AP Precalculus In a Nutshell

1. Rates of Change

A Summary of Relations vs. Functions, Function Notation and Evaluation, Graphs of Functions, Algebraic Domain Rules, Intercepts and Zeros, Vertical Line Test, Increasing and Decreasing Intervals, Concavity, Average Rate of Change, Instantaneous Rate, Linear Functions, Examples Using Tables and Graphs

2. Polynomial Functions

A Summary of Structure of Polynomial Functions, Rates of Change and Relative Extrema, Absolute Extrema and Inflection Points, Zeros of Polynomial Functions, Symmetry of Polynomial Functions, End Behavior, Graphing Polynomial Functions (7-Step Strategy), Binomial Theorem and Pascal’s Triangle, and Polynomial Inequalities

 

3. Rational Functions

A Summary of What Is a Rational Function, Long Division of Rational Expressions, Intercepts and Zeros, Vertical Asymptotes, Holes (Removable Discontinuities), End Behavior Asymptotes, Seven-Step Strategy to Graph Rational Functions, Symmetry, Rational Inequalities

4. Parent Functions

A Summary of Basic Parent Functions and Graphs, Piecewise-Defined Functions, Function Transformations, Function Models and Applications, Regression Models, Rational and Quadratic Modeling Examples, Composition of Functions, Inverse Functions

5. Exponential Functions

A Summary of Definition and Graph of Exponential Functions, End Behavior, Laws of Exponents, Graph Transformations, Modeling Real-World Data, Finding Equations from Data, Continuous Growth and Decay, Competing Model Validation, Real-World Examples

6. Sequences

Arithmetic Sequences
Geometric Sequences
Change in Linear and Exponential Functions

7. Logarithmic Functions

Logarithmic Expressions
Inverses of Exponential Functions
Logarithmic Functions
Logarithmic Function Manipulation
Exponential and Logarithmic Equations and Inequalities
Logarithmic Function Context and Data Modeling
Semi-log Plots

8. Trigonometric Functions

Periodic Phenomena
Sine, Cosine, and Tangent
Sine and Cosine Function Values
Sine and Cosine Function Graphs
Sinusoidal Functions
Sinusoidal Function Transformations
Sinusoidal Function Context and Data Modeling
The Tangent Function
Inverse Trigonometric Functions
Trigonometric Equations and Inequalities
The Secant, Cosecant, and Cotangent Functions
Equivalent Representations of Trigonometric Functions

9. Polar Functions

Trigonometry and Polar Coordinates
Polar Function Graphs
Rates of Change in Polar Functions

10. Parametric Functions

Parametric Functions
Parametric Functions Modeling Planar Motion
Parametric Functions and Rates of Change
Parametrically Defined Circles and Lines
Implicitly Defined Functions
Conic Sections
Parameterization of Functions

11. Vectors

Algebraic and Graphical Properties of Vectors
Vector-Valued Functions

12. Matrices

Matrix Operations
The Inverse and Determinant of a Matrix
Linear Transformations and Matrices
Matrices as Functions
Matrices Modeling Context