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.

Buy the entire 10 volumes for $151.56.
 

Volume 1 The Mass Points Method

Table of Contents

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

Table of Contents

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

Table of Contents

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

Table of Contents

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

Table of Contents

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

Table of Contents

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

Table of Contents

Chapter 1. Discriminant: Basic Knowledge 1

Chapter 2. Factoring Quadratic Trinomials8

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

Table of Contents

Part I Skills of the Substitution Method 1

Chapter 1. Linear Substitution6

Chapter 2. Radical Substitution14

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

Table of Contents

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

Table of Contents

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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