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【纪念当年的帖子（2008）】高級數學纲要笔记
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发表于 5-5-2008 03:25 PM
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发表于 5-5-2008 11:09 PM
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发表于 5-5-2008 11:11 PM
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发表于 5-5-2008 11:20 PM
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发表于 5-5-2008 11:25 PM
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楼主 |
发表于 6-5-2008 09:47 PM
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发表于 9-5-2008 12:58 AM
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真得太感谢你了！！
你能在今年SPM之前做完比较重要和容易拿分的Chapter 吗？
很难的才找到这样的贴...
因为你的付出，我会努力好好学的...
谢谢你咯... |
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发表于 9-5-2008 06:19 PM
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楼主 |
发表于 10-5-2008 05:59 PM
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发表于 10-5-2008 06:30 PM
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发表于 10-5-2008 07:03 PM
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我有问题要问！！忘完了~~
1. The equation x^2-6x+7=h(2x-3) has roots which are equal. Find the values of h.
2. Given that Alpha and Beta are roots of the equation x^2-2x+k=0, while 2Alpha and 2Beta are the roots of the equation x^2+mx+9=0. Determine the possible values of k and m.
3.One of the roots of the equation 2x^2+6x=2k-1 is twice the other. Find the value of k and the roots of the equation.
4.Solve the quadratic equation 2x(x-4)=(1-x)(x+2). Give your answer correct to 4 significant figures.
5.The quadratic equation x(x+1)=px-4 has two distinct roots. Find the range of values of p. |
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楼主 |
发表于 10-5-2008 08:19 PM
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以后遇到什么难题自己先试试做看，
改次我不允许你们这样放题目在我的帖子请求大家解答，
念在你初犯，下不为例。
1. The equation x^2-6x+7=h(2x-3) has roots which are equal. Find the values of h.
x^2-6x-2hx+7+3h=0
Since the roots are equal,b^2-4ac=0
(-6-2h)^2-4(1)(7+3h)=0
...
h = -1 or h = -2
2. Given that Alpha and Beta are roots of the equation x^2-2x+k=0, while 2Alpha and 2Beta are the roots of the equation x^2+mx+9=0. Determine the possible values of k and m.
x^2-2x+k=0 ---(1)
x^2+mx+9=0---(2)
from (1),SOR = A+B = 2
POR = AB = k
from (2), 2A + 2B = -m
2(A+B) = -m
2(2) = -m
m = -4
2A2B = 4AB = 4(k) = 9
k = 9/4
3.One of the roots of the equation 2x^2+6x=2k-1 is twice the other. Find the value of k and the roots of the equation.
Let the roots = A and 2A
From the equation, 2x^2+6x-2k+1 =0
SOR = A+2A = -(b/a) = -(6/2)
A = -1
POR = A(2A) = c/a = 2A^2 = (-2k+1)/2
Substitute A = -1
Finally k = -3/2
4.Solve the quadratic equation 2x(x-4)=(1-x)(x+2). Give your answer correct to 4 significant figures.
Just use the formula：x = - 0.2573 or x = 2.591
5.The quadratic equation x(x+1)=px-4 has two distinct roots. Find the range of values of p.
Rearrange the equation, x^2+x-px+4=0
Since two distinct roots, b^2 - 4ac>0
a = 1 , b = 1-p , c = 4
...
Finally p > - 3 or p > 5
[ 本帖最后由 乙劍真人 于 10-5-2008 08:24 PM 编辑 ] |
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发表于 10-5-2008 08:38 PM
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拜托~~
我就是试过了才来问的~~
如果会的就不会来问了~~ |
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楼主 |
发表于 10-5-2008 08:41 PM
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发表于 10-5-2008 08:48 PM
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原帖由 乙劍真人 于 10-5-2008 08:41 PM 发表 
嗯！
如果我的语气重还请海涵。
第一题的b^2-4ac开始可以做得仔细点吗？？我就是那里不知道的~~
怎样做completing the square的~~很乱 |
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发表于 10-5-2008 09:02 PM
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我最不明白就是function的咯。。。
我真的很不明白偶=。=‘’ |
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楼主 |
发表于 10-5-2008 09:03 PM
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原帖由 jesselton 于 10-5-2008 08:48 PM 发表
第一题的b^2-4ac开始可以做得仔细点吗？？我就是那里不知道的~~
怎样做completing the square的~~很乱
嗯..
如果你要做 b^2 - 4 ac，
首先必须将那个 equation 排成 general form： ax^2 + bx + c = 0，
过后只要找到 a , b 及 c 就可以 substitute 进去那个 b^2 - 4 ac 里面..
e.g.：7x^2 - 4x + 3 = 0
a = 7，b = - 4，c = 3
我在做着笔记，多几天就可以上载了.. |
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发表于 10-5-2008 09:19 PM
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发表于 10-5-2008 09:21 PM
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原帖由 乙劍真人 于 10-5-2008 08:41 PM 发表
嗯！
如果我的语气重还请海涵。
我也是被你的语气吓倒了
以后选择做旁观者就好了
看你表演 |
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楼主 |
发表于 10-5-2008 09:29 PM
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原帖由 vincent5081 于 10-5-2008 09:21 PM 发表
我也是被你的语气吓倒了
以后选择做旁观者就好了
看你表演
嗯..
可能我被我的教授训练惯了吧！
每当我们有问题要请教他们，我们是必须先做足功课的，要问也是要问对那个关键..
不然肯定被骂..
你看我表演真的感到很大压力哩..
你就替我压阵吧！
如果有什么错误，请你指正.. |
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