CONTENTS
To the Students vi
Part A – Math Review
I. Heart of Algebra
Chapter 1: The Language and Tools of Algebra 5
1-1 Variables and Expressions 5
1-2 Exponents and Order of Operations 7
1-3 Simplifying Algebraic Expressions 9
1-4 Rational, Irrational, and Decimal 11
Chapter 1 Practice Test 13
Answers and Explanations 15
Chapter 2: Solving Linear Equations 19
2-1 Writing Equations 19
2-2 Solving Equations 21
2-3 Solving Equations with Variables on Both Sides 23
2-4 Equations with No Solution and Identity 25
2-5 Solving for a Specific Variable 27
Chapter 2 Practice Test 29
Answers and Explanations 31
Chapter 3: Functionsand Linear Equations 37
3-1 Relations and Functions 37
3-2 Rate of Change and Slope 40
3-3 Slope-Intercept Form and Point-Slope Form 42
3-4 Parallel and Perpendicular Lines 44
3-5 Solving Systems of Linear Equations 46
3-6 Absolute Value Equations 50
Chapter 3 Practice Test 52
Answers and Explanations 54
Chapter 4: Linear Inequalities and Graphs 61
4-1 Solving Inequalities 61
4-2 Compound and Absolute Value Inequalities 63
4-3 Graphing Inequalities in Two Variables 65
4-4 Graphing Systems of Inequalities 67
Chapter 4 Practice Test 69
Answers and Explanations 71
,ii • Contents
Chapter 5: Word Problems in Real-Life Situation 77
5-1 Solving Word Problems Using Linear Models 77
5-2 Solving Word Problems with Equations 79
5-3 Solving Word Problems Using Systems of Equations 81
5-4 Solving Word Problems Using Inequalities 83
Chapter 5 Practice Test 85
Answers and Explanations 87
II. Statistics and Data Analysis
Chapter 6: Ratios, Rates, and Proportions 95
6-1 Ratios and Rates 95
6-2 Proportions 97
6-3 Ratios, Rates, and Proportions Word Problems 99
Chapter 6 Practice Test 101
Answers and Explanations 103
Chapter 7: Percents 109
7-1 Percent of Change 109
7-2 Percents and Equations 111
7-3 Percent Word Problems 113
Chapter 7 Practice Test 115
Answers and Explanations 117
Chapter 8: Statistics 121
8-1 Mean, Median, Mode, and Range 121
8-2 Standard Deviation 123
8-3 Graphical Displays 125
8-4 Scatter Plots 127
8-5 Populations, Samples, and Random Selection 129
Chapter 8 Practice Test 131
Answers and Explanations 133
Chapter 9: Categorical Data and Probability 139
9-1 Permutations and Combinations 139
9-2 Rules of Probability 141
9-3 Categorical Data and Conditional Probabilities 143
Chapter 9 Practice Test 145
Answers and Explanations 147
, Contents • iii
III. Advanced Math
Chapter 10: Law of Exponents and Polynomials 153
10-1 Laws of Exponents and Scientific Notation 153
10-2 Adding, Subtracting, Multiplying, and Dividing Polynomials 156
10-3 FOIL Method and Special Products 159
10-4 Prime Factorization, GCF, and LCM 161
10-5 Factoring Using the Distributive Property 164
Chapter 10 Practice Test 166
Answers and Explanations 168
Chapter 11: Quadratic Functions 173
11-1 Graphs of Quadratic Equations 173
11-2 Factoring Trinomials 176
11-3 Factoring Differences of Squares and Perfect Square Trinomials 179
11-4 Solving Quadratic Equations by Completing the Square 181
11-5 Quadratic Formula and the Discriminant 183
11-6 Solving Systems Consisting Linear and Quadratic Equations 186
Chapter 11 Practice Test 188
Answers and Explanations 190
Chapter 12: Composition, Recursion, and Exponential Functions 197
12-1 Composition of Functions 197
12-2 Recursive Formula 199
12-3 Exponential Functions and Graphs 201
12-4 Exponential Growth and Decay 203
Chapter 12 Practice Test 205
Answers and Explanations 207
Chapter 13: Polynomial and Radical Functions 213
13-1 Polynomial Functions and Their Graphs 213
13-2 Remainder Theorem and Factor Theorem 215
13-3 Radical Expressions 217
13-4 Solving Radical Equations 220
13-5 Complex Numbers 222
Chapter 13 Practice Test 225
Answers and Explanations 227
, iv • Contents
Chapter 14: Rational Expressions 233
14-1 Rational Expressions 233
14-2 Solving Rational Equations 236
14-3 Direct, Inverse, and Joint Variation 238
14-4 Solving Word Problems Using Rational Equations 240
Chapter 14 Practice Test 242
Answers and Explanations 244
Chapter 15: Trigonometric Functions 251
15-1 Trigonometric Ratios of Acute Angles 251
15-2 The Radian Measure of an Angle 253
15-3 Trigonometric Functions of General Angles and the Unit Circle 255
Chapter 15 Practice Test 259
Answers and Explanations 261
IV. Geometry
Chapter 16: Lines and Angles 267
16-1 Lines, Segments, and Rays 267
16-2 Angles 269
16-3 Parallel and Perpendicular Lines 271
Chapter 16 Practice Test 273
Answers and Explanations to Exercises and Practice Test 275
Chapter 17: Triangles 279
17-1 Angles of a Triangles 279
17-2 Pythagorean Theorem and Special Right Triangles 281
17-3 Similar Triangles and Proportional Parts 283
17-4 Area of a Triangle 285
Chapter 17 Practice Test 287
Answers and Explanations 289
Chapter 18: Polygons 295
18-1 Parallelograms 295
18-2 Rectangles, Squares, and Trapezoids 297
18-3 Regular Polygons 299
Chapter 18 Practice Test 301
Answers and Explanations 303
To the Students vi
Part A – Math Review
I. Heart of Algebra
Chapter 1: The Language and Tools of Algebra 5
1-1 Variables and Expressions 5
1-2 Exponents and Order of Operations 7
1-3 Simplifying Algebraic Expressions 9
1-4 Rational, Irrational, and Decimal 11
Chapter 1 Practice Test 13
Answers and Explanations 15
Chapter 2: Solving Linear Equations 19
2-1 Writing Equations 19
2-2 Solving Equations 21
2-3 Solving Equations with Variables on Both Sides 23
2-4 Equations with No Solution and Identity 25
2-5 Solving for a Specific Variable 27
Chapter 2 Practice Test 29
Answers and Explanations 31
Chapter 3: Functionsand Linear Equations 37
3-1 Relations and Functions 37
3-2 Rate of Change and Slope 40
3-3 Slope-Intercept Form and Point-Slope Form 42
3-4 Parallel and Perpendicular Lines 44
3-5 Solving Systems of Linear Equations 46
3-6 Absolute Value Equations 50
Chapter 3 Practice Test 52
Answers and Explanations 54
Chapter 4: Linear Inequalities and Graphs 61
4-1 Solving Inequalities 61
4-2 Compound and Absolute Value Inequalities 63
4-3 Graphing Inequalities in Two Variables 65
4-4 Graphing Systems of Inequalities 67
Chapter 4 Practice Test 69
Answers and Explanations 71
,ii • Contents
Chapter 5: Word Problems in Real-Life Situation 77
5-1 Solving Word Problems Using Linear Models 77
5-2 Solving Word Problems with Equations 79
5-3 Solving Word Problems Using Systems of Equations 81
5-4 Solving Word Problems Using Inequalities 83
Chapter 5 Practice Test 85
Answers and Explanations 87
II. Statistics and Data Analysis
Chapter 6: Ratios, Rates, and Proportions 95
6-1 Ratios and Rates 95
6-2 Proportions 97
6-3 Ratios, Rates, and Proportions Word Problems 99
Chapter 6 Practice Test 101
Answers and Explanations 103
Chapter 7: Percents 109
7-1 Percent of Change 109
7-2 Percents and Equations 111
7-3 Percent Word Problems 113
Chapter 7 Practice Test 115
Answers and Explanations 117
Chapter 8: Statistics 121
8-1 Mean, Median, Mode, and Range 121
8-2 Standard Deviation 123
8-3 Graphical Displays 125
8-4 Scatter Plots 127
8-5 Populations, Samples, and Random Selection 129
Chapter 8 Practice Test 131
Answers and Explanations 133
Chapter 9: Categorical Data and Probability 139
9-1 Permutations and Combinations 139
9-2 Rules of Probability 141
9-3 Categorical Data and Conditional Probabilities 143
Chapter 9 Practice Test 145
Answers and Explanations 147
, Contents • iii
III. Advanced Math
Chapter 10: Law of Exponents and Polynomials 153
10-1 Laws of Exponents and Scientific Notation 153
10-2 Adding, Subtracting, Multiplying, and Dividing Polynomials 156
10-3 FOIL Method and Special Products 159
10-4 Prime Factorization, GCF, and LCM 161
10-5 Factoring Using the Distributive Property 164
Chapter 10 Practice Test 166
Answers and Explanations 168
Chapter 11: Quadratic Functions 173
11-1 Graphs of Quadratic Equations 173
11-2 Factoring Trinomials 176
11-3 Factoring Differences of Squares and Perfect Square Trinomials 179
11-4 Solving Quadratic Equations by Completing the Square 181
11-5 Quadratic Formula and the Discriminant 183
11-6 Solving Systems Consisting Linear and Quadratic Equations 186
Chapter 11 Practice Test 188
Answers and Explanations 190
Chapter 12: Composition, Recursion, and Exponential Functions 197
12-1 Composition of Functions 197
12-2 Recursive Formula 199
12-3 Exponential Functions and Graphs 201
12-4 Exponential Growth and Decay 203
Chapter 12 Practice Test 205
Answers and Explanations 207
Chapter 13: Polynomial and Radical Functions 213
13-1 Polynomial Functions and Their Graphs 213
13-2 Remainder Theorem and Factor Theorem 215
13-3 Radical Expressions 217
13-4 Solving Radical Equations 220
13-5 Complex Numbers 222
Chapter 13 Practice Test 225
Answers and Explanations 227
, iv • Contents
Chapter 14: Rational Expressions 233
14-1 Rational Expressions 233
14-2 Solving Rational Equations 236
14-3 Direct, Inverse, and Joint Variation 238
14-4 Solving Word Problems Using Rational Equations 240
Chapter 14 Practice Test 242
Answers and Explanations 244
Chapter 15: Trigonometric Functions 251
15-1 Trigonometric Ratios of Acute Angles 251
15-2 The Radian Measure of an Angle 253
15-3 Trigonometric Functions of General Angles and the Unit Circle 255
Chapter 15 Practice Test 259
Answers and Explanations 261
IV. Geometry
Chapter 16: Lines and Angles 267
16-1 Lines, Segments, and Rays 267
16-2 Angles 269
16-3 Parallel and Perpendicular Lines 271
Chapter 16 Practice Test 273
Answers and Explanations to Exercises and Practice Test 275
Chapter 17: Triangles 279
17-1 Angles of a Triangles 279
17-2 Pythagorean Theorem and Special Right Triangles 281
17-3 Similar Triangles and Proportional Parts 283
17-4 Area of a Triangle 285
Chapter 17 Practice Test 287
Answers and Explanations 289
Chapter 18: Polygons 295
18-1 Parallelograms 295
18-2 Rectangles, Squares, and Trapezoids 297
18-3 Regular Polygons 299
Chapter 18 Practice Test 301
Answers and Explanations 303
