Mathematics 2009 | Study Mode

Question 31
A
A circle of radius 4 cm and the center 0
B
The perpendicular bisector of the chords
C
A straight line passing through 0
D
A circle of radius 6 cm and with center 0
Explanation
x2 + 33 = 52
x2 + 9 = 25
x2 = 25 9
x2 = 16

x = 16

= 4 cm
The locus is a circle of radius 4 cm with the center 0

Question 32
A
-2
B
-1
C
1
D
2
Explanation
 Gradient = y2 - y1 x2 - x1

 2 3
= 4-p
p-(-1)

 2 3
= 4-p
p+1

3(4-p) = 2(p+1)
12 - 3p = 2p + 2
12 2 = 2p + 3p
10 = 5p
 p = 10 5

= 2

Question 33
A
1
B
2
C
3
D
4
Explanation
A(4,2) and B(1,r), AB = 3 units

3 = (x2- x1)2 + (y2-y1)2

3 = (4-1)2 + (2-r)2

3 = 32 + (2-r)2

3 = 9 + 4 4r + r2

3 = r2 - 4r + 13

9 = r2 - 4r + 13 By squaring both sides
r2 - 4r + 4 = 0
(r-2)(r-2) = 0
r = 2

Question 34
A
6 sin 8x
B
-24 sin 4x
C
12 sin 4x
D
-12 sin 4x
Explanation
y = 3 cos 4x
dy/dx = 3x -4 sin 4x
= -12sin 4x

Question 35
A
$$\frac{2+\sqrt{3}}{4}$$
B
$$\frac{\sqrt{2}+\sqrt{3}}{4}$$
C
$$\frac{\sqrt{2}+\sqrt{3}}{2}$$
D
$$\frac{\sqrt{2}-\sqrt{3}}{2}$$
Explanation
$$Sin 45 - cos 30\\ \frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{2}\\ =\frac{\sqrt{2}-\sqrt{3}}{2}$$

Question 36
A
100m
B
753 m
C
1003m
D
2003m
Explanation
 Tan 60 = 300 x

 x = 300 Tan 60

 x = 300 3

x = (300/3) x (3/3)
 x = 3003 .....3

x = 1003

Question 37
A
0 units per sec
B
15 units per sec
C
22 unit per sec
D
26 units per sec
Explanation
x = (2+3t)(5t-4)
Let u = 2+3t du/dt = 3
and v = 5t-4 dv/dt = 5
dx/dt = Vdu/dt + Udv/dt
= (5t-4)3 + (2+3t)5
= 15t - 12 + 10 + 15t
= 30t - 2
= 30x4/5 - 2
= 24 - 2
= 22

Question 38
A
4
B
3
C
2
D
1
x(4-x) = 4x-x2
dy/dx = 4-2x
As dy/dx = 0
4-2x = 0
2x = 4
x = 2

Question 39
A
2.3 cm
B
4.0 cm
C
5.2 cm
D
6.0 cm
Explanation
S = t3 - t2 - t + 5
ds/dt = 3t2 - 2t - 1
As ds = 0
3t2 - 2t - 1 = 0
(3t+1)(t-1) = 0
t = 1 or -1/3
At min pt t = -1/3
S = t3 - t2 - t + 5 put t = -1/3
= (-1/3)3 - (-1/3)2 - (-1/3) + 5
= -1/27 - 1/9 + 1/3 + 5
= 140 / 27
= 5.2

Question 40
A
sec tan + k
B
tan + k
C
2sec + k
D
sec + k
Explanation
sec2 d = 1/cos2 d
(cos)-2 d,
let u = cos
u-2 = 1/u + c
cos = sin + c
sec-2 = 1/u sin + c
= (sin / cos) + c
= Tan + c

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