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JAMB Mathematics Past Questions & Answers - Page 273

1,361.

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?

$\frac{5√3m}{3}$

5√3m

10√3m

$\frac{10√3m}{3}$

View answer & explanation

Correct answer is C

RQP = 90^o

PQS = 30^o but

RQS = 90^o = $\frac{RS}{10}$

RS = 10 tan 60^o

RS = 10 tan 60^o

RS = 10√3m

1,362.

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

P = 2, q = 4

p = 3, q = 1

p = 5, q = 3

p = 6, q = 2

View answer & explanation

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

1,363.

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 90^o?

the perpendicular bisector of XY

a right-angled triangle

a circle

a semi circle

View answer & explanation

Correct answer is D

Since XY is a fixed line and

XPY = 90^o P is on one side of XY

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

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

1,364.

Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45^o

2 $\pi$

8 + 2 $\pi$

16 + 2 $\pi$

16 + 16 $\pi$

View answer & explanation

Correct answer is C

Perimeter = OP + OQ + PQ

= 8 + 8 + PQ

length PQ = $\frac{\theta}{360 \times 2\pi r}$

= $\frac{45}{360}$ x 2 x $\pi$ x 8

= 2 $\pi$

Perimeter of sector 2r + L

Where l = length of arc and r = radius

∴ P = 2(8) + 2 $\pi$

= 16 + 2 $\pi$

1,365.

An open rectangular box is made of wood 2cm thick. If the internal dimensions of the box are 50cm long, 36cm wide and 20cm deep, the box volume of wood in the box is

11 520cm³

36 000cm³

38 200cm³

47 520cm³

View answer & explanation

Correct answer is A

Internal dimension are 50cm, 36cm and 20cm

internal volume = 50 x 36 x 20cm³

1000 x 36cm³

= 36000cm³

External dimension are 54cm x 40cm x 22cm

= 2160cm² x 22cm = 47520cm³

Volume of wood = Ext. volume - Int. volume

= 47,520cm³ - 36,000cm³

= 11,520cm³