# Math Competition Books Series

## 10 Volumes

### PDF files

#### Prepare for Mathcounts, AMC 8/10/12, and AIME (American Invitational Mathematics Examination).

Each chapter consists of:
(1) basic skill and knowledge section with plenty of examples,
(2) exercise problems,
(3) detailed solutions to all problems.

## Volume 1 The Mass Points Method

Chapter 1. Terms and Properties1

Chapter 2. Direct Application of Mass Points 20

Chapter 3. Removing Line Segments47

Chapter 4. Splitting Mass Points 62

Chapter 5. Length and Area Problems 77

Index 177

## Volume 2 Balls and Boxes

Chapter 1. Permutations And Combinations1

Chapter 2. Number Separations 23

Chapter 3. Indistinguishable Balls And Distinguishable Boxes56

Chapter 4. Distinguishable Balls And Distinguishable Boxes81

Chapter 5. Distinguishable Balls And Indistinguishable Boxes 119

Chapter 7. Mixed Problems 170

Index 181

## Volume 3 The Area Method

Chapter 1. Base and Height Formula1

Chapter 2. Trigonometry Formulas 12

Chapter 3. Heron's Formula 23

Chapter 4. The Square Ratio Formula31

Chapter 5. The Perimeter and Radius Formulas 47

Chapter 6. The Theorems of the Areas Ratio 56

Chapter 7. The Common Side Theorems 81

Chapter 8. The Parallel Sides Theorem 106

Chapter 9. The Common Angle Theorems 118

Index 152

## Volume 4 Problem Solving Using Cauchy’s Inequalities

Chapter 1. Cauchy’s Inequality and Other Forms 1

Chapter 2. Circles, Ellipses, and Hyperbolas 8

Chapter 3. Finding the Maximum or Minimum Values 12

Chapter 4. Solving Geometry Problems 40

Chapter 5. Solving Radical Problems 101

Chapter 6. Solving Equation and Inequality Problems 117

Chapter 7. Proving Inequalities 128

Index 143

## Volume 5 Problem Solving Using AM – GM Inequalities

Chapter 1. Introduction: AM- GM Inequality 1

Chapter 2. Different forms of AM – GM inequalities 20

Chapter 3. Finding Largest / Smallest Values 35

Chapter 4. Solving Geometry Problems 84

Chapter 5. Solving Equations and Inequalities 110

Chapter 6. Using AM – GM to Prove Inequalities 122

Index 147

## Volume 6 The Completing the Square Method

Chapter 1. Introduction 1

Chapter 2. Factoring10

Chapter 3. Finding Values 20

Chapter 4. Finding Maximum/Minimum Values 45

Chapter 5. Solving Equations and Inequalities 84

Chapter 6. Proving Problems 106

Index 121

## Volume 7 Problem Solving Using the Discriminant

Chapter 1. Discriminant: Basic Knowledge 1

Chapter 3. Solving Quadratic Equation Problems 8

Chapter 4. Solving Quadratic Function Problems 12

Chapter 5. Finding the Maximum or Minimum Values39

Chapter 6. Solving Radical Problems 102

Chapter 7. Solving Analytic Geometry Problems 118

Chapter 8. Applying Discriminant by Construction 129

Chapter 9. Applying Discriminant to Prove Problems129

Index 144

## Volume 8 The Substitution Method

Part I Skills of the Substitution Method 1

Chapter 1. Linear Substitution6

Chapter 3. Inverse Substitution 24

Chapter 4. Variable Expression Substitution 40

Chapter 5. Average Value Substitution 53

Chapter 6. Ratio Substitution 61

Chapter 7. Other Substitutions 69

Part II Problem Solving Using the Substitution Method76

Chapter 8. Simplifications 76

Chapter 9. Factoring Polynomials91

Chapter 10. Solving Equations99

Chapter 11. Proving Equality And Inequality131

Chapter 12. Finding The Greatest/Smallest Values139

Index 152

## Volume 9 Problem Solving Using Auxiliary Lines

Chapter 1. Draw the auxiliary lines with Medians 1

Chapter 2. Draw the auxiliary lines with Midlines 28

Chapter 3. Draw the auxiliary lines with Angle Bisectors 49

Chapter 4. Draw the auxiliary lines with Perpendicular Lines 70

Chapter 5. Draw the auxiliary lines with Parallel Lines97

Chapter 6. Draw the auxiliary lines with Circles 143

Index 210

## Volume 10 Problem Solving Using Vieta’s Theorem

Chapter 1. Vieta’s Theorem1

Chapter 2. Converse of Vieta’s Theorem35

Chapter 3. Symmetric functions of the roots of quadratic equations 77

Chapter 4. Non-symmetric functions of the roots of quadratic equations102

Chapter 5. The roots and the coefficients of cubic/quartic equations 144

Chapter 6. Solving the system of nonlinear equations 172

Index 220

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