Quod Erat Demonstrandum

2008/06/30

Filed under: HKCEE,Report — johnmayhk @ 5:18 下午
Tags:

【有關會考數學】

1. 不要臨會考前才操練 past paper
2. 要取 A，不能忽略初中數學
3. 可在中四暑假做初中數學的溫習（針對 A1 部分）
4. 留意以下題種：

(1) Approximation

(2) Centres of triangle

(3) 數型或看 pattern 的數種（如參考考評局方經理在 SBA 會上公佈的 exemplar）。

(4) Transformation of graphs

(5) Further application

【有關附加數】

Express $\tan 22.5^o$ in surd form.

Solve $|x - 1| = |x| - 1$

2008 年又玩
Solve $|x - 3| + 3 = x$

General solution 絕跡新高中，同樣絕跡於 2008 年的附加數卷，三角短題問的是以下一道題：

Find the maximum and minimum value of $\sin x + \sqrt{3}\cos x$ for $0^o \le x \le 90^o$.

7 則迴響 »

1. John sir, 唔駛唔開心既….

你已經盡o左最大既能力，
其餘的，做學生的都要努力……

cheers

迴響 由 Ricky — 2008/06/30 @ 7:20 下午 | 回應

2. Thank you Ricky, am I 盡o左最大既能力? Frankly speaking, not really, I always think that ‘有心無力’ is the truth…Anyway, thank you again!

I met 森林木 on 30/6 afternoon near sfxc, but I was in hurry, no more sharing.

迴響 由 johnmayhk — 2008/07/02 @ 8:18 上午 | 回應

3. For the problem, |x – 3| = x – 3.

This implies x – 3 >= 0, since |x – 3| >= 0.
Therefore, |x – 3| = x – 3, and the equation is true iff x >= 3. Done.

For the problem, |x – 1| = |x| – 1. Here is how I would do it:

|x| – 1 = |x – 1| >= ||x| – 1| >= |x| – 1.

Hence |x| – 1 = ||x| – 1|. The solution to this equation is |x| >= 1 as before.
Thus the solution to the original problem is x >= 1 or x<= -1. Done.

迴響 由 koopa — 2008/07/02 @ 11:50 上午 | 回應

4. on post 3:

I wonder |x|-1 = |x-1| if x is negative, e.g -3 ?

I would do it:

|x| >=1 definitly,

by double checking and observing |x-1|-|x| = -1

or |x-1| < |x|

迴響 由 Ringo — 2008/07/03 @ 8:31 下午 | 回應

http://intranet.sfxc.edu.hk/it-school/homepage/nwc/20080703gif01.gif
Hence the solution is $x \ge 1$.

迴響 由 johnmayhk — 2008/07/03 @ 9:13 下午 | 回應

6. Thanks for pointing out the mistake. Just want to do the problem in non-standard ways, but then I was too careless to not checking the solution works.

迴響 由 koopa — 2008/07/05 @ 10:22 上午 | 回應

7. i typed it wrong in last line.

never thought of using graph for solving it.

迴響 由 ringo — 2008/07/05 @ 1:04 下午 | 回應