F5 maths - Ans.fyi 參考答案

F5 maths

2011-06-12 5:07 am

1. There are 20 members in the school choir. A team of four members will be selected randomly to participate in the joint-school singing contest.

(a) What is the number if different teams can be formed.

(b) Joey is one of the member on the choir and must be selected to take part in the singing contest. How many different teams can be formed?

2.(a) Solve 2sin^2 x- cos x- 1 for 0°≦x ≦360°
(b) Find the maximum value of 2sin^2 x- cos x -1 for any real number x.

回答 (2)

知識就是力量

2011-06-12 5:42 am

✔ 最佳答案

1.(a) No. of different teams = 20C4 = 4845
(b) Since Joey has been chosen, there are 19 members left and only 3 members have to be chosen.
So no. of different teams (20 - 1)C(4 - 1) = 19C3 = 969

2(a) 2sin^2 x - cos x - 1 = 0
2(1 - cos^2 x) - cos x - 1 = 0
-2cos^2 x - cos x + 1 = 0
2cos^2 x + cos x - 1 = 0
(2 cos x - 1)(cos x + 1) = 0
cos x = 1/2 or cos x = -1
x = 60 or 300 or x = 180
So x = 60, 180 or 300
(b) y = 2sin^2 x - cos x - 1
= 2(1 - cos^2 x) - cos x - 1
= -2cos^2 x - cos x + 1
= -2[cos^2 x + (1/2)cos x] + 1
= -2[cos^2 x + (1/2)cos x + (1/4)^2 - (1/4)^2] + 1
= -2(cos x + 1/4)^2 + 9/8
Hence max. value is attained at 9/8.

2011-06-11 21:44:34 補充：
I think the question 2(a) should be Solve 2sin^2 x - cos x - 1 = 0 for 0°≦x ≦360°
while for (b) Find the maximum value of y = 2sin^2 x - cos x - 1 for any real number x.

參考: Knowledge is power.

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[匿名]

2011-06-12 5:37 am

q2 typing mistake??

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