【纪念当年的帖子（2010）】Add Maths功课讨论区

Enceladus

我现在很烦恼，SPM要到了，每科功课都还没准备好。这几天正在赶add maths。我现在遇到麻烦，form 4第二课有几题不会。

Enceladus

Given that -3 and k are the roots of the quadratic equation.(2x+1)(x-1)=p(1-3x), where p is a constant, find the value of p and of k.
不会不会，救命。

Enceladus

Given that -3 and k are the roots of the quadratic equation.(2x+1)(x-1)=p(1-3x), where p is a constant, find the value of p and of k.
不会不会，救命。

Enceladus

The roots of the quadratic equation x^2+3x=10 are p+1 and q-1. Find the values of p and the corresponding values of q.这题也是不会。。。

walrein_lim88

回复 183# Enceladus

walrein_lim88

回复 184# Enceladus

Enceladus

walao,原来是同样做法，我懂了，谢谢你的教导。

永遠愛著許瑋倫

xy=(-2/3)(x+y)+6
xy:Y,(-2/3)=m,x+y=X,6=C
Find the y in terms of x.
最不不会就是in terms of这些了

superliong

x(x-7)<18
find value of x .

看看这题

walrein_lim88

回复 189# superliong


    x^2-7x<18
    x^2-7x-18<0
   (x-9)(x+2)<0
     -2<x<9

walrein_lim88

xy=(-2/3)(x+y)+6
xy:Y,(-2/3)=m,x+y=X,6=C
Find the y in terms of x.
最不不会就是in terms of这些了: ...
永遠愛著許瑋倫 发表于 9-3-2010 10:59 PM

superliong

Given  f(x)=6-3k+6kx-3x^2
where k is constant.
Show that the equation of the axis of symmetry of the graph of f(x) is x = k.
Then , find the value of k if f(x)has a maximum value of 12

walrein_lim88

Given  f(x)=6-3k+6kx-3x^2
where k is constant.
Show that the equation of the axis of symmetry of the graph of f(x) is x = k.
Then , find the value of k if f(x)has a maximum value of 12
superliong 发表于 10-3-2010 04:43 PM

有两个办法：
一：completing the square
f(x)=-3x^2+6kx+6-3k
=-3(x^2-2kx)+6-3k
=-3[(x-k)^2-k^2]+6-3k
=-3(x-k)^2+3k^2-3k+6
Hence maximum value is at x=k which is also axis of symmetry of the graph of f(x)
If maximum value =12
Then 3k^2-3k+6=12
        3k^2-3k-6=0
        k^2-k-2=0
        (k-2)(k+1)=0
        k=-1,2
        x=-1,2
二：Differentiation
f(x)=6-3k+6kx-3x^2
f'(x)=6k-6x
Maximum when f'(x)=0
6k-6x=0
k=x,x=k (line of symmetry)
maximum value, f(k)=12
When x=k, 6-3k+6k^2-3k^2=12
3k^2-3k-6=0
k^2-k-2=0
(k-2)(k+1)=0
k=-1,2
x=-1,2

superliong

回复 193# walrein_lim88


        哇，你好厉害哦！！
这是chapter 2 的 ， 也可以用differentiation 来解嘢！

walrein_lim88

回复 194# superliong


    可以啊。。。别忘了dy/dx = 0是可以找出MAX/MINIMUM VALUE 的

dollyeye

1.  if the sum of an arithmetic progression, log y+log y^2+log y^3+...+log y^n is given by n(n+1),find the value of y.


2.   given that sin x°, 2 cos x° and 2 sin x° are three consecutive terms in an arithemetic progression.find the value of x° in radians.


3.(i) find the sum of all the integers from 1 to 100 that are divisible by 5.
   (ii)hence ,find the sum of all the integers from 1 to 100 that are not divisible by            
       5.

这3题怎样做？

walrein_lim88

回复 196# dollyeye


   

数学神

2.   given that sin x°, 2 cos x° and 2 sin x° are three consecutive terms in an arithemetic progression.find the value of x° in radians.

2 cos x° - sin x° =  2 sin x° - 2 cos x°
2 cos x° + 2 cos x° =  2 sin x° + sin x°
4 cos x° =  3 sin x°
4/3 =  （sin x°）/（cos x°）
tan x° = 4/3
x° = 53.13° = 0.927 rad

walrein兄，那天我做的也是没错咯？！

乙劍真人

回复  dollyeye
walrein_lim88 发表于 23-3-2010 01:01 PM

这个格式很美..

walrein_lim88

回复 199# 乙劍真人


    什么叫做格式很美？？