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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.

2,296.

Ice forms on a refrigerator ice-box at the rate of (4 - 06t)g per minute after t minutes. If initially there are 2g of ice in the box, find the mass of ice formed in 5 minutes

A.

19.5

B.

17.0

C.

14.5

D.

12.5

Correct answer is C

dmdt = 4 - 0.6t

dm = (4 - 0.6t)dt

m = 4t0.3t2+c, when t = 0, m = 2g

∴ c = 2

m = 4t0.3t2+2, when t = 5 minutes

m = 4(5)0.3(5)2+2=207.5+2

= 14.5

2,297.

If y = x sin x, Find d2yd2x

A.

2 cosx - x sinx

B.

sinx + x cosx

C.

sinx - x cosx

D.

x sinx - 2 cosx

Correct answer is A

y=xsinx

dydx=xcosx+sinx

d2ydx2=x(sinx)+cosx+cosx

= 2cosxxsinx

2,298.

Evaluate lim

A.

7

B.

2

C.

3

D.

4

Correct answer is B

\lim \limits_{x \to 2} \frac{(x - 2)(x^2 + 3x - 2)}{x^2 - 4}

\frac{(x - 2)(x^{2} + 3x - 2)}{x^{2} - 4} = \frac{(x - 2)(x^{2} + 3x - 2)}{(x - 2)(x + 2)}

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

\therefore \lim \limits_{x \to 2} \frac{(x - 2)(x^2 + 3x - 2)}{x^2 - 4} = \lim \limits_{x \to 2} \frac{x^{2} + 3x - 2}{x + 2}

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

= \frac{4 + 6 - 2}{4} = 2

2,299.

Given that \theta is an acute angle and sin \theta = \frac{m}{n}, find cos \theta

A.

\frac{\sqrt{n^2 - m^2}}{m}

B.

\frac{\sqrt{(n + m)(n - m)}}{n}

C.

\frac{m}{\sqrt{n^2 - m^2}}

D.

\sqrt{\frac{n}{n^2 - m^2}}

Correct answer is B

sin \theta = \frac{m}{n} 

Opp = m; Hyp = n

Adj = \sqrt{n^{2} - m^{2}}

\cos \theta = \frac{\sqrt{n^{2} - m^{2}}}{n}

= \frac{\sqrt{(n + m)(n - m)}}{n}

2,300.

Find then equation line through (5, 7) parallel to the line 7x + 5y = 12

A.

5x + 7y = 120

B.

7x + 5y = 70

C.

x + y = 7

D.

15x + 17y = 90

Correct answer is B

Equation (5, 7) parallel to the line 7x + 5y = 12

5Y = -7x + 12

y = \frac{-7x}{5} + \frac{12}{5}

Gradient = \frac{-7}{5}

∴ Required equation = \frac{y - 7}{x - 5} = \frac{-7}{5} i.e. 5y - 35 = -7x + 35

5y + 7x = 70