Table of Contents
Introduction ix
Chapter 1 Basic Algebraic Skills 1
Working with Real Numbers 1
Questions 1-40
Complex Numbers 5
Questions 41-55
The Cartesian Coordinate System 6
Questions 56-65
Chapter 2 Precalculus Function Skills 9
Basic Function Concepts 9
Questions 66-78
Operations with Functions 10
Questions 79-120
Chapter 3 Graphs of Functions 13
Basic Graphing Concepts 13
Questions 121-130
Increasing and Decreasing Behavior and Extrema 14
Questions 131-137
Function Transformations 17
Questions 138-165
Chapter 4 Linear and Quadratic Functions, Equations, and Inequalities 21
Linear Functions 21
Questions 166-174
Linear Equations and Inequalities 22
Questions 175-182
Quadratic Functions 23
Questions 183-196
Quadratic Equations and Inequalities 25
Questions 197-207
Average Rate of Change and Difference Quotients for Linear and Quadratic Functions 26
Questions 208-220
Linear and Quadratic Function Models and Applications 27
Questions 221-230
Chapter 5 Polynomial and Rational Functions 29
Polynomial Functions 29
Questions 231-236
Remainder Theorem, Factor Theorem, and Fundamental Theorem of Algebra 30
Questions 237-245
Descartes' Rule of Signs and Rational Root Theorem 31
Questions 246-250
Rational Functions 32
Questions 251-256
Vertical, Horizontal, and Oblique Asymptotes and Holes in Graphs of Rational Functions 33
Questions 257-266
Behavior of Polynomial and Rational Functions Near ± ∞ 36
Questions 267-272
Chapter 6 Exponential, Logarithmic, and Other Common Functions 37
Exponential Functions 37
Questions 273-281
Logarithmic Functions 39
Questions 282-294
Exponential and Logarithmic Equations 41
Questions 295-302
Other Common Functions 42
Questions 303-312
Chapter 7 Matrices and Systems of Linear Equations 45
Basic Concepts of Matrices 45
Questions 313-322
Determinants and Inverses 46
Questions 323-332
Solving Systems of Linear Equations Using Inverse Matrices 48
Questions 333-334
Solving Systems of Linear Equations Using Cramer's Rule 49
Questions 335-339
Solving Systems of Linear Equations Using Elementary Row Transformations 50
Questions 340-342
Chapter 8 Sequences, Series, and Mathematical Induction 53
Sequences 53
Questions 343-362
Series 55
Questions 363-372
Mathematical Induction 56
Questions 373-382
Chapter 9 Trigonometric Functions 59
Angle Measurement 59
Questions 383-392
Trigonometric Functions 60
Questions 393-407
Trigonometric Graphs and Transformations 64
Questions 408-432
Chapter 10 Analytic Trigonometry 69
Fundamental Trigonometric Identities 69
Questions 433-442
Sum and Difference Identities 70
Questions 443-455
Double- and Half-Angle Identities 71
Questions 456-460
Trigonometric Equations 72
Questions 461-472
Solving Triangles 74
Questions 473-482
Chapter 11 Conic Sections 77
The Circle 77
Questions 483-488
The Ellipse 78
Questions 489-493
The Hyperbola 79
Questions 494-497
The Parabola 80
Questions 498-501
Answers 81