Question 2 (a) John, a renowned plumber, wishes to purchase 20 metal pipes at Shs 35,000 per pipe. He wants to take advantage of a trade discount of 15%. Required: Determine the amount of money the plumber will pay for the pipes. (4 marks) (b) A supplier has electrical appliances worth Shs 3,000,000 in the store. He informed his customers that the following cash discounts are available for early payment purchases in April as follows: Within 7 days 10.0 % Within 14 days 7.5 % Within 28 days 2.5 %. Required: How much will a customer pay for the appliances if payment is made on the; (i) 5th day (ii) 21st day. (iii) 30th day. (c) A saving club wishes to have Shs 40,000,000 in five years' time. Required: (2 marks) (2 marks) (2 marks) How much should be invested now at 12% per annum simple interest to achieve the target? (4 marks) (d) Kato's loan of Shs 4 million with an interest rate of 5% compounded every 6 months is amortised by equal semi-annual payments over the next 2 years. Required: Determine the value of each payment

Question 3 (a) (b) State any two limitations of index numbers. (2 marks) The table shows prices and quantities for four commodities in two periods. 2017 Quantity 2018 Quantity Business Mathematics & Statistics-Paper 3 Commodity Price Shs A 1,000 B 1,800 C 3,000 D 4,500 kg 100 50 20 10 Price Shs 1,200 2,000 3,500 4,500 kg 120 60 25 12 as the base year. (c) POKOT limited manufactures iron sheets in two gauge types A and B . The total revenue from 15 pieces of type 10 pieces of type B was Shs 600,000 while the total revenue from 5 pieces of type 8 pieces of type B was Shs 340,000.

Required: Form a simultaneous equation for the data and solve the equations to determine the selling price of each type. (6 marks) Njovu sugar factory has a total cost function given by C ? 20 ? 4x and revenuefunction,R?24x?4x2 where xisthelevelofoutputintons, C and R are both in million shillings.

Required: Calculate the level of output that maximises profit and hence obtain the maximum profit.

Question 4 (a) (i) Distinguish between a permutation and a combination. (ii) A village council of 5 members is to be chosen from 6 men and 3 women. Required: In how many ways can the council be chosen so as to include 3 men and 2 women? (b) (i) Distinguish between a universal set and a subset. (ii) Lwengo College has 30 students. 18 of these paid tuition, 15 registered for the ATD exams. If only 5 students who paid tuition registered for the ATD exams. Required: Determine the number of students who neither paid tuition nor register for ATD exams. (4 marks) (c) Three ladies, Eva, Jane and Mary went shopping in a supermarket. Eva picked four bars of soap, two boxes of mineral water and five packs of chicken. Jane picked five bars of soap, four boxes of mineral water, and three packs of chicken. Mary picked three bars of soap, two boxes of mineral water, and three packs of chicken. A bar of soap costs Shs 4, 000 box of mineral water Shs 12, 000 and a pack of chicken Shs 15, 000. Required:

(i) Form 3 x 3 quantity matrix and 3 x 1 cost matrix. (4 marks)

ii)Using matrix multiplication, find the total amount spent by the three ladies at the supermarket.

FORMULAE Combination "C, = n! (n-r)!r! Permutations " p, = n! 2 (n-r)! 3. Harmonic mean (ungrouped data) hm = n 4. Harmonic mean (grouped data) hm = n 5 . Mean, x = A+2fd Ef or Mean, x = Geometric mean = V(1+p,)(1+P12)....(1+P,) 6. Where p is the proportional increase. N - Cfb 7. Median = Lb+ 2 C fm 8. Mode = Im + d, + d 2 C 9. Variance Var(x) = Efx' 6 = VEf 10. Sample standard deviation or E( x -x)? S = n-1 11. Standard deviation S = E fd2 (E fd VES Ef 12. Pearson coefficient of skewness Sk = (x -mode) 3 x- median or Sd Sk = Sa 13. Price relatives = P x 100 PoQuestion 5 (a) (i) Distinguish between primary data and secondary data. (2 marks) (ii) Describe any two features of a good questionnaire. (2 marks) (b) Three aero planes flying from Nairobi to Entebbe recorded the following averae seeds (in kmlhr) on their journeys. Required: Using the harmonic mean method. determine the average speed of the three planes from Nairobi to Entebbe airports. (3 marks) (c) A security guard at a busy international airport recorded the planes arriving every day and the number of passengers each delivered. The table below shows the sample data he captured in a day: No. of No. of passengers planes 100 - 114 2 115 - 119 5 120 - 124 12 125 - 129 20 130 - 134 8 135 - 139 8 140 - 144 5 Required: Using the assumed (working mean) of 127 determine the; (i) mean number of passengers. (4 marks) (ii) standard deviation of the number of passengers. (4 marks) (iii) plot a histogram and use it to estimate the modal number of passengers that landed at the airport. (5 marks) (Total 20 marks) Question 6 (a) (i) Distinguish between discrete and continuous random variable. (2 marks) (ii) The table below shows statistics of the number of radio adverts in each of the four adult programs over a period of one week. No. of Adverts x 6 _ 7 8 _10 _ _Likelihood P(X =x) 0.45 0.30 _ 0.2 _0.05 _ Required: Compute the expected number of adverts for the data above. (4 marks) (b) Mr. Richard invested his Shs 30 million savings in a iuice factory and hardware stores. Market statistics showed that profits earned from the Juice factory and hardware stores are 5% and 8% of the amount invested respectively. The total profit earned on this investment was Shs 2.100.000. Required: (i) Calculate how much money was invested in each sector i.e. the juice factory and hardware stores. (9 marks) (ii) Determine the new total investment if he increases the investmenf in iuice by 7% and hardware by 6%. (5 marks) (Total 20 marks)