JAMB Mathematics Past Questions & Answers - Page 225

1,121.

If a u2 - 3v2 and b = 2uv + v2 evaluate (2a - b)(a - b2), when u = 1 and v = -1

A.

9

B.

15

C.

27

D.

33

Correct answer is A

a = u2 - 3y2 = (1)2 - 3(-1) = -2

b = 2uu + v2 + v2

= 2(1)(-1) + (-1)2 = -1

∴ 2(2a - b)(a - b∴) = [2(-2) - 1](-2 - (-1)2)

= -3 - 3

= 9

1,122.

If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1

A.

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

B.

\(\frac{1}{3}\)

C.

3

D.

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

Correct answer is D

If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1

p = \(\frac{2(1 - r^2)}{3n^2}\) when r = \(\frac{1}{3}\) and p = 1

1 = \(\frac{2}{3}\) \(\frac{(1 - (\frac{1}{3})^2)}{n^2}\)

n2 = \(\frac{2(3 - 1)}{3 \times 3}\)

n2 = \(\frac{2 \times 2}{3 \times 3}\)

= \(\frac{4}{9}\)

n = \(\frac{4}{9}\)

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

1,123.

Simplify without using tables \(\frac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}\)

A.

\frac{3\sqrt{14}}{4}\)

B.

\(\frac{3\sqrt{2}}{4}\)

C.

\(\frac{3\sqrt{14}}{28}\)

D.

\(\frac{3\sqrt{2}}{28}\)

Correct answer is D

\(\frac{2\sqrt{14} \times 3\sqrt{21}}{7 \sqrt{24} \times 2\sqrt{98}}\) = \(\frac{6\sqrt{14} \times 3 \times \sqrt{7} \times \sqrt{3}}{7 \times 2 \sqrt{6} \times \sqrt{7} \times \sqrt{14}}\)

= \(\frac{3\sqrt{3}}{14\sqrt{6}}\)

= \(\frac{3\sqrt{3}}{14\sqrt{2} \times \sqrt{3}}\)



= \(\frac{3\sqrt{2}}{28}\)

1,124.

Simplify without using tables \(\frac{log_26}{log_28}\) - \(\frac{log_23}{2log_2\frac{1}{2}}\)

A.

\(\frac{1}{5}\)

B.

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

C.

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

D.

(\frac{log_23}{log_27}\)

Correct answer is A

log\(_2\)6 - log\(_2\)3 = log\(_2\) (\(\frac{6}{3}\))

= log\(_2\)2... A

log\(_2\)8 - 2log\(_2\)\(\frac{1}{2}\)

log\(_2\)8 - log\(_2\)\(\frac{1}{2}\)\(^2\)

log\(_2\)8 - log\(_2\)\(\frac{1}{4}\)

= log\(_2\) 32... B

\(\frac{A}{B}\) = \(\frac{log_22}{log_232}\)

N.B. log\(_2\)2 = 1

= \(\frac{1}{5}\)
 

1,125.

Evaluate without using tables (0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\)

A.

\(\frac{625}{8}\)

B.

\(\frac{8}{625}\)

C.

\(\frac{1}{8}\)

D.

8

Correct answer is A

(0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\) = (8 x 10-3)10-3 x (16 x 10-2)-\(\frac{3}{2}\)

= \(\frac{(2^3)}{10^3}\) - 3 x \(\frac{(2^4)}{10}\) - \(\frac{-3}{2}\)

= \(\frac{625}{8}\)