中三數學功課問題(20分)就黎考試

1.
weighted mean of the data
=(7×0.1+11x0.2+5×0.3+21×0.4+4x0.5)/(0.1+0.2+0.3+0.4+0.5 )
=9.87
2.
curved surface area
=pi×15×18
=270π cm^2
3.A(0,2) B(0,3) C(4,6)
D(4,y)
AB=√(0-0)^2+(2-3)^2
=√1
CD=√(4-4)^2+(6-y)^2
=√((6-y)^2
√((6-y)^2=√1
y=7
D(4,7)

4.

圖片參考：http://imgcld.yimg.com/8/n/HA00510450/o/701006060080113873419730.jpg

3(πr^2)=πxrxl+(πr^2)
2πr^2=πxrxl
2r=l

πxrxl=π×l^2×θ/360°
2πr^2=π×l^2×θ/360°
2πr^2=π×(2r)^2×θ/360°
θ=180°
∴ㄥ180° of sector can be turn to form this cone

5.
a^2 - (a-b)^2
=[a-(a-b)][a+(a-b)]
=(a-a+b)(a+a-b)
=b(2a-b)
6.
(x+17+20+15+12+40)/6-(x+17+20+15+12)/5=4
[5(x+17+20+15+12+40)-6(x+17+20+15+12)]/30=4
5x+85+100+75+60+200-6x-102-120-90-72=120
-x=-16
x=16

7. Let θ be the inclination
mPQ=(0+3)/(7+1)
=3/8
tanθ =3/8
θ =21°
∴The inclination is 21°





2010-06-06 18:01:37 補充：
a^2-b^2≡(a-b)(a+b)

咁
a^2 - (a-b)^2
=[a-(a-b)][a+(a-b)]
=(a-a+b)(a+a-b)
=b(2a-b)

a-a+b
咪剩番b囉

∴(a-a+b)(a+a-b)
=b(2a-b)

2010-06-06 18:07:32 補充：
the total surface areas of two similar solid pyramids made of iron are in the ratio 81:36. if the smaller one weighs 1KG, then the large one weights?

Let y KG be the large one weights
(√81)^3 / (√36)^3=y / 1
729 / 216=y / 1
y=3.375
∴ The large one weights is 3.375 KG

2010-06-06 18:50:39 補充：
http://img576.imageshack.us/img576/8968/57972951.jpg
The men not classifying as 'Fail'=40-40X25%
=30

http://img7.imageshack.us/img7/9321/mc001k.jpg
Let hcm be the lower circular cone
h/(h+3)=1/2
h=3

Volume=1/3×π×3^2x6 - 1/3×π×1^2x3
=17πcm^3

2010-06-06 18:50:44 補充：
http://img534.imageshack.us/img534/6703/mc002.jpg
modal class =70-79marks

http://img257.imageshack.us/img257/1306/mc003.jpg
∵O is the incentre of △ABC
∴ㄥACB=45°,ㄥABC=45°

ㄥBAC=180°-45°-45°
=90°

Area of △ABC=8×8/2
=32cm^2

在這題,O是△ABC的內心,
即FB平分ㄥABC,DC平分ㄥACB

2010-06-06 18:53:10 補充：
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