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JAMB Mathematics Past Questions & Answers - Page 34

166.

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?

180 $^o$

36 $^o$

60 $^o$

108 $^o$

View answer & explanation

Correct answer is B

Total number of acres = 2 + 5 + 3 + 11 + 9 = 30

The angle of acres = 2 + 5 + 3 + 11 + 9 = 30

The angle of the sector for cassava in a pie chart = $\frac{3}{30} \times 360^o = 36^o$

167.

A cylindrical tank has a capacity of 3080m $^3$ . What is the depth of the tank if the diameter of its base is 14m?

25m

23m

22m

20m

View answer & explanation

Correct answer is D

V = 2080cm $^3$ , h = ?

r = 7cm

V = V $\pi r^2h$

h = $\frac{V}{\pi r^2} = \frac{3080}{\frac{22}{7} \times 49}$

$\frac{3080}{54}$ = 20cm

168.

A sector of circle of radius 7.2cm which substends an angle of 300 $^o$ at the centre is used to form a cone. What s the radius of the base of the cone?

8cm

9cm

6cm

7cm

View answer & explanation

Correct answer is C

No explanation has been provided for this answer.

169.

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST

$\frac{\pi r}{3}$

$\frac{\pi r}{2}$

$\frac{\pi r}{12}$

$\frac{\pi r}{6}$

View answer & explanation

Correct answer is A

$\frac{ \frac{r}{2}}{r}$ Sin $\theta$ = $\frac{1}{2}$

$\theta$ = sin $^{-1}$ ( $\frac{1}{2}$ ) = 30 $^o$ = 60 $^o$

Length of arc (minor)

ST = $\frac{\theta}{360}$ x 2 $\pi r$

$\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}$

170.

A binary operation x is defined by a x b = a $^b$ . If a x 2 = 2 - a, find the possible values of a?

1, -2

2, -1

2, -2

1, -1

View answer & explanation

Correct answer is A

a = b = a $^2$

a + 2 = a $^2$ .....(i)

a + 2 = 2 - a..............(ii)

a $^2$ = 2 - a

a $^2$ + a - 2 = a $^2$ + a - 2 = 0

= (a + 2)(a - 1) = 0

a = 1 or - 2

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