The Essential Guide to ALGEBRA 2 - 개정2판 <*> 미국 수학 시리즈 4

유하림 (지은이)헤르몬하우스

2023-01-31

Algebra 2를 배울 때 기본 개념과 그 응용 외에 무엇을 더 알아야만 학교 시험뿐 아니라 SAT 2 및 AMC 10/12 문제풀이까지 도달할 수 있을까 고민하면서 집필하였다. 특히, 미국 명문 Boarding School 및 국내외 외국인학교에 다니는 9학년(10학년) 학생들 이 반드시 숙지하고, 생각의 방향을 올바르게 키워나가서 결국 AMC와 같은 수학 경 시대회에서도 우수한 성적을 거둘 수 있을까 고민을 많이 한 교재다.

목차

Preface 2

저자 소개 3

이 책의 구성과 특징 4

Topic 1 Real Number System

1.1 Properties of Real Numbers............................................... 10

1.2 Real Number Line.............................................................. 12

1.3 Algebraic Expressions....................................................... 15

1.4 Solving Linear Equations and Word Problems................... 17

1.5 Solving Inequalities........................................................... 19

1.6 Compound Inequality........................................................ 20

1.7 Absolute Value................................................................... 21

Topic 2 Function and Linear Graph

2.1 Relation and Function........................................................ 32

2.2 Direct Variation.................................................................. 34

2.3 Linear Function and Slope-Intercept Form........................ 36

2.4 Perpendicular and Parallel Lines........................................ 39

2.5 Transformation of Linear Function.................................... 41

2.6 Absolute Value Function and Graph.................................. 43

2.7 Two-Variable Inequalities.................................................. 45

Topic 3 System of Equations and Inequalities

3.1 System of Linear Equations............................................... 58

3.2 Two Methods : Substitution and Elimination..................... 61

3.3 System of Linear Inequalities............................................ 64

3.4 Linear Programming.......................................................... 66

3.5 System of Equations in 3 Variables.................................... 70

3.6 Matrices............................................................................. 73

3.7 Multiplication of Matrix.................................................... 75

Topic 4 Quadratic Equations and Factoring

4.1 Quadratic Function............................................................ 86

4.3 Standard Form of a Quadratic Functions........................... 93

4.4 Completing the Square....................................................... 95

4.5 Quadratic Formula............................................................. 97

4.6 Complex Numbers............................................................. 99

4.7 Application of Quadratic Function and Equations............. 102

4.8 Quadratic Inequalities........................................................ 106

Topic 5 Polynomials and Polynomial Function

5.1 Classification of Polynomials............................................ 118

5.2 End-Behavior of Polynomial Function.............................. 120

5.3 The Shape of Cubic Graph................................................. 121

5.4 Table Values and Polynomial Degrees............................... 122

5.5 Finding x-intercepts........................................................... 123

5.6 Finding Zeros..................................................................... 124

5.7 Given Zeros....................................................................... 125

Topic 6 Application of Polynomials

6.1 Factorization...................................................................... 132

6.2 Long Division.................................................................... 134

6.3 Factor Theorem.................................................................. 136

6.4 Synthetic Division............................................................. 137

6.5 Rational Root Theorem...................................................... 139

6.6 Two guidelines for finding roots........................................ 141

Topic 7 Radical Expression and Radical Function

7.1 Introduction to Radicals..................................................... 148

7.2 Multiplying Radical Expressions....................................... 152

7.3 Rational Exponents............................................................ 157

7.4 Solving Radical Equations................................................. 159

7.5 Radical Function................................................................ 162

Topic 8 Rational Expression and Rational Function

8.1 Inverse Variation................................................................ 176

8.2 Graphs of Rational Functions............................................ 179

8.3 Reciprocal Function........................................................... 181

8.4 Hole or Vertical Asymptote................................................ 183

8.5 Rational Inequality............................................................. 184

8.6 Word Problems.................................................................. 185

8.7 Solving Rational Equations................................................ 186

Topic 9 Exponential and Logarithmic Expressions and Functions

9.1 Exponential Function......................................................... 198

9.2 Exponential Equation......................................................... 200

9.3 Logarithmic Function........................................................ 204

9.4 Logarithmic Equation........................................................ 205

9.5 Using Logarithm to Solve Equations................................. 209

Topic 10 Sequence and Series

10.1 Sequence............................................................................ 222

10.2 Arithmetic Sequence and Series........................................ 223

10.3 Geometric Sequence and Series......................................... 225

10.4 Arithmetic Mean and Geometric Mean.............................. 228

10.5 Difference Sequence.......................................................... 229

10.6 The Σ Notation................................................................... 231

Topic 11 Counting : Permutation and Combination

11.1 From a to b......................................................................... 242

11.2 Multiplication Principle..................................................... 243

11.3 Permutation : Counting Successive Events........................ 248

11.4 Principle of Addition.......................................................... 252

11.5 Combination : Another Tool for Overcounts...................... 255

11.6 Permutation vs. Combination............................................. 258

11.7 Binomial Theorem............................................................. 260

Topic 12 Probability

12.1 Probability......................................................................... 270

12.2 Probability and Tree Diagrams.......................................... 281

Topic 13 Probability Distribution Functions

13.1 Discrete Random Variable................................................. 294

13.2 Binomial Distribution........................................................ 296

13.3 Normal Distribution........................................................... 300

Solution Manual 309