星期六去補習，學生問對數的題目，其中一條如下：
若 log 3 2 = a, log 3 5 = b，以 a 和 b 表示 log 10 5。
當時栗用眼尾掃了題目一下，便開口說：「哦，這可是經典呢，只要將 log 10 5 變成 log 10 (10/2)，然後寫成 log 10 10 - log 10 2，即是……」
且慢！log 10 10 是 1 沒錯，但題目中的 log 2，底數是 3 不是10，怎麼辦？
栗定一定神，再換個方法計：
log 10 5 = (log 3 5) / (log 3 10) = b / [log 3 (5 x 2)] = b / [log 3 5 + log 3 2]
= b / (b + a)
驚險過後，牢騷便來。話說換底數這條公式，在本地的中學課程已經消失了近十年，連讀附加數的學生也不用學，現在怎麼又鹹魚翻生？要知學生的能耐，一代不如一代，課程發展組的人，你們別玩吧！
what grade level is this stuff?
回覆刪除[版主回覆12/15/2009 20:06:00]Teacher: F4 Maths, Compulsory section
不知怎的，感覺這個算題有點無聊，想 log 的 base 除了 base 10 和 base e 之外， 其他的 base 大抵都很少用，若要學生明瞭 base 的意義， 乾脆用 base 10 豈不是好。不知道這個算式 用base 3 跟 base r ( r = real number) 有何分別？
回覆刪除[版主回覆12/15/2009 20:10:00]絕對認同乏言先生所言。對一般中學生而言，知道常用對數已經足夠，換底數的把戲，用來填塞官員空洞的腦袋比較合適。
Maybe I shouldn't have signed up for the CEE math. I don't have a clue on how to do this. Oh well, too late
回覆刪除[版主回覆12/15/2009 20:23:00]Don't worry, Teacher. This type of question will only appear in the HKDSE exam, not the HKCEE.
you said F4, so CEE will include them, no?
回覆刪除[版主回覆12/15/2009 21:42:00]No, Teacher. I'm talking about the new NSS syllabus and you're going to do the old one.
嘩, 點解我完全不懂.......
回覆刪除Thanks for reintroduce that property of Logarithm to me... I vaguely remember I learned that property back in school, but clearly know how useful that property is...(the second part is a joke... )
回覆刪除So the new one is much more advanced than the old one?
回覆刪除[版主回覆12/16/2009 08:06:00]Yes, Teacher. It's quite similar to the one introduced more than 10 years ago.
So they're raising the math standards and dumbing down the English ones. Any public rationale on that?
回覆刪除[版主回覆12/20/2009 08:45:00]I'm not sure if the authority is dumbing down the English standards. On the public exam level, I think the HKDSE English exam is much more difficult than the HKCEE (and even HKALE). I wonder how students can write 600 words within 1.5 hours. Only very clever students can make it, right?
咪話，我都諗唔起點解 log 10 5 = (log 3 5) / (log 3 10)
回覆刪除「你們便玩吧」-->「你們別玩吧」﹖
[版主回覆12/16/2009 13:42:00]謝謝！你栗姐老花益發嚴重了
十多年前學過的東西，不記得絕對不出奇呢！不過如果我唔識做，咁就冇面啲~~~
哈哈，睇完都唔知你講乜 因為我已經完全忘記這些數學
回覆刪除[版主回覆12/20/2009 08:47:00]淇淇：忘了倒好。我倒是不明白，為何過了十多年，自己還會記得這條公式... (我沒備課都識教~)
??
回覆刪除我最近正在學log，但絕大部分時間也只做base 10，
回覆刪除那可怕的base 3該不會隨之而來吧？
[版主回覆12/20/2009 08:49:00]yuenyee：不只 base 3，還有其他的 base 呢！
這條換底數公式屬非剪裁部分，我看大部分中四學生都要讀，只能祝君好運了
But the 600 words are on two different subjects, 200 on one and 400 on the other, up only slightly from the current CEE of 150 and 350. The current A-level has 500 words on a single subject.
回覆刪除[版主回覆12/24/2009 08:19:00]Teacher: But they are in the same paper, and only 1.5 hours are given. Intimidating to less able students ...
這些數學公是我都忘光了^^
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[版主回覆12/24/2009 08:20:00]不要緊的, 我看連工程上也很少用到這種公式吧? 根本就是純數學的範疇~
I thought intimidation was the whole idea They used to have two exams two years apart to declare 80% of the kids failures. Now they have to "do" the entire 80% in a single exam, since they are not increasing the number of U spots. (how's that usage of the word "do"?)
回覆刪除[版主回覆12/30/2009 08:23:00]You've got a really good here, Teacher. I haven't thought about it before.
In fact, I don't see why the bureau wants students to stay at school for one more year. To lower the unemployment rate of teengers?
The reason is that the gov't wants to show the world that they're enhancing public education, which is true only if you believe in the nonsense that spending time in a classroom is the same as learning. But don't laugh, they got this nonsense from the US "educrats".
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