JAMB Mathematics Past Questions & Answers - Page 417

2,081.

A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?

A.

(1,1) only

B.

(1,1) and (1,2)

C.

(0,0) and (1,1)

D.

(√2,√2) only

Correct answer is A

x2 + y2 = (√2)2
x2 + y2 = 2
but y = x

Thus; x2 + x2 = 2
2x2 = 2
x2 = + or - 1

But x2 + y2 = 2
12 + y2 = 2
1 + y2 = 2
y2 = 2 - 1
y2 = 1
y = + or - 1

Thus point (x,y) = (1,1) only.

2,082.

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.

A.

8

B.

6

C.

4

D.

3

Correct answer is B

2x + x = 180°, => 3x = 180°, and thus x = 60°

Each exterior angle = 60° but size of ext. angle = 360°/n
Therefore 60° = 360°/n
n = 360°/60° = 6 sides

2,083.

if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is

A.

A straight line

B.

a circle

C.

the bisector of angle PXQ

D.

the perpendicular bisector of PQ

Correct answer is D

No explanation has been provided for this answer.

2,084.

3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.

A.

-4/3

B.

-3/4

C.

3/4

D.

4/3

Correct answer is A

Grad of 3y = 4x - 1
y = 4x/3 - 1/3
Grad = 4/3

Grad of Ky = x + 3
y = x/k + 3/4
Grad = 1/k

Since the two lines are perpendicular,
1/k = -3/4
-3k = 4
k = -4/3

2,085.

An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.

A.

2/3 cm

B.

2 cm

C.

1 cm

D.

3 cm

Correct answer is C

Since the inscribed triangle is equilateral, therefore the angles at all the points = 60°

Using the formula for inscribed circle, 

2R = \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)

where R = radius of the circle; a, b and c are the sides of the triangle.

⇒ 2R = \(\frac{\sqrt{3}}{\sin 60}\)

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

2R = 2

R = 1cm