Mathematics questions and answers

Mathematics Questions and Answers

How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.

3,751.

If dy/dx = x + cos x, find y

A.

x2 - sin x + c

B.

x2 + sin x + c

C.

x2/2 - sin x + c

D.

x2/2 + sin x + c

Correct answer is D

dy/dx = x + cos x
y = ∫(x + cos x)dx
y = 1/2x2 + sin x + C

3,752.

Find the value of x for which the function 3x\(^3\) - 9x\(^2\) is minimum

A.

zero

B.

2

C.

3

D.

5

Correct answer is B

y = 3x\(^3\) - 9x\(^2\)
dy/dx = 9x\(^2\) - 18x
As dy/dx = 0
9x\(^2\) - 18x = 0
9x(x-2) = 0
9x = 0 which implies x = 0
x-2 = 0 implies x = 2
d2y/dx2 = 18x - 18
when x = 0
d2y/dx2 < 0 ∴ x is is minimum
when x = 2d\(^2\)y/dx\(^2\) = 18
∴ the value > 0 x is minimum

3,753.

Differentiate (x2 - 1/x)2 with respect to x

A.

4x2 - 4x - 2/x

B.

4x2 - 2 + 2/x3

C.

4x2 - 2 - 2/x3

D.

4x2 - 3x + 2/x

Correct answer is C

y = (x2 - 1/x)2
y = (x2 - 1/x)(x2 - 1/x)
y = x4 - x - x + 1/x2
y = x4 - 2x + 1/x2
y= x4 - 2x + x-2
dy/dx = 4x2 - 2 - 2x-3
= 4x2 - 2 - 2/x3

3,754.

The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.

A.

y = x2 + 7x + 9

B.

y = x2 + 7x - 18

C.

y = x2 + 7x + 18

D.

y = x2 + 14x + 11

Correct answer is B

dy/dx = 2x + 7
y = ∫2x + 7
y = x2 + 7x + C at (2,0)
0 = 22 + 7(2) + C
0 = 4 + 14 + C
0 = 18 + C
C = -18
∴ The equation is y = x2 + 7x - 18

3,755.

For what of n is n+1C3 = 4(nC3)?

A.

6

B.

5

C.

4

D.

3

Correct answer is D

\(^{n+1}C_3 = 4(^nC_3)\\\frac{(n+1)!}{(n+1-3)!3!} = 4\left(\frac{n!}{(n-3)!3!}\right)\\\frac{(n+1)n!}{(n-2)(n-3)!}=4\left(\frac{n!}{n-3!}\right)\\=\frac{n+1}{n-2}=\frac{4}{1}\\n+1 = 4(n-2)\\n+1 = 4n-8\\-3n = -9\\\frac{-9}{-3}\\n=3\)