Quod Erat Demonstrandum

2009/04/27

2009 CE Mathematics Paper

Filed under: HKCEE,mathematics — johnmayhk @ 3:38 下午

今天考會考數學,同事看卷後,感到題目很淺,考生出來,紛紛說「太淺了,怕取不到 A」云云。

聊舉數例

2009 CE Mathematics Paper I Q.17

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Given

A, B, C and D lie on the horizontal ground. CE is perpendicular to the plane ABE.
AC = 28 cm, BC = 25 cm, BD = 6 cm, BE = 24 cm, \angleABC = 57^o.

Find the shortest distance from E to the horizontal ground.

估計考生會誤以為 CD 垂直 AB,或 ED 垂直 AB 之類。

這題考核一個概念:已知直線垂直某平面,則該直線會和該平面上任何一條線互相垂直。

相信本題的破題關鍵,就是因為 CE 垂直平面 ABE,則 CE 垂直 BE,即 \angleCEB = 90^o.

隨即,考慮(比如)角錐體 EDBC 的體積,設題目要求的距離為 h cm,則

h * [CBD] = CE * [DBE]

從而得 h。

2009 CE Mathematics Paper II Q.48

jksdhichsil1

Given: AB is a diameter. AC intersects DB at E. Let \angleAED = \theta, then \frac{CD}{AB} = ?

本題,考生可能以為 “equal chord, equal angle",誤以為 \frac{CD}{AB} 等於 \frac{\angle DAC}{\angle ADB},錯!

[超快解法可參考 comment 6 or 8]

其他的幾何和解釋幾何的題目也是十分淺易。比較有趣,最尾一題(Q.54)竟然是:

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The broken line graphs above show the annual revenue (in million dollars) of Company X and Company Y in 2008 and 2009. Which of the following statements about the increases of the annual revenue of the two companies from 2008 to 2009 is true?

A. The percentage increases of the annual revenue of company X and company Y are the same.
B. The percentage increases of the annual revenue of company X is twice that of company Y.
C. The percentage increases of the annual revenue of company X is five times that of company Y.
D. The percentage increases of the annual revenue of company X is ten times that of company Y.

PS 1 等我學下補習社授課員先:我貼中o左的士收費果條…XP
PS 2 中三同學考這份,應該可以及格。

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11 則迴響 »

  1. 今年份paper 1 都幾有得意
    Section A1 居然出有效數字(3 分)
    Section A2 出prove
    可能過去三年d證明題太少人揀
    所以要迫d考生做返d證明題(陰謀論)
    Section B 無圓形
    出左straight line + linear programming (時光倒流二十年)

    而的士收費好考學生既presentation skills
    易諗但難寫得靚

    總括而言
    今年份甲一淺
    甲二要諗多d
    乙部估唔到

    btw
    我mc都貼中左數制出十六進制(懶醒中….)

    迴響 由 溟天凱 — 2009/04/27 @ 6:51 下午 | 回覆

  2. >Section B 無圓形
    係,捉錯路。

    >易諗但難寫得靚
    用 ceiling function Ok 嗎?

    >貼中左數制出十六進制
    好有補習社廣告 feel…

    迴響 由 johnmayhk — 2009/04/27 @ 10:08 下午 | 回覆

  3. 1.其實考試局
    一年出二進制
    一年出十六進制
    係人都估到

    2.學生懂得甚麼是ceiling function 嗎?

    3.舊年出稅制
    今年出的士收費
    估唔到下年會出乜野
    在334新學制下
    「生活中的數學」的題目可能會越來越多

    迴響 由 溟天凱 — 2009/04/27 @ 10:39 下午 | 回覆

  4. 我呀妹佢考完之後比份卷我睇

    當中第 48 題 MC 我足足諗左起碼 20 分鐘
    點知都係錯

    我覺得 MC 都算係幾難 wo,難過舊年啦
    反而 LQ 聽講幾易,係 A2 最後一題聽講唔多人做得到

    * btw, 我呀妹錯左 20 題 MC,能 C 嗎?

    迴響 由 Wong Kwok Hei — 2009/04/29 @ 10:44 下午 | 回覆

  5. Q48題我也想了很久…
    但真的很難會想到sine law…=.="

    迴響 由 Patrick Wong — 2009/04/29 @ 10:48 下午 | 回覆

  6. For 48, here is a solution without using the sine law:

    It is clear that AEB is similar to DEC.
    Therefore, CD/AB = DE/AE.
    Since AB is the diameter, angle ADB is a right angle. Therefore, DE/AE = cos(theta).
    Done.

    迴響 由 koopa — 2009/05/01 @ 6:20 下午 | 回覆

    • Nice method! Thank you Koopa!!

      迴響 由 johnmayhk — 2009/05/04 @ 11:07 上午 | 回覆

  7. 我5系你o既學生,但我想問下第十二條……急!
    多謝……

    迴響 由 TorresWong — 2009/10/23 @ 7:42 下午 | 回覆

    • 對不起,現在才覆,且手中沒有題目,答不到你。

      迴響 由 johnmayhk — 2009/10/26 @ 10:31 下午 | 回覆

  8. 2009 CE Mathematics Paper II Q.48
    最正確的方法應該是cos theta=ED/EA=CE/AB
    sin law 太花時間,亦不乎合設題要求

    迴響 由 roviury — 2010/03/09 @ 11:31 下午 | 回覆

    • Yes, the method you’d mentioned is the same as what was given in comment 6.

      迴響 由 johnmayhk — 2010/03/10 @ 10:54 上午 | 回覆


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