Quod Erat Demonstrandum

2011/03/18

某兩題中四數

Filed under: NSS — johnmayhk @ 5:02 下午

1.

以下是中四上學期,教科書中某題:

A wire of 80 cm long is cut into two pieces and each wire is bent into a square.
The length of each side of the smaller square is x cm.

(a) Express the total area of the two squares in terms of x.
(b) Find the minimum area of the two squares in total.

易得答案

(a) (2x^2-40x+400) cm^2
(b) 200 cm^2

問題不在計數。

葉同學說:「題目有問題!」

因為 (b) 的答案是當 x=10 時得出,但當 x=10,代表那兩個正方形的邊長是一樣的,有違 x 的原來設定:"The length of each side of the smaller square is x cm"

心中暗喜,同學很細心,我也不察,唯有說擬題要注意一下。

2.

又是教科書某題。

A rectanglar lawn with a length of x m and a width y m is to be planted with flowers. The relevent information of the lawn is as follows.

I. The perimeter of the lawn should be between 20 m and 46 m inclusive.

II. The length of the lawn should be greater than the width, but not greater than 5 times the width.

Write down all the constraints.

教科書的答案是

10 \le x+y\le 23
y<x\le 5y
x>0
y>0

但梁同學隨即指出,最後兩條不等式是多餘的(Why?)。

心中暗喜,同學很細心,我也不察,但在公開試中,寫以下答案

10 \le x+y\le 23
y<x\le 5y

會否被扣分?不會吧。

1 則迴響 »

  1. 寧願寫多, 不要寫少

    迴響 由 roviury fung — 2011/03/27 @ 12:49 下午 | 回覆


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