# Quod Erat Demonstrandum

## 2008/09/29

### Just a question of applied math. from a F.7 boy

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 6:13 下午
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Just discuss an easy AL Applied Mathematics (II) Question with students.

Let $f(x), g(x), h(x)$ be twice differentiable functions such that $f(x) = g^2(x) + x^3h(x)$.

(a) Let $p(x) = \frac{f(x)}{g(x)}$, where $g(0) \ne 0$. Show that $p(0) = g(0), p'(0) = g'(0), p''(0) = g''(0)$.

(b) Using (a), or otherwise, find Taylor’s expansion of the function $\frac{2x^4 - 3x^3 + x + 4}{\sqrt{x + 4}}$ about $x = 0$, up to the term in $x^2$. (more…)

## 2008/09/27

### 一本數學參考書

Filed under: Uncategorized — johnmayhk @ 10:40 上午

http://press.princeton.edu/releases/m8350.html

http://gowers.wordpress.com/2008/09/17/princeton-companion-errata/

## 2008/09/26

### 中二數學問題之有效數字

Filed under: Junior Form Mathematics — johnmayhk @ 9:37 上午

## 2008/09/24

### 比較係數

Filed under: Pure Mathematics — johnmayhk @ 10:05 下午
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$f(x) = ax^2 + bx + c$$a \ne 0$），滿足 $f(f(x)) \equiv f^2(x)$，求 $a, b, c$ 的值。 (more…)

## 2008/09/22

### 論商餘 (一)

Filed under: HKCEE,Junior Form Mathematics,Pure Mathematics — johnmayhk @ 10:34 下午
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## 2008/09/20

### 利用插值法找餘式

Filed under: Additional / Applied Mathematics,HKALE,Pure Mathematics — johnmayhk @ 2:33 下午

## 2008/09/19

### 太空原子筆

Filed under: Fun — johnmayhk @ 6:01 下午

## 2008/09/18

### 究竟「打從」個「打」字是什麼意思？

Filed under: Fun — johnmayhk @ 5:48 下午

## 2008/09/16

### 什麼是無限

Filed under: Fun,Pure Mathematics — johnmayhk @ 5:14 下午

## 2008/09/13

### 太太入院

Filed under: Family — johnmayhk @ 10:28 下午

## 2008/09/10

### 一個多星期。推介網頁。IES

Filed under: Life,School Activities — johnmayhk @ 10:50 下午
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## 2008/09/07

### 初中數學堂之：正負數加減

Filed under: Junior Form Mathematics,Teaching — johnmayhk @ 2:02 下午

http://intranet.sfxc.edu.hk/it-school/homepage/nwc/temp/1_plus_1_equal_2.pdf

## 2008/09/06

### 純數習題：代數數

Filed under: HKALE,Pure Mathematics — johnmayhk @ 1:04 上午

$\sqrt{2} + \sqrt{3}$ 是代數數（algebraic number）。 (more…)

## 2008/09/04

### F.2 Mathematics: significant figures

Filed under: Junior Form Mathematics — johnmayhk @ 10:30 下午

F.2 students, please fill in the following blanks.

(a) $-0.0012000$ has __________ significant figures.

(b) $12000$ has __________ significant figures.
(more…)

## 2008/09/03

### Prerequisite of F.4 algebra

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 5:17 下午

As usual, we start with basic algebraic computation drilling at the beginning of F.4 mathematics lessons. But, I just did some useless mathematical chatting and gave something about infinity (e.g. the discussion of 1 – 1 + 1 – 1 + … ) and they showed their excitment with hands clapping. Well, of course, I switched to serious matter very soon. As expected, most of the students did not know the fact that “zero is an even number" (even, they did not know that zero is an integer). I went through some ‘prerequisite’ questions with them, one is:

(a) $\sqrt{9} = \pm3$ 　[True or false?]
(b) If $x^2 = 9$, then $x = 3$.　[True or false?]
(c) The square roots of 9 are 3 and -3.　[True or false?]
(d) If $x^2 = 9$, then $x = 3$ and $x = -3$.　[True or false?]

F.4 students, here are the answers. (more…)