JAMB Mathematics Past Questions & Answers - Page 237

1,181.

A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?

A.

336

B.

420

C.

576

D.

720

Correct answer is A

Total floor area = 720 x 420

Area of one tile = 30 x 30

No. of tile required = \(\frac{720 \times 420}{30 \times 30}\)

= 24 x 14

= 336 tiles

1,182.

4sin2 x - 3 = 0, find x if 0 \(\geq\) x \(\geq\) 90o

A.

30o

B.

45o

C.

60o

D.

9o

Correct answer is C

4 sin2x - 3 = 0

sin2x = \(\frac{3}{4}\)

Sin x = \(\pm\) \(\sqrt{\frac{3}{4}}\)

= \(\pm\) \(\sqrt{\frac{3}{4}}\)

= 60o

1,183.

The pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have angles of depression of 35o and 55o. Find the distance between the two points of observation

A.

10(sin 35o - sin 55o)

B.

10 cos35o - cos 55o

C.

10(tan35o - tan55o)

D.

10(cot35o - cot55o)

Correct answer is D

x = 10 cot35o - 10 cot55o

= 10(cot35o - cot55o)

1,184.

If x : y = 5 : 12 and z = 52cm, find the perimeter of the triangle.

A.

68cm

B.

84cm

C.

100cm

D.

120cm

Correct answer is D

13 = 52

1 = \(\frac{52}{13}\)

= 4

5 + 12 + 13 = 30

Total perimeter = 30 x 4

= 120cm

1,185.

In XYZ, y = z = 30° and XZ = 3cm. Find YZ

A.

\(\frac{\sqrt{3}}{2}\) cm

B.

3\(\frac{\sqrt{3}}{2}\) cm

C.

3\(\sqrt{3}\) cm

D.

2\(\sqrt{3}\) cm

Correct answer is C

Y \(\to\) 30°

X \(\to\) 120°

Z \(\to\) 30°

\(\frac{3}{\text{sin 30}}\) = \(\frac{YZ}{\text{sin 120}}\)

YZ = \(\frac{3\times \sin 120}{\sin 30}\)

\(3 \times \frac{\sqrt{3}}{2} \times 2 = 3\sqrt{3}\)