AP® Precalculus Study Notes - Effective Fall 2023
AP® Precalculus – Study Notes- New Syllabus
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AP Precalculus - Study Notes
Unit 1: Polynomial and Rational Functions
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 1.7 Rational Functions and End Behavior
- 1.8 Rational Functions and Zeros
- 1.9 Rational Functions and Vertical Asymptotes
- 1.10 Rational Functions and Holes
- 1.11 Equivalent Forms of Polynomial and Rational Expressions
- 1.12 Transformations of Functions
- 1.13 Function Models: Selection and Assumptions
- 1.14 Function Models: Construction and Application
Unit 2: Exponential and Logarithmic Functions
- 2.1 Arithmetic and Geometric Sequences
- 2.2 Linear and Exponential Change
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Modeling
- 2.6 Competing Function Models
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Modeling
- 2.15 Semi-log Plots
Unit 3: Trigonometric and Polar Functions
- 3.1 Periodic Phenomena
- 3.2 Sine, Cosine, and Tangent
- 3.3 Sine and Cosine Values
- 3.4 Sine and Cosine Graphs
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Transformations
- 3.7 Sinusoidal Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.11 Secant, Cosecant, and Cotangent
- 3.12 Equivalent Trigonometric Forms
- 3.13 Trigonometry and Polar Coordinates
- 3.14 Polar Function Graphs
- 3.15 Rates of Change in Polar Functions
Unit 4: Parameters, Vectors, and Matrices
- 4.1 Parametric Functions
- 4.2 Parametric Modeling of Planar Motion
- 4.3 Parametric Rates of Change
- 4.4 Parametrically Defined Circles and Lines
- 4.5 Implicitly Defined Functions
- 4.6 Conic Sections
- 4.7 Parametrization of Implicit Functions
- 4.8 Vectors
- 4.9 Vector-Valued Functions
- 4.10 Matrices
- 4.11 Inverse and Determinant of a Matrix
- 4.12 Linear Transformations and Matrices
- 4.13 Matrices as Functions
- 4.14 Matrix Modeling