      Home Math Competition Books Series

## All books are in pdf file format, not hard copy books.

These books can be used by students preparing for math competitions such as Mathcounts, AMC 8/10/12, and AIME (American Invitational Mathematics Examination).

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

## \$95.56

Click the button to purchase: Each Volume (10 volumes in total):

 Titles The Mass Points Method \$8.11 USD Problem SolvBalls and Boxes \$8.25 USD The Area Method \$10.39 USD Problem Solving Using Cauthy's Inequalities \$11.56 USD Problem Solving Using AM – GM Inequalities \$8.98 USD The Completing the Square Method \$7.38 USD Problem Solving Using the Discriminant \$9.23 USD The Substitution Method \$8.56 USD Problem Solving Using Auxiliary Lines \$17.43 USD Problem Solving Using Vieta's Theroem \$14.91 USD Volume 1.       The Mass Points Method

1. Terms and Properties                                                               1

2. Direct Application of Mass Points                                           20

3. Removing Line Segments                                                              47

4. Splitting Mass Points                                                                     62

5. Length and Area Problems                                                           77

Index                                                                                                117

Volume 2.       Balls and Boxes

Chapter 1 Permutations And Combinations       1

Chapter 2 Number Separations                         23

Chapter 3 Indistinguishable Balls And Distinguishable  Boxes                    56

Chapter 4 Distinguishable Balls And Distinguishable Boxes                     81

Chapter 5 Distinguishable Balls And Indistinguishable Boxes                      119

Chapter 6 Indistinguishable Balls And Indistinguishable Boxes                   152

Chapter 7 Mixed Problems                            152

Index                                                               181

Volume 3.       The Area Method

Chapter 1. Base and Height Formula                                                              1

Chapter 2. Trigonometry Formulas                                                                12

Chapter 3. Heron's Formula                                                                            23

Chapter 4. The Square Ratio Formula                                                            31

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 Cauthy’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 Proving Inequalities                                     122

Index                                                                                                               147

Volume 6.       The Completing the Square Method

Chapter 1. Introduction                                                                                  1

Chapter 2 Factoring                                                                                        10

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 2. Factoring Quadratic Trinomials                                                     8

Chapter 3. Solving Quadratic Equation Problems                                          8

Chapter 4. Solving Quadratic Function Problems                                          12

Chapter 5. Finding the Maximum or Minimum Values                                 39

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 Problems                                   129

Index                                                                                                               144

Volume 8.       The Substitution Method

Part I Skills of the Substitution Method                                                         1

Chapter 1 Linear Substitution                                                             6

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 Method                               76

Chapter 8 Simplifications                                                                   76

Chapter 9 Factoring Polynomials                                                        91

Chapter 10 Solving Equations                                                            99

Chapter 11 Proving Equality And Inequality                                     131

Chapter 12 Finding The Greatest/Smallest Values                            139

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 the midlines                                                28

Chapter 3 Draw the auxiliary lines with the angle bisector                            49

Chapter 4 Draw the auxiliary lines with perpendicular line                           70

Chapter 5 Draw the auxiliary lines with parallel lines                                   97

Chapter 6 Draw the auxiliary lines with circles                                              143

Index                                                                                                               210

Volume 10.     Problem Solving Using Vieta’s Theorem

Chapter 1 Vieta’s Theorem                                                                             1

Chapter 2 Converse of Vieta’s Theorem                                                        35

Chapter 3 Symmetric functions of the roots of quadratic equations              77

Chapter 4 Non-symmetric functions of the roots of quadratic equations       102

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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