JAMB Mathematics Past Questions & Answers

1,256.

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

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

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

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

$\frac{uw}{pw + qu}$

View answer & explanation

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 $\frac{uw}{pw + qu}$

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

1,257.

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

- $\frac{3}{5}$

$\frac{3}{5}$

-3

View answer & explanation

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

1,258.

Multiply (x² - 3x + 1) by (x - a)

x³ - (3 + a) x² + (1 + 3a)x - a

x³ - (3 - a)x² + 3ax - a

x³ - (3 - a)x² - (1 = 3a) - a

x³ + (3 - a)x² + (1 + 3a) - a

View answer & explanation

Correct answer is A

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

= x³ - (3 + a) x² + (1 + 3a)x - a

1,259.

Rationalize $\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}$

5 - 2 $\sqrt{6}$

5 + 2 $\sqrt{6}$

5 $\sqrt{6}$

View answer & explanation

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 $\sqrt{6}$

1,260.

Simplify $\frac{1}{1 + \sqrt{5}}$ - $\frac{1}{1 - \sqrt{5}}$

- $\frac{1}{2}\sqrt{5}$

$\frac{1}{2}\sqrt{5}$

-- $\frac{1}{4}\sqrt{5}$

View answer & explanation

Correct answer is B

$\frac{1}{1 + \sqrt{5}}$ - $\frac{1}{1 - \sqrt{5}}$

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

= $\frac{-2\sqrt{5}}{1 - 5}$

= $\frac{-2\sqrt{5}}{- 4}$

= $\frac{1}{2}\sqrt{5}$