# Quod Erat Demonstrandum

## 2008/02/29

### Taylor’s polynomials@濟濟一堂

Filed under: Additional / Applied Mathematics,HKALE,Pure Mathematics — johnmayhk @ 3:14 下午

From『濟濟一堂學術討論區』2003-11-05 09:28:45

## 2008/02/28

### Evaluate cube roots

Filed under: Additional / Applied Mathematics,HKCEE,Junior Form Mathematics — johnmayhk @ 4:02 下午

A F.5 student, Yan, asked me to do the following without using calculator

$\sqrt[3]{10 + 6\sqrt{3}} + \sqrt[3]{10 - 6\sqrt{3}}$

## 2008/02/27

### F.5 last day

Filed under: Life,School Activities — johnmayhk @ 5:45 下午

Today is the last normal school day of F.5 students. This is the song chosen

### To senior form mathematics students

Filed under: Information — johnmayhk @ 4:15 下午

Mathematics Curricula
http://www.edb.gov.hk/index.aspx?nodeid=2899&langno=1

Examination Syllabuses
http://www.hkeaa.edu.hk/en/hkale/Subject_and_Syllabuses/

Seminar and Workshop Handouts (For Mathematics Teachers)
http://www.edb.gov.hk/index.aspx?nodeid=4651&langno=1

In the link just above, it is quite interesting to find the NSS (New senior secondary 新高中) Enriching Knowledge for the Mathematics Curriculum (Advanced Topics in Mathematics) Rainbow in Mathematics, just click and read. If secondary students could come across and understand topics mentioned in the handout like

Homology
Pascal’s Theorem
Bézout’s Theorem
Cayley-Bacharach Theorem
Elliptic Curve
Mordell-Weil Theorem
Mazur’s Theorem
Birch and Swinnerton-Dyer conjecture

in NSS, then HK secondary mathematics education will take the lead over this lonely planet for sure! But there’s a long way to go, at least, I just heard about (not understand) some of the names mentioned in the list above. How poor I am.

## 2008/02/26

### Book tomb

Filed under: Life — johnmayhk @ 10:48 下午

Recent weeks, whenever I checked the blog stats, I must find the following blog in the Top WordPress.com blog

http://lawchiwah.wordpress.com/

What an ironic tragedy that books became the tomb of a book lover. This event may be symbolic. Is that a sign for HK culture in future?

When talking about reading, just forword the following, saluting to Art Garfunkel!

http://www.wretch.cc/blog/giawgwan&article_id=7104149

### Something to say about F.7 Pure Mathematics (II) Mock Exam (part 1)

Filed under: HKALE,Pure Mathematics — johnmayhk @ 6:08 下午

$f'' \ge 0$ on I – – – – – – (*)

$f$ is concave upwards on I" means

$pf(x) + (1 - p)f(y) \ge f(px + (1 - p)y)$ for all $p \in [0 , 1]$ and $x , y \in I$" – – – – – – (**)

## 2008/02/24

### Hilbert tells stories

Filed under: Family — johnmayhk @ 11:20 下午

Hilbert, a 2.5-year-old boy, was very exciting because my old friends from my old church visited us today. He had fun with sisters. We asked him to tell a story, he did. What a suprise that he told us a very short story created on his own. We all laughed and enjoyed the precious moment with the gift from God. I do want to record Hilbert’s every funny moment. However, he is really growing very fast and I’m too old to catch up with all the swift changes. Just picture some of his joyful times here.

Hello to the world! Perhaps, someone had put that funny little green hat on your brain some days in your life… (more…)

## 2008/02/23

### Quadratic formula program @ CASIO 3950p/3650p

Filed under: HKCEE,Junior Form Mathematics — johnmayhk @ 11:17 下午
Tags:

Factorize $4x^2 - 4xy + y^2$.

（不變金句：教了，不等於學了）

## 2008/02/20

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 11:01 上午

1. 口訣：一冇 trigo，即寫 general

$\sin(2\theta) = \sin30^o$
$2\theta = 30^o$
$\theta = 15^o$
$\therefore \theta = 180^on + (-1)^n(15^o)$

$\sin(2\theta) = \sin30^o$
$2\theta = 180^on + (-1)^n(30^o)$

$\sin(2\theta) = \sin30^o$
$2\theta = 180^on + (-1)^n(30^o)$
$\therefore \theta = 90^on + (-1)^n(15^o)$

2. 又 degree 又 radian；個樣衰過 Edit 神

## 2008/02/19

### A beautiful question in binomial theorem

Filed under: Additional / Applied Mathematics,HKALE,HKCEE,Pure Mathematics — johnmayhk @ 5:02 下午

$\frac{(m + n)!}{(m + n)^{m + n}} < \frac{m!}{m^m}\frac{n!}{n^n}$

## 2008/02/16

### 五稜鏡評陳冠希事件

Filed under: Life,Report,Teaching — johnmayhk @ 10:22 上午

## 2008/02/09

### 本誌消息

Filed under: Uncategorized — johnmayhk @ 3:19 上午

Don’t you believe that I spent 3 or 4 days on marking the F.7C pre-mock paper! Just have a look at the results.

### [PM] Fixed point (不動點)

Filed under: Pure Mathematics,Teaching — johnmayhk @ 3:16 上午

Let $f : [a , b] \longrightarrow [a , b]$ such that $f(x)$ is continuous on [$a , b$]. Prove that there exist $c\in [a , b]$ such that $f(c) = c$

$f$ 的值域（range of $f$）為 [$a , b$]，故

$g(x) = f(x) - x$，則

$g(a) = f(a) - a \ge 0$ – – – (1)
$g(b) = f(b) - b \le 0$ – – – (2)

### [Gag] 自貼

Filed under: Fun — johnmayhk @ 3:16 上午

（設計對白）再嘈！打爆你個 $\theta$！！

## 2008/02/06

### 數學應用題：拍賣

Filed under: Junior Form Mathematics — johnmayhk @ 12:55 上午
Tags:

【場景】