Blogs about: Hkcee
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十進制轉二進制
同事在中二的數學考卷擬了一道題：把 表達成二進制的數字。 整數部分，同學易求，現在的關注點是 如何轉成二進數？這個也簡單， 對卷後，梁同學問我，那麼 如何轉成二進數？ 這又是我這個授課員不能秒殺題。 同學，試探究一下：是否任何有理數都可轉成二進數？ 對我來說，這仍是開放問題。高手見笑。 最無聊（trivial）的結果是 (a) 任何形如 的有理數必可轉成二進數。（其中 , 為正整數） … more →
Quod Erat Demonstrandum
十進制轉二進制
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johnmayhk wrote 1 week ago: 同事在中二的數學考卷擬了一道題：把 表達成二進制的數字。 整數部分，同學易求，現在的關注點是 如何轉成二進數？這個也簡單， 對卷後，梁同學問我，那麼 如何轉成二進數？ 這又是我這個授課員不能秒 … more →
閒談一些基本東西：導數符號，函數，解釋
johnmayhk wrote 2 weeks ago: 1. 高階導數的符號 同學問，為何 D 兩次（即求二階導數）的符號是 而不是 或 ？ 記得 CJ 老師曾經出上面的來考同學。 我不知其來源，只是靠估兼無聊地說： 比如求 的導數（w.r.t. x … more →
橢圓規
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johnmayhk wrote 4 weeks ago: 不知有沒有授課員用過橢圓規這個教具？（實情我不知這名稱是否正確，網上找到 Ellipsograph 這個字，不知是否橢圓規的正確英文名稱。） 我「靜靜雞」用科組錢買了一個，操作見下： （是 … more →
溫書題
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johnmayhk wrote 1 month ago: 這是溫書時期。 1. 有關數列的題目 這是校內 2007-2008 年度純數期終試其中一題： ======================================= Let {} be a s … more →
點數差的期望值
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johnmayhk wrote 1 month ago: 擲兩顆公平骰子一次，求兩個點數差的期望值。 學生甲： 嗯，擲一顆骰子，點數的期望是 。無論擲兩顆，三顆，它們的點數期望值皆是 ，故此，兩個點數差的期望值就是 。 學生乙： 設 分別是兩顆骰子的點數， … more →
用 logarithm 計出頭幾個位
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johnmayhk wrote 2 months ago: 昨天匆匆出了份中四 logarithm 的習作，其中一題： Find the first digit of . 留意，我們不是找「個位」，而是找「第一個位」是什麼。 其實不止找到第一個位，頭幾個位都可 … more →
2009 CE Additional Mathematics Paper Section B
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johnmayhk wrote 2 months ago: 重點題目： 以下是 2009 CE Additional Mathematics Q.18，同學，看看你可否在 16 分鐘內正確地完成它： The following figure shows a p … more →
有關圓形方程和軌跡的無聊討論
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johnmayhk wrote 2 months ago: 【其一】 上課材料 To 4E students: you may download the worksheet (2009-04-24) at f4-additional-mathematics-w … more →
2009 CE Mathematics Paper
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johnmayhk wrote 2 months ago: 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 Given A, B, C a … more →
Discussion of F.4 General Mathematics Test Paper (2009-03-26)
johnmayhk wrote 3 months ago: To F.4E students Please visit my forum and do some exploration on some easy geometry questions in th … more →
Just answer an easy additional mathematics question
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johnmayhk wrote 3 months ago: A F.5 student asked me the following question some days ago, reply now. A(-3,0) and B(-1,0) are two … more →
Minor point in differentiation
johnmayhk wrote 4 months ago: This is a simple question in differentiation. Let for any real number , determine at (1,-1). Some … more →
Some F.4 textbook questions
johnmayhk wrote 4 months ago: Students may find the following textbook questions difficult. Question 1 Refer to the figure below, … more →
Just an old question about F.4 trigonometry
johnmayhk wrote 4 months ago: It is glad that F.4 students asked me how to evaluate Here is a way. Knowing that Hence the requi … more →
出現 A 先於 B 的機會
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johnmayhk wrote 5 months ago: 常見題目：擲一顆公平骰子若干次，求得到 1 點先於得到 6 點的概率。 此例容易，因 1 點和 6 點在地位上無異，易知要求概率為 。 改一改題：擲兩顆公平骰子若干次，求得到總點數為 4 點先於得到總 … more →
錯在哪裡系列：零是不定義？
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johnmayhk wrote 6 months ago: When giving the following basic trigonometry question in F.4 additional mathematics lesson: Given , … more →
做數雕蟲小技系列：看整體
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johnmayhk wrote 7 months ago: 看整體有時比看局部好。舉例 1. Factorize . 部分同學把焦點集中在 和 這兩個部分，他們會採取「爆破」的策略，把 和 分別爆開，即 和 。但如果看整體，即 其實已是 這個形式 … more →
Exist or does not exist
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johnmayhk wrote 7 months ago: Is giving hints a good way to help students in solving mathematics problems? Urm, sometimes it may n … more →
Create an m.i. question
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johnmayhk wrote 7 months ago: It is not difficult to create questions like: Prove by mathematical induction that for any positive … more →
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