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
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
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
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
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
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
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
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
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
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
Please email ourmathcounts@gmail.com if you have any questions. Thanks.