JAMB Mathematics Past Questions & Answers - Page 245

1,221.

The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?

A.

perpendicular bisector of the two lines

B.

angle bisector of the two lines

C.

bisector of the two lines

D.

line parallel to the two lines

Correct answer is B

The required locus is angle bisector of the two lines

1,222.

If the heights of two circular cylinder are in the ratio 2 : 3 and their volumes?

A.

27 : 32

B.

27 : 23

C.

23 : 32

D.

27 : 23

Correct answer is A

\(\frac{h_1}{h_2}\) = \(\frac{2}{3}\)

h2 = \(\frac{2h_1}{3}\)

\(\frac{r_1}{r_2}\) = \(\frac{9}{8}\)

r2 = \(\frac{9r_1}{8}\)

v1 = \(\pi\)(\(\frac{9r_1}{8}\))2(\(\frac{2h_1}{3}\))

= \(\pi\)r1 2h1 x \(\frac{27}{32}\)

v = \(\frac{\pi r_1 2h_1 \times \frac{27}{32}}{\pi r_1 2h_1}\) = \(\frac{27}{32}\)

v2 : v1 = 27 : 32

1,223.

A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pope is 10cm.Find the volume of metal used in making 3m of the pipe.

A.

153\(\pi\)cm3

B.

207\(\pi\)cm3

C.

15 300\(\pi\)cm3

D.

20 700\(\pi\)cm3

Correct answer is D

Volume of a cylinder = πr\(^2\)h

First convert 3m to cm by multiplying by 100

Volume of External cylinder = π \times 13\(^2\) \times 300

Volume of Internal cylinder = π \times 10\(^2\) \times 300

Hence; Volume of External cylinder - Volume of Internal cylinder

Total volume (v) = π (169 - 100) \times 300

V = π \times 69 \times 300

V = 20700πcm\(^3\)

1,224.

If Cos \(\theta\) = \(\frac{12}{13}\). Find \(\theta\) + cos2\(\theta\)

A.

\(\frac{169}{25}\)

B.

\(\frac{25}{169}\)

C.

\(\frac{169}{144}\)

D.

\(\frac{144}{169}\)

Correct answer is A

Cos \(\theta\) = \(\frac{12}{13}\)

x2 + 122 = 132

x2 = 169- 144 = 25

x = 25

= 5

Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\)

If cos2\(\theta\) = 1 + \(\frac{1}{tan^2\theta}\)

= 1 + \(\frac{1}{\frac{(5)^2}{12}}\)

= 1 + \(\frac{1}{\frac{25}{144}}\)

= 1 + \(\frac{144}{25}\)

= \(\frac{25 + 144}{25}\)

= \(\frac{169}{25}\)

1,225.

Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?

A.

9

B.

8

C.

7

D.

5

Correct answer is A

For a regular polygon of n sides

n = \(\frac{360}{\text{Exterior angle}}\)

Exterior < = 180° - 140°

= 40°

n = \(\frac{360}{40}\)

= 9 sides