中三數學(20點)

👨🏻‍🏫 學術台數學

nganliyan

2009-12-28 9:40 pm

[color=Blue]
全部題目都要有步驟

化簡下列各式:
1,
(a)x^3+2x^-5x+3x-4x^3

(b)(4y+1)-(2-3y)

(c)9ab^3
---------
3a^4b

(d)-8 3a^2b^4
-----------x-------------
16a^3b^2 b

2.展開
(a) 4x(5x-2)
(b)(y+5)(y-2)
3.解未知數
(a)7x-6=5x-8
(b)4x-1 5x
------ -3=------- +2
2 3

4.400減少了20%後,再增加30%,求新值

5.若巴士的車費由16減少至15,求車費的百分改變

6.已知一部機器現時的價值為20 000,若這部機器每年的折舊率為20什麼,求4年後該部機器的價值(答案須準確至最接近的元)

7.若年利率為6%,並以單利息計算,存款期3年,可得利息1080,求本金

8.某住宅單位的應課差餉租值為240 000,若差餉徵收率為每年4%,求每季應繳交的差餉

9.圖中,ABCD為一邊平行四邊形,E為AD上的一點使得AB=AE,已知角BCD=75度,求角BAE及角CDE
B C
75

A E D

10.在圖中,ABCD是一個菱形,若角ACD=63,求角ABD
A D

E

63
B C

11.在圖中,AD是BC的垂直平分線
(a)證明三角形ADB全等三角形ADC
(b)由此,證明AD是角BAC上的角平分線
A

直角
B l D l C

13.求A(-3,4),B(1,-2),求AB的距離

14.若A(3,a),B(1,-2),求AB的斜率

15.林太從銀行提取了共142張$20和$50的新鈔票,總值$3800,問林太提取了$20和$50新鈔票各多少張?

16.偉明每日的工作時間由8小時增加至10小時,但他每小時的工資卻減少25%,求偉明每日收入的百分改變

17.若(x,y)=(-2,1)為聯立方程
( ax-by+8=0
~
( bx+ay+1=0 的解,求a及b

18.某觀光遊覽船只有頭等和普通等兩類船票出售,已知共出售出600張船票,其中售出的普通等船票為售出的頭等數目之三倍,若一張頭等船票的售價為$850,而一張普通等船票的售價為$500,求售出船票的總值[/color]

更新1:

多謝你了,但係有d題我諗住整個圖形俾你睇,點知唔得,同埋個d-----<<尼d係分線少少修正: 1(c)9ab^3分線3a^4b 1(d)-8分線16a^3 x3a^2b^4分線b 3(b)4x-1分線2 -3等於乘3a^2b^4分線b

回答 (2)

匿名

2009-12-29 1:10 am

✔ 最佳答案

1,(a)x^3+(2x^-5 x)+3x-4x^3
= -3x^3+(2x^-4)+3x
= -3x^3+(2/x^4)+3x
(b)(4y+1)-(2-3y)
= -8y+12y^2-2+3y
= 12y^2-5y-2
(c)(9ab^3)/3a^4 b)
= 3(a^-3)b^2
= 3b^2/a^3
(d)-8/(16a^3 b^2)*(3a^2b^4)/b
= (-1/2a^3 b^2) * 3a^2 b^3
= -3ab/2
2.(a) 4x(5x-2)
= 20x^2 - 8x
(b)(y+5)(y-2)
= y^2 +3y-10
3.(a)7x-6=5x-8
2x=-2
x=-1
(b)[(4x-1)/2]-3= (5x/3)+2
3(4x-1) - 18 = 2(5x) + 12
12x-3-18=10x+12
2x=33
x=33/2
x=16.5
4.新值= 400*(1-20%)*(1+30%)
= 400 * 0.8 *1.3
= 416
5.車費的百分改變 = (15-16)/16 *100%
= -1/16 * 100%
= -6.25%
6.4年後該部機器的價值
= 20000 * (1-20%)^4
= 20000 * 0.4096
= $8192
7.設本金為$C,
C(6%)*3 = 1080
C=6000
所以本金為$6,000
8.每季應繳交的差餉 = 240,000 * (4%/4)
= $2,400
9.<BAE = 75 deg (properties of // gram)
AB//CD(properties of //gram)
<BAE+<CDE=180deg(int.<s, AB//CD)
<CDE=105 deg
10.Given that AC perpendicular to BD (properties of rhombus)
<CAB=<ACD= 63 deg (properties of rhombus)
<ABD+<CAB+90deg=180deg (<s sum in triangle)
<ABD=27deg
11.(a)Let the meet point of two lines be K, i.e. AK=DK, BK=CK
AD = AD (common line)
AB^2=(AK^2+BK^2)
AC^2=AK^2+CK^2
AC^2=AB^2
AC=AB
所以三角形ADB全等三角形ADC(SS)
(b)Since triangle ADB = triangle ADC (from (a))
<CAD=<BAD
所以AD是角BAC上的角平分線
無12題[skipped]
13.AB^2=(1-(-3))^2+(4-(-2))^2
AB^2=52
AB=2√13
14.AB的斜率 = (-2-a)(1-3)
= (-2-a)/-2
= (2+a)/2
15.設林太提取了$20新鈔票x張,,,所以林太提取了$50新鈔票(142-x)張
20x+(142-x)50 = 3800
20x - 50x + 7100 = 3800
30x = 3300
x = 110
所以林太提取了$20新鈔票110張,提取了$50新鈔票(142-110 = 32)張
16.設偉明每日收入為$x,
偉明每日收入的百分改變
= [x(1-25%)(10) - x(8)]/8x * 100%
= (7.5x-8x)/8x *100%
= -6.25%
17.
( -2a-b+8)=0 --------(1)

( -2b+a+1)=0 --------(2)
(1)*2-(2), -4a-2b+16+2b-a-1=0
-5a+15=0
a=3
Sub a=3 into(1),
-2(3)-b+8=0
b=8-6
b=2
18.設售出普通等船票x張,,,所以售出的頭等數目為x/3 張,,,
x + x/3 = 600
3x+x=1800
x = 450
售出船票的總值
= x(500)+(x/3)(850)
= (450)(500)+(450/3)(850)
= $352,500

2009-12-28 17:10:44 補充：
好累~~一次做咁多~~~xD:P

2009-12-28 17:56:39 補充：
1(c)9ab^3分線3a^4b
=9ab^3/3a^4 b
= 3a^-1 b^2
= 3b^2/a
1(d)-8分線16a^3 x3a^2b^4分線b
= -8/16a^3 x 3a^2 b^4/b
= -1/2a^3 x 3a^2 b^3
= -3b^3/2a
3(b)4x-1分線2 -3等於x乘3a^2b^4分線b
(4x-1)/2 - 3 = x(3a^2 b^4/b)
4x-1 - 6 = x(9a^2 b^3)
x(4-9a^2 b^3) = 6
x = 6/(4-9a^2 b^3)

2009-12-28 17:57:11 補充：
3(b)4x-1分線2 -3等於乘3a^2b^4分線b 即係咩?

2009-12-28 19:13:00 補充：
(4x-1)/2 -3 = 5x/3 +2
3(4x-1) - 18 = 10x + 12
12x - 3 - 18 = 10x + 12
2x = 33
x = 33/2

2009-12-28 19:13:28 補充：
okay~ I have posted the answer~~^^"

參考: Hope can help you~~, Finish ^^"~

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nganliyan

2009-12-29 3:01 am

4x-1..........5x....
~~~ -3= ~~~...+2
...2............3........

咁樣會唔會清楚d

2009-12-28 21:53:33 補充：
擅長領域：數學 | 物理

你物理都掂?
我有d物理題都未搞掂

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