Mathematics - Applications and Interpretation
5セクション · 40チャプター
IB Diploma Programme (DP) - SL & HL の学習者向けの無料Mathematics - Applications and Interpretation学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
Topic 1 — Number and algebra
Standard form, approximation and error
Arithmetic sequences and series
Geometric sequences and series
Financial mathematics: interest, depreciation, annuities
Exponents and logarithms
Solving equations and systems with technology
Complex numbers (HL)
Matrices, eigenvalues and Markov chains (HL)
Topic 2 — Functions
Straight lines and gradients
Functions, domain, range and inverses
Graphs, key features and intersections
Modelling with standard functions
Modelling skills: fitting, testing and using models
Composite and inverse functions; transformations (HL)
Logarithmic, sinusoidal, logistic and piecewise models (HL)
Linearizing data; log-log and semi-log graphs (HL)
Topic 3 — Geometry and trigonometry
Three-dimensional geometry: solids, distance and angles
Right-angled and non-right-angled trigonometry
Circles, arcs, sectors and radians
Perpendicular bisectors and Voronoi diagrams
Unit circle, identities and trigonometric equations (HL)
Vectors, scalar and vector products (HL)
Vector lines, kinematics and matrix transformations (HL)
Graph theory and network algorithms (HL)
Topic 4 — Statistics and probability
Sampling, data types and bias
Presenting data: tables, histograms and box plots
Central tendency and dispersion
Correlation and regression
Probability: sample space, combined and conditional events
Discrete random variables and the binomial distribution
Normal distribution, estimators and confidence intervals
Hypothesis testing and further distributions
Topic 5 — Calculus
Limits, derivatives and rates of change
Differentiating polynomials; tangents and normals
Stationary points and optimisation
Integration, areas and the trapezoidal rule
Further differentiation rules and the second derivative (HL)
Further integration, volumes of revolution and kinematics (HL)
Differential equations, slope fields and Euler's method (HL)
Coupled systems and phase portraits (HL)
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