IB AA HL

IB Analysis and Approaches HL

Unit 1: Number and Algebra

Unit 2: Functions

- 2.1 Transformations on Functions
- 2.2 Composite Functions, Inverse Functions, Symmetry
- 2.3 Factor/Remainder Theorem
- 2.4 Vieta's Formula
- 2.5 Inequalities
- Quiz
- 2.6 Polynomial Functions
- 2.7 Graphing Rational Functions
- 2.8 Exponential/Logarithmic Functions
- 2.9 Trigonometric Functions
- 2.10 Inverse Trig Functions
- Review
- Test
- Paper 3 practice

Unit 3: Probability and Statistics

Unit 4: Differential Calculus

- 4.1 Limits
- 4.2 Continuity
- 4.3 Average and Instantaneous Rate of Change
- 4.4 Definition of Derivative
- 4.5 Simple Differentiation Rules
- 4.6 Product, Quotient, Chain Rules
- Derivatives Quiz
- 4.7 Implicit Differentiation
- 4.8 Derivatives of Other Functions
- 4.9 Second Derivative and Applications
- 4.10 L'hopital's Rule
- 4.11 Curve Sketching
- 4.12 More Curve Sketching
- Curve Sketching Quiz
- 4.13 Optimization
- 4.14 Optimizing Non-Polynomials
- 4.15 Related Rates
- Review
- Test
- Paper 3 practice

Unit 5: Vectors

- 5.1 Introduction and Operations on Vectors
- 5.2 3D Vectors and Special Vectors
- 5.3 Dot Product
- 5.4 Cross Product
- 5.5 Equations of Lines
- 5.6 Equations of Planes
- 5.7 Intersections of Lines and Planes; Lines and Lines
- 5.8 Intersections of Planes
- 5.9 The Foot incl. distances
- Review
- Test
- Paper 3 Practice

Unit 6: Complex Numbers

- 6.1 Introduction to Complex Numbers (Fundamental Theorem of Algebra)
- 6.2 Complex Plane Geometry and Polar Form
- 6.3 Operations on Complex Numbers in Polar Form/Euler Form
- 6.4 DeMoivre's Theorem and Roots of Unity
- 6.5 Another Day of Complex Numbers Problems
- 6.6 Binomial Theorem (n is negative or rational)
- 6.7 Partial Fractions
- 6.8 Proof by Induction - Divisibility - Crossover to previous units
- Review
- Test
- Paper 3 Practice

Unit 7 Probability Distributions

- 7.0.1 Probability Review
- 7.0.2 Stats Review
- 7.1 Discrete Probability Distributions
- 7.2 Expectation Problems
- 7.3 Binomial Distribution
- 7.4 The Normal Distribution
- 7.5 IB Questions on Normal Distributions
- Review
- Test
- Paper 3 Practice

Unit 8: Integration

- 8.0 Calculus Review
- 8.1 Basic Integration
- 8.2 Definite Integrals
- 8.3 Integration by Substitution
- 8.3.2 Trigonometric Substitutions
- 8.4.1 Integration By Parts
- 8.4.2 Integration By Parts II
- Integration Quiz
- 8.5 Areas Between Curves
- 8.6 Volumes of Revolution 8.6.2 Volumes of Between Curves
- 8.7 Connections to Previous Units, induction, functions, derivatives, improper integrals
- Review
- Test
- Paper 3 Practice

Unit 9: Applications of Integration

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