Quod Erat Demonstrandum

2009/04/29

純數小技

Filed under: HKALE,Pure Mathematics — johnmayhk @ 5:53 下午
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一.Chain rule 秘技:不要忘記「D 那星」

在下師承我的啟蒙中學教師馬 sir,他喜歡用星星 \star 代表一個 expression,比如要求

\frac{d}{dx}e^{\sin x}

不妨視 \sin x 為一個 expression,以 \star 代之,曰 (more…)

廣告

2009/04/28

有關圓形方程和軌跡的無聊討論

Filed under: HKCEE,mathematics — johnmayhk @ 4:28 下午
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【其一】 上課材料

To 4E students: you may download the worksheet (2009-04-24) at

f4-additional-mathematics-worksheet-20090424

together with some exploration at

http://www.hkedcity.net/ihouse_tools/forum/read.phtml?forum_id=27877&current_page=&i=1247383&t=1247383

【其二】 笑到喊

形如下式的二元二次方程

x^2 + y^2 + Dx + Ey + F = 0 – – – – – – (*)

中四的同學知道,其圖像代表著圓形(指實圓圓周 circumference of real circle)。

現在反過來,代表著圓形的方程式,是否一定形如 (*)?(即二元二次)

不一定,以下是一條二元四次方程方程

x^4 + 2x^3 + (2y^2 - 2y - 1)x^2 + (2y^2 - 2y - 2)x + y^4 - 2y^3 - y^2 + 2y + 1 = 0

其圖像,也是圓形。為何? (more…)

2009/04/27

[FW][YouTube] 我阿媽係外星人 My mom is an alien

Filed under: Fun — johnmayhk @ 10:01 下午

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

image002

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. (more…)

2009/04/22

中二數學:累積頻數曲線

Filed under: Junior Form Mathematics — johnmayhk @ 6:10 下午

1.

同學問:「有累積頻數多邊形不是已經足夠嗎?為何還要學累積頻數曲線?」

2. (more…)

一些有關不能使用 l’Hôpital’s rule 的例子

Filed under: HKALE,Pure Mathematics — johnmayhk @ 9:31 上午
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昨天和同事討論 l’Hôpital’s rule,我就是忘記了一個例子,以說明就算運用 l’Hôpital’s rule 找到 \lim \frac{f'}{g'} (有限值),它也未必等於 \lim \frac{f}{g},今早補貼一下: (more…)

2009/04/21

Trivial reflection of mathematics teaching

Filed under: HKALE,Pure Mathematics — johnmayhk @ 6:04 下午
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Pure Mathematics is a subject of mathematical “techniques". It provides students with certain tools and procedures to solve certain mathematical problems.

However, for me, Pure Mathematics is a subject of “art".

“Techniques" can be taught, while “art" cannot be taught easily. (more…)

2009/04/20

Just reply to my so-called ETV

Filed under: Fun,Junior Form Mathematics — johnmayhk @ 12:45 上午

Here is just a reply to my primary school mathematics ETV (magic square).

When I was a primary school boy, my mathematics teacher taught us how to construct magic square, today, I still remember what she had taught me. For your reference, here is an easy way to construct magic square of odd order:

http://en.wikipedia.org/wiki/Magic_square#A_method_for_constructing_a_magic_square_of_odd_order

Students, try to construct magic squares (more…)

2009/04/19

等我教下小學數啦

Filed under: Fun — johnmayhk @ 12:11 上午

以下是在下自編自導自演自拍的極速小學數學 ETV,上住四堂先,遲下再教。

1. 圓周率

(more…)

2009/04/17

可導性

Filed under: HKALE,Pure Mathematics — johnmayhk @ 5:23 下午
Tags: , ,

這是有關「可導性」(differentiablity)的討論,寫給那天沒有上復活假期補課班的中六同學。注:討論純粹以中學數學的觀點出發。

先請同學回答下面三道是非題:

1. Put x = 0 into the expression of f'(x) and it is undefined, then f(x) is not differentiable at x = 0. True?
2. If \lim_{x \rightarrow 0^-}f'(x) = \lim_{x \rightarrow 0^+}f'(x), then f(x) is differentiable at x = 0. True?
3. If \lim_{x \rightarrow 0^-}f'(x) is finite, then the value of \lim_{h \rightarrow 0^-}\frac{f(h) - f(0)}{h} is also finite. True? (more…)

2009/04/15

純數生活例子(無聊篇)

Filed under: Pure Mathematics — johnmayhk @ 8:09 上午

中四數學教科書中,有關於圓的切線(tangent)之主題,當中舉了一個「生活例子」:太陽從海面初升,代表了圓形交直線於兩個不同點;當整個圓形剛剛從海面出現,就是直線切圓於一點的情況云云。 (more…)

2009/04/14

家庭小片段-0009

Filed under: Family,Life — johnmayhk @ 2:13 上午

記一些片段而已。

img_4964_renamed_993

家近山,附近很容易找到昆蟲。太太捉了一些,諸如飛蛾,蜘蛛,臭蟲等等做兒子的「學具」,有一些昆蟲已經給了幼稚園老師。2009-03-30,我和太太捉了一隻小班蟬(已是第三隻了,之後捉了一隻大蝴蝶),非常高興可以和兒子上生物課,見下: (more…)

2009/04/08

電腦,對你又愛又恨。

Filed under: Family,Life — johnmayhk @ 9:58 下午

那天出中七應數 mock 卷,已是晚上十時許,輸入了大部分內容,辛苦地畫了圖,突然,WORD2007 彈出錯誤信息:文件損壞。 (more…)

2009/04/01

[FW] 網絡民主 01.04.2009

Filed under: Life — johnmayhk @ 12:12 下午

世界進入電子網絡時代,金融海嘯亦都係金融嘅電子化,成也網絡,敗也網絡。有人提出一個新嘅口號,就係全球網絡(即係internet)已經改變哂不分國界,不分種族、文化、宗教嘅人類生活習慣。

呢派學者認為,網絡興起代表住人類一場真正嘅民主,點解咁講呢?因為網絡出現之後,全球無哂專家,無哂明星,無哂好似莫扎特、貝多芬咁嘅經典音樂才華巨匠,導演方面亦都慢慢唔會再有史匹堡。 (more…)

Discussion of F.4 General Mathematics Test Paper (2009-03-26)

Filed under: HKCEE,mathematics — johnmayhk @ 9:22 上午
Tags:

To F.4E students

Please visit my forum and do some exploration on some easy geometry questions in the previous quiz by clicking the following.

http://www.hkedcity.net/ihouse_tools/forum/read.phtml?forum_id=27877&current_page=&i=1247268&t=1247268

在WordPress.com寫網誌.