JAMB Mathematics Past Questions & Answers - Page 296

1,476.

\(\begin{array}{c|c} \text{Average hourly earnings(N)} & 5 - 9 & 10 - 14 & 15 - 19 & 20 - 24\\ \hline \text{No. of workers} & 17 & 32 & 25 & 24\end{array}\)

Estimate the mode of the above frequency distribution

A.

12.2

B.

12.27

C.

12.9

D.

13.4

Correct answer is B

\(\begin{array}{c|c} \text{Class intervals} & F & \text{Class boundary}\\ \hline 5 - 7 & 17 & 4.5 - 9.5\\ 10 - 14 & 32 & 9.5 - 14.5\\ 15 - 19 & 25 & 14.5 - 19.5\\ 20 - 24 & 24 & 19.5 - 24.5 \end{array}\)

mode = 9.5 + \(\frac{D_1}{D_2 + D_1}\) x C

= 9.5 + \(\frac{5(32 - 17)}{2(32) - 17 - 25}\)

= 9.5 + \(\frac{75}{27}\)

= 12.27

\(\approx\) 12.3

1,477.

If m and n are the mean and median respectively of the set of numbers 2, 3, 9, 7, 6, 7, 8, 5, find m + 2n to the nearest whole number

A.

19

B.

18

C.

13

D.

12

Correct answer is A

mean(x) = \(\frac{\sum x}{N}\)

= \(\frac{48}{8}\)

= 5.875

re-arranging the numbers;

2, 3, 5, 6, 2, 7, 8, 9

median = \(\frac{6 + 7}{2}\)

= \(\frac{1}{2}\)

= 6.5

m + 2n = 5.875 + (6.5)2

= 13 + 5.875

= 18.875

= \(\approx\) = 19

1,478.

find the equation of the curve which passes through by 6x - 5

A.

6x2 - 5x + 5

B.

6x2 + 5x + 5

C.

3x2 - 5x - 5

D.

3x2 - 5x + 3

Correct answer is D

m = \(\frac{dy}{dv}\) = 6x - 5

∫dy = ∫(6x - 5)dx

y = 3x2 - 5x + C

when x = 2, y = 5

∴ 5 = 3(2)2 - 5(2) +C

C = 3

∴ y = 3x2 - 5x + 3

1,479.

Evaluate ∫\(^{\pi}_{2}\)(sec2 x - tan2x)dx

A.

\(\frac{\pi}{2}\)

B.

\(\pi\) - 2

C.

\(\frac{\pi}{3}\)

D.

\(\pi\) + 2

Correct answer is B

∫\(^{\pi}_{2}\)(sec2 x - tan2x)dx

∫\(^{\pi}_{2}\) dx = [X]\(^{\pi}_{2}\)

= \(\pi\) - 2 + c

when c is an arbitrary constant of integration

1,480.

Differentiate \(\frac{x}{cosx}\) with respect to x

A.

1 + x sec x tan x

B.

1 + sec2 x

C.

cos x + x tan x

D.

x sec x tan x + secx

Correct answer is D

let y = \(\frac{x}{cosx}\) = x sec x

y = u(x) v (x0

\(\frac{dy}{dx}\) = U\(\frac{dy}{dx}\) + V\(\frac{du}{dx}\)

dy x [secx tanx] + secx

x = x secx tanx + secx