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Hps2205:Quantitative Methods Question Paper
Hps2205:Quantitative Methods
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2014
QUESTION ONE (30 MARKS)
a) Highlight the significance of mathematics in business decision making. (4 Marks) b) Solve the following equations i. 8?? - 6 = 5?? + 9 (2 Marks) ii. 2??2 - 7?? - 9 = 0 (2 Marks) iii. 3?? - 2?? = 0 ?? - 2?? = -4 (4 Marks) c) Given that ?? = {1,2,3} ?? = {2 3 4 5} ?? = {5,7} ?????? ?? = {??:1 = ?? = 12,?? ? ??} Evaluate the following operations and present them in a Venn diagram. i. ?? ? ?? ? ?? ii. ?? n ?? n ?? iii. (?? ? ??)' (8 Marks) d) Briefly explain the following terms as used in statistics; i. Population ii. Sample iii. Data iv. Variable (4 Marks)
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e) Given the following data set 11, 22, 10, 13, 17, 11, 15, 9, 19
Determine the; i. Arithmetic mean. (2 Marks) ii. Mode (1 Mark) iii. Median. (1 Mark) iv. Geometric mean. (2 Marks)
QUESTION TWO (20 MARKS)
a) In a bid to launch a new type of plant in the market, an entrprenuer contracted a biologist who after a genetic experiment, the number of pea plants having certain characteristics was tallied with the following characteristics. 22 were tall 25 had green peas 39 had smooth peas 9 were tall and had green peas 17 were tall and had smooth peas 20 had grean peas and smooth peas 6 had all the three characteristics 4 had none of the characteristics
Draw a Venn diagram and hence; i. Find the total number of plants counted; ii. How many plants were tall and had peas that were neither smooth or green iii. How many plants were not tall but had peas that were smooth and green. (10 Marks) b) Derive the quadratic formula by solving ????2 + ???? + ?? = 0 where ?? ? 0 using a completing square method. (5 Marks) c) Solve for x given that i. 3 - ?? - 2??2 = -0 ii. ?? = log64 4 (5 Marks)
QUESTION THREE (20 MARKS)
a) The following data relates to daily wages in K£ of 40 firm workers.
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Daily wages K£ No. of workers 30-34 6 35-39 10 40-44 11 45-49 6 50-54 4 55-59 2
i. Calculate the; (i) Mean (3 Marks) (ii) Mode (3 Marks) (iii)Standard deviation (3 Marks) ii. Present the data using a histogram. (4 Marks)
b) State three properties of a good average. (3 Marks) c) Distinguish between mutually exclusive and exhaustive events with independent events. (4 Marks)
QUESTION FOUR (20 MARKS)
a) State and explain two types of annuities citing examples in each case. (4 Marks) b) On commencing employment a man is paid a basic salary of Ksh. 7200 per annum and receives annual increments of Ksh.350. Determine his salary in the 9th year and calculate the total he will have received in the first 12 year. (5 Marks) c) Top Notch consultant Ltd has fixed cost of Ksh.15,000 for its product and variable cost given by 140+0.04x shillings per unit where x is the total number of units and the selling price of the product is given by 300-6x shillings per unit i. Formulate the function of the total cost and total revenue. (4 Marks) ii. Find the breakeven point. (3 Marks) d) A group of young men decided to raise sh. 480,000 to start a business. Before the actual payment was made, 4 of the members pulled out and each those remaining had to pay an additional sh.20,000. Determine the original number of the members. (4 Marks)
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