JAMB Mathematics Past Questions & Answers - Page 386

1,926.

Three teachers shared a packet of chalk. The first teacher got 2/5 of the chalk and the second teacher received 2/15 of the remainder. What fraction the the third teacher receive?

A.

8/15

B.

11/25

C.

12/25

D.

13/25

Correct answer is D

First teacher received \(\frac{2}{5}\) ∴Remainder \(= 1 - \frac{2}{5} = \frac{3}{5}\)
2nd teacher received; \(\frac{2}{15} of \frac{3}{5} = \frac{2}{15} \times \frac{3}{5} = \frac{2}{25}\)
3rd teacher will receive; \(1-\frac{2}{5}-\frac{2}{25}=\frac{25-10-2}{15}\\=\frac{13}{25}\)

1,927.

The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum whose period is 9 sec

A.

96 cm

B.

324 cm

C.

36 cm

D.

144 cm

Correct answer is B

\(L \propto T^2\)

\(L = kT^2\)

\(k = \frac{L}{T^2}\)

when T = 4, L = 64.

\(k = \frac{64}{4^2} = 4\)

\(L = 4T^2\)

when T = 9,

\(L = 4 \times 9^2 = 324cm\)

1,928.

Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....

A.

2/3

B.

1/3

C.

3/4

D.

1

Correct answer is C

\(a=\frac{1}{2}\\r=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{6}\times\frac{2}{1}=\frac{1}{3}\\S_\infty = \frac{a}{1-r}\\S_\infty = \frac{\frac{1}{2}}{1-\frac{1}{3}}\\=\frac{\frac{1}{2}}{\frac{3}{2}}\\=\frac{1}{2}\times\frac{3}{2}\\=\frac{3}{4}\)

1,929.

Factorize completely ac - 2bc - a + 4b2

A.

(a - 2b)(c - a - 2b)

B.

(a - 2b)(c + a +2b)

C.

(a - 2b)(c - a + 2b)

D.

(a - 2b)(c + a - 2b)

Correct answer is A

ac - 2bc - a2 + 4b2
ac - 2bc - (a2 - 4b2)
ac - 2bc - (a2 -(2b)2)
c(a - 2b) - {(a - 2b)(a + 2b)}
(a - 2b)(c - (a + 2b))
(a - 2b)(c - a - 2b)

1,930.

The nth term of two sequences are Qn = 3 . 2n - 2 and Um = 3 . 22m - 3. Find the product of Q2 and U2.

A.

18

B.

12

C.

6

D.

3

Correct answer is A

Qn = 3 * 2n - 2
Um = 3 * 22m - 3
Q2 * U2 = (3 * 22 - 2) * (3 * 22(2) - 3)
= 3 * 20 * 3 * 21
= 3 * 1 * 3 * 2
= 18