IB Maths: Applications and Interpretation HL Lessons
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1Number and algebra15 subtopics
- 1.1 Scientific notation
- 1.2 Arithmetic sequences and series
- 1.3 Geometric sequences and series
- 1.4 Financial applications of geometric sequences and series
- 1.5 Laws of exponents and introduction to logarithms
- 1.6 Approximation and error
- 1.7 Amortization and annuities
- 1.8 Solving systems of linear equations and polynomial equations with technology
- 1.9 Laws of logarithms
- 1.10 Rational exponents
- 1.11 Sum of infinite geometric sequences
- 1.12 Complex numbers: Cartesian form
- 1.13 Complex numbers: polar and exponential forms
- 1.14 Matrices
- 1.15 Eigenvalues and eigenvectors
2Functions10 subtopics
- 2.1 Equation of a straight line
- 2.2 Concept of a function, domain, range and inverse
- 2.3 Graphs of functions and sketching
- 2.4 Key features of graphs
- 2.5 Modelling with functions
- 2.6 Modelling skills
- 2.7 Composite and inverse functions
- 2.8 Transformations of graphs
- 2.9 Further modelling functions
- 2.10 Logarithmic scaling and linearizing data
3Geometry and trigonometry16 subtopics
- 3.1 Three-dimensional geometry
- 3.2 Trigonometry in triangles
- 3.3 Applications of trigonometry
- 3.4 Arc length and sector area
- 3.5 Perpendicular bisectors
- 3.6 Voronoi diagrams
- 3.7 Radian measure
- 3.8 Unit circle and trigonometric identities
- 3.9 Matrix transformations
- 3.10 Vectors: concepts and algebra
- 3.11 Vector equation of a line
- 3.12 Vector applications to kinematics
- 3.13 Scalar and vector products
- 3.14 Graph theory: definitions and representation
- 3.15 Adjacency matrices and walks
- 3.16 Graph algorithms: trees, cycles and routes
4Statistics and probability19 subtopics
- 4.1 Sampling, data quality and outliers
- 4.2 Presenting data
- 4.3 Measures of central tendency and dispersion
- 4.4 Correlation and linear regression
- 4.5 Probability basics
- 4.6 Combined events and conditional probability
- 4.7 Discrete random variables and expected value
- 4.8 Binomial distribution
- 4.9 Normal distribution
- 4.10 Spearman's rank correlation
- 4.11 Hypothesis testing: chi-squared and t-tests
- 4.12 Data collection, reliability and validity
- 4.13 Non-linear regression
- 4.14 Linear combinations of random variables and unbiased estimates
- 4.15 Central limit theorem
- 4.16 Confidence intervals
- 4.17 Poisson distribution
- 4.18 Hypothesis testing: means, proportions, correlation and errors
- 4.19 Transition matrices and Markov chains
5Calculus18 subtopics
- 5.1 Limits and the derivative
- 5.2 Increasing and decreasing functions
- 5.3 Differentiating polynomials
- 5.4 Tangents and normals
- 5.5 Integration and area under a curve
- 5.6 Stationary points
- 5.7 Optimisation
- 5.8 Trapezoidal rule
- 5.9 Differentiation rules and related rates
- 5.10 Second derivative and concavity
- 5.11 Further integration
- 5.12 Areas and volumes of revolution
- 5.13 Kinematics
- 5.14 Differential equations: separation of variables
- 5.15 Slope fields
- 5.16 Euler's method
- 5.17 Phase portraits
- 5.18 Second order differential equations