Year : 
1986
Title : 
Mathematics (Core)
Exam : 
JAMB Exam

Paper 1 | Objectives

31 - 40 of 48 Questions

# Question Ans
31.

A regular polygon of n sides has 160o as the size of each interior angle. Find n

A. 18

B. 16

C. 14

D. 12

A
32.

A girl walks 45 meters in the direction 050o from a point Q to a point X. She then walks 24 meters in the direction 140o from X to a point Y. How far is she then from Q?

A. 69m

B. 57m

C. 51m

D. 21m

Detailed Solution

QY = 452 + 242 = 2025 + 576

= 2601

QY = \(\sqrt{2601}\)

= 51
33.

An arc of a circle of radius 6cm is 8cm long. Find the area of the sector

A. 5\(\frac{1}{3}\)cm2

B. 24cm2

C. 36cm2

D. 84cm2

Detailed Solution

Radius of the circle r = 6cm, Length of the arc = 8cm

Area of sector = \(\frac{\theta}{360}\) x \(\pi\)r2........(i)

Length of arc = \(\frac{\theta}{360}\) x 2\(\pi\)r........(ii)

from eqn. (ii) \(\theta\) = \(\frac{240}{\pi}\), subt. for \(\theta\) in eqn (i)

Area x \(\frac{240}{1}\) x \(\frac{1}{360}\) x \(\frac{\pi 6}{1}\)

= 24cm\(^2\)
34.

Find the total surface area of solid cone of radius 2\(\sqrt{3}\)cm and slanting side 4\(\sqrt{3}\)

A. 8\(\sqrt{3}\pi \)cm2

B. 24\(\pi \)cm2

C. 15\(\sqrt{3}\pi \)cm2

D. 36\(\pi \)cm2

Detailed Solution

Total surface area of a solid cone

r = 2\(\sqrt{3}\)

= \(\pi r^2\) + \(\pi\)rH

H = 4\(\sqrt{3}\), \(\pi\)r(r + H)

∴ Area = \(\pi\)2\(\sqrt{3}\) [2\(\sqrt{3}\) + 4\(\sqrt{3}\)]

= \(\pi\)2\(\sqrt{3}\)(6\(\sqrt{3}\))

= 12\(\pi\) x 3

= 36\(\pi \)cm2
35.

If U and V are two distinct fixed points and W is a variable points such that UWV is a right angle, what is the locus of W?

A. The perpendicular bisector of UV

B. A circle with UV as radius

C. A line parallel to the line UV

D. A circle with the line UV as the diameter

D
36.

An open rectangular box externally measures 4m x 3m x 4m. Find the total cost of painting the box externally if it costs N2.00 to paint one square meter

A. N96.00

B. N112.00

C. N136.00

D. N160.00

Detailed Solution

Total surface area(s) = 2(4 x 3) + 2(4 x 4)

= 2(12) + 2(16)

= 24 + 32

= 56cm2

1m2 costs N2.00

∴ 56m∴ will cost 56 x N2.00

= N112.00
37.

Of the nine hundred students admitted in a university in 1979, the following was the distribution by state: Anambrs 185, Imo 135, Kaduna 90, Kwara 110, Ondo 155, Oyo 225. In a pie chart drawn to represent this distribution, The angle subtended at the centre by anambra is

A. 50o

B. 65o

C. 74o

D. 88o

Detailed Solution

Anambra = \(\frac{185}{900}\) x \(\frac{360}{1}\)

= 74o
38.

Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

A. 131

B. 125

C. 123

D. 120

Detailed Solution

Arrange in ascending order

89, 100, 108, 119, |120, 130|, 131, 131, 141, 161

Median = \(\frac{120 + 130}{2}\)

= 125
39.

Find the probability that a number selected at random from 40 to 50 is a prime

A. \(\frac{3}{11}\)

B. \(\frac{5}{11}\)

C. \(\frac{3}{11}\)

D. \(\frac{4}{11}\)

Detailed Solution

From 40 to 50 = 11 & number are prime i.e. 41, 43, 47

prob. of selecting a prime No. is \(\frac{3}{11}\)
40.

A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?

A. \(\frac{1}{7}\)

B. \(\frac{11}{18}\)

C. \(\frac{7}{18}\)

D. \(\frac{7}{11}\)

Detailed Solution

Prob. of purple shirt is \(\frac{7}{18}\)
31.

A regular polygon of n sides has 160o as the size of each interior angle. Find n

A. 18

B. 16

C. 14

D. 12

A
32.

A girl walks 45 meters in the direction 050o from a point Q to a point X. She then walks 24 meters in the direction 140o from X to a point Y. How far is she then from Q?

A. 69m

B. 57m

C. 51m

D. 21m

Detailed Solution

QY = 452 + 242 = 2025 + 576

= 2601

QY = \(\sqrt{2601}\)

= 51
33.

An arc of a circle of radius 6cm is 8cm long. Find the area of the sector

A. 5\(\frac{1}{3}\)cm2

B. 24cm2

C. 36cm2

D. 84cm2

Detailed Solution

Radius of the circle r = 6cm, Length of the arc = 8cm

Area of sector = \(\frac{\theta}{360}\) x \(\pi\)r2........(i)

Length of arc = \(\frac{\theta}{360}\) x 2\(\pi\)r........(ii)

from eqn. (ii) \(\theta\) = \(\frac{240}{\pi}\), subt. for \(\theta\) in eqn (i)

Area x \(\frac{240}{1}\) x \(\frac{1}{360}\) x \(\frac{\pi 6}{1}\)

= 24cm\(^2\)
34.

Find the total surface area of solid cone of radius 2\(\sqrt{3}\)cm and slanting side 4\(\sqrt{3}\)

A. 8\(\sqrt{3}\pi \)cm2

B. 24\(\pi \)cm2

C. 15\(\sqrt{3}\pi \)cm2

D. 36\(\pi \)cm2

Detailed Solution

Total surface area of a solid cone

r = 2\(\sqrt{3}\)

= \(\pi r^2\) + \(\pi\)rH

H = 4\(\sqrt{3}\), \(\pi\)r(r + H)

∴ Area = \(\pi\)2\(\sqrt{3}\) [2\(\sqrt{3}\) + 4\(\sqrt{3}\)]

= \(\pi\)2\(\sqrt{3}\)(6\(\sqrt{3}\))

= 12\(\pi\) x 3

= 36\(\pi \)cm2
35.

If U and V are two distinct fixed points and W is a variable points such that UWV is a right angle, what is the locus of W?

A. The perpendicular bisector of UV

B. A circle with UV as radius

C. A line parallel to the line UV

D. A circle with the line UV as the diameter

D
36.

An open rectangular box externally measures 4m x 3m x 4m. Find the total cost of painting the box externally if it costs N2.00 to paint one square meter

A. N96.00

B. N112.00

C. N136.00

D. N160.00

Detailed Solution

Total surface area(s) = 2(4 x 3) + 2(4 x 4)

= 2(12) + 2(16)

= 24 + 32

= 56cm2

1m2 costs N2.00

∴ 56m∴ will cost 56 x N2.00

= N112.00
37.

Of the nine hundred students admitted in a university in 1979, the following was the distribution by state: Anambrs 185, Imo 135, Kaduna 90, Kwara 110, Ondo 155, Oyo 225. In a pie chart drawn to represent this distribution, The angle subtended at the centre by anambra is

A. 50o

B. 65o

C. 74o

D. 88o

Detailed Solution

Anambra = \(\frac{185}{900}\) x \(\frac{360}{1}\)

= 74o
38.

Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

A. 131

B. 125

C. 123

D. 120

Detailed Solution

Arrange in ascending order

89, 100, 108, 119, |120, 130|, 131, 131, 141, 161

Median = \(\frac{120 + 130}{2}\)

= 125
39.

Find the probability that a number selected at random from 40 to 50 is a prime

A. \(\frac{3}{11}\)

B. \(\frac{5}{11}\)

C. \(\frac{3}{11}\)

D. \(\frac{4}{11}\)

Detailed Solution

From 40 to 50 = 11 & number are prime i.e. 41, 43, 47

prob. of selecting a prime No. is \(\frac{3}{11}\)
40.

A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?

A. \(\frac{1}{7}\)

B. \(\frac{11}{18}\)

C. \(\frac{7}{18}\)

D. \(\frac{7}{11}\)

Detailed Solution

Prob. of purple shirt is \(\frac{7}{18}\)