IB Mathematics AI HL-Questions 2025
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Topic 1
Number & Algebra
1.1
Number & Skills
Approximation, Rounding, Decimal Places, Significant Figures, Scientific Notation, Percentage Error…
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1.2
Sequences & Series
Arithmetic & Geometric Sequences & Series, Finding Terms & Sum of Terms, Infinite Sum, Sigma Notation…
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1.3
Financial Mathematics
Compound Interest, Depreciation, Loans & Amortization, Annuities, Using Finance Solver on the Calculator…
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1.4
Complex Number
Cartesian/ Polar/ Euler Form, Operations (+-x/) & Powers, Argand Diagrams, Applications with Sin/ Cos Waves…
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1.5
Matrices
Operations (+-x), Identity/ Determinant/ Inverse, Systems of Linear Equations, Eigenvalues & Eigenvectors…
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1.6
System of Linear Equations
Simultaneous equations, Quadratic equations, Cubic Equations, Applications…
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Topic 2
Functions
2.1
Linear Equations & Graphs
Forms of Linear Lines, Gradient, Intercepts, Parallel & Perpendicular Lines, Perpendicular Bisectors…
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2.2
Applications of Functions
Linear, Quadratic, Exponential, Log, Sinusoidal, Logistic, Piecewise. Scaling & Linearizing using Logs…
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2.3
Properties of Functions
Understanding the Domain & Range of a Function, Finding & Interpreting Composite & Inverse Functions…
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2.4
Transformation
Horizontal & Vertical Translations, Reflections in X & Y Axes, Stretches with Scale Factors, Composite…
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Topic 3
Geometry & Trigonometry
3.1
Geometry of 3D Shapes
Dimensions, Surface Area, Volume. 3D Shapes Including Spheres, Hemispheres, Cones, Prisms & Pyramids…
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3.2
Trigonometry
Right & Non-Right Triangles: Sin/Cos/Tan, Sin & Cosine Rule, Area, Circles: Arcs & Sectors, Radians…
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3.3
Voronoi Diagram
Sites/ Edges/ Cells/ Vertices, Perpendicular Bisectors, Nearest Neighbour Interpolation, Toxic Waste Dump…
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3.4
Trigonometric Functions
The Unit Circle, Trig Identities, Ambigious Case of Sine Rule, Solving Trig Equations, Trig Functions & Graphs…
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3.5
Geometric Transformation
Transformation of Shapes & Points Using Matrices. Reflections/ Stretches/ Enlargements/ Translations/ Rotations…
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3.6
Vectors
Vector Basics, Scalar & Vector Product, Vector Eqn of a Line, Angle Between, Applications to Kinematics…
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3.7
Graph Theory
Graph Basics, Walks/Trails etc, Eulerian/ Hamiltonian, Kruskal’s/ Prim’s, Chinese Postman, Travelling Salesman…
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Topic 4
Statistics & Probability
4.1
Descriptive Statistics
Mean/ Median/ Mode, Interquartile Range, Histograms, Box & Whisker Plots, Cumulative Freq, Grouped Data…
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4.2
Bivariate Statistics
Scatter Plots, Correlation (Pearson/ Spearman), Linear & Non-Linear Regression, Coefficient of Determination…
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4.3
Probablity
Basic Prob, Tree/ Venn/ Sample Space Diagrams, Conditional Prob, Transition Matrices & Markov Chains…
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4.4
Distributions
Probability/ Binomial/ Normal/ Poission Distributions. Random Variables & Combinations of Random Variables…
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4.5
Hypothesis Testing
Ho/H1, Sig Levels, p-values, chi-squared tests, t-tests, Critical Val/ Reg, Type 1/2 Errors, Pop Mean & Proportion…
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4.6
Estimation & Confidence Intervals
Reliability & Validity of Data Collection, Unbiased Estimators, Central Limit Theorem, Confidence Intervals…
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Topic 5
Calculus
5.1
Differentiation
Product/ Chain/ Quotient Rules, Double Derivative Test, Tangents/ Normals, Max/ Min/ Optimisation, Related Rates…
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5.2
Integration
Anti-Diff, Area Under & Beneath Curves, Trapezoidal Rule, Integration by Substitution, Volumes of Revolution…
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5.3
Kinematics
Displacement, Velocity, Acceleration, Total Distance Travelled, Kinematic Graphs…
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5.4
Differential Equations
Solving Differential Eqs, Slope Fields, First Order & Coupled Differential Eqs, Euler’s Methods, Phase Portraits…
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