JAMB Mathematics Past Questions & Answers - Page 347

1,731.

No. of Days 1 2 3 4 5 6
No. of students 20 2x 60 40 x 50


The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term?

A.

180

B.

120

C.

110

D.

40

Correct answer is B

20 + 2x + 60 + 40 + x + 50 = 260
170 + 3x = 260
3x = 260 - 170
3x = 90
x = 90/3 = 30
At least 4 days
4 days = 40
5 days = 30
6 days = 50
Total = 120

1,732.

Evaluate ∫sec\(^2\)θ dθ?

A.

sec θ tan θ + k

B.

tan θ + k

C.

2sec θ + k

D.

sec θ + k

Correct answer is B

∫sec2θ dθ = ∫ 1/cos2 dθ
∫(cos)-2 dθ,
let u = cos θ
∴∫u-2 = 1/u + c
∫cos θ = sin θ + c
∫sec-2θ = 1/u sin θ + c
= (sinθ / cosθ) + c
= Tan θ + c

1,733.

The distance traveled by a particle from a fixed point is given as s = (t\(^3\) - t\(^2\) - t + 5)cm. Find the minimum distance that the particle can cover from the fixed point?

A.

2.3 cm

B.

4.0 cm

C.

5.2 cm

D.

6.0 cm

Correct answer is B

S = t\(^3\) - t\(^2\) - t + 5
ds/dt = 3t\(^2\) - 2t - 1
As ds = 0
3t\(^2\) - 2t - 1 = 0
(3t+1)(t-1) = 0
∴ t = 1 or -1/3
At min pt t = 1
S = t\(^3\) - t\(^2\) - t + 5

put t = 1
= 1\(^3\) - \1(^2\) - 1 + 5
= 1 - 1 - 1 + 5

= 4

1,734.

If s = (2 + 3t)(5t - 4), find ds/dt when t = 4/5 secs

A.

0 units per sec

B.

15 units per sec

C.

22 unit per sec

D.

26 units per sec

Correct answer is C

x = (2+3t)(5t-4)
Let u = 2+3t ∴du/dt = 3
and v = 5t-4 ∴dv/dt = 5
dx/dt = Vdu/dt + Udv/dt
= (5t-4)3 + (2+3t)5
= 15t - 12 + 10 + 15t
= 30t - 2
= 30x4/5 - 2
= 24 - 2
= 22

1,735.

A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is 60º, find the width of the river?

A.

100m

B.

75√3 m

C.

100√3m

D.

200√3m

Correct answer is C

Tan 60 = 300
x

 

x = 300
Tan 60

 

 

x = 300
√3


x = (300/√3) x (√3/√3)

 

 

x = 300√3
.....3

 


x = 100√3