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IB Mathematics AI HL
Questionbank

The IB Mathematics Applications & Interpretation (AI) 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 2A

Functions I

Topic 2B

Functions II

Topic 3

Geometry & Trigonometry

Topic 4A

Statistics & Probability I

Topic 4B

Statistics & Probability II

Topic 5

Calculus

Topic 1

Number & Algebra

Topic 2A

Functions I

Topic 2B

Functions II

Topic 3

Geometry & Trigonometry

Topic 4A

Statistics & Probability I

Topic 4B

Statistics & Probability II

Topic 5

Calculus

Topic 1

Number & Algebra

Topic 1 All

All Questions in Topic 1 Number & Algebra

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Number Skills

Approximation, Rounding, Decimal Places, Significant Figures, Scientific Notation, Percentage Error...

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Sequences & Series

Arithmetic & Geometric Sequences & Series, Finding Terms & Sum of Terms, Infinite Sum, Sigma Notation...

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Financial Mathematics

Compound Interest, Depreciation, Loans & Amortization, Annuities, Using Finance Solver on the Calculator...

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Complex Numbers

Cartesian/Polar/Euler Form, Operations (+-x/) & Powers, Argand Diagrams, Applications with Sin/Cos Waves...

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Matrices

Operations (+-x), Identity/ Determinant/Inverse, Systems of Linear Equations, Eigenvalues & Eigenvectors...

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Systems of Linear Equations

Simultaneous Equations, Quadratic Equations, Cubic Equations, Applications...

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Topic 2A

Functions I

Topic 2A All

All Questions in Topic 2A Functions I

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Straight Line Equations

Forms of Linear Lines, Gradient, Intercepts, Parallel & Perpendicular Lines, Perpendicular Bisectors...

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Linear Functions

Linear Functions, Domain & Range, Rate of Change, Modeling & Real-World Applications...

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Quadratic Functions

Forms of Quadratic Functions, Vertex & Axis of Symmetry, Roots & Discriminant, Modeling & Real-World Applications...

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Cubic Functions

Forms of Cubic Functions, Graphing, Modeling & Real-World Applications...

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Direct & Inverse Variation

Constants of Proportionality, Direct Variation Equations, Inverse Variation Equations, Graphical Representations...

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Exponential Functions

Exponential Growth & Decay, Asymptotes & Intercepts, The Natural Base e, Financial & Scientific Modeling...

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Logarithmic Functions

Logarithmic Bases, Laws of Logarithms, Logarithmic Modeling & Scales, Real-World Applications...

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Topic 2B

Functions II

Topic 2B All

All Questions in Topic 2B Functions II

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Sinusoidal Functions

Amplitude & Principal Axis, Period & Frequency, Sine and Cosine Graphs, Harmonic Motion & Modeling...

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Logistic Functions

Carrying Capacity, Initial Growth Rate, Maximum Growth Rate, Population & Epidemic Modeling...

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Piecewise Functions

Sub-Domains & Intervals, Component Functions, Evaluating Piecewise Expressions, Step Functions & Real-World Rates...

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Other Functions

Combinations of Functions, Maxima, Minima, Domain and Range, Real World Applications...

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Composite Functions

Nested Notation & Structure, Evaluating Composite Expressions, Domain of Composite Functions, Algebraic Composition...

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Inverse Functions

Swapping Domain & Range, Reflection across line y = x, Algebraic Operations, Interpretation in Context...

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Function Transformations

Vertical & Horizontal Translations & Stretches, Reflections across Axes, Order of Transformations...

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Topic 3

Geometry & Trigonometry

Topic 3 All

All Questions in Topic 3 Geometry & Trigonometry

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Geometry of 3D Shapes

Dimensions, Surface Area, Volume. 3D Shapes Including Spheres, Hemispheres, Cones, Prisms & Pyramids...

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Triangle Geometry

Right-Angled Trigonometry, Sine & Cosine Rules, Area of Triangles, Angles of Elevation & Depression, Bearings...

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Circle Geometry

Radians and Degrees, Arc Length and Sector Area, Area between to Arcs...

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Mixed Geometry

Combinations of Circles and Triangles, Segments, Composite Shapes...

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Voronoi Diagrams

Sites/Edges/Cells/Vertices, Perpendicular Bisectors, Nearest Neighbour Interpolation...

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Geometric Transformations

Transformation of Shapes & Points Using Matrices. Reflections/ Stretches/Enlargements/ Translations/ Rotations...

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Vectors

Vector Basics, Scalar & Vector Product, Vector Equation of a Line, Angle Between Vectors, Kinematics...

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Graph Theory

Graph Basics, Walks/Trails etc, Eulerian/Hamiltonian, Kruskal's/ Prim's, Chinese Postman, Travelling Salesman...

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Topic 4A

Statistics & Probability I

Topic 4A All

All Questions in Topic 4A Statistics & Probability I

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Descriptive Statistics

Mean/Median/Mode, Interquartile Range, Histograms, Box & Whisker Plots, Cumulative Freq, Grouped Data...

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Probability

Basic Probability, Tree Diagrams, Venn Diagrams, Sample Space Diagrams, Conditional Probability...

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Transition Matrices & Markov Chains

States & Transition Diagrams, Multi-Step State Transitions, Steady-State Probabilities, Power Formula for Matrices...

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Discrete Probability Distributions

Discrete Random Variables & Sample Spaces, Probabilities, Expected Values, Fair Games...

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The Binomial Distribution

Bernoulli Trials & Binomial Conditions, Expectation & Variance, Cumulative Probabilities, Real-World Modeling...

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The Poisson Distribution

Poisson Conditions & Rates, Mean & Variance Equality, Cumulative Probabilities, Queueing & Event Rate Modeling...

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The Normal Distribution

The Bell Curve, Cumulative Areas & Graph Shading, Inverse Normal Calculations, Linear Combinations...

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Topic 4B

Statistics & Probability II

Topic 4B All

All Questions in Topic 4B Statistics & Probability II

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Linear Regression

Scatter Plots, Lines of Best Fit, Pearson's Product Moment Correlation Coefficient, Extrapolation...

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Spearman's Rank

Ranking Data, Non-Linear Data, Ordinal Data, Monotonic Relationships...

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Non-Linear Regression

Coefficients of Determination, Residual Sum of Squares, Polynomial Regression, Exponential Regression...

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Chi Squared Tests

Tests for Independence, Goodness of Fit Tests, Degrees of Freedom, Expected Frequencies...

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t-Tests and z-Tests

One Sample & Two Sample Tests, Paired Tests, Variance/Standard Deviation Known or Unknown...

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Confidence Intervals

Confidence Levels, Interval Construction, t-Intervals, z-Intervals, Assumptions, Interpretation...

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Linear Regression Tests

Hypothesis Formulation (rho = 0), Conditions & Assumptions, Degrees of Freedom & p-Values, Statistical Significance...

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Tests for Population Mean and Proportion

Hypothesis Testing, Critical Regions, Type I and Type II Errors, Binomial and Poisson Distributions...

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Topic 5

Calculus

Topic 5 All

All Questions in Topic 5 Calculus

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Differentiation

Product/Chain/Quotient Rules, 2nd Derivative Test, Tangents/Normals, Max/Min, Related Rates...

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Optimization

Functions & Constraints, The Derivative & Critical Points, First & Second Derivative Tests, Real-World Applications...

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Anti-Differentiation

Equation of a Curve, Constant of Integration (+C), The Power Rule for Integration, Indefinite Integrals...

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Integration & Areas

Definite Integrals, Area Underneath a Curve, Area Between Two Curves...

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The Trapezoidal Rule

Trapezoidal Intervals, The Trapezoidal Rule Formula, Overestimation vs. Underestimation, Percentage Error...

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Integration & Volumes

Volumes of Revolution About the x-axis and y-axis, Lower and Upper Bounds...

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Kinematics

Displacement, Velocity, Acceleration, Total Distance Travelled, Kinematic Graphs...

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Differential Equations

First Order Diff Eqs, Coupled Diff Eqs, Euler's Method, Slope Fields, Phase Portraits, Predator/Prey Models...

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More IB Mathematics AI 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 AI 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 Applications and Interpretation (AI) 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 AI 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 AI Higher Level course.
The AI HL Questionbank is designed to help IB students practice AI 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 AI HL Question bank. For example, if you want to practice AI HL exam style questions involving Matrices, you can go to AI HL Topic 1 (Number & Algebra) and go to the Matrices area of the question bank. On this page there is a carefully designed set of IB Math AI 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 AI HL Questionbank is perfect for revising a particular topic or concept, in-depth. For example, if you wanted to improve your knowledge of Complex Numbers, there is a designed set of full length IB Math AI HL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AI HL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AI 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 Applications and Interpretation (AI) HL exam style questions in the AI 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 AI HL Question bank, then a popular option would be to go to the AI 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 AI HL exam.