IB Mathematics: Analysis and Approaches SL

IB Math AA SL Questionbank: Practice Questions by Topic

Updated October 2026

Exam-style IB Math AA 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.

32 topics
1297 questions
95 worked examples

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Rational and Reciprocal Functions · Paper 1 · 4 marks · medium

The function $f$ is defined by $f (x) = \frac{3 x - 1}{x + 2}$ for $x \neq - 2$ . Find an expression for $f^{- 1} (x)$ .

Worked answer

Let $y = f (x)$ and swap $x$ and $y$ : $x = \frac{3 y - 1}{y + 2}$ . M1
Multiply by the denominator: $x (y + 2) = 3 y - 1 ⟹ x y + 2 x = 3 y - 1$ . M1
Collect the $y$ terms: $x y - 3 y = - 2 x - 1$ . M1
Factorise and divide: $y (x - 3) = - 2 x - 1 ⟹ f^{- 1} (x) = \frac{- 2 x - 1}{x - 3}$ (or $\frac{2 x + 1}{3 - x}$ ). A1

More Rational and Reciprocal Functions questions →

Unit 1: Number and Algebra

Binomial Theorem 46 questions · 3 worked10 easy · 19 medium · 12 hard · 5 very hardPaper 1: 39 · Paper 2: 7
Exponentials and Logarithms 73 questions · 3 worked18 easy · 35 medium · 16 hard · 4 very hardPaper 1: 61 · Paper 2: 12
Financial Math 25 questions · 3 worked10 easy · 10 medium · 3 hard · 2 very hardPaper 1: 3 · Paper 2: 22
Proof 18 questions · 3 worked5 easy · 10 medium · 3 hardPaper 1: 15 · Paper 2: 3
Sequences and Series 64 questions · 3 worked15 easy · 30 medium · 13 hard · 6 very hardPaper 1: 45 · Paper 2: 19

Practise all of Unit 1 →

Unit 2: Functions

Equations of Straight Lines 30 questions · 3 worked9 easy · 12 medium · 5 hard · 4 very hardPaper 1: 23 · Paper 2: 7
Exponential and Logarithmic Functions 25 questions · 3 worked7 easy · 9 medium · 7 hard · 2 very hardPaper 1: 16 · Paper 2: 9
Function Fundamentals 53 questions · 3 worked10 easy · 28 medium · 9 hard · 6 very hardPaper 1: 43 · Paper 2: 10
Graphing Functions 34 questions · 3 worked9 easy · 13 medium · 9 hard · 3 very hardPaper 1: 2 · Paper 2: 32
Quadratic Functions 39 questions · 3 worked8 easy · 19 medium · 8 hard · 4 very hardPaper 1: 31 · Paper 2: 8
Rational and Reciprocal Functions 45 questions · 3 worked8 easy · 23 medium · 10 hard · 4 very hardPaper 1: 38 · Paper 2: 7
Transformations of Graphs 49 questions · 3 worked16 easy · 19 medium · 10 hard · 4 very hardPaper 1: 41 · Paper 2: 8

Practise all of Unit 2 →

Unit 3: Geometry and Trigonometry

Geometry and Right Angled Trigonometry 62 questions · 3 worked14 easy · 25 medium · 17 hard · 6 very hardPaper 1: 33 · Paper 2: 29
Non Right Angled Trigonometry 45 questions · 3 worked8 easy · 19 medium · 16 hard · 2 very hardPaper 1: 19 · Paper 2: 26
Radians 44 questions · 3 worked10 easy · 20 medium · 10 hard · 4 very hardPaper 1: 29 · Paper 2: 15
Solving Trigonometric Equations 30 questions · 3 worked4 easy · 16 medium · 7 hard · 3 very hardPaper 1: 23 · Paper 2: 7
The Unit Circle and Exact Values of Trigonometric Ratios 27 questions · 3 worked6 easy · 13 medium · 5 hard · 3 very hardPaper 1: 25 · Paper 2: 2
Trigonometric Functions 28 questions · 3 worked6 easy · 10 medium · 9 hard · 3 very hardPaper 1: 16 · Paper 2: 12
Trigonometric Identities 18 questions · 3 worked4 easy · 8 medium · 6 hardPaper 1: 13 · Paper 2: 5

Practise all of Unit 3 →

Unit 4: Statistics and Probability

Bivariate Data and Correlation 49 questions · 3 worked13 easy · 23 medium · 10 hard · 3 very hardPaper 1: 15 · Paper 2: 34
Discrete Random Variables 50 questions · 3 worked14 easy · 20 medium · 11 hard · 5 very hardPaper 1: 32 · Paper 2: 18
Measures of Central Tendency 24 questions · 3 worked6 easy · 9 medium · 6 hard · 3 very hardPaper 1: 17 · Paper 2: 7
Normal Distribution 41 questions · 3 worked11 easy · 14 medium · 11 hard · 5 very hardPaper 1: 9 · Paper 2: 32
Presentation of Data 43 questions · 3 worked15 easy · 17 medium · 8 hard · 3 very hardPaper 1: 33 · Paper 2: 10
Probability 72 questions · 3 worked16 easy · 36 medium · 16 hard · 4 very hardPaper 1: 57 · Paper 2: 15

Practise all of Unit 4 →

Unit 5: Calculus

Applications of Differentiation 42 questions · 3 worked4 easy · 12 medium · 23 hard · 3 very hardPaper 1: 22 · Paper 2: 20
Definite Integrals 32 questions · 3 worked5 easy · 17 medium · 7 hard · 3 very hardPaper 1: 23 · Paper 2: 9
Graphical Behaviour and the Second Derivative 22 questions · 3 worked4 easy · 9 medium · 6 hard · 3 very hardPaper 1: 15 · Paper 2: 7
Integration 41 questions · 3 worked12 easy · 16 medium · 10 hard · 3 very hardPaper 1: 30 · Paper 2: 11
Kinematics 34 questions · 3 worked4 easy · 12 medium · 15 hard · 3 very hardPaper 1: 19 · Paper 2: 15
Limits and Rates of Change 41 questions · 2 worked11 easy · 15 medium · 10 hard · 5 very hardPaper 1: 31 · Paper 2: 10
Rules of Differentiation 51 questions · 3 worked12 easy · 23 medium · 13 hard · 3 very hardPaper 1: 44 · Paper 2: 7

Practise all of Unit 5 →

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More AA SL revision

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

FAQ

Are these official IB AA 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 AA SL past papers page.

Do the AA 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 AA SL questions are there?

1297 questions in 32 topics, sorted by syllabus unit, plus 95 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 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.

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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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