F2數學 2 types Q (20 point!)

2013-01-20 3:36 am

There are 5 service groups, total has 200 students joined the service groups.
The pie chart shows the distribution of students in service groups
( I use words to describe the pie chart)
1. Community Youth Club: y%
2. Girl Guides: 18%, it has 36 students
3. Scouts: 38%
4. Hong Kong Red Cross: x%
5. St. John: 24%

b) How many students joined the scouts?
c) It is known that 20 more students joined the Hong Kong Red Cross than
Community Youth Club.
ci) Find the number of students who joined the Community Youth Club
cii) Find the % of students who joined the Hong Kong Red Cross

the difference of two squares identity
use identity : a^2-b^2 = (a+b) (a-b) or (a+b) (a-b) = a^2-b^2
expand following expressions
1. 1/3(3y+1) (3y-1)
2. (-4p+12p) (6q+2p)
3. 8(a/2+b/4) (a/2-b/4)

Must list every steps

回答 (1)

用戶26240

2013-01-20 5:42 am

✔ 最佳答案

b)
Number of students joined the scout
= 200 * 38%
= 76

ci)
Total percentage :
y + 18 + 38 + x + 24 = 100 ...... [1]

20 more students joined the Hong Kong Red Crossthan Community Youth Club :
200 * x% - 200 * y% = 20 ...... [2]

From [1] :
x + y = 20 ...... [3]

From [2] :
2x - 2y = 20
x - y = 10 ...... [4]

[3] - [4] :
2y = 10
y = 5

Number of students joined the Community Youth Club
= 200 * 5%
= 10

cii)
[3] + [4] :
2x = 30
x = 15

Students who joined the Hong Kong Red Cross = 15%

=====
1.
(1/3) (3y + 1) (3y - 1)
= (1/3) [(3y)² - 1²]
= (1/3) (9y² - 1)
= 3y² - (1/3)

=====
2.
(-4p + 12q) (6q + 2p)
= (12q - 4p) (6q + 2p)
= [4(3q - p)] [2(3q + p)]
= 8 (3q - p) (3q + p)
= 8 [(3q)² - p²]
= 8 (9q² - p²)
= 72q² - 8p²

=====
3.
8 [(a/2) + (b/2)] [(a/2) - (b/4)]
= 8 [(a/2)² - (b/4)²
= 8 [(a²/4) - (b²/16)]
= 2a² - (b²/2)

參考: 土扁

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