JAMB Mathematics Past Questions & Answers - Page 37

181.

Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio 

A.

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

B.

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

C.

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

D.

\(\frac{1}{4}\)

Correct answer is A

\(\frac{h}{n - 2} = \frac{n + 3}{n}\)

n\(^2\) = (n + 3) (n - 2) 

n\(^2\) = n\(^2\) + n - 6

n\(^2\) + n - 6 - n\(^2\) = 0

n - 6 = 0

n = 6

Common ratio: \(\frac{n}{n - 2} = \frac{6}{6 - 2} = \frac{6}{4}\) = \(\frac{3}{2}\) 

182.

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart? 

A.

180\(^o\)

B.

36\(^o\)

C.

60\(^o\)

D.

108\(^o\)

Correct answer is B

Total number of acres = 2 + 5 + 3 + 11 + 9 = 30

The angle of acres = 2 + 5 + 3 + 11 + 9 = 30

The angle of the sector for cassava in a pie chart = \(\frac{3}{30} \times 360^o = 36^o\) 

183.

A cylindrical tank has a capacity of 3080m\(^3\). What is the depth of the tank if the diameter of its base is 14m?

A.

25m

B.

23m

C.

22m

D.

20m

Correct answer is D

V = 2080cm\(^3\), h = ? 

r = 7cm

V = V\(\pi r^2h\)

h = \(\frac{V}{\pi r^2} = \frac{3080}{\frac{22}{7} \times 49}\) 

\(\frac{3080}{54}\) = 20cm

185.

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST

A.

\(\frac{\pi r}{3}\)

B.

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

C.

\(\frac{\pi r}{12}\)

D.

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

Correct answer is A

\(\frac{ \frac{r}{2}}{r}\) Sin \(\theta\) = \(\frac{1}{2}\) 

\(\theta\) = sin\(^{-1}\) (\(\frac{1}{2}\)) = 30\(^o\) = 60\(^o\) 

Length of arc (minor)

ST = \(\frac{\theta}{360}\) x 2\(\pi r\) 

\(\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}\)