IB Math AI HL Notes

Mathematics: Applications and Interpretation

Unit 1

1.1Standard form

1.2Sequences and sigma notation

1.3Geometric sequences

1.4Financial applications: compound interest and annual depreciation

1.5Exponents and logarithms

1.6Approximating and estimating

1.7Loan repayments and amortization

1.8Technology methods for linear and polynomial systems

1.9Log laws (HL only)

1.10Non-integer exponents (HL only)

1.11Infinite geometric series (HL only)

1.12Complex numbers: intro (HL only)

1.13Complex numbers: continued (HL only)

1.14Matrices (HL only)

1.15Eigenvalues & eigenvectors (HL only)

Unit 2

2.1Equations of a line

2.2Functions, domains, ranges, and graphs

2.3Graph of a function

2.4Features of a graph

2.5Modeling functions

2.6Modeling skills

2.7Composite & inverse functions (HL only)

2.8Graph transformations (HL only)

2.9HL modelling (HL only)

2.10Log-log & semi-log graphs (HL only)

Unit 3

3.13D space, volume, angles, and midpoints

3.22D and 3D trigonometry

3.3Angles of elevation and depression

3.4Circle arc length and area of sector (degrees)

3.5Line intersections and perpendicular bisectors

3.6Voronoi diagrams

3.7Radians (HL only)

3.8Unit circle & trig equations (HL only)

3.9Matrix transformations (HL only)

3.10Vector definitions (HL only)

3.11Vector equation of a line (HL only)

3.12Vectors & kinematics (HL only)

3.13Scalar & vector products (HL only)

3.14Graph theory (HL only)

3.15Adjacency matrices (HL only)

3.16Route algorithms (HL only)

Unit 4

4.1Introduction to statistics

4.2Presentation of data

4.3Mean, median, and mode

4.4Correlation of data

4.5Trial and outcome

4.6Venn diagrams

4.7Discrete random variables

4.8Binomial distribution

4.9Normal distribution

4.10Spearman rank correlation coefficient

4.11Expected, observed, hypotheses, chi-squared, goodness of fit, and t-test

4.12Data collection & validity (HL only)

4.13Non-linear regression (HL only)

4.14E(X), Var(X) & estimators (HL only)

4.15Central limit theorem (HL only)

4.16Confidence intervals (HL only)

4.17Poisson distribution (HL only)

4.18t & z tests, errors (HL only)

4.19Markov chains (HL only)

Unit 5

5.1Introduction to limits

5.2Increasing and decreasing functions

5.3Introduction to derivatives

5.4Tangents and normals

5.5Introduction to integration

5.6Stationary points, local maximum and minimum

5.7Optimization

5.8Trapezoid rule

5.9Differentiation rules (HL only)

5.10Second derivatives (HL only)

5.11Integration techniques (HL only)

5.12Areas & volumes of revolution (HL only)

5.13Kinematics (HL only)

5.14Differential equations (HL only)

5.15Slope fields (HL only)

5.16Euler's method (1st order) (HL only)

5.17Phase portraits (HL only)

5.18Euler's method (2nd order) (HL only)

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