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 (Apply to Exponential Functions), Graph Transformations, Modeling Real-World Data, Finding Equations from Data, Continuous Growth and Decay, Competing Model Validation, Real-World Examples

6. Sequences

A Summary of Introduction to Sequences, Domain and Range of Sequences, Arithmetic Sequences, Geometric Sequences, Comparing Sequences to Functions, Example: Identifying Types, Domain and Range Differences

7. Logarithmic Functions

A Summary of Logarithmic Expressions and Evaluation, Inverse of Exponential Functions, Properties of Logarithmic Functions, The Natural Log Function ln(x), Solving Logarithmic and Exponential Equations, Logarithmic Inequalities, Transformations and Inverses, Modeling with Logarithmic Functions, Semi-log Plots, Linearizing Exponential Data

8. Trigonometric Functions

A Summary of Periodic Phenomena and the Unit Circle, Sine and Cosine Functions, Sinusoidal Transformations, Tangent and Reciprocal Functions, Inverse Trigonometric Functions, Trig Equations and Inequalities, Modeling with Trigonometric Functions, Graphing Summary, Trig Identities and Simplification

9. Polar Functions

A Summary of Polar Coordinates and Definitions, Coordinate Conversion, Complex Numbers in Polar Form, Graphing Polar Functions, Interpreting Polar Graph Behavior, Average Rate of Change in Polar Functions

10. Parametric Functions

A Summary of Parametric Functions and Graphing, Motion Modeling and Extrema, Average Rate of Change and Slope, Parametric Forms of Lines and Circles, Implicit Functions and Intercepts, Converting Forms, Conic Sections, Inverses and Representations

11. Vectors

A Summary of Vector Basics, Equality and Negation, Vector Addition and Subtraction, Scalar Multiplication, Dot Product and Angle Between Vectors, Word Problems with Vectors, Component Form and Unit Vectors, Vector-Valued Functions

12. Matrices

A Summary of What Is a Matrix, Matrix Operations, Applications: Area and Geometry, Linear Transformations, Inverse of Linear Transformations, Matrices as Functions, Markov Chains and Transition Matrices