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IB Mathematics · Applications and Interpretation

Question Bank

Practice questions across the Applications & Interpretation syllabus with clear, step-by-step solutions. Choose Standard Level (SL) or Higher Level (HL), then focus on the concepts that matter most.

Standard Level (SL)Higher Level (HL)

Topic 1 · Number & Algebra

All ConceptsAll questions in Topic 1 Number & AlgebraSequences & SeriesArithmetic and geometric sequences and seriesExponents & LogsInteger exponent laws, logarithms (base 10 and e), Laws of logarithms, Rational exponentsInterest & AnnuitiesCompound interest, depreciation and inflation, Amortization and annuities with technologyNumbers & CalculationsScientific notation and calculations, Approximation, bounds, percentage error and estimationLinear systems & Polynomial EquationsTechnology-based solution of linear systems and polynomial equationsComplex NumbersComplex numbers in Cartesian form and Argand diagrams, Polar/exponential forms of complex numbers and applicationsMatrix ConceptsMatrix arithmetic, determinants, inverses and applicationsArgand Diagrams and Eigen VectorsFurther matrix concepts including eigenvalues/eigenvectors

Topic 2 · Functions

All ConceptsAll questions in Topic 2 FunctionsLinear and Quadratic FunctionsLinear equations, gradients and straight-line graphs, Key Features, Forms of equations, Quadratic Formula, Discriminant, Equations, InequalitiesExponential and cubic functionsAsymptotes, Key Features, Graphs, Domain and RangeFunctionsFunction notation, domain, range and inverse functionsModelling cycleChoose, fit, validate and interpret a modelSinusoidal ModelsSine, Cosine functionsAdvanced Functions analysisMore advanced functions, transformations and modellingLogarithmic models and scalingLogarithmic models and scaling

Topic 3 · Geometry and Trigonometry

All ConceptsAll questions in Topic 3 Geometry and TrigonometryThree-dimensional geometryDistance, surface area and volumeTrigonometryRight angle,bearings and elevation/depression, Sine rule, cosine rule and triangle areaVoronoi diagrams and applicationsVoronoi diagrams and applicationsAdvanced TrigonometryTrigonometric functions, identities and equations, Radians, arc lengths and sectorsVectors and MatricesMatrices as geometric transformations, Vectors and vector applications

Topic 4 · Statistics and Probability

All ConceptsAll questions in Topic 4 Statistics and ProbabilityStatisticsSampling, data collection, bias, reliability, representing and interpreting data, mean median mode, quartiles, variance and standard deviation Bivariate DataPearson coefficient and linear regressionProbabilityVenn diagrams, tree diagrams and conditional probabilityDistributionsBinomial and normals distributions and applicationsHypothesis testingChi squared testsProbability distributions and statistical inferenceProbability distributions and statistical inferenceMarkov chains and transition matricesMarkov chains and transition matrices

Topic 5 · Calculus

All ConceptsAll questions in Topic 5 CalculusIntroduction to calculusLimits, derivatives rates of change conceptsDifferentiationPolynomial derivatives, gradients, tangent equationsApplications of differentiationsStationary points. Local extrema, optimization. modellingIntegrationsNumerical integration. Definite integrals, areas under curvesAdvanced DifferentiationAdvanced derivative rules, related ratesAdvanced integrationAdvanced integration techniques and applicationKinematicsDisplacement, velocity and acceleration using calculusDifferential EquationsNumerical methods, phase portaits, dynamical systems