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JAMB Mathematics Past Questions & Answers - Page 288

1,436.

$\frac{d}{dx}$ cos(3x $^2$ - 2x) is equal to

-sin(6x - 2)

-sin(3x² - 2x)dx

(6x - 2) sin(3x² - 2x)

-(6x - 2)sin(3x² - 2x)

View answer & explanation

Correct answer is D

Let $3x^{2} - 2x = u$

$y = \cos u \implies \frac{\mathrm d y}{\mathrm d u} = - \sin u$

$\frac{\mathrm d u}{\mathrm d x} = 6x - 2$

$\therefore \frac{\mathrm d y}{\mathrm d x} = (6x - 2) . - \sin u$

= $- (6x - 2) \sin (3x^{2} - 2x)$

1,437.

Differentiate $\frac{6x^3 - 5x^2 + 1}{3x^2}$ with respect to x

$\frac{2 + 2}{3x^3}$

2 + $\frac{1}{6x}$

2 - $\frac{2}{3x^3}$

$\frac{1}{5}$

View answer & explanation

Correct answer is C

$\frac{6x^3 - 5x^2 + 1}{3x^2}$

let y = 3x²

y = $\frac{6x^3}{3x^2}$ - $\frac{6x^2}{3x^2}$ + $\frac{1}{3x^2}$

Y = 2x - $\frac{5}{3}$ + $\frac{1}{3x^2}$

$\frac{dy}{dx}$ = 2 + $\frac{1}{3}$ (-2)x^-3

= 2 - $\frac{2}{3x^3}$

1,438.

In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ.

√23cm

√13cm

2√5cm

2√3cm

View answer & explanation

Correct answer is B

(XZ)² = 3² + 4² - 2 x 3 x 4 cos60^o

= 25 - 24 $\frac{1}{2}$

XZ = √13cm

1,439.

The angle of elevation of a building from a measuring instrument placed on the ground is 30°. If the building is 40m high, how far is the instrument from the foot of the building?

$\frac{20}{√3}$ m

$\frac{40}{√3}$ m

20√3m

40√3m

View answer & explanation

Correct answer is D

$\frac{40}{x}$ = tan 30°

x = $\frac{40}{tan 30}$

= $\frac{40}{1\sqrt{3}}$

= 40√3m

1,440.

Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2

3√10

3√5

√26

√13

View answer & explanation

Correct answer is D

2x - y .....(i)

x + y.....(ii)

from (i) y = 2x - 4

from (ii) y = -x + 2

2x - 4 = -x + 2

x = 2

y = -x + 2

= -2 + 2

= 0

$x_1$ = 2

$y_1$ = 0

$x_2$ = 4

$y_2$ = 3

Hence, dist. = $\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$

= $\sqrt{(3 - 0)^2 + (4 - 2)^2}$

= $\sqrt{3^2 + 2^2}$

= $\sqrt{13}$