p3 Question 2 (a) Explain why weights are used in index number calculations. (2 marks) (b) Farmers in Ntusi Parish are categorised as small, medium and large according to the capital invested and the earnings. A survey was carried out and a sample of five poultry farmers showed the following earnings. Farmer Ntende Bintu Bwomezi Bulamu Kitundu Earnings (Shs) 2,165,000 1,072,000 887,000 776,000 704,000 Required: (i) Compute simple earnings indices for Ntende, Bintu,Bulamu and Kitundu using Bwomezi's earnings as the base earning. (6 marks) (ii) Comment on the index earning of Ntende. (1 mark) (c) The hourly wages of Ajilong and Bolingo engaged in the same kind of work were Shs 48,000 and Shs 37,000 respectively. When a uniform amount was added to each one's wage, Ajilong's wage became 6 of Bolingo's 5 wage. Required: Determine the amount that was added to each one's wage. (d) Lok Oroma Auto Limited rents out vehicles and charges a fixed daily rate plus a fixed amount per kilometre covered. In the first week, the total charge was Shs 830,000 for 1,250 km covered while in the second week; the total charge was Shs 710,000 with 850 km covered.

Required: Calculate the fixed daily rate and the fixed amount per km. (6 marks)

Question 3 (a) (b) (c) Explain the following terms as applied in business: (i) trade margin (2 Marks) (ii) depreciation. (2 Marks) Matafari cooperative society is planning to borrow Shs 50 million to build a new brick factory. The bank charges a compound interest of 18% per annum on all borrowed money. Required: (i) calculate the amount the cooperative should save and pay in a bank every month for 5 years in order to clear the loan. (5 Marks) (ii) determine the interest accrued on this loan. (3 Marks) A smart phone costs Shs 600,000 and has a scrap value of Shs 150,000 with a useful life of 5 years. Required:

(i) determine the depreciation values at the end of each year using sum The chief executive officer (CEO) in an authority in government asked the human resource manager to update him on staffing. The Human Resource Manager presented the following data: of the digits method.

(ii) find the total depreciation value. (6 Marks) (2 marks) (Total 20 marks) Distinguish between primary data and secondary data. The budget allocation to the welfare department of Kizinda Technical Institute is Shs 48 million per annum. The welfare officer appropriates it as indicated in table below:

Question 4 Item Housing Medical Transport Others

Required: Represent the data on a pie chart.

(c) The chief executive officer (CEO) in an authority in government asked the human resource manager to update him on staffing. The Human Resource Manager presented the following data:

Age (years) 10-20 20-30 30-40 40-50 50-60 60-70 Required: Number of employees 03 06 09 11 10 01 (i) Calculate the median age in complete years. (ii) Construct the cumulative frequency curve for the data. (iii) Using the curve in (ii) above estimate the number of employees between the ages of 35 and 55 years. (4 marks (Total 20 marks) Question 5 (a) Distinguish between the following terms as used in mathematics: (i) quartiles and percentiles. (2 marks) (ii) linear and quadratic equations. (2 marks) (b) The following table shows categories of wages (Shs '000') that the corresponding workers in a shoe manufacturing company received in the year ended Wage 110 - 144 145 - 179 180 - 214 215 - 249 250 - 284 285 - 319 320 - 354 Required: 31 December, 2017. Number of workers 03 19 31 25 14 10 03 Calculate the: (i) quartile deviation. (ii) 45th percentile (7 marks) (4 marks) (c) A group of youth agreed to do business together. They decided to hire a small office at a monthly rent of Shs 100,000 per member of the group. If one member of the groups drops out at last minute, each of the remaining members will have to pay Shs 120,000 in order to rent the same office.

Required: Determine the original number of members in the group. (5 marks)

Question 6 (a) (b) Distinguish between dependent and conditional probability (2 marks) Coloured T-shirts are placed in bags of 20 each. There are 5 different colours of T-shirts. The probability of picking a T-shirt of certain colour at random among 5 colours is shown in the table. Colour Orange White Yellow Green Red Probability 0.05 - 0.2 0.25 0.35

Required: (i) Find the probability of picking a white T-shirt. (2 marks) (ii) How many T- shirts of each colour would you expect to find in a bag? The profit function of a juice making company is given by P(x)?1x3 ?7x2 ?10x?2000 where xisinthousandsofshillings. 32 (c) Required: Determine the: i)marginal profit function, dp . dx ii)values of x for which dp ? 0. dx iii)the maximum and minimum values of P(x).

FORMULAE Combination "C, =- n! 1 (n-r)!r! Permutations " p, =- n! 2 (n-r)! 3. Harmonic mean (ungrouped data) hm = 4 . Harmonic mean (grouped data) hm = n M 5 . Mean, x = A+ or Mean, x= MM 6. Geometric mean = (1+p,)(1+P12).....(1+Pm) where p is the proportional increase. N 7 . Median = Lb+ 2 - Cfb C fm 8. Mode = Im +|c d, + d2 ) 9. Variance Var(x) = 10. Sample standard deviation S = VES 11. Sample standard deviation (x -5) S = n-1 12. Pearson coefficient of skewness Sk = (x -mode) 3 x - median or Sa Sk = S 13. Price relatives = P x 100 Po 14. Laspeyre's price index Z(P, X 90) x 100 E(P. xq.)