JAMB Mathematics Past Questions & Answers - Page 333

1,661.

If the variance of 3+x, 6, 4, x and 7-x is 4 and the mean is 5, find the standard deviation

A.

\(\sqrt{3}\)

B.

2

C.

3

D.

\(\sqrt{2}\)

Correct answer is B

Let \(\delta^2\) and \(\delta\) denote the variance and standard deviation of the distribution respectively.

But \(\delta^2\) = 4 (given)

Hence \(\delta\) = \(\sqrt{4}\) = 2

1,662.

\(\begin{array}{c|c}Age & 20 & 25 & 30 & 35 & 40 & 45 \\
\hline \text{No. of people} & 3 & 5 & 1 & 1 & 2 & 3 \end{array}\)

Calculate the median age of the frequency distribution in the table above

A.

25

B.

30

C.

35

D.

20

Correct answer is A

N = \(\sum f\) = 15

Hence the median age is the \(\frac{N + 1}{2}\)th age, i.e.

\(\frac{15 + 1}{2}\)th = 8th

From the table, the age that falls on the 8th position when arranged in ascending order is 25years

1,663.

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

A.

6

B.

8

C.

14

D.

2

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

1,664.

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

A.

t + 1

B.

2t

C.

2t + 1

D.

t

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

1,665.

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.

A.

0.75cm2S-1

B.

0.53cm2S-1

C.

0.35cm2S-1

D.

0.88cm2S-1

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