Official ACT Mathematics Guide (eBook)

ACT (Iowa City, IA) is a not-for-profit organization providing assessment, research, information, and program management services to support education and workforce development. Known most widely as the makers of the ACT exam--the college readiness and placement assessment taken by some 1.8 million high school students each year--ACT produces a number of assessments and services reaching more than 10 million people along the kindergarten through career continuum. ACT's rigorous research informs policy decisions and helps develop programs that boost lifelong learning potential in schools and workplaces around the world. To learn more, visit www.act.org.

Introduction v

Chapter 1: The ACT Math Test 1

Reporting Categories: Score Reporting 2

Reporting Categories: Topic Overview 2

Chapter 2: Number and Quantity 5

Real and Complex Number Systems 5

Number Line and Absolute Value 6

Exponents 17

Imaginary and Complex Numbers 21

Vectors 25

Matrices 28

Chapter 2: Quiz Answers 33

Chapter 3: Algebra 37

Scientific Notation 37

Equations 39

Linear Equations 45

System of Equations 48

Roots 61

Logarithmic Equations 65

Chapter 3: Quiz Answers 66

Chapter 4: Functions 73

Series, Sequences, and Consecutive Numbers 73

Slope-Intercept Form of a Linear Equation 76

Chapter 4: Quiz Answers 84

Chapter 5: Geometry 87

Coordinate Geometry 87

Lines and Angles 88

Two-Dimensional Shapes 91

Three-Dimensional Shapes 116

Trigonometry 121

Chapter 5: Quiz Answers 131

Chapter 6: Statistics and Probability 139

Probability 139

Sets of Numbers 141

Charts 144

Chapter 6: Quiz Answers 146

Chapter 7: Practice Questions 149

Chapter 8: Answers and Explanations 195

Answer Key 196

Explanatory Answers 197