2013 - JAMB Mathematics Past Questions and Answers - page 3

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

y = (2x +2)³

Then \(\frac{\delta y}{\delta x}\) = 3(2x +2)²2

=6(2x +2)²

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

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

N = 4_

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

= 2t

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

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

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

Range = Highest score - Lowest score

= 10 - 3

= 7

A student can select 2 subjects from 5 subjects in;

⁵C₃ ways, i.e. = \(\frac{5!}{2!(5 - 2)!}\)

= \(\frac{5!}{2!3!}\)

5 people can take 3 places in;

⁵P₃ ways, = \(\frac{5!}{(5 - 3)!}\) = \(\frac{5!}{2!}\)

= \(\frac{5 \times 4 \times 3 \times 2!}{2!}\)

= 5 x 4 x 3

= 60 ways