Blogs about: Additional Applied Mathematics

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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 →

Tags: HKALE, HKCEE, Pure Mathematics, Basic, Differentiation, Probability

應用純數4 comments

johnmayhk wrote 3 weeks ago: 有人強調數學在生活中的應用,有人指出所謂「數學在生活中的應用」是牽強的。經驗使我比較贊成後者。 無論如何,以趣味的角度向學生介紹(所謂的)數學在生活中應用的例子,或許可以達到某些教學的成效。 讓我在這 … more →

Tags: HKALE, Pure Mathematics

橢圓規7 comments

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 →

Tags: HKALE, HKCEE, Pure Mathematics

點數差的期望值5 comments

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 →

Tags: HKALE, HKCEE, mathematics

數數唸1 comment

johnmayhk wrote 2 months ago: 一. 以下數字是「旋轉對稱」的嗎? 1961 是?嗯,問題係「旋轉對稱」應該是描述圖形,而不是數字…如果我把它寫成 那這個數字還是「旋轉對稱」的嗎? 二. ” is differenti … more →

Tags: HKALE, Junior Form Mathematics, Pure Mathematics, limit, mathematical induction, Probability, SBA

2009 CE Additional Mathematics Paper Section B5 comments

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 →

Tags: HKCEE

大數值的乘階2 comments

johnmayhk wrote 3 months ago: 中四同學在學期初已接觸乘階(factorial) 的運算。比如 理論上,這個正整數 ,可以「要幾大,有幾大」;但實際上,我們日常接觸的運算工具,必有其限制;用 EXCEL 2003,只可以算 … more →

Tags: HKALE, Pure Mathematics, University Mathematics, idea of setting question, SBA, limit

Just answer an easy additional mathematics question1 comment

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 →

Tags: HKCEE

Reply to a F.7 student

johnmayhk wrote 3 months ago: To estimate , please refer to the normal table, you may see Now, to evaluate , what substitution ne … more →

Tags: HKALE

Just answer questions from F7 student

johnmayhk wrote 4 months ago: Q.1 sin x 同cos x 既taylor’s theorem expansion say the last term of sin x is (-1)^(n-1)*x^(2n-1) … more →

Tags: HKALE

boring discussion on limit of sequence

johnmayhk wrote 4 months ago: Here is just a typical, basic, level-zero question about the limit of sequence for formative assessm … more →

Tags: HKALE, Pure Mathematics

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 →

Tags: HKCEE, Basic, Differentiation

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 →

Tags: HKCEE, Teaching, trigonometry

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 →

Tags: HKCEE, Trick, trigonometry

Asymptotic Behavior of Solutions to Linear Equations

johnmayhk wrote 4 months ago: Apart from the interesting article in the last post, Justin also sent me the following interesting q … more →

Tags: HKALE, Pure Mathematics, idea of setting question

出現 A 先於 B 的機會3 comments

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 →

Tags: HKCEE, Teaching, HKALE, idea of setting question

拉 curve6 comments

johnmayhk wrote 5 months ago: 中二的同學問我如何「拉 curve」(即調整分數),讓我略談。 比如數學科某次考試結果,最高和最低分數分別為 79 分及 4 分,但因為及格率只有三成,太低,於是把原本得 42 分的變成及格,即 50 … more →

Tags: Junior Form Mathematics, SBA

錯在哪裡系列:零是不定義?5 comments

johnmayhk wrote 6 months ago: When giving the following basic trigonometry question in F.4 additional mathematics lesson: Given , … more →

Tags: HKCEE, trigonometry

做數雕蟲小技系列:看整體4 comments

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 →

Tags: HKCEE, Junior Form Mathematics, Teaching, Factorization, trigonometry