桃子

>>for y= ax^2 + bx +c, it is a function, but not a equation, it includes infinite points of coordinates such that y value depends on x value

First of all, y= ax^2 + bx +c is BOTH a function and an equation. Even junior form students should know it.

>>for ax^2 + bx +c = 0, which is the genuine form of quadratic equation, is a particular condition that y = 0.

Setting y=0 is a way to solve the equation. However, it is not a condition.

>>Then the question is simplified as converting a function into a equation.
Your image is correct. This is a fairly basic technique taught in Core. A typical question would be:
y=3x/(x^2+3)
Find the range of y.

yx^2-3x+3y=0
discriminant
=9-9y^2>=0
y^2<=1
-1<=y<=1

The question in M1 paper is a bit trickier and you need to know the symmetry of a quadratic function.

>>Turning a function into an equation under limited conditions as stated in the question is illogical, as my teacher said.

This technique is logical and should definitely be taught in Core.

[ 本帖最後由 桃子 於 2014-5-1 12:17 AM 編輯 ]

桃子

引用:

原帖由 D.Y. 於 2014-4-30 11:59 PM 發表

As stated in HKDSE Core Maths Curriculum,
for general form of quadratic equation, ax^2 +bx +c = 0,

a,b,c must be constants.
Apparently, in your claim, a,b,c all compose of y, which are not cons ...

I don't care about how it is expressed in the syllabus.
I am sure this technique was taught in Maths and A.Maths in the past (although normally used in conjunction with discriminant).
I think it should not be excluded in DSE.

D.Y.

引用:

原帖由 桃子 於 2014-5-1 12:12 AM 發表
>>for y= ax^2 + bx +c, it is a function, but not a equation, it includes infinite points of coordinates such that y value depends on x value

First of all, y= ax^2 + bx +c is BOTH a function and an  ...

Thank you for comment. I just don't wanna argue, but I just wanna discuss rationally.

The sticking point in your claim is that a,b,c, are not constants, they depend on y, which in turn depend on x.

I guess you could not use discriminant to find the range as a,b,c are not constant.


According to wiki, the coef., a,b,c must be constants
http://en.wikipedia.org/wiki/Quadratic_equation

D.Y.

引用:

原帖由 桃子 於 2014-5-1 12:16 AM 發表

I don't care about how it is expressed in the syllabus.
I am sure this technique was taught in Maths and A.Maths in the past (although normally used in conjunction with discriminant).
I think it s ...

ya, "determination of discriminant" was included in CE AMaths but not in CE Maths in the past,
but now it is added in HKDSE syllabus,

indeed I have done all the past paper questions in Joint-us, more than 30 years,
I have no impression that I deal with question s.t. the coef. of quadratic equation that are not constant,
most likely, the coef. of a.b.c are something like (k-4), (2k+3), etc, where k is a constant
then we used discriminant to find the k value or k's range

Could you find a question for finding discriminant s.t. coef a,b,c are not constants in all the exams held by HKEAA?

桃子

It is nothing strange, just the same technique you re-express a rational function of degree 2 to find its range.

Originally, I did this problem by symmetry of quadratic equation. I also note it is possible (and perhaps easier to understand) to do it by sum of roots.

In any case, you need to start with the QE shown above.

D.Y.

引用:

原帖由 桃子 於 2014-5-1 12:56 AM 發表
It is nothing strange, just the same technique you re-express a rational function of degree 2 to find its range.

Originally, I did this problem by symmetry of quadratic equation. I also note it is  ...

Anyway, 多謝ctze先，maths 有時系要有爭論先好玩同有挑戰性，

甘樣先至諗到新野，有時就算系數學家ge理論都會被后人推翻，對數學有質疑系好事。

btw, 好奇問 ctze 系咪大學讀數學系/工程系的 ？？



而家好夜了。。。。好眼訓。。。。訓先了

lwc_1995

12c ii 應該錯，因為manager B 應該係 after training 後再抽樣本，所以標準差應該係4.2/n^0.5

t105

12b唔見左

D.Y.

引用:

原帖由 lwc_1995 於 2014-5-1 02:40 AM 發表
12c ii 應該錯，因為manager B 應該係 after training 後再抽樣本，所以標準差應該係4.2/n^0.5

Thanks. 應該系4.7 吧
Please look at the revised one. Thanks

[ 本帖最後由 D.Y. 於 2014-5-1 06:20 AM 編輯 ]

D.Y.

引用:

原帖由 t105 於 2014-5-1 03:43 AM 發表
12b唔見左

sorry 寫漏左，請看2樓。

privatechitutor

13ci  個ans要-1
因為係between two bad day

舉個例子  我合格既機會係0.2
咁我每考5次 就有1次合格
假設第一次係fail
fail pass pass pass pass fail
由此可見 between two fail 只有4 個pass

所以 條式係 1/0.2-1

正如ci 一樣

maths23456

容我說句公道話。
數學和物理不一定要有必然的關係，物理是其中一個數學的應用，但數學領域自身可獨立存在而不需要受到物理的規範。
例如，愛因斯坦 proved 物理只有 4 dimensions (x,y,z, time).  Vectors in Maths can have n-dimensions.  There are many formulas deduced from n-dimensional space, for any positive integer n.
For ax^2 + bx + c = 0, even though a, b, c are parametized by y, once you regard y as a constant, then a, b, c are constants.
雖說 y depends on x, we can also say "once y is fixed, we can deduce x (although x can have no solution for certain values of y)".

利申：數學愛好者，曾在歷屆 Pure Maths 拿 A(1)。

17561791

thx so much

clavin369

有操過past paper都識要1/p - 1
名校第一？

D.Y.

引用:

原帖由 privatechitutor 於 2014-5-1 08:48 AM 發表
13ci  個ans要-1
因為係between two bad day

舉個例子  我合格既機會係0.2
咁我每考5次 就有1次合格
假設第一次係fail
fail pass pass pass pass fail
由此可見 between two fail 只有4 個pass

所以 條 ...

你睇下隔離個版。。。。我有-1 窩。。。