# Mathematics 2008 | Study Mode

Question 21
A
1
B
zero
C
-1/2
D
-1
##### Explanation
mn = m+n+mn
Let e be the identity element
me = em = m
m+e+me = m
e+me = m-m
e+me = 0
e(1+m) = 0
e = 0 / (1+m)
e = 0

Question 22
A

100o

B

80o

C

50o

D

30o

##### Explanation

Exterior angle = sum of two interior opposite angles
y = 50o (vert. opp >s are equal)
X = y + 30
X = 50 + 30
X = 80o

Question 23
A
12o
B
24o
C
25o
D
30o
##### Explanation
Exterior angle = 360 / n
= 360 / 12
= 30o

Question 24
A
90o
B
53o
C
36o
D
26o
##### Explanation
a = a(base s of Iss )
a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
OPQ = 53o

Question 25
A
12.5 cm2
B
75.0 cm2
C
78.5 cm2
D
84.8 cm2
##### Explanation
Area of the figure = Area of rect + area of semi circle
$$=L \times h + \frac{1}{2}\pi r^2\\ 5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times \left(\frac{5}{2}\right)^2\\ =75+\frac{(22\times 25)}{2\times7}\\ =75 + 9\frac{23}{28}\\ =84.8cm$$

Question 26
A
30o
B
45o
C
60o
D
90o
##### Explanation
If a length of a chord is equal to the length of a radius in the same circle, the triangle formed y the chord and the radii is an equilateral triangle
each angle = 60o

Question 27
A
44,000 liters
B
4,400 liters
C
440 liters
D
44 liters
##### Explanation
V = r2h
1m = 100cm
14cm = 1400cm
$$V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\ = 44, 000 liters$$

Question 28
A
(2,5)
B
(5,2)
C
(1,0)
D
(0,1)
##### Explanation
$$X = \frac{6+2}{2}=\frac{10}{2}=5\\ Y = \frac{2+2}{2}=\frac{4}{2}=2\\ X,Y = (5,2)$$

Question 29
A
3/2
B
2/3
C
-2/3
D
-3/2
##### Explanation
3X + 2Y + 1 = 0
2Y = -3X - 1
$$\frac{-3}{2}X - \frac{1}{2}$$
Gradient of 3X + 2Y +1 = 0 is -3/2
Gradient of a line perpendicular to 3X + 2Y + 1 = 0
$$=-1 \div \frac{3}{2}\\ =-1 \times \frac{-2}{3}=\frac{2}{3}$$

Question 30
A
3/4
B
3/5
C
2/5
D
1/4
##### Explanation
sin = 3/5
x2 = 52 - 32

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