“AI가 문제를 다 풀어주는 시대에, 왜 Algebra II를 배워야 할까?”

 

Algebra II는 단순히 공식을 외우고 정답을 찾는 과목이 아닙니다. Algebra I에서 미지수의 값을 구하는 법을 배웠다면, Algebra II에서는 함수와 그래프를 통해 세상의 다양한 ‘관계’를 이해하는 법을 배웁니다.

공부한 시간과 성적의 관계, 시간에 따른 자산의 변화, 정보가 퍼지는 속도처럼 우리 삶의 많은 현상은 수학적 관계로 설명할 수 있습니다. 복잡해 보이는 문제도 식으로 정리하면 그 안에 숨어 있던 단순한 관계가 드러납니다.

AI는 답을 알려줄 수 있지만, 그 답이 왜 맞는지 이해하고 판단하는 힘은 직접 생각하고 문제를 풀어보는 과정에서 길러집니다.

『I Know You Can Do Algebra II』는 Algebra II를 어렵게 느끼는 학생들이 개념을 이해하고, 문제 속 관계를 발견하며 수학의 즐거움을 경험하도록 돕는 책입니다.

 

I Know You Can Do Algebra II.

당신은 충분히 해낼 수 있습니다.

[목 차]

Preface .......................................................................................................4

저자소개 .......................................................................................................5

이 책의 특징 ..................................................................................................5

 

1. Functions and Their Graphs......................................................................9

1.1 Functions and Their Properties....................................................... 10

1.2 Linear Functions......................................................................... 15

1.3 Transformations of Functions......................................................... 21

1.4 Absolute Value Functions.............................................................. 25

 

2. Quadratic Functions............................................................................... 31

2.1 Quadratic Functions..................................................................... 32

2.2 Quadratic Equations..................................................................... 36

2.3 Completing the Square.................................................................. 44

2.4 Complex Numbers....................................................................... 48

 

3. Polynomial Functions and Rational Functions...................................... 57

3.1 Polynomial Functions................................................................... 58

3.2 Synthetic Division and Long Division................................................ 66

3.3 Theorems for Determining Zeros of Polynomial Functions..................... 71

3.4 Rational Functions....................................................................... 77

3.5 Rational Expressions and Equations.................................................. 81

3.6 Polynomial and Rational Inequalities................................................. 86

 

4. Radical Functions and Equations........................................................... 91

4.1 Rational Exponents...................................................................... 92

4.2 Radical Functions and Equations...................................................... 96

4.3 Operations on Functions and Inverse Functions.................................. 104

 

5. Exponential Functions and Logarithmic Functions ............................ 113

5.1 Exponential Functions................................................................. 114

5.2 Functions involving e.................................................................. 119

5.3 Exponential Modeling.................................................................. 121

5.4 Logarithmic Functions.................................................................. 125

5.5 Properties of Logarithms............................................................... 133

5.6 Exponential and Logarithmic Equations............................................ 138

5.7 Compound Interest..................................................................... 142

 

6. Trigonometric Functions...................................................................... 145

6.1 Angle Measure........................................................................... 146

6.2 Trigonometry in Unit Circle........................................................... 151

6.3 Trigonometric Function Graphs...................................................... 157

6.4 Trigonometric Identities............................................................... 167

6.5 Inverse Trigonometric Functions.................................................... 177

6.6 Trigonometric Equations.............................................................. 184

6.7 Solving Triangles........................................................................ 188

 

7. Sequences and Series.......................................................................... 197

7.1 Sequences................................................................................ 198

7.2 Series...................................................................................... 204

 

8. Answer Key........................................................................................... 211