Shatin Pui Ying College
F.5 Additional Mathematics (2005-06)
Test on Chapter 17 & 18
Class : 5D (
)
Marks:
/40
Name :
Signature :
FORMULAS FOR REFERENCE
sin (A  B) = sin A cos B  cos A sin B
cos A + cos B = 2 cos A  B cos
2
AB
2
cos (A  B) = cos A cos B  sin A sin B
cos A – cos B = –2 sin A  B sin
2
AB
2
tan (A  B) =
1.
tan A  tan B
1  tan A tan B
2 sin A cos B = sin (A + B) + sin (A – B)
sin A + sin B = 2 sin A  B cos
2
AB
2
2 cos A cos B = cos (A + B) + cos (A – B)
sin A – sin B = 2 cos A  B sin
2
AB
2
2 sin A sin B = cos (A – B) – cos (A + B)
Evaluate the following integrals :
(a)

(c)
 tan
3
2x  2005dx
2
d
(3 marks)
(b)
 x
(3 marks)
(d)
 cos 5x sin 4xdx
2

3
 2 dx
(3 marks)
(4 marks)
(e)
 cos x  sin x cos x  sin x dx
(f)
 sin x cos x sin 2xdx
(4 marks)
(g)

x 2  6x
dx
x  32
(4 marks)
(4 marks)
(h)

x
dx (Bonus question : 5 marks)
x 3
2.
The slope at any point (x, y) of a curve is 3x + cosx. If the curve cuts the y-axis at the point
(0, 3), find its equation.
(5 marks)
3.
A man drives from town A to town B on a straight road without stopping while travelling.
His velocity at time t hours after leaving A is (60t – 30t2) km/h. Find
(a) his travelling time,
(b) the distance between town A and town B and
(c) the maximum velocity of the car.
(10 marks)