JAMB Mathematics Past Questions & Answers - Page 278

1,386.

If y = 3t3 + 2t2 - 7t + 3, find \(\frac{dy}{dt}\) at t = -1

A.

-1

B.

1

C.

-2

D.

2

Correct answer is C

y = 3t3 + 2t2 - 7t + 3

\(\frac{dy}{dt}\) = 9t2 + 4t - 7

When t = -1

\(\frac{dy}{dt}\) = 9(-1)2 + 4(-1) - 7

= 9 - 4 -7

= 9 - 11

= -2

1,387.

What is the value of sin(-690)?

A.

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

B.

-\(\frac{\sqrt{3}}{2}\)

C.

\(\frac{-1}{2}\)

D.

\(\frac{1}{2}\)

Correct answer is D

Sin(-690o) = Sin(-360 -3300

sin - 360 = sin 0

∴ sin(-690o) = sin(330o)

Negative angles are measured in clockwise direction

The acute angle equivalent of sin(-330o) = sin(30o)

sin(-330o) = sin(30o)

= \(\frac{1}{2}\)

= 0.5

1,388.

The angle of depression of a boat from the top of a cliff 10m high is 30. How far is the boat from the foot of the cliff?

A.

\(\frac{5√3m}{3}\)

B.

5√3m

C.

10√3m

D.

\(\frac{10√3m}{3}\)

Correct answer is C

RQP = 90o

PQS = 30o but

RQS = 90o = \(\frac{RS}{10}\)

RS = 10 tan 60o

RS = 10 tan 60o

RS = 10√3m

1,389.

If M(4, q) is the mid-point of the line joining L(p, -2) and N(q, p). Find the values of p and q

A.

P = 2, q = 4

B.

p = 3, q = 1

C.

p = 5, q = 3

D.

p = 6, q = 2

Correct answer is D

\(\frac{p + q}{2}\) = 4

p + q = 8 ....(i)

\(\frac{p - 2}{2}\) = q

p - 2q 2 ....(ii)

q = 2, p = 6

3q = 6

1,390.

What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 90o?

A.

the perpendicular bisector of XY

B.

a right-angled triangle

C.

a circle

D.

a semi circle

Correct answer is D

Since XY is a fixed line and

XPY = 90o P is on one side of XY

P1P2P3......Pn are all possible cases where

XPY = 90o the only possible tendency is a semicircle because angles in semicircle equals 90o