Section A
Answer all questions in the boxes provided. Working may be continued below the lines if necessary.
1. [Maximum mark: 6]
A discrete random variable X has the following probability distribution.
(a) Find p. [3]
(b) Find E (X). [3]
2. [Maximum mark: 5]
The following diagram shows a circle with centre O and a radius of 10cm. Points A, B and C lie on the circle
Angle AOB is 1.2 radians.
(a) Find the length of arc ACB. [2]
(b) Find the perimeter of the shaded region. [3]
3. [Maximum mark: 6]
(a) Given that 2m = 8 and 2n = 16, write down the value of m and of n. [2]
(b) Hence or otherwise solve 
. [4]
4. [Maximum mark: 7]
The following diagram shows the graph of a function f .
5. [Maximum mark: 7]
Given that sin x = 3/4, where x is an obtuse angle, find the value of
(a) cos x ; [4]
(b) cos 2x . [3]
6. [Maximum mark: 6]
Let f (x) = px² + (10 − p) x + 5/4 p −5 .
(a) Show that the discriminant of f (x) is 100 − 4p² . [3]
(b) Find the values of p so that f (x) = 0 has two equal roots.
7. [Maximum mark: 8]
Let f (x) = cos x , for 0 ≤ x ≤ 2π . The following diagram shows the graph of f .
There are x-intercepts at x =π/2,3π/2.
The shaded region R is enclosed by the graph of f , the line x = b , where b > 3π/2, and the x-axis. The area of R is (1-
/2). Find the value of b .
Section B部分省略。。。。。
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