JAMB Mathematics Past Questions & Answers

136.

Factorize m $^3$ - m $^2$ + 2m - 2

(m² + 1)(m - 2)

(m - 1)(m + 1)(m + 2)

(m - 2)(m + 1)(m - 1)

(m² + 2)(m - 1)

View answer & explanation

Correct answer is D

Using trial expansion of each option

(m $^2$ + 2) (m - 1)

137.

If g(x) = x $^2$ + 3x find g(x + 1) - g(x)

(x + 2)

2(x + 2)

(2x + 1)

(x² + 4)

View answer & explanation

Correct answer is B

g(x) = x2 + 3x

When g(x + 1) = (x + 1)^2 + 3(x + 1)

= x $^2$ + 1 + 2x + 3x + 3

= x $^2$ + 5x + 4

g(x + 1) - g(x) = x2 + 5x + 8 - (x $^2$ + 3x)

= x $^2$ + 5x + 4 - x2 -3x

= 2x + 4 or 2(x + 4)

= 2(x + 2)

138.

If w varies inversely as $\frac{uv}{u + v}$ and w = 8 when

u = 2 and v = 6, find a relationship between u, v, w.

uvw = 16(u + v)

16uv = 3w(u + v)

uvw = 12(u + v)

12uvw = u + v

View answer & explanation

Correct answer is C

W $\alpha$ $\frac{\frac{1}{uv}}{u + v}$

∴ w = $\frac{\frac{k}{uv}}{u + v}$

= $\frac{k(u + v)}{uv}$

w = $\frac{k(u + v)}{uv}$

w = 8, u = 2 and v = 6

8 = $\frac{k(2 + 6)}{2(6)}$

= $\frac{k(8)}{12}$

k = 12

i.e 12 ( u + v) = uwv

139.

Find the probability that a number selected at random from 41 to 56 is a multiple of 9

$\frac{1}{8}$

$\frac{2}{15}$

$\frac{3}{16}$

$\frac{7}{8}$

View answer & explanation

Correct answer is A

Given from 41 to 56

41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56

The nos multiple of 9 are: 45, 54

P(multiple of 9) = $\frac{2}{16}$

= $\frac{1}{8}$

140.

Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

View answer & explanation

Correct answer is B

$\begin{array}{c|c} 1 & 2 & 3 & 4\\\hline 1(1, 1) & (1, 2) & (1, 3) & (1, 4)\\ \hline 2(2, 1) & (2 , 2) & (2, 3) & (2, 4) \\ \hline 3(3, 1) & (3, 2) & (3, 3) & (3, 4)\\ \hline 4(4, 1) & (4, 2) & (4, 3) & (4, 4)\end{array}$

sample space = 16

sum of nos. removed are (2), 3, (4), 5

3, (4), 5, (6)

(4), 5, (6), 7

(5), 6, 7, (8)

Even nos. = 8 of them

Pr(even sum) = $\frac{8}{16}$

= $\frac{1}{2}$