## Mathematics 2018 | Study Mode

Question 41
A
x = 240$$^o$$ - y - z
B
x = 180$$^o$$ - y - z
C
x = 360$$^o$$ + y -z
D
x = 360$$^o$$ - y - z
Explanation.

In the diagram,

a = z (alternate angles)

b = 180$$^o$$ - a (angles on a straight line)

b = 180$$^o$$ - z

c = 180$$^o$$ - x (angles on a straight line)

y = b + c (sum of oposite interior angles)

y = 180$$^o$$ - z + 180$$^o$$ - x

y = 360$$^o$$ - z - x

x = 360$$^o$$ - y - z

Question 42
A
N26,792.00
B
N26,972.00
C
N62.792.00
D
N62,972.00
Explanation.

Total donation = 4 x 500 + 7 x 2000 + 20 x 1000 + 9 x 700 + 4 x 500 + 5 x 100 + 3 x 50 + 1 x 2 + 2 x 10

= 20000 + 14000 + 20000 + 6300 + 2000 + 500 + 150 + 2 + 20

= N62,972

Question 43
A
90$$^o$$
B
60$$^o$$
C
45$$^o$$
D
30$$^o$$
Explanation.

In the diagram, < WOZ = 180$$^o$$ (angle on a straight line)

< WOX = < XOY = < YOZ

(|WX| = |XY| = |YZ|)

$$\frac{180^o}{3}$$ = 60$$^o$$

= 60$$^o$$

M + m =2m (base angles of isosceles $$\bigtriangleup$$, |OY| and |OZ| are radii)

< YOZ + 2m (base angles of a $$\bigtriangleup$$)

60$$^o$$ + 2m = 180$$^o$$ (sum of a $$\bigtriangleup$$)

60$$^o$$ + 2m = 180$$^o$$

2m = 180$$^o$$ - 60$$^o$$

2m = 120$$^o$$

m = $$\frac{120^o}{2}$$

= 60$$^o$$

Question 44
A
2 : 3 : 4
B
3 : 4 : 5
C
4 : 5 : 6
D
5 : 6 : 7
Explanation.

m + n = 110$$^o$$, (n + r) = 130$$^o$$

(m + n) = 120$$^o$$

then, r = 130$$^o$$ - n

and;

m + (130^o - n) = 120$$^o$$

m - n = -10$$^o$$

2m + (n + r) = 110 + 120 = 230

2m + 130 = 230

2m = 230 - 130

m = $$\frac{100}{2}$$ = 50$$^o$$

n = 110$$^o$$ - 50$$^o$$

= 60$$^o$$

r = 130$$^o$$ - 60$$^o$$ = 70$$^o$$

Hence, the ratio m : n : r

= 50 : 60 : 70

= 5 : 6 : 7

Question 45
A
170$$^o$$
B
177$$^o$$
C
182$$^o$$
D
192$$^o$$
Explanation.

Length of arc, L = 21.4 - 2 x 4.2cm

= 21.4 - 8.4

= 13cm

But L = $$\frac{\theta}{360^o}$$ x 2$$\pi r$$

i.e 13 = $$\frac{\theta}{360^o}$$ x 2 x $$\frac{22}{7}$$ x 4.2

= 13 x 360$$^o$$ x 7

= $$\theta$$ x 2 x 22 x 4.2

$$\theta$$ = $$\frac{13 \times 360^o \times 7}{44 \times 4.2}$$

= $$\approx$$ 177.27$$^o$$

$$\approx$$ 177$$^o$$ (to the nearest degree)

Question 46
A
$$\frac{1}{10}$$
B
$$\frac{1}{5}$$
C
$$\frac{5}{12}$$
D
1$$\frac{2}{5}$$
Explanation.

From the diagram,

h$$^2$$ = 4$$^2$$ + 3$$^2$$ (pythagoras')

h$$^2$$ = 16 + 9 = 25

h = $$\sqrt{25}$$ = 5

Hence, sin x - cos x

= $$\frac{4}{5} - \frac{3}{5}$$

= $$\frac{2}{5}$$

Question 47
A
10cm
B
15cm
C
25cm
D
30cm
Explanation.

In $$\bigtriangleup$$YSC, sin 30$$^o$$ = $$\frac{YS}{20}$$

|YS| = 20 sin 30$$^o$$

= 20 x 0.5

10m

Question 48
A
42cm
B
48cm
C
52cm
D
60cm
Explanation.

Let the length of a side of the rhombus be n

Then, n$$^2$$ = 5$$^2$$ + 12$$^2$$

= 25 + 144 = 169

n = $$\sqrt{169}$$

= 13cm

Hence, perimeter of rhombus = 4n = 4 x 13

= 52cm

Question 49
A
18
B
20
C
30
D
38
Explanation.

Let n(M $$\cup$$ N \) = x

Then 20 - x + x + 30

- x = n(M $$\cup$$ N)

50 - x = 40

50 - 40 = x

10 = x

x = 10

Hence, n(M $$\cup\N)' = 8 + (20 - 10) + (30 + 10) = 8 + 10 + 20 = 38 Question 50 A (0,0), (1,1) B (0,0), (0,1) C (1, 0), (0, 0) D (0, 0) (0, 0) Explanation. y = x\(^2$$ ....(1)

y = x ......(2)

y = y

x$$^2$$ - x

x$$^2$$ - x = 0

x(x - 1) = 0

x = 0 or x - 1 = 0

x = 0 or x = 1

when x = 0, y = 0$$^2$$ = 0

when x = 1, y = 1$$^2$$ = 1

Hence; the two graphs interest at (0, 0) and (1, 1)

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