# Quod Erat Demonstrandum

## 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

$\theta = n\pi + (-1)^n30^o$

$\pi$ is in radian but $30^o$ is in degree, don’t mix them up! You may write either

$\theta = n\pi + (-1)^n\frac{\pi}{6}$

or

$\theta = 180^on + (-1)^n30^o$

3. 向量：寫箭咀，冇得除，有點要露點，寫 square 好危險！

(a) 寫箭咀

(b) 冇得除

Suppose A,B,C lie on the same line with B divides A and C internally.
Given $\frac{AB}{BC} = 3$, express $\overrightarrow{AB}$ in terms of $\overrightarrow{BC}$

$\frac{AB}{BC} = 3 \Rightarrow AB = 3BC \Rightarrow \overrightarrow{AB} = 3\overrightarrow{BC}$

(c) 有點要露點

$\overrightarrow{a} \bullet \overrightarrow{b}$，啱！
$\overrightarrow{a}\overrightarrow{b}$，錯！
$\overrightarrow{a}(\overrightarrow{b} + \overrightarrow{c})$，都錯！

(d) 寫 square 好危險

$\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}$
$\overrightarrow{a}^2 = (\overrightarrow{b} + \overrightarrow{c})^2$

$\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}$
$\overrightarrow{a}\bullet\overrightarrow{a} = (\overrightarrow{b} + \overrightarrow{c})\bullet(\overrightarrow{b} + \overrightarrow{c})$

4. unit vector 唔係 1，你寫 $\overrightarrow{u} = 1$ 就死得。

$|\overrightarrow{u}| = 1$

5. 向量相減唔會零，點解講極都唔明

$\overrightarrow{a} - \overrightarrow{a} = 0$ 錯！
$\overrightarrow{a} - \overrightarrow{a} = \overrightarrow{0}$ 啱！

6. 求向量長度口訣：有 i,j 畢氏定理；冇 i,j 用 dot 無死

$\overrightarrow{p} = 3\overrightarrow{i} + 4\overrightarrow{j}$
$|\overrightarrow{p}| = \sqrt{3^2 + 4^2}$（這是畢氏定理也）

$\overrightarrow{p} = 3\overrightarrow{a} + 4\overrightarrow{b}$

$|\overrightarrow{p}| = \sqrt{3^2 + 4^2}$，錯錯錯錯錯錯錯錯錯錯錯錯錯！

$\overrightarrow{p} \bullet \overrightarrow{p} = |\overrightarrow{p}|^2$

$|\overrightarrow{p}|^2 = (3\overrightarrow{a} + 4\overrightarrow{b}) \bullet (3\overrightarrow{a} + 4\overrightarrow{b})$

$|\overrightarrow{p}|^2$
$= 9\overrightarrow{a} \bullet \overrightarrow{a} + 24\overrightarrow{a} \bullet \overrightarrow{b} + 16\overrightarrow{b} \bullet \overrightarrow{b}$
$= 9|\overrightarrow{a}|^2 + 24\overrightarrow{a} \bullet \overrightarrow{b} + 16|\overrightarrow{b}|^2$

…寫住咁多先…想死中…

## 2 則迴響 »

1. I see that the symbal will be taught at the end of the book…
Chinese lesson is completely terrible, that situation has never happened in the worst primary school class, not that I experienced!
So how’s the New Year?
How comes there’s a little sheet of paper asking who on earth I think is the worst guy in class? Is that the class idea or…
Sent you a letter, dunno if you’d seen…

迴響 由 Ed' — 2008/02/20 @ 8:55 下午 | 回覆

2. Yep.

I and Ms JD will take the situation of Chi lesson seriously. Hopefully, Ms LTW will be back before Talentine.

My holiday was fine because I’d left HK with my wife for 7 days without doing any work.

The sheet is an idea of the class association, some kinds of statistics to be posted on board.

The letter? Oops, forget about it.

迴響 由 johnmayhk — 2008/02/21 @ 5:16 下午 | 回覆