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유하림 커리큘럼 Essential Math Series의 핵심 교재 중 한 권입니다. 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 집필하였습니다. 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 교재라고 단언컨대 말 씀 드릴 수 있습니다.

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