Further Mathematics Past Questions and Answers

(a) If \(^{18}C_{r} = ^{18}C_{r + 2}\), find \(^{r}C_{5}\).
(b) In a community, 10% of the people tested positive to the HIV virus. If 6 persons from the community are selected at random, one after the other with replacement, calculate, correct to four decimal places, the probability that : (i) exactly 5 (ii) none (iii) at most 2; tested positive to the virus.

The table below shows the distribution of ages of workers in a company.

Age/ yr	17 - 21	22 - 26	27 - 31	32 - 36	37 - 41	42 - 46	47 - 51	52 - 56
Workers	12	24	30	37	45	25	10	7

(a) Using an assumed mean of 39, calculate the (i) mean (ii) standard deviation; of the distribution.
(b) If a worker is selected at random from the company for an award, what is the probability that he is at most 36 years old?

The table shows the marks obtained by some candidates in Physics (y) and Mathematics (x) tests.

Mathematics	43	46	48	39	30	60	8	45	40
Physics	54	53	63	30	44	75	20	33	49

(a)(i) Represent this information on a scatter diagram.
(ii) Find \(\bar{x}\) and \(\bar{y}\), the mean of x and y respectively.
(iii) Draw the line of best fit to pass through (x, y).
(b) Find the equation of the line in a(iii).
(c) Use your equation in (b) to find, correct to one decimal place, the mark in Physics for a candidate who scored 28 in Mathematics.

Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)

Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)