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압구정 현장 강의를 통해 Prealgebra부터 AP Calculus까지 가르치면서, 강사로서 느낀 점은, 학부모님들이 선택할 수 있는 국내에서 판매되는 전문 교재가 몇 개 없다는 것과 충분히 많은 연구와 노력을 통 해 개발된 교재들은 더더욱 부족하다는 점이었습니다.
국내 수능 시장에서는 "OOO" 커리큘럼으로 진행되는 수업들과 교재 들이 많은 데 비해, 미국 SAT 시장과 유학 시장은 그렇지 않았기 때문에, 이렇게 유하림 커리큘럼의 시작을 알리는 것이 기대되면서도 떨립니다.
Algebra 1을 처음 배우는 학생들이 흥미롭게 배우길 희망하면서 교재를 썼습니다. 또한, 강의나 교재가 너무 쉽다고 느껴지진 않을 정도 의 개념 강의 수준을 유지하기 위해 노력했으며, 지금까지 수업해왔 던 내용들을 많이 담았기 때문에 국내에서 유학을 준비하는 학생이나 해외에서 공부하고 있는 학생들에게 도움이 되길 진심으로 희망해봅니다.
국내 수능 시장에서는 "OOO" 커리큘럼으로 진행되는 수업들과 교재 들이 많은 데 비해, 미국 SAT 시장과 유학 시장은 그렇지 않았기 때문에, 이렇게 유하림 커리큘럼의 시작을 알리는 것이 기대되면서도 떨립니다.
Algebra 1을 처음 배우는 학생들이 흥미롭게 배우길 희망하면서 교재를 썼습니다. 또한, 강의나 교재가 너무 쉽다고 느껴지진 않을 정도 의 개념 강의 수준을 유지하기 위해 노력했으며, 지금까지 수업해왔 던 내용들을 많이 담았기 때문에 국내에서 유학을 준비하는 학생이나 해외에서 공부하고 있는 학생들에게 도움이 되길 진심으로 희망해봅니다.
저자: 유하림
Preface 2
저자 소개 3
이 책의 구성과 특징 4
Topic 1 Mathematical Expressions
1.1 Mathematical Expressions................................................. 10
1.2 Arithmetic with Expressions.............................................. 11
1.3 Manipulation of Expressions............................................. 13
Topic 2 More Variables
2.1 One-Variable Equation....................................................... 22
2.2 Multivariable Expressions................................................. 24
2.3 Multivariable Arithmetic ................................................... 25
2.4 Expansion and Simplification............................................ 27
2.5 Multivariable Fractions...................................................... 29
2.6 Multivariable Equations..................................................... 30
Topic 3 Two-Variable Equations
3.1 Two-Variable Equations..................................................... 38
3.2 Substitution........................................................................ 39
3.3 Elimination ....................................................................... 41
3.4 Word Problems ................................................................. 43
Topic 4 Proportion
4.1 Direct Proportion............................................................... 50
4.2 Inverse Proportion............................................................. 51
4.3 Joint Proportion................................................................. 52
4.4 Rate in Algebra 1............................................................... 53
Topic 5 Linear Graphs
5.1 The Real Number Line and the Cartesian Plane................ 62
5.2 Graphing Linear Equations................................................ 65
5.3 Slope Problems.................................................................. 68
5.4 Finding Line Equations...................................................... 70
5.5 Slope and Intercepts........................................................... 73
5.6 Parallel and Perpendicular lines......................................... 75
Topic 6 Basic Inequalities
6.1 Introduction ...................................................................... 84
6.2 Comparison ....................................................................... 86
6.3 Linear Inequalities............................................................. 88
6.4 Graphing Linear Inequalities............................................. 91
6.5 Linear Optimization........................................................... 93
Topic 7 Introduction to Quadratics
7.1 Quadratic Equations........................................................... 100
7.2 Factorization for a = 1....................................................... 102
7.3 Factorization for a ≠ 1....................................................... 104
Topic 8 More Factorization
8.1 Square of Binomials........................................................... 116
8.2 Difference of Squares........................................................ 120
8.3 Four-Term Quadratics........................................................ 122
Topic 9 Complex Number
9.1 x2 = -1................................................................................ 130
9.2 Complex Numbers............................................................. 132
Topic 10 Completing the Squares
10.1 The Perfect Squares........................................................... 140
10.2 Completing the Squares..................................................... 143
10.3 Quadratic Formula............................................................. 145
Topic 11 Graphing Quadratics and Inequalities
11.1 Parabola ............................................................................ 156
11.2 Circle ................................................................................ 161
11.3 Quadratic Inequalities ....................................................... 165
11.4 Trivial Inequalities............................................................. 169
11.5 Quadratic Optimization...................................................... 170
Topic 12 Functions
12.1 Function ............................................................................ 180
12.2 Function Arithmetic........................................................... 185
12.3 Composition of Two Functions.......................................... 188
Topic 13 Graphs and Transformation
13.1 Graphing Functions............................................................ 200
13.2 Transformation .................................................................. 206
13.3 Graphs of Inverse Functions.............................................. 211
Topic 14 Polynomial Arithmetic
14.1 Polynomials....................................................................... 224
14.2 Polynomial Division.......................................................... 227
14.3 Rational Equations............................................................. 231
Topic 15 Statistics
15.1 Measures of Central Tendency........................................... 238
15.2 Measures of Spread............................................................ 239
15.3 Line of Best Fit.................................................................. 241
Solution Manual 247
저자 소개 3
이 책의 구성과 특징 4
Topic 1 Mathematical Expressions
1.1 Mathematical Expressions................................................. 10
1.2 Arithmetic with Expressions.............................................. 11
1.3 Manipulation of Expressions............................................. 13
Topic 2 More Variables
2.1 One-Variable Equation....................................................... 22
2.2 Multivariable Expressions................................................. 24
2.3 Multivariable Arithmetic ................................................... 25
2.4 Expansion and Simplification............................................ 27
2.5 Multivariable Fractions...................................................... 29
2.6 Multivariable Equations..................................................... 30
Topic 3 Two-Variable Equations
3.1 Two-Variable Equations..................................................... 38
3.2 Substitution........................................................................ 39
3.3 Elimination ....................................................................... 41
3.4 Word Problems ................................................................. 43
Topic 4 Proportion
4.1 Direct Proportion............................................................... 50
4.2 Inverse Proportion............................................................. 51
4.3 Joint Proportion................................................................. 52
4.4 Rate in Algebra 1............................................................... 53
Topic 5 Linear Graphs
5.1 The Real Number Line and the Cartesian Plane................ 62
5.2 Graphing Linear Equations................................................ 65
5.3 Slope Problems.................................................................. 68
5.4 Finding Line Equations...................................................... 70
5.5 Slope and Intercepts........................................................... 73
5.6 Parallel and Perpendicular lines......................................... 75
Topic 6 Basic Inequalities
6.1 Introduction ...................................................................... 84
6.2 Comparison ....................................................................... 86
6.3 Linear Inequalities............................................................. 88
6.4 Graphing Linear Inequalities............................................. 91
6.5 Linear Optimization........................................................... 93
Topic 7 Introduction to Quadratics
7.1 Quadratic Equations........................................................... 100
7.2 Factorization for a = 1....................................................... 102
7.3 Factorization for a ≠ 1....................................................... 104
Topic 8 More Factorization
8.1 Square of Binomials........................................................... 116
8.2 Difference of Squares........................................................ 120
8.3 Four-Term Quadratics........................................................ 122
Topic 9 Complex Number
9.1 x2 = -1................................................................................ 130
9.2 Complex Numbers............................................................. 132
Topic 10 Completing the Squares
10.1 The Perfect Squares........................................................... 140
10.2 Completing the Squares..................................................... 143
10.3 Quadratic Formula............................................................. 145
Topic 11 Graphing Quadratics and Inequalities
11.1 Parabola ............................................................................ 156
11.2 Circle ................................................................................ 161
11.3 Quadratic Inequalities ....................................................... 165
11.4 Trivial Inequalities............................................................. 169
11.5 Quadratic Optimization...................................................... 170
Topic 12 Functions
12.1 Function ............................................................................ 180
12.2 Function Arithmetic........................................................... 185
12.3 Composition of Two Functions.......................................... 188
Topic 13 Graphs and Transformation
13.1 Graphing Functions............................................................ 200
13.2 Transformation .................................................................. 206
13.3 Graphs of Inverse Functions.............................................. 211
Topic 14 Polynomial Arithmetic
14.1 Polynomials....................................................................... 224
14.2 Polynomial Division.......................................................... 227
14.3 Rational Equations............................................................. 231
Topic 15 Statistics
15.1 Measures of Central Tendency........................................... 238
15.2 Measures of Spread............................................................ 239
15.3 Line of Best Fit.................................................................. 241
Solution Manual 247
