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.
Volume 1. The
Mass Points Method
Table
of Contents
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
Table
of Contents
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
Table
of contents
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
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 Proving
Inequalities 122
Index 147
Volume 6. The
Completing the Square Method
Table of Contents
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
Table of Contents
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
Table of Contents
Part I Skills of the Substitution Method 1
Chapter 1 Linear Substitution
6
Chapter 2 Radical Substitution 14
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
Table
of Contents
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
Table of Contents
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
