## Dec 16, 2012

1. [PDF]

### 8. Farey Fractions

IMO 2000 TRAINING. 991009. Farey Fractions. Definition. The set of Farey fractions of order n, denoted by n. F , is the set of reduced fractions in the closed ...
2. [PDF]

### 68. 第八屆培正數學邀請賽，初賽（中四組）

1. 第八屆培正數學邀請賽. 8th Pui Ching Invitational Mathematics Competition. 初賽（中四組）. Heat Event (Secondary 4). 時限：1 小時15 分. Time allowed: 1 hour ...
3. [PDF]

### 67. 第八屆培正數學邀請賽，初賽（中三組）

1. 第八屆培正數學邀請賽. 8th Pui Ching Invitational Mathematics Competition. 初賽（中三組）. Heat Event (Secondary 3). 時限：1 小時15 分. Time allowed: 1 hour ...
4. [PDF]

### 69. 第八屆培正數學邀請賽，初賽（高中組）

1. 第八屆培正數學邀請賽. 8th Pui Ching Invitational Mathematics Competition. 初賽（高中組）. Heat Event (Senior Secondary). 時限：1 小時15 分. Time allowed: 1 ...
5. [PDF]

### 66. 第八屆培正數學邀請賽，初賽（中二組）

1. 第八屆培正數學邀請賽. 8th Pui Ching Invitational Mathematics Competition. 初賽（中二組）. Heat Event (Secondary 2). 時限：1 小時15 分. Time allowed: 1 hour ...
6. [PDF]

### 3. Probability

Mathematical Database. Page 1 of 13. PROBABILITY. In everyday life, we would frequently encounter questions like “What is the chance that our team will win in ...
7. [PDF]

### INTRODUCTORY THEORY OF DIFFERENTIATION

8. [PDF]

1. Worksheet for Teaching Module. Countability (Lesson 2). Topic: Proof by Contradiction and One-to-One Correspondence. Introduction. In this lesson we will ...
9. [PDF]

### number theory unit 3 diophantine equations

Mathematical Database. Page 1 of 10. NUMBER THEORY. UNIT 3 DIOPHANTINE EQUATIONS. 1. Introduction. A Diophantine equation is an equation for which ...
10. [PDF]

### inequalities unit 1 classical inequalities

Mathematical Database. Page 1 of 15. INEQUALITIES. UNIT 1 CLASSICAL INEQUALITIES. 1. Inequality of the Means. To motivate our discussion, let's look at ...
11. [PDF]

### INEQUALITIES

Mathematical Database. Page 1 of 7. INEQUALITIES. UNIT 3 GEOMETRIC INEQUALITIES. A geometric inequality is an inequality which appears in a geometric ...
12. [PDF]

### BINOMIAL THEOREM

Mathematical Database. Page 1 of 13. BINOMIAL THEOREM. 1. Introduction. When we expand. 2. ( 1) x + and. 3. ( 1) x + , we get. 2. 2. 2. ( 1) ( 1)( 1). 1. 2 1 ...
13. [PDF]

### INEQUALITIES

Mathematical Database. Page 1 of 12. INEQUALITIES. UNIT 2 TECHNIQUES IN PROVING INEQUALITIES. In Unit 1 we learnt several classical inequalities.
14. [PDF]

### RAMSEY'S THEORY

Mathematical Database. Page 1 of 1. RAMSEY'S THEORY. You probably have heard of this interesting fact: among any six people in the world, there exist ...
15. [PDF]

### PIGEONHOLE PRINCIPLE

Mathematical Database. Page 1 of 12. PIGEONHOLE PRINCIPLE. Pigeonhole principle is a fundamental but powerful tool in combinatorics. Unlike many other ...
16. [PDF]

### SETS AND FUNCTIONS

Mathematical Database. Page 1 of 22. SETS AND FUNCTIONS. 1. Introduction of Sets. The concept of sets is the foundation of modern mathematics and ...
17. [PDF]

### logic

Mathematical Database. Page 1 of 7. LOGIC. One of the most important criteria in studying mathematics is having a logical mind. In the following texts, some ...
18. [PDF]

### convergence and limits

Mathematical Database. CONVERGENCE AND LIMITS. 1. Introduction. In “Introductory Theory of Differentiation” we introduced the theory of limits of functions.
19. [PDF]

### Number theory unit 1 divisibility

Mathematical Database. Page 1 of 14. NUMBER THEORY. UNIT 1 DIVISIBILITY. 1. Divisibility. Definition 1.1. Let a and b be integers, 0 a ≠ . We say that a ...
20. [PDF]

### chapter 10 physical treatments of some mathematical problems

Page 1 of 11. CHAPTER 10. PHYSICAL TREATMENTS OF SOME MATHEMATICAL PROBLEMS. Mathematics is the study of the relationships between ...
21. [PDF]

### number theory unit 4 some special numbers

Mathematical Database. Page 1 of 11. NUMBER THEORY. UNIT 4 SOME SPECIAL NUMBERS. 1. Introduction. In the previous units we have come across ...
22. [PDF]

1. Worksheet for Teaching Module. Countability (Lesson 4). Topic: Countable Sets. Introduction. In the previous lesson we studied finite sets. In this lesson we ...
23. [PDF]

1. Worksheet for Teaching Module. Countability (Lesson 6). Topic: Algebraic Numbers. Introduction. In this lesson we shall apply the theory of countability to ...
24. [PDF]

### MATHEMATICAL INDUCTION

Mathematical Database. Page 1 of 21. MATHEMATICAL INDUCTION. 1. Introduction. Mathematics distinguishes itself from the other sciences in that it is built ...
25. [PDF]

### 拉姆賽理論（Ramsey's Theory） - 數學資料庫

數學資料庫. 第1 頁，共6 頁. 拉姆賽理論（Ramsey's Theory）. 世界上任何六個人之中，必定有三個是互相認識或互相不認識的。這樣有趣的. 事實相信很多人都會聽過， ...
26. [PDF]

### number theory unit 0 introduction

Mathematical Database. Page 1 of 3. NUMBER THEORY. UNIT 0 INTRODUCTION. The history of number theory dates back to almost as far as the history of ...
27. [PDF]

### 3. Baire's theorem

Page 1 of 5. To see how powerful the Baire's theorem is, we demonstrate an application: we shall show that there exist continuous functions that are nowhere ...
28. [PDF]

### inequalities unit 0 introduction

Mathematical Database. Page 1 of 2. INEQUALITIES. UNIT 0 INTRODUCTION. Inequalities are mathematical statements involving one or more inequality signs: ...
29. [PDF]

### Introduction

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Introduction. In mathematics, Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle. It is named after Blaise. Pascal in much of the ...
30. [PDF]

### Summary:

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Summary: The three classical problems in greek mathematic were squaring the circle, doubling the cube and trisecting an angle. And this essay is about ...
31. [PDF]

### 小費費微積分長佂

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第1 頁. - 註：此故事純屬虛構,絕不含任何史實–. -. 那是一個風和日麗的早上，挨過了考試卻挨不過數學課的小費費頓生一個念頭：上. 山拜訪sum 山老人，順道請教他 ...
32. [PDF]

### 搶

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... 「搶」. 相信大家也玩過「搶廿一」這個數學遊戲。遊戲有廿一枚棋子，規則是雙方玩家. 輪流拿取1-4 枚棋子，拿取最後一枚棋子者為勝。要找出這個遊戲的「上策」並 ...
33. [PDF]

### Understanding Basic Calculus

i. Preface. This book is a revised and expanded version of the lecture notes for Basic Calculus and other similar courses offered by the Department of ...
34. [PDF]

### 皇牌

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相信大家一定看過魔術,以下是我為 大家介紹的一种紙牌魔術。 當觀眾現楊抽出5張牌時,交給助手,再轉交給魔術師,而2人在其中的过程中是. 沒有任何交流的喔!
35. [PDF]

### 談幾何原本

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引言. “如果歐幾里得未能激起你少年時代的熱情，那麼你就不是一個天才的科學. 家。” 愛因斯坦說的很對。一直以來，數學對於我來說，只是一門特別容易的學 ...
36. [PDF]

### hour hand, minute hand, second hand

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Question: In a circle clock, what time(s) will let three hands (hour hand, minute hand, second hand) divide the clock in three equal parts? To solve question, we ...
37. [PDF]

### 1.1.2.3.5.8…… - 數學資料庫

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頁2 / 15. 目錄：. 一. 引言. 二. 求斐波那契數列1.1.2.3.5.8……的通項. 三. 找出所有. 0. 1. 2. = +. +. +. + n n n. cT. bT. aT. 的通項 i). 0. 4 b2. > - ac ii). 0. 4 b2. = - ac iii). 0 ...
38. [PDF]

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Part-time Administrative Assistant Wanted. About Us. Mathematical Database (MD) is a non-profit organization registered under the Societies Ordinance in ...
39. [PDF]

### 邏輯學和概率－悖論探討考慮一個情況： 在你面前有兩個信封，信封旁 ...

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邏輯學和概率－悖論探討. 考慮一個情況：. 在你面前有兩個信封，信封旁的紙寫著以下的句子。 「一個信封有１元，另一個有１０元」有1/2 的概率，. 「一個信封有１０元， ...
40. [PDF]

### Full page photo print

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Page 1. lj. LS. L wa. Mm. »I4 ma. LNX. ¿L. UN. HLM: Page 2. Page 3. Page 4. Page 5. Page 6. Page 7.
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### 63. 第七屆培正數學邀請賽，決賽 - 數學資料庫

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1. 第七屆培正數學邀請賽. 7th Pui Ching Invitational Mathematics Competition. 決賽（高中組）. Final Event (Senior Secondary). 時限：2 小時. Time allowed: 2 hours ...
42. [PDF]

### Mathematical Excalibur

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Olympiad Corner. 37th. International. Mathematical. Olympiad, July 5-17, 1996, Mumbai,. India. First Day (10 July, 1996). Time: 4 hours. (Each problem is worth ...
43. [PDF]

### 中三組

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1. 第十一屆培正數學邀請賽（2012 年）. 11th Pui Ching Invitational Mathematics Competition (2012). 初賽（中三組）. Heat Event (Secondary 3). 時限：1 小時15 分 ...
44. [PDF]

### 中三組 - 數學資料庫

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1. 第五屆培正數學邀請賽. The 5th Pui Ching Invitational Mathematics Competition. 決賽（中三組）. Final Event (Secondary 3). 時限：2 小時. Time allowed: 2 hours ...
45. [PDF]

### 85. 第九屆培正數學邀請賽 - 數學資料庫

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1. 第九屆培正數學邀請賽. 9th Pui Ching Invitational Mathematics Competition. 決賽（中三組）. Final Event (Secondary 3). 時限：2 小時. Time allowed: 2 hours ...
46. [PDF]

### 4th Pui Ching Invitational Mathematics Competition Final Event ...

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1. 4th Pui Ching Invitational Mathematics Competition. Final Event (Secondary 2). 2. Time allowed: 2 hours. Instructions to Contestants: 1. 100. This paper is ...
47. [PDF]

### x

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1. Chapter 5: Applications of Differentiation. • Curve Sketching. • Applied Extremum Problems. Objectives. • To sketch graphs of functions (polynomials etc) using ...
48. [PDF]

### 4th Pui Ching Invitational Mathematics Competition Final Event ...

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1. 4th Pui Ching Invitational Mathematics Competition. Final Event (Secondary 1). 2. Time allowed: 2 hours. Instructions to Contestants: 1. 100. This paper is ...
49. [PDF]

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50. [PDF]

### Point Set Combinatorics

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Volume 13, Number 1. February-April, 2008. Point Set Combinatorics. Kin Y. Li. Olympiad Corner. The 2008 APMO was held in March. Here are the problems.
51. [PDF]

### ∫ (2x − 3)( x + 1) d x.

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1. Example Find. ∫. (2x − 3)(x. 2. + 1) dx. Wrong solution. ∫. (2x − 3)(x. 2. + 1) dx = ∫. (2x − 3) dx ·. ∫. (x. 2. + 1) dx. = (. 2 · x2. 2. − 3x. ) ·. ( x3. 3. + x. ) + C ...
52. [PDF]

### Harmonic Series (I)

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Volume 15, Number 5. February-April 2011. Harmonic Series (I). Leung Tat-Wing. Olympiad Corner. Below are the problems of the 2011. Canadian Math ...
53. [PDF]

### x

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1. Strategy for u-substitution. • Consider the integrand as product of two functions. ∫ α(x) · β(x)dx. • Choose u = an expression appearing in one function such ...
54. [PDF]

### From How to Solve It to Problem Solving - Department of ...

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Volume 12, Number 2. May 2007 – August 2007. From How to Solve It to. Problem Solving in Geometry (II). K. K. Kwok. Munsang College (HK Island). Olympiad ...
55. [PDF]

### IMO Shortlisted Problems - Department of Mathematics - The Hong ...

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Volume 15, Number 3. October 2010 - December, 2010. IMO Shortlisted Problems. Kin Y. Li. Olympiad Corner. Below are the problems of the 2010. Chinese ...
56. [PDF]

### ∫ f(x)dx ∫ f(t)dt

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1. Summary To find. ∫ b a f(x)dx. Introduce F(x) = ∫ x a f(t)dt. Required integral is F(b). It is shown that F (x) = f(x). Definition Let f be a function. Suppose G is a ...
57. [PDF]

### 中三組

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1. 第十屆培正數學邀請賽. 10th Pui Ching Invitational Mathematics Competition. 初賽（中三組）. Heat Event (Secondary 3). 時限：1 小時15 分. Time allowed: 1 hour ...
58. [PDF]

### 中三組

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1. 第十一屆培正數學邀請賽（2012 年）. 11th Pui Ching Invitational Mathematics Competition (2012). 決賽（中三組）. Final Event (Secondary 3). 時限：2 小時 ...
59. [PDF]

### Mathematical Achievement Contest 2010

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Mathematics Achievement Contest 2010. Appendix I. Information Sheet. The Mathematics Achievement Contest (MAC) is a comprehensive mathematics contest ...
60. [PDF]

### 中二組

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1. 第十一屆培正數學邀請賽（2012 年）. 11th Pui Ching Invitational Mathematics Competition (2012). 初賽（中二組）. Heat Event (Secondary 2). 時限：1 小時15 分 ...
61. [PDF]

### x

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1. Criteria for Increasing / Decreasing Functions. • If f (x) > 0 for all x in (a,b), then f is increasing on (a,b). Definition If f (x0) = 0, we say that x0 is a critical point of f.
62. [PDF]

### 團體賽（初級組）

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1. 香港培正中學第一屆數學邀請賽. Pui Ching Middle School 1st Invitational Mathematics Competition. 團體賽（初級組）. Group Event (Junior Section). 時限：45...
63. [PDF]

### 簡介費馬數 - Department of Mathematics - The Hong Kong ...

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Volume 7, Number 4. October 2002 – November 2002. 簡介費馬數. 梁達榮. Olympiad Corner. The 2002 Canadian Mathematical. Olympiad. Problem 1. Let S be ...
64. [PDF]

### 中一組 - 數學資料庫

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1. 第五屆培正數學邀請賽. 5th Pui Ching Invitational Mathematics Competition. 初賽（中一組）. Heat Event (Secondary 1). 時限：1 小時15 分. Time allowed: 1 hour ...
65. [PDF]

### 3. Exercises on invariants

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Invariance Principle (May 13, 2000). 1. Given 0 x and 0 y such that 0. 0. 0. x y. > > . Define, for. 0,1, 2, n = ",. 1. 1. 2. ,. 2 n n. n n n n n n. x y. x y x y. x y. +. +. +. = = ...
66. [PDF]

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%"('#)1 02'434"5 67 "(89'#6 @9 AB6 #CEDF6 "(GEHI \$&89DFP#CQ "5 "(89'. RS R R R U TTTTI VVVVXWWWW¦YYYYa```` b CE6 d ce34CE'% ...
67. [PDF]

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%"('#)1 02'434"5 67 "(89'#6 @9 AB6 #CEDF6 "(GEHI \$&89DFP#CQ "5 "(89'. RS R R R U TTTTI VVVV¦WWWWYXXXXa```` b CE6 d ce34CE'% ...
68. [PDF]

### 計數機程式（適用於Casio fx-3900Pv）

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第1 頁，共8 頁. 計數機程式（適用於Casio fx-3900Pv）. ○ ㆒般程式﹕. 小數轉分數第㆔版（47 個程序步）. Kin 1. 1. X↔Y. K × 2. K × 3. K × 4. K × 5. 1 cos− sin. K × 1 ...
69. [PDF]

### Lagrange Interpolation Formula - Department of Mathematics - The ...

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Volume 15, Number 2. July - September, 2010. Lagrange Interpolation Formula. Kin Y. Li. Olympiad Corner. Below are the problems used in the selection of the ...
70. [PDF]

### Double Counting - Department of Mathematics - The Hong Kong ...

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Volume 13, Number 4. November-December, 2008. Double Counting. Law Ka Ho, Leung Tat Wing and Li Kin Yin. Olympiad Corner. The following were the ...
71. [PDF]

### x

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1. Course Outline. 0. Revision. Part I. 1. Sets, Real Numbers and Inequalities. - Set notations and Real Number System. - Solving Polynomial Inequalities ...
72. [PDF]

### 答案

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第十一屆培正數學邀請賽（2012 年）. 11th Pui Ching Invitational Mathematics Competition (2012). 初賽答案. Answers to Heat Event. 題號. No. 中一組. Secondary 1...
73. [PDF]

### 1. 三次方程的判別式

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㆔次方程的判別式. ㆖期我們討論過如何利用卡爾丹公式去解方程. 0. 2. =+. + qpx x. ，. 同學可能會問﹕㆔方次程可否像㆓次方程那樣利用判別式判斷出實. 根的數目？
74. [PDF]

### L' Hospital's Rule

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Page 1 of 4. L' Hospital's Rule. In the following we are going to establish the L' Hospital Rule. For convenience, we will consider right-hand limits at a point a; ...
75. [PDF]

### 17. 香港培正中學第三屆數學邀請賽，團體賽

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香港培正中學第三屆數學邀請賽. Pui Ching Middle School 3rd Invitational Mathematics Competition. 團體賽（初級組）. Group Event (Junior Section). 時限：45 分鐘 ...
76. [PDF]

### 96. 第十屆培正數學邀請賽，決賽（中二） - 數學資料庫

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1. 第十屆培正數學邀請賽. 10th Pui Ching Invitational Mathematics Competition. 決賽（中二組）. Final Event (Secondary 2). 時限：2 小時. Time allowed: 2 hours ...
77. [PDF]

### 中三組 - 數學資料庫

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1. 第六屆培正數學邀請賽. 6th Pui Ching Invitational Mathematics Competition. 決賽（中三組）. Final Event (Secondary 3). 時限：2 小時. Time allowed: 2 hours ...
78. [PDF]

### Teaching Module (Probability)∗ Teachers' Guide

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Teaching Module (Probability)∗. Teachers' Guide. Mathematical Database (http://www.mathdb.org). Lesson 1 (Basic Concepts and Definitions). To clarify the ...
79. [PDF]

### From How to Solve It to Problem Solving in Geometry

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Volume 12, Number 1. March 2007 – April 2007. From How to Solve It to. Problem Solving in Geometry. K. K. Kwok. Munsang College (HK Island). Olympiad ...
80. [PDF]

### 中四組

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1. 第七屆培正數學邀請賽. 7th Pui Ching Invitational Mathematics Competition. 初賽（中四組）. Heat Event (Secondary 4). 時限：1 小時15 分. Time allowed: 1 hour ...
81. [PDF]

### Recurrence Relations

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IMO/KKK/Recurrence Relations/Note/1. Recurrence Relations. In this lecture, we show how to formulate a counting problem in terms of recurrence relations and ...
82. [PDF]

### 11. 香港培正中學第二屆數學邀請賽，團體賽

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香港培正中學第二屆數學邀請賽. Pui Ching Middle School 2nd Invitational Mathematics Competition. 團體賽（初級組）. Group Event (Junior Section). 時限：45 分鐘 ...
83. [PDF]

### IMO Problems on Functional Equation

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Page 1 of 3. IMO Problems on Functional Equation. 1968/5. Let f be a real-valued function defined for all real numbers x such that, for some positive constant a ...
84. [PDF]

### 中四組

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1. 第十一屆培正數學邀請賽（2012 年）. 11th Pui Ching Invitational Mathematics Competition (2012). 決賽（中四組）. Final Event (Secondary 4). 時限：2 小時 ...
85. [PDF]

### Famous Geometry Theorems - Department of Mathematics - The ...

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Volume 10, Number 3. August 2005 – September 2005. Famous Geometry Theorems. Kin Y. Li. Olympiad Corner. The 2005 International Mathematical ...
86. [PDF]

### 六個頂點的多面體 - Department of Mathematics - The Hong Kong ...

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Volume 6, Number 4. Volume 6, Number 4. October 2001. October 2001 – December 2001. December 2001. December 2001. 六個頂點的多面體 ...
87. [PDF]

### Using GW-BASIC for Drawing Mandelbrot Sets

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GW-BASIC. Using GW-BASIC for Drawing Mandelbrot Sets. Mr. LEUNG Chi Kit. The Hong Kong Taoist Association Ching Chung Secondary School. For a given ...
88. [PDF]

### Base n Representations - Department of Mathematics - The Hong ...

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Olympiad Corner. The 2000 Canadian Mathematical. Olympiad. Problem 1. At 12:00 noon, Anne, Beth and Carmen begin running laps around a circular track of ...
89. [PDF]

### 中四組

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1. 第十屆培正數學邀請賽. 10th Pui Ching Invitational Mathematics Competition. 初賽（中四組）. Heat Event (Secondary 4). 時限：1 小時15 分. Time allowed: 1 hour ...
90. [PDF]

### 4th Pui Ching Invitational Mathematics Competition c [ m 4 m 4 m 4 ...

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1. 4th Pui Ching Invitational Mathematics Competition c [ m 4 m 4 m 4 –. Heat Event (Secondary 4). · ß 1 [ · 15. Time allowed: 1 hour 15 minutes. [ C 5. [ C 5 ...
91. [PDF]

### 高中組 - 數學資料庫

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1. 第五屆培正數學邀請賽. The 5th Pui Ching Invitational Mathematics Competition. 決賽（高中組）. Final Event (Senior Secondary). 時限：2 小時. Time allowed: 2 ...
92. [PDF]

### 3. 香港培正中學第一屆數學邀請賽，個人賽

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1. 香港培正中學第一屆數學邀請賽. Pui Ching Middle School 1st Invitational Mathematics Competition. 個人賽（中三組）. Individual Event (Secondary 3). 時限：1...
93. [PDF]

### Geometry via Complex Numbers

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Volume 9, Number 1. January 2004 – April 2004. Geometry via Complex Numbers. Kin Y. Li. Olympiad Corner. The Sixth Hong Kong (China). Mathematical ...
94. [PDF]

### Problem Solving I - Department of Mathematics - The Hong Kong ...

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Volume 7, Number 2. May 2002 – June 2002. Problem Solving I. Kin-Yin LI. Olympiad Corner. The 31st. United States of America. Mathematical Olympiad 2002 ...
95. [PDF]

### Difference Operator - Department of Mathematics - The Hong Kong ...

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Volume 11, Number 5. January 2007 – February 2007. Difference Operator. Kin Y. Li. Olympiad Corner. Below are the 2006 British Math lympiad (Round 2) ...
96. [PDF]

### 13. 香港培正中學第三屆數學邀請賽，個人賽

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香港培正中學第三屆數學邀請賽. Pui Ching Middle School 3rd Invitational Mathematics Competition. 個人賽（中一組）. Individual Event (Secondary 1). 時限：1 ...
97. [PDF]

### 87. 第九屆培正數學邀請賽，決賽

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1. 第九屆培正數學邀請賽. 9th Pui Ching Invitational Mathematics Competition. 決賽（高中組）. Final Event (Senior Secondary). 時限：2 小時. Time allowed: 2 hours ...
98. [PDF]

### 中二組

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1. 第七屆培正數學邀請賽. 7th Pui Ching Invitational Mathematics Competition. 初賽（中二組）. Heat Event (Secondary 2). 時限：1 小時15 分. Time allowed: 1 hour ...
99. [PDF]

### Jensen's Inequality - Department of Mathematics - The Hong Kong ...

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Olympiad Corner. The 41st. International Mathematical. Olympiad, July 2000: Time allowed: 4 hours 30 minutes. Each problem is worth 7 points. Problem 1.
100. [PDF]

### 14. Mathematical Excalibur Vol. 3 No. 4

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Volume 3, Number 4. Septe mber-N ovember, 199'? Olympiad Corner. British Maiheinaiicaf O{_vmpicsd: Round 1. (January 15, 1997). Time Allowed: 3% hours.