JAMB Mathematics Past Questions & Answers - Page 257

1,281.

A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin

A.

\(\frac{(p + q)}{pw + qu}\)

B.

\(\frac{uw(p + q)}{pw + qu}\)

C.

\(\frac{uw(p + q)}{pw}\)

D.

\(\frac{uw}{pw + qu}\)

Correct answer is B

Average speed = \(\frac{total Distance}{Total Time}\)

from Calabar to Enugu in time t1, hence

t1 = \(\frac{P}{U}\) also from Enugu to Benin

t2 \(\frac{q}{w}\)

Av. speed = \(\frac{p + q}{t_1 + t_2}

= p + q * \frac{p}{u} + \frac{q}{w}\)

= p + q x \(\frac{uw}{pw + qu}\)

= \(\frac{uw(p + q)}{pw + qu}\)

1,282.

Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy^1}\) When x = -2 and y = 3

A.

3

B.

-\(\frac{3}{5}\)

C.

\(\frac{3}{5}\)

D.

-3

Correct answer is D

\(\frac{xy^2 - x^2y}{x^2 - xy^1}\)

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

= \(\frac{-30}{10}\)

= -3

1,283.

Multiply (x2 - 3x + 1) by (x - a)

A.

x3 - (3 + a) x2 + (1 + 3a)x - a

B.

x3 - (3 - a)x2 + 3ax - a

C.

x3 - (3 - a)x2 - (1 = 3a) - a

D.

x3 + (3 - a)x2 + (1 + 3a) - a

Correct answer is A

(x2 - 3x + 1)(x - a) = x3 - 3x2 + x - ax2 + 3ax - a

= x3 - (3 + a) x2 + (1 + 3a)x - a

1,284.

Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)

A.

5 - 2\(\sqrt{6}\)

B.

5 + 2\(\sqrt{6}\)

C.

5\(\sqrt{6}\)

D.

5

Correct answer is B

\(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)

= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\)

\(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\)

\(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\)

= \(\frac{30 + 12\sqrt{6}}{6}\)

= 5 + 2\(\sqrt{6}\)

1,285.

Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)

A.

- \(\frac{1}{2}\sqrt{5}\)

B.

\(\frac{1}{2}\sqrt{5}\)

C.

-- \(\frac{1}{4}\sqrt{5}\)

D.

5

Correct answer is B

\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)

= \(\frac{1 - \sqrt{5} - 1 - \sqrt{5}}{(1 + \sqrt{5}) (1 - \sqrt{5}}\)

= \(\frac{-2\sqrt{5}}{1 - 5}\)

= \(\frac{-2\sqrt{5}}{- 4}\)

=  \(\frac{1}{2}\sqrt{5}\)