IB

IB Mathematics AA HL
Questionbank

The IB Mathematics Analysis & Approaches (AA) Higher Level (HL) Questionbank is a great source of practice questions, coming from the entire syllabus! Each question comes with a clear markscheme and solution video, with an experienced IB teacher going through the question step-by-step. The questions are organized by topic and arranged by difficulty, making it the perfect resource for studying a particular concept.

Topic 1

Number & Algebra

Topic 2

Functions

Topic 3

Geometry & Trigonometry

Topic 4

Statistics & Probability

Topic 5A

Calculus I

Topic 5B

Calculus II

Topic 1

Number & Algebra

Topic 2

Functions

Topic 3

Geometry & Trigonometry

Topic 4

Statistics & Probability

Topic 5A

Calculus I

Topic 5B

Calculus II

Topic 1

Number & Algebra

Topic 1 All

All Questions in Topic 1 Number & Algebra

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Sequences & Series

Arithmetic & Geometric Progressions, Series, Sigma Notation, Infinite Sum...

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Financial and Growth Models

Compound Interest & Depreciation, Exponential Growth & Decay, Real-World Financial Modelling...

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Exponents & Logarithms

Exponent & Log Laws, Solving Exponential & Logarithmic Equations…

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The Binomial Theorem

Pascal's Triangle, the Binomial Coefficient nCr, Binomial Expansions, Fractional & Negative Indices...

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Counting Principles

Permutations & Combinations, Factorial Notation, Product Principle, Sum Principle…

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Complex Numbers: Algebraic Operations

Sums & Products of Roots, Factorising, Solving Equations, Real Polynomials...

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Complex Numbers: Geometric Representations

Different Forms, De Moivre’s Theorem, Argand Diagram, Geometric Applications…

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Proof by Deduction, Contradiction, and Counterexample

Simple Deductive Proofs, LHS to RHS Proofs, Proof by Contradiction & Counterexample...

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Proof by Induction: Series, Divisibility, and Inequalities

Proof by Induction including Propositions with Series, Divisibility and Inequalities...

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Proof by Induction: Differentiation & Integration

Proof by Induction for Calculus Propositions, including Differentiation & Integration...

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Systems of Linear Equations

Solving 3 x 3 Systems of Linear Equations, Row Operations, Unique/No/Infinite Solutions…

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Topic 2

Functions

Topic 2 All

All Questions in Topic 2 Functions

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Composite & Inverse Functions

Composite Functions, One-to-One Functions, Domain & Range, Finding Inverses...

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Linear and Quadratic Functions

Equations, Discriminant, Intercepts, Vertex Form, Roots, Modelling, Function Properties...

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Rational Functions

Asymptotes, Intercepts, Sketching, Reciprocal Functions, GDC…

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Polynomials

Factor & Remainder Theorems, Sum & Product of Roots, Zeros, Roots, Factors…

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Transformations

Translations, Reflections, Stretches, Graphs, Composite Transformations…

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Modulus Equations and Functions

Absolute-Value/Modulus Functions, Solving Equations & Inequalities…

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Function Sketching

Intercepts, Turning Points, Asymptotes, Symmetry, Transformations, End Behaviour...

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Exponential and Logarithmic Functions

Exponential & Logarithmic Functions & Graphs, Asymptotes, Intercepts…

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Topic 3

Geometry & Trigonometry

Topic 3 All

All Questions in Topic 3 Geometry & Trigonometry

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Triangle Geometry

Sine & Cosine Rule, Area of a Triangle, Ambiguous Case, Right-Angled Trigonometry & 3D Applications...

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Circle Geometry

Radians & Degrees, Arc Length & Area of Sector, Area of Segment, Problem-Solving & Applications...

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Mixed Geometry

Sine & Cosine Rule, Arc Length & Sector Area, Triangles in Circles, Composite Areas & Applications...

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Trigonometric Identities & Equations

Reciprocal Trig Functions, Compound & Double Angle Identities, Inverse Trig Functions, Symmetry Properties...

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Trigonometric Functions & Graphs

Circular Functions, Amplitude, Period & Transformations, Domain, Range & Asymptotes, Modelling & Applications...

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Vectors, Points & Lines

Vector Basics & Components, Scalar (Dot) Product & Angles, Vector Equation of a Line, Intersecting & Skew Lines...

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Vectors & Planes

Vector (Cross) Product, Equations of a Plane, Line & Plane Intersections, Angles Between Lines & Planes...

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Topic 4

Statistics & Probability

Topic 4 All

All Questions in Topic 4 Statistics & Probability

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Descriptive Statistics

Mean-Median-Mode, Variance, Standard Dev., IQR, Stem/Box Plot, Cumulative Freq…

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Bivariate Statistics

Equation of Regression Line y=ax+b, Correlation Coefficient ‘r’, Strength, Applications…

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Probability

Basics, Venn & Tree Diagrams, Combined Events, Independent, Mutually Exclusive, Conditional…

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Discrete Random Variables

Probability Distributions, Expected Value, Variance, Applications...

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Continuous Random Variables

Density Functions, Expected Value, Variance, Continuous Models...

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The Binomial Distribution

Binomial Experiments, Parameters, Probabilities, Mean & Variance...

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The Normal Distribution

Normal Models, Inverse Normal, Standardisation, z-Scores, Probabilities, Applications...

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Topic 5A

Calculus I

Topic 5A All

All Questions in Topic 5A Calculus I

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Differentiation Fundamentals

Power Rule & Standard Derivatives, Chain, Product & Quotient Rules, Tangents & Normals, Second Derivative...

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Trigonometric Differentiation

Derivatives of Sine, Cosine & Tangent, Reciprocal Trig Derivatives, Inverse Trig Derivatives, Chain Rule Applications...

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Optimization

Setting Up & Solving Problems, First & Second Derivative Tests, Points of Inflexion, Real-World Applications...

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L'Hopital's Rule

Indeterminate Forms, Evaluating Limits, L'Hôpital's Rule, Repeated Application & Maclaurin Series...

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Implicit Differentiation

Differentiating Implicit Functions, Gradients of Implicit Curves, Tangents & Normals, Higher Order Derivatives...

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Related Rates of Change

Chain Rule & Connected Rates, Rates of Change Over Time, Geometric & Physical Models, Problem-Solving Applications...

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Kinematics I: Differentiation

Displacement, Velocity & Acceleration, Differentiating Position Functions, Speed & Direction, Analysing Motion...

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Topic 5B

Calculus II

Topic 5B All

All Questions in Topic 5B Calculus II

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Integration Fundamentals and Areas

Antiderivatives, Definite Integrals, Area Under Curves, Fundamental Theorem of Calculus...

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Volumes of Revolution

Volumes About the x- and y-axes, Definite Integrals, Geometric Applications...

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Integration by Parts and by Substitution

Integration by Parts, Repeated Techniques, Applications, Trigonometric Substitutions...

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Trigonometric Integration

Trig Identities, Powers of Trig Functions, Trigonometric Substitution...

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Kinematics II: Integration and Mixed

Displacement, Velocity, Acceleration, Total Distance Traveled, Graphs, Applications using GDC…

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Differential Equations

First Order DE’s, Euler’s Method, Variables Separable, Homogeneous, Integrating Factor, Applications…

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Maclaurin Series

Common Expansions, Use of Substitution, Products, Integration, Differentiation, Differential Equations…

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More IB Mathematics AA HL Resources

Questionbank

All the questions you could need! Sorted by topic and arranged by difficulty, with mark schemes and video solutions for every question.

Paper 3

This resource offers a collection of mathematical modeling and investigation-style questions designed to help you prepare for the IB Math AA HL Paper 3 exam.

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Practice Exams

Choose your revision tool! Contains topic quizzes for focused study, Revision Village mock exams covering the whole syllabus, and the revision ladder to precisely target your learning.

Key Concepts

Helpful refreshers summarizing exactly what you need to know about the most important concepts covered in the course.

Past Papers

Full worked solutions to all past paper questions, taught by experienced IB instructors.

Bootcamps & IA Toolkit

This resource combines topic-based Bootcamps and an IA Toolkit. Bootcamps review key concepts, while the IA Toolkit supports your Internal Assessment.

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Flashcards

Use multiple-choice questions and study crucial terminology on desktop or mobile app to improve your marks!

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Frequently Asked Questions

The IB Math Analysis and Approaches (AA) HL Questionbank is a comprehensive set of IB Mathematics exam style questions, categorised into syllabus topic and concept, and sorted by difficulty of question. The bank of exam style questions are accompanied by high quality step-by-step markschemes and video tutorials, taught by experienced IB Mathematics teachers. The IB Mathematics AA HL Question bank is the perfect exam revision resource for IB students looking to practice IB Math exam style questions in a particular topic or concept in their AA Higher Level course.
The AA HL Questionbank is designed to help IB students practice AA HL exam style questions in a specific topic or concept. Therefore, a good place to start is by identifying a concept that you would like to practice and improve in and go to that area of the AA HL Question bank. For example, if you want to practice AA HL exam style questions that involve Complex Numbers, you can go to AA SL Topic 1 (Number & Algebra) and go to the Complex Numbers area of the question bank. On this page there is a carefully designed set of IB Math AA HL exam style questions, progressing in order of difficulty from easiest to hardest. If you’re just getting started with your revision, you could start at the top of the page with Question 1, or if you already have some confidence, you could start at the medium difficulty questions and progress down.
The AA HL Questionbank is perfect for revising a particular topic or concept, in-depth. For example, if you wanted to improve your knowledge of Counting Principles (Combinations & Permutations), there is a set of full length IB Math AA HL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AA HL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AA HL Key Concepts, where students can learn and revise the underlying theory, if missed or misunderstood in class.
With an extensive and growing library of full length IB Math Analysis and Approaches (AA) HL exam style questions in the AA HL Question bank, finishing all of the questions would be a fantastic effort, and you will be in a great position for your final exams. If you were able to complete all the questions in the AA HL Question bank, then a popular option would be to go to the AA HL Practice Exams section on Revision Village and test yourself with the Mock Exam Papers, to simulate the length and difficulty of an actual IB Mathematics AA HL exam.