JAMB Mathematics Past Questions & Answers - Page 286

1,426.

Two variables x and y are such that \(\frac{dy}{dx}\) = 4x - 3 and y = 5 when x = 2. Find y in terms of x

A.

2x2 - 3x + 5

B.

2x2 - 3x + 3

C.

2x2 - 3x

D.

4

Correct answer is B

∫dy = ∫(4x - 3)dx, y = 2x2 - 3x + C

when y = 5, x = 2, C = 3

y = 2x2 - 3x + 3

1,427.

For what value of x is the tangent to the curve y = x\(^2\) - 4x + 3 parallel to the x-axis?

A.

3

B.

2

C.

1

D.

6

Correct answer is B

At the point where the tangent is parallel to the x- axis, the slope of the curve = 0.

Given: \(y = x^{2} - 4x + 3\)

\(\frac{\mathrm d y}{\mathrm d x} = 2x - 4\)

\(2x - 4 = 0 \implies 2x = 4 \)

\(x = 2\)

When x = 2, the tangent of the curve is parallel to the x- axis.

1,428.

The derivative of cosec x is

A.

tan x cosec x

B.

-cot x cosec x

C.

tan x sec x

D.

-cot x sec x

Correct answer is B

\(\csc x = \frac{1}{\sin x}\)

Using the quotient rule,

\(\frac{\mathrm d y}{\mathrm d x} = \frac{vdu - udv}{v^{2}}\)

= \(\frac{\sin x (0) - 1 (\cos x)}{(\sin x)^{2}}\)

= \(\frac{- \cos x}{\sin^{2} x}\)

= \((\frac{- \cos x}{\sin x}) (\frac{1}{\sin x})\)

= \(- \cot x \csc x\)

1,430.

P is on the locus of points equidiatant from two given points X and Y. UV is a straight line throuh Y parallel to the locus. If < PYU is 40°, find < XPY.

A.

100o

B.

80 o

C.

50 o

D.

40 o

Correct answer is B

< PYU = < YPQ = 40°(Alternative) = PQ\(\parallel\)UV

< XPQ = < YPQ = 40°, Since QX = QY

therefore < XPY = 80°