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