JAMB Mathematics Past Questions & Answers - Page 62

306.

If the midpoint of the line PQ is (2,3) and the point P is (-2, 1), find the coordinate of the point Q.

A.

(8,6)

B.

(5,6)

C.

(0,4)

D.

(6,5)

Correct answer is D

Midpoint of a line PQ where P has coordinates (x\(_{1}\), y\(_{1}\)) and Q has coordinates (x\(_{2}\), y\(_{2}\)) is given as 

\((\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})\).

\(\therefore\) If Q has coordinates (r, s), then

\(\frac{-2 + r}{2} = 2\) and \(\frac{1 + s}{2} = 3\)

\(-2 + r = 4 \implies r = 6\)

\(1 + s = 6 \implies s = 5\)

Q = (6, 5)

307.

The locus of the points which is equidistant from the line PQ forms a

A.

perpendicular line to PQ

B.

circle centre P

C.

circle centre Q

D.

pair of parallel lines to PQ

Correct answer is A

No explanation has been provided for this answer.

308.

A chord of a circle subtends an angle of 120° at the centre of a circle of diameter \(4\sqrt{3} cm\). Calculate the area of the major sector.

A.

32\(\pi\) cm\(^2\)

B.

4\(\pi\) cm\(^2\)

C.

8\(\pi\) cm\(^2\)

D.

16\(\pi\) cm\(^2\)

Correct answer is C

Angle of major sector = 360° - 120° = 240°

Area of major sector : \(\frac{\theta}{360} \times \pi r^{2}\)

r = \(\frac{4\sqrt{3}}{2} = 2\sqrt{3} cm\)

Area : \(\frac{240}{360} \times \pi \times (2\sqrt{3})^{2}\)

= \(8\pi cm^{2}\)

309.

Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8 cm.

A.

\(8\sqrt{3}\) cm

B.

4 cm

C.

8 cm

D.

\(8\sqrt{2}\) cm

Correct answer is D

Length of chord = \(2r \sin (\frac{\theta}{2})\)

= \(2 \times 8 \times \sin (\frac{90}{2})\)

= \(16 \times \frac{\sqrt{2}}{2}\)

= \(8\sqrt{2} cm\)

310.

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

A.

720

B.

336

C.

420

D.

576

Correct answer is B

Length of the tile = 30 cm = 0.3m

Area of the tile = 0.3 \(\times\) 0,3 = 0.09 m\(^2\)

Area of the room = (7.2 \(\times\) 4.2)m\(^2\)

Number of tiles = \(\frac{7.2 \times 4.2}{0.09}\)

= 336