2000 - JAMB Mathematics Past Questions and Answers - page 3
21
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 option: c
Users' Answers & Comments22
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 option: 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 two lines are perpendicular,
1/k = -3/4
-3k = 4
k = -4/3
Users' Answers & Commentsy = 4x/3 - 1/3
Grad = 4/3
Grad of Ky = x + 3
y = x/k + 3/4
Grad = 1/k
Since two lines are perpendicular,
1/k = -3/4
-3k = 4
k = -4/3
23
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 option: d
Users' Answers & Comments24
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 option: 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
Users' Answers & CommentsEach exterior angle = 60° but size of ext. angle = 360°/n
Therefore 60° = 360°/n
n = 360°/60° = 6 sides
25
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 option: 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.
Users' Answers & Commentsx2 + 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.
26
Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
A
π
B
π/2
C
-π/2
D
-π
correct option: d
\(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta = \int^{\pi}_{0}\frac{-sin^{2}\theta}{sin^{2}\theta}\ = \int^{\pi}_{0}d\theta = -\pi\)
Users' Answers & Comments27
If y = 2x - sin2x, find dy/dx when x = π/4
A
π
B
-π
C
π/2
D
-π/2
correct option: d
y = 2x cos2x - sin2x
dy/dx = 2 cos2x +(-2x sin2x) - 2 cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x sin2x
= -2 x (π/4) sin2 x (π/4)
= -(π/2) x 1 = -(π/2)
Users' Answers & Commentsdy/dx = 2 cos2x +(-2x sin2x) - 2 cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x sin2x
= -2 x (π/4) sin2 x (π/4)
= -(π/2) x 1 = -(π/2)
28
A bowl is designed by revolving completely the area enclosed by y = x2 - 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?
A
7π cubic units
B
15π/2 cubic units
C
8π cubic units
D
17π/2 cubic units
29
If the volume of a hemisphere is increasing at a steady rate of 18π m/s, at what rate is its radius changing when its is 6m?
A
2.30m/s
B
2.00 m/s
C
0.25 m/s
D
0.20 m/s
correct option: c
Users' Answers & Comments30
X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.
A
0.30
B
0.50
C
0.57
D
1.80
correct option: a
P (X or Y) = P(X) + P(Y), when they are independent as given.
0.7 = 0.4 + P(Y)
P(Y) = 0.7 - 0.4 = 0.30
Users' Answers & Comments0.7 = 0.4 + P(Y)
P(Y) = 0.7 - 0.4 = 0.30