB Math AI SL Questionbank: Practice Questions by Topic

Updated October 2026

Exam-style IB Math AI SL 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.

36 topics
1015 questions
127 worked examples

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Sequences and Series · Paper 1 · 4 marks · medium

The second term of a geometric sequence is $- 6$ and the fifth term is $162$ .

Find the common ratio, $r$ .
Find the first term, $u_{1}$ .

Worked answer

$u_{2} = u_{1} r = - 6$ and $u_{5} = u_{1} r^{4} = 162$ . (M1)
$\frac{u_{1} r^{4}}{u_{1} r} = \frac{162}{- 6} ⟹ r^{3} = - 27$ . (M1)
$r = - 3$ . A1
$u_{1} (- 3) = - 6 ⟹ u_{1} = 2$ . A1

Unit 1: Number and Algebra

Approximations and Error 45 questions · 5 worked16 easy · 16 medium · 8 hard · 5 very hardPaper 1: 35 · Paper 2: 10
Financial Mathematics 47 questions · 4 worked6 easy · 18 medium · 15 hard · 8 very hardPaper 1: 15 · Paper 2: 32
Logarithms and Exponentials 16 questions · 3 worked3 easy · 4 medium · 5 hard · 4 very hardPaper 1: 11 · Paper 2: 5
Sequences and Series 36 questions · 4 worked6 easy · 15 medium · 7 hard · 8 very hardPaper 1: 23 · Paper 2: 13
Systems of Equations 45 questions · 5 worked10 easy · 18 medium · 13 hard · 4 very hardPaper 1: 9 · Paper 2: 36
Volume and Surface Area 35 questions · 5 worked7 easy · 15 medium · 10 hard · 3 very hardPaper 1: 20 · Paper 2: 15

Practise all of Unit 1 →

Unit 2: Functions

Applications of Functions 40 questions · 5 worked10 easy · 13 medium · 9 hard · 8 very hardPaper 1: 18 · Paper 2: 22
Direct/Inverse Variation and Cubic Models 14 questions · 3 worked3 easy · 6 medium · 3 hard · 2 very hardPaper 1: 9 · Paper 2: 5
Exponential Modelling 16 questions · 3 worked5 medium · 8 hard · 3 very hardPaper 1: 1 · Paper 2: 15
Functions: Domain, Range & Inverses 28 questions · 5 worked4 easy · 9 medium · 7 hard · 8 very hardPaper 1: 21 · Paper 2: 7
Graphing Linear, Quadratic, Exponential and Logarithmic Functions 85 questions · 3 worked24 easy · 31 medium · 20 hard · 10 very hardPaper 1: 49 · Paper 2: 36
Linear Modelling 19 questions · 3 worked1 starter · 8 easy · 7 medium · 1 hard · 2 very hardPaper 1: 14 · Paper 2: 5
Quadratic Modelling 27 questions · 3 worked3 easy · 13 medium · 10 hard · 1 very hardPaper 1: 6 · Paper 2: 21
Sinusoidal Modelling 13 questions · 3 worked2 easy · 5 medium · 3 hard · 3 very hardPaper 1: 3 · Paper 2: 10
Solving Equations 12 questions · 3 worked2 easy · 2 medium · 4 hard · 4 very hardPaper 1: 6 · Paper 2: 6

Practise all of Unit 2 →

Unit 3: Geometry and Trigonometry

3D Coordinate Geometry 13 questions · 3 worked3 easy · 6 medium · 2 hard · 2 very hardPaper 1: 11 · Paper 2: 2
3D Trigonometry 13 questions · 3 worked5 easy · 8 mediumPaper 1: 13
Arcs and Sectors 13 questions · 3 worked2 easy · 11 mediumPaper 1: 4 · Paper 2: 9
Coordinate Geometry 31 questions · 5 worked7 easy · 9 medium · 8 hard · 7 very hardPaper 1: 18 · Paper 2: 13
Non-Right-Angled Trigonometry 42 questions · 5 worked9 easy · 17 medium · 12 hard · 4 very hardPaper 1: 10 · Paper 2: 32
Right-Angled Trigonometry 11 questions · 3 worked6 easy · 4 medium · 1 hardPaper 1: 4 · Paper 2: 7
Three-Figure Bearings and Navigation 10 questions · 3 worked2 easy · 2 medium · 4 hard · 2 very hardPaper 1: 3 · Paper 2: 7
Voronoi Diagrams 33 questions · 4 worked5 easy · 11 medium · 11 hard · 6 very hardPaper 1: 19 · Paper 2: 14

Practise all of Unit 3 →

Unit 4: Statistics and Probability

Bivariate Data 45 questions · 3 worked12 easy · 15 medium · 12 hard · 6 very hardPaper 1: 21 · Paper 2: 24
Descriptive Statistics 36 questions · 3 worked7 easy · 19 medium · 5 hard · 5 very hardPaper 1: 21 · Paper 2: 15
Probability 60 questions · 3 worked13 easy · 18 medium · 20 hard · 9 very hardPaper 1: 36 · Paper 2: 24
Probability Distributions 29 questions · 3 worked4 easy · 13 medium · 7 hard · 5 very hardPaper 1: 8 · Paper 2: 21
Sampling Techniques 15 questions · 3 worked3 easy · 7 medium · 5 hardPaper 1: 11 · Paper 2: 4
Statistical Testing 30 questions · 3 worked9 easy · 9 medium · 8 hard · 4 very hardPaper 1: 15 · Paper 2: 15
Two-Sample T-Test 12 questions · 3 worked2 easy · 5 medium · 3 hard · 2 very hardPaper 1: 4 · Paper 2: 8
Venn Diagrams & Hard Probability 15 questions · 3 worked2 medium · 10 hard · 3 very hardPaper 1: 6 · Paper 2: 9

Practise all of Unit 4 →

Unit 5: Calculus

Differentiation Rules 28 questions · 3 worked8 easy · 13 medium · 4 hard · 3 very hardPaper 1: 23 · Paper 2: 5
Integration 35 questions · 3 worked4 easy · 19 medium · 8 hard · 4 very hardPaper 1: 20 · Paper 2: 15
Limits, Derivatives & Rates of Change 23 questions · 3 worked5 easy · 9 medium · 6 hard · 3 very hardPaper 1: 17 · Paper 2: 6
Optimisation 15 questions · 3 worked1 starter · 4 medium · 5 hard · 5 very hardPaper 1: 5 · Paper 2: 10
Tangents & Normals 28 questions · 5 worked3 easy · 9 medium · 9 hard · 7 very hardPaper 1: 16 · Paper 2: 12

Practise all of Unit 5 →

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5 quick questions from across AI SL. No sign-in needed.

Work out

\frac{1}{6} + \frac{3}{4}

. Give your answer as a fraction in its simplest form.

Choose your answer · keys 1–4

\frac{11}{12}

\frac{1}{8}

\frac{2}{5}

\frac{1}{6}

$x$	0	1	2
$P (X = x)$	$\frac{1}{4}$	$\frac{1}{2}$	$\frac{1}{4}$

More AI SL revision

IB Maths AI SL past papers (official IB papers)
AI SL formula booklet
AI SL revision notes
Concept guides for every sub-topic
AI SL knowledge organisers: each topic on one printable page, and the AI SL formulas to memorise (not in the booklet)
AI SL 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 AA HL · IB Maths AI HL

FAQ

Are these official IB AI SL 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 SL past papers page.

Do the AI SL 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 SL questions are there?

1015 questions in 36 topics, sorted by syllabus unit, plus 127 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 SL 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.

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