Quod Erat Demonstrandum

2008/02/23

Quadratic formula program @ CASIO 3950p/3650p

Filed under: HKCEE,Junior Form Mathematics — johnmayhk @ 11:17 下午
Tags:

驚恐中。我班的中五同學不懂做

Factorize 4x^2 - 4xy + y^2.

(不變金句:教了,不等於學了)

在中二的課,談到 cross method,我教同學用計算機。Casio 3950p (or 3650p) 較以往好,是它顯示的根(roots)是分數,不是點數,這樣可方便同學寫出答案。中五的同學,若你的 Casio 3950p 還未有 quadratic formula,快快看:

http://intranet.sfxc.edu.hk/it-school/homepage/nwc/casio_%20fx_3950p_quadratic_formula_program.doc

那天,中五同學問,如何用計算機做 factorization?唉。按上面連結的 note,照樣輸入程式。

舉例

(1) Factorize 6x^2 - 6y^2 + 5xy

步驟一:把 x 的項按指數由大至小排好,即

6x^2 + 5xy - 6y^2

步驟二:把系數(coefficients)輸入計算機

a=6, b=5, c=-6

計算機將出現答案如下:

2┘3 及 -3┘2

\frac{2}{3}, -\frac{3}{2}

步驟三:寫答案

6x^2 + 5xy - 6y^2
= 6(x - ?)(x - ?)

第一,不理三七二十一,把 x^2 的系數(即是 6)抄出來。
第二,加上兩個括弧 6(x - ?)(x - ?)
第三,填上 ?
這例,? 就是計算機出現的答案 2┘3 及 -3┘2,還要貼上 y,即 \frac{2}{3}y, -\frac{3}{2}y,所以

6x^2 + 5xy - 6y^2
= 6(x - \frac{2}{3}y)(x - (-\frac{3}{2}y))
= 3\times2(x - \frac{2}{3}y)(x - (-\frac{3}{2}y))
= (3x - 3(\frac{2}{3}y))(2x - 2(-\frac{3}{2}y))
= (3x - 2y)(2x + 3y)

(2) Factorize 15x^2 + xy^2 - 2y^4

15x^2 + xy^2 - 2y^4
= 15x^2 + x(y^2) - 2(y^2)^2

Enter a=15, b=1, c=-2 into calculator, the answer will be

-2┘5 , 1┘3

Hence

15x^2 + xy^2 - 2y^4
= 15x^2 + x(y^2) - 2(y^2)^2
= 15(x - (-\frac{2}{5}y^2))(x - \frac{1}{3}y^2)
= (5x - 5(-\frac{2}{5}y^2))(3x - 3(\frac{1}{3}y^2))
= (5x + 2y^2)(3x - y^2)

注:這裡,答案貼上的是 y^2,不是 y

愈寫愈墮落,不寫了。

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

想詳細研究 CASIO 3950P / 3650P,看看說明書吧

http://intranet.sfxc.edu.hk/it-school/homepage/nwc/fx3650_3950P_menu.pdf

對於運用計算機方面,我屬幼稚園級;網絡內外高手如雲,比如大師級黃 sir。有興趣研究一下他的作品吧:

http://lpl.hkcampus.net/~lpl-wwk/

那天,用 EXCEL generates 數字,再用這裡(wordpress)把形如 3x^2 – 4x + 1 輕易轉成 3x^2 - 4x + 1,我便輕易出了百幾題(所謂)中二的數,隨便用:

http://intranet.sfxc.edu.hk/it-school/homepage/nwc/f2_quadratic_factorization_drilling.doc

不寫了,愈寫愈墮落。冇眼睇。

3 則迴響 »

  1. 感謝你, 我一直在找, 現在有program用了-)

    迴響 由 thankyouverymuch — 2011/06/12 @ 11:00 下午 | 回覆

  2. I remember a few years ago when I learnt the quadratic formula, I swore I would not use the programme as I always wanted to rely on my own, to rely on my memory, entering every number, every operation sign by my fingers. Now, I have to break my promise just because I have to get fast in the exam…

    迴響 由 Bruce Leung — 2012/11/08 @ 11:08 下午 | 回覆

  3. Now I have even surrendered to Heron’s formula and I don’t even bother to memorize radius = sqrt(D^2 / 4 + E^2 / 4 – F) for a circle in general form. What a degeneration of my brain.

    迴響 由 Bruce Leung — 2012/11/08 @ 11:10 下午 | 回覆


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