Blogs about: Teaching
特色網誌
小心重覆數算
6 對夫婦，隨機選出 4 人，求僅有一對夫婦被選出的概率。 中六的 A 同學答：。 他解釋：P(僅有一對夫婦) = P(起碼一對夫婦) – P(兩對夫婦) 易知 P(兩對夫婦) = ，理由是兩對夫婦，就是從 6 對夫婦選出 2 對，共 種可能。 至於 P(起碼一對夫婦)，可這樣想： 先從 6 對夫婦選出 1 對，選法為 種。餘下的 2 人，可從 人當中，隨意選取 2 個，選法共 種。故… more →
Quod Erat Demonstrandum
小心重覆數算
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johnmayhk wrote 1 week ago: 6 對夫婦，隨機選出 4 人，求僅有一對夫婦被選出的概率。 中六的 A 同學答：。 他解釋：P(僅有一對夫婦) = P(起碼一對夫婦) – P(兩對夫婦) 易知 P(兩對夫婦) = ，理由 … more →
A nice coordinate geometry problem (suitable for Form 7 pure)
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koopakoo wrote 1 month ago: Let be a point on the curve Let be the tangent line at Given intersects the curve again at Prove tha … more →
For my IMO Students (Basic and Advanced)
koopakoo wrote 1 month ago: Here is good problem for my IMO students. Given a real number . Find the greatest area of triangle A … more →
For my Form 7 Pure students: A proof of the Rational Root Theorem
koopakoo wrote 1 month ago: Let Suppose , where is a rational root. Then we have . Multiplying both sides by yields: Since , we … more →
To my Form 7 students: I am impressed!
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koopakoo wrote 1 month ago: Just finished my CB class tonight and I am impressed by two students. They both expressed interests … more →
lego identity research
cally wrote 2 months ago: 這個讓參與者用lego來represent自己的research 很有趣，雖然我愛文字，但也同意作者 David Gauntlett的結論，不是人人都擅用文字來表達自己，也需要時間來消化，因此，傳統研 … more →
Selected solutions for my F7 Pure (Polynomials)
koopakoo wrote 2 months ago: Book 2, pg 14. (00IQ12)(c) (i) Let y = x^2, then we have ay^2 – by + a. Considering the discri … more →
Selected solutions for my A.maths students (theory of quadratics)
koopakoo wrote 2 months ago: Notes L1b, Page 14. Given are roots of Suppose , determine the values of Solution: We consider two c … more →
IMO phase II training Homework Solution
koopakoo wrote 2 months ago: Here is my solution to the following problem given in IMO phase II training for the basic group: Pro … more →
Find dy/dx at a point not on the curve
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johnmayhk wrote 2 months ago: When distributing the marked test paper to students, one student, Carman, reminded me that there was … more →
類似地？
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johnmayhk wrote 2 months ago: 小心，對一些運算法則，我們定要正本清源，不能單以一句「類似地」便隨便進行「類似」運算。 e.g. 1 循環小數 正確，但不是「類似地」得到： （錯！） 事實上， e.g. 2 二階導數 正確（設考 … more →
i 是開方負 1？
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johnmayhk wrote 3 months ago: 新高中數學教科書出現了 這個命題。 接著是一些例題： 暗暗地在 teaching note 出現了以下句子： but 時而可以，時而不可；同學，你感到有點問題嗎？ 我想說 不是被定義為 。 是一個確定 … more →
拼出 $100
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johnmayhk wrote 3 months ago: 老題：利用面值 $10，$20 及 $50 紙幣若干張，要拼出 $100，問有多少組合方式？ 可以拿 2 張 $50 紙幣，這是一種組合； 可以拿 3 張 $10，1 張 $20 及 1 張 $50， … more →
Finding general term by generating function
johnmayhk wrote 3 months ago: It is extremely easy to set up questions on number pattern, like 1, 3, 8, 19, 42, 89, ? for more det … more →
Challenging problem in Linear Algebra
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koopakoo wrote 3 months ago: Let Solve the following matrix equation where … more →
Answers to Linear Algebra Concept Check
koopakoo wrote 3 months ago: Let (E) be the following system: Let be the augmented matrix. Determine whether the following statem … more →
Mental exercises for my Pure Complex Class (1)
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koopakoo wrote 3 months ago: Dear Students, Please avoid as much calculations as possible. In ideal situation, you should not do … more →
Selected Solutions to My Pure Complex Class (1)
koopakoo wrote 3 months ago: Lesson 1: Page 26 where the last line follows from part a(ii). Page 27 (i) Hence Note that we have i … more →
Solutions to selected problems for my Olympiad Class
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koopakoo wrote 3 months ago: Book 1 Page 1 Answer which can be looked up from the Pascal Triangle. Page 2 Answer: Page 2 Answer: … more →
