# Mathematics 2009 | Study Mode

Question 71
A
7 cm
B
9 cm
C
12 cm
D
24 cm
##### Explanation
132 = 52 + b2

169 = 25 + b2

b2 = 144

b = $$\sqrt{144}$$

= 12 cm

Question 72
A
7.00cm
B
3.50cm
C
3.00cm
D
1.75cm
##### Explanation
Surface area of a sphere = 4$$\pi$$r2

4$$\pi$$r2 = 154 cm2

$$\pi$$r2 = $$\frac{154}{4}$$

= 38.5

$$\pi$$r2 = 38.5

r2 = 38.5 + $$\frac{22}{7}$$ $$\to$$ r2 = 38.5 x $$\frac{7}{22}$$

r2 12.25 $$\to$$ r = $$\sqrt{12.25}$$

= 3.5 cm

Question 73
A
x + y = 0
B
x - y = 0
C
x + y + k = 0
D
x - y - k = 0
##### Explanation

Question 74
A
A circle of radius 4 cm and with centre O
B
The perpendicular bisector of the chords
C
a straight line passing through centre O
D
A circle of radius 6 cm and with centre O

Question 75
A
-2
B
-1
C
1
D
2
##### Explanation
$$\frac{y_1 - y_o}{x_1 - x_o}$$ = m

$$\frac{4 - p}{p + 1}$$ = $$\frac{2}{3}$$

2p + 2 = 12 - 3p

5p = 10

p = $$\frac{10}{5}$$

= 2

Question 76
A
1
B
2
C
3
D
4
##### Explanation
Applying the formula

(x - a)2 + (y - b)2 = r2

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

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

9 + ( 4 - 4r + r2) = 9

13 - 4r + r2 = 9

r2 - 4r + 13 - 9 = 0

(r2 - 2r) - (2r + 4) = 0

r(r - 2) -2(r - 2) = 0

(r - 2) (r - 2)

r = 2 or -2

Question 77
A
$$\frac{2 + \sqrt{6}}{4}$$
B
$$\frac{ \sqrt{2} + \sqrt{3}}{4}$$
C
$$\frac{ \sqrt{2} + \sqrt{3}}{6}$$
D
$$\frac{ \sqrt{2} - \sqrt{3}}{2}$$
##### Explanation
sin 45o - cos 30o

$$\frac{1}{\sqrt{2}}$$ - $$\frac{\sqrt{3}}{2}$$

= $$\frac{2 - \sqrt{2} \times \sqrt{3}}{2\sqrt{2}})$$

= $$\frac{2 - \sqrt{6} \times \sqrt{2}}{2\sqrt{2} \sqrt{2}}$$

= $$\frac{2\sqrt{2} - \sqrt{12}}{4}$$

= $$\frac{2\sqrt{2} - 2\sqrt{3}}{4}$$

= $$\frac{2(\sqrt{2} - \sqrt{3})}{4}$$

= $$\frac{\sqrt{2} - \sqrt{3}}{2}$$

Question 78
A
753m
B
1003m
C
2003m
D
100m
##### Explanation
Tan 60o = $$\frac{300}{x}$$

x Tan 60o = 300

x3 = 300

x = $$\frac{300}{\sqrt{3}}$$ x $$\frac{\sqrt{3}}{\sqrt{3}}$$

x = $$\frac{300\sqrt{3}}{3}$$ x 100$$\sqrt{3}$$

Question 79
A
6 sin 8x
B
-24 sin 4x
C
12 sin 4x
D
-12 sin 4x
##### Explanation
If y = 3 cos 4x, $$\frac{dy}{dx}$$ equals

$$\frac{dy}{dx}$$ = 3(4 - sin 4x)

= -12 sin 4x

Question 80
A
0 units per sec.
B
15 units per seconds
C
22 units per seconds
D
26 units per seconds
##### Explanation
s = (2 + 3t)(5t - 4), find $$\frac{dy}{dx}$$ when t = $$\frac{4}{5}$$ sec

= 10t - 8 + 15t2 - 12t

$$\frac{ds}{dt}$$ = 15t2 - 2t - 8

= 30t - 2 ; t = $$\frac{4}{5}$$

= 30t - 2

= 30 x $$\frac{4}{5}$$ - 2 $$\to$$ 24 - 2

= 22 sec

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