Processing math: 100%

JAMB Mathematics Past Questions & Answers - Page 328

1,636.

The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.

Correct answer is B

Using x = $\frac{\sum x}{N}$ in each case, we get;

$\sum_{6}^{i=1} x_i$ = 10 x 7 = 70

$\sum_{7}^{i=1} x_i$ = 2 + 4 + 8 + 14 + 16 + 18 = 62

Hence the missing number can be obtained from

$\sum_{6}^{i=1} x_i - \sum_{7}^{i=1} x_i$ = 70 - 62 = 8

So, all the seven numbers are 2, 4, 8, 8, 14, 16, 18

Mode = 8

1,637.

Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.

t + 1

2t + 1

View answer & explanation

Correct answer is B

$\sum x$ = (t + 2) + (2t + 4) + (3t + 2) + 2t = 8t

N = 4_

∴ Mean, x = $\frac{\sum x}{N} = \frac{8t}{4} = 2t$

= 2t

1,638.

The radius of a circle is increasing at the rate of 0.02cms^-1. Find the rate at which the area is increasing when the radius of the circle is 7cm.

0.75cm²S^-1

0.53cm²S^-1

0.35cm²S^-1

0.88cm²S^-1

View answer & explanation

Correct answer is D

A = $\pi$ r², $\frac{\delta A}{\delta r}$ = 2πr

So, using $\frac{\delta A}{\delta t}$ = $\frac {\delta A}{\delta r}$ x $\frac {\delta A}{\delta t}$

= 2 $\pi$ r x 0.02

= 2 $\pi$ x 7 x 0.02

= 2 x $\frac{22}{7}$ x 0.02

= 0.88cm²s^-1

1,639.

If y = (2x + 2) $^3$ , find $\frac{\delta y}{\delta x}$

3(2x +2)²

6(2x +2)

3(2x +2)

6(2x +2)²

View answer & explanation

Correct answer is D

$y = (2x + 2)^{3}$

$\frac{\mathrm d y}{\mathrm d x} = 3(2x + 2)^{3 - 1} . 2$

= $6(2x + 2)^{2}$

1,640.

If y = x sin x, find $\frac{\delta y}{\delta x}$

sin x - cos x

cos x - x sin x

cos x + x sin x

sin x + x cos x

View answer & explanation

Correct answer is D

y = x sin x

Where u = x and v = sin x

Then $\frac{\delta u}{\delta x}$ = 1 and $\frac{\delta v}{\delta x}$ = cos x

By the chain rule, $\frac{\delta y}{\delta x} = v\frac{\delta u}{\delta x} + u\frac{\delta v}{\delta x}$

= (sin x)1 + x cos x

= sin x + x cos x