IB Mathematics: Applications and Interpretation HL practice

Independent practice matched to the topics of this course. It is not official course material, so check your own course outline for exactly what your teacher covers. This page includes all the IB Math AI SL skills plus the higher-level ones (marked HL).

Functions

• Functions: notation, domain, range and the vertical line test
• Inverse functions
• Composite functions f(g(x)) HL
• Transformations: y = a f(k(x − d)) + c

Quadratic Functions

• Roots, zeros and x-intercepts
• Quadratic models in real life

Polynomial and Rational Functions

• Choose a model: linear, quadratic or exponential

Exponential and Logarithmic Functions

• Exponential growth and decay models
• Log laws and change of base
• Solve exponential and logarithmic equations
• Semi-log plots and linearizing exponential data

Sequences and Series

• Arithmetic sequences: general term
• Geometric sequences: general term
• Arithmetic series
• Geometric series
• Pascal's triangle and the binomial theorem

Financial Mathematics

• Compound interest
• Present value
• Annuities: future value and present value
• Loans, mortgages and the cost of owning a car
• Rounding, significant figures and percentage error

Trigonometry

• Radians and the unit circle HL
• Trigonometry in 3D and with bearings

Periodic and Sinusoidal Functions

• Transformations: amplitude, period, phase shift and axis
• Sinusoidal models: Ferris wheels, tides and daylight

Complex Numbers, Counting and Proof

• Complex numbers: add, subtract, multiply and divide HL
• Complex numbers in polar form and De Moivre's theorem HL
• Combinations: selections where order doesn't matter

Vectors, Matrices and Conics

• Matrices: add, multiply and use in context HL
• Determinant and inverse of a 2 × 2 matrix HL
• Matrices as transformations HL
• Eigenvalues of a 2 × 2 matrix HL

3D Geometry, Voronoi Diagrams and Graphs

• Distance and midpoint in 3D
• 3D solids: volume, surface area and angles
• Voronoi diagrams and nearest neighbours
• Graph theory: degrees, Euler paths and minimum spanning trees HL

Statistics

• Sampling methods, bias and study design
• Summary statistics, IQR and outliers
• Regression lines, residuals and r²
• Spearman's rank correlation
• Sampling distributions and the central limit theorem HL
• Confidence intervals HL
• Hypothesis tests, p-values and errors
• Chi-squared tests

Probability

• Probability rules: complements, or, and independence
• Discrete random variables and expected value
• The binomial distribution
• The normal distribution and z-scores
• The Poisson distribution HL
• Markov chains and steady states HL

Introduction to Calculus

• Optimization problems
• Introduction to integration and area
• Differential equations: slope fields and Euler's method HL

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