50 Mathcounts Lectures


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Volume 2
Volume 3

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Chapter 1. Logic (click to read chapter)1

Chapter 2. Addition and Subtraction15

Chapter 3. Multiplication and Division30

Chapter 4. Parity47

Chapter 5. Operations and Fractions62

Chapter 6. Operations with Decimals81

Chapter 7. Operations with Percents96

Chapter 8. Pigeonhole Principle 112

Chapter 9. Converting Fractions, Decimals, and Percents 125

Chapter 10. Ratios and Proportions (click to read chapter) 140

Chapter 11. Perimeter and Area 152

Chapter 12. Counting Principles 177

Chapter 13. Exponents195

Chapter 14. Radicals205

Chapter 15. Place Value and Scientific Notation 222

Chapter 16. Absolute Values 234

Chapter 17. Order of Operations 247

Chapter 18. Simplifying Algebraic Expressions 256

Index 271

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Chapter 19. Evaluating Algebraic Expressions 1

Chapter 20. Divisibility14

Chapter 21. Solving Equations32

Chapter 22. Solving Inequalities 46

Chapter 23. Venn diagrams 63

Chapter 24. Combinatorics (click to read chapter) 83

Chapter 25. Angles and triangles 104

Chapter 26. Classification of triangles 115

Chapter 27. Similar triangles 130

Chapter 28. Pythagorean Theorem 137

Chapter 29. Quadrilaterals163

Chapter 30. Trapezoids177

Chapter 31. Parallelograms191

Chapter 32. Angle bisectors and medians 205

Chapter 33. Triangular inequality218

Chapter 34. Area Method 227

Chapter 35. Polygons241

Chapter 36. Circles262

Index283

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Chapter 37. Factors1

Chapter 38. Prime Numbers 21

Chapter 39. Least Common Multiples And Greatest Common Factors39

Chapter 40. Methods Of Factoring 57

Chapter 41. Venn Diagram 2 74

Chapter 42. Congruence86

Chapter 43. Last Digits108

Chapter 44. Remainder 119

Chapter 45. Coordinate System 134

Chapter 46. Lines And Equations 149

Chapter 47. Systems Of Equations 174

Chapter 48. Mean, Median, Mode, And Range 198

Chapter 49. Volume 220

Chapter 50. Probability 247

Index 279


ACKNOWLEDGEMENTS
We would like to thank the following math contests:
The Mathcounts Competitions: the nation's premier middle school math enrichment, coaching, and competition program.
The AMC 8: a 25 question, 40 minute multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem solving skills.
The AIME (American Invitational Mathematics Examination): an intermediate examination between the AMC 10 or AMC 12 and the USAMO.
The China Middle School Math Competition.

We would also like to thank the hundreds of families who participated in the 50 Mathcounts Lectures 2011 Summer Program. Without their support and trust, this program would not be possible. Thanks goes to these parents and students who reviewed the draft of the lectures, made corrections to errors, and provided excellent insights to solutions.