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Hbc2103:Mathematics For Business Question Paper
Hbc2103:Mathematics For Business
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) i) Define a set. (2 Marks) ii) Given the set ,,, list down all its subsets. (3 Marks) b) The sum of the first three terms of a geometric series is 26. If the common ratio is 3, find the sum of the first 6 terms. (4 Marks) c) An economy is forecast to grow continuously at a rate of 2.5% p.a. if the Gross National Product (G.N.P) is currently 56 billion pounds, what will the forecast for G.N.P be at the end of 21 months. (4 Marks) d) Solve by elimination method the system of linear equations. 2 + - = 2 + 3 + 2 = 1 + + = 2 (5 Marks) e) Integrate by parts = . (4 Marks) f) Solve for x in the equation 2 + + ?? = 0 by completing the square method. (4 Marks) g) Differentiate using the first principles the function = 2 + 3. (4 Marks)
QUESTION TWO (20 MARKS)
a) Given the sets; = 1,2,3,4, = 7,8,9, ?? = Find; i. (2 Marks)
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ii. (2 Marks) iii. (2 Marks) b) A survey of 100 randomly selected students gave the following information. 45 students are taking Mathematics 41 students are taking English 40 students are taking History 15 students are taking Mathematics and English. 18 students are taking mathematics and History 17 students are taking English and History 7 are taking all the three subjects Let M= {Students taking Mathematics} E= {Students taking English} H= {students taking History} Required: i. Draw a Venn diagram to illustrate the above information. (4 Marks) ii. Find how many students are; (i) Taking only Mathematics (2 Marks) (ii) Taking only English (2 Marks) (iii) Taking only History (2 Marks) (iv) Not taking any of these courses. (2 Marks) (v) Not taking Mathematics. (2 Marks)
QUESTION THREE (20 MARKS)
a) Solve the inequalities i. 2 - 6 4 - 7 (2 Marks) ii. -4 < 2-3 3 < 4 (3 Marks) b) Evaluate the given limits; lim2 2-4 -2 (3 Marks) c) For the function = 42 - 3 + 1, obtain the coordinates of the vertex and state whether it is a maximum or minimum. (4 Marks) d) A nutritionist wishes to prepare a food mixture that contains 40g of Vitamin A and 50g of Vitamin B. The two mixtures that are available contain the following percentage of Vitamin A and B. Vitamin A Vitamin B Mixture I 10% 4% Mixture II 5% 12% How many grams of each mixture should be used to obtain the desired diet? (4 Marks) e) Suppose that the amount, A(t) of a certain radio-active substance present at time t is given by = 1000-0.1 where t is measured in days and A(t) in grams. What is the original amount of the radioactive substance present? Find the amount of substance present after 5 days. (4 Marks)
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QUESTION FOUR (20 MARKS)
a) Differentiate the following using the indicated techniques in the bracket. i. = + 3(2 - 5) (product rule) (2 Marks) ii. = 3 +1 (Quotient) (2 Marks) iii. = (2 + )3 . (chain rule) (2 Marks) b) Determine the determinant of the matrix
=
1 2 0 1 0 -1 -1 3 2 (6 Marks)
c) An object is dropped from a cliff which is 1,296 feet above the ground. The height of the object is described as a function of time. The function is = = -162 + 1,296, where h is equals the height in feet and t equals time measured in seconds from the time the object is dropped. i. How far will the object drop 2 seconds? (2 Marks) ii. What is the instantaneous velocity of the object at t=2? (2 Marks) iii. What is the velocity of the object at the instant it hits the ground? (4 Marks)
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