JAMB Mathematics Past Questions & Answers - Page 294

1,466.

The angle of elevation of a building from a measuring instrument placed on the ground is 30°. If the building is 40m high, how far is the instrument from the foot of the building?

A.

\(\frac{20}{√3}\)m

B.

\(\frac{40}{√3}\)m

C.

20√3m

D.

40√3m

Correct answer is D

\(\frac{40}{x}\) = tan 30°

x = \(\frac{40}{tan 30}\)

= \(\frac{40}{1\sqrt{3}}\)

= 40√3m

1,467.

Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2

A.

3√10

B.

3√5

C.

√26

D.

√13

Correct answer is D

2x - y .....(i)

x + y.....(ii)

from (i) y = 2x - 4

from (ii) y = -x + 2

2x - 4 = -x + 2

x = 2

y = -x + 2

= -2 + 2

= 0

\(x_1\) = 2

\(y_1\) = 0

\(x_2\) = 4

\(y_2\) = 3

Hence, dist. = \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\)

= \(\sqrt{(3 - 0)^2 + (4 - 2)^2}\)

= \(\sqrt{3^2 + 2^2}\)

= \(\sqrt{13}\)

1,468.

A point P moves so that its equidistant from point L and M. If LM is16cm, find the distance of P from LM when P is 10cm from L

A.

12cm

B.

10cm

C.

8cm

D.

6cm

Correct answer is D

p from LM = \(\sqrt{10^2 - 8^2}\) 

= \(\sqrt{36}\) = 6cm

1,469.

The angle between the positive horizontal axis and a given line is 135°. Find the equation of the line if it passes through the point (2,3)

A.

x - y = 1

B.

x + y = 1

C.

x + y = 5

D.

x - y = 5

Correct answer is C

m = tan 135° = -tan 45° = -1

\(\frac{y - y_1}{x - x_1}\) = m

\(\frac{y - 3}{x - 2}\) = -1

= y - 3 = -(x - 2)

= -x + 2

x + y = 5

1,470.

A cone with the sector angle of 45° is cut out of a circle of radius r of the cone.

A.

\(\frac{r}{16}\) cm

B.

\(\frac{r}{6}\) cm

C.

\(\frac{r}{8}\) cm

D.

\(\frac{r}{2}\) cm

Correct answer is C

The formula for the base radius of a cone formed from the sector of a circle = \(\frac{r \theta}{360°}\)

= \(\frac{r \times 45°}{360°}\)

= \(\frac{r}{8} cm\)