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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:2014
QUESTION ONE – (30MARKS)
(a) What are real numbers? (2 Marks) (b) Discuss the rational numbers with examples. (2 Marks) (c) Given that two sets A and B ?? = 2,4,6,8,10,12 ?? = 3,6,9,12
(i) Define a universal set. (1 Mark) (ii) Find ?? n ?? (1 Mark) (iii) Find ?? ? ?? (1 Mark)
(d) Given that ?? = 1,2,3,4,5 , list the members of the following sets. (i) ??2:?? ? ?? (1 Marks)
(ii) 1 ?? :?? ? ?? (2 Marks)
(iii) 2 ?? :?? ? ?? (2 Marks)
2
(e) Find the values of x for which the following expression do not exist.
6
52 ?? ? xx x
(3 Marks)
(f) Simplify; (i) 3 × 5 - 2 + 6 - 2 × 3 + 3 + 8 - 2 × 3 (1 Mark) (ii) 1 4 ????16 × 2 - 20 - 2 × 6 (1 Mark) (iii) Expand the following expression ?? + ?? 8 (2 Marks) (iv) Use Pascal’s triangle to determine the co-efficients of the terms in (iii) above. (2 Marks) (g) Solve the simultaneous equation using substitution method 3?? + 4?? = 4 ?? - 4?? = 16 (3 Marks)
(h) Solve the simultaneous equation using matrix algebra 3?? + 4?? = 2 9?? + 12?? = 16 (3 Marks)
QUESTION TWO – (20 MARKS)
(a) Solve
34 96
12 23
? ?
?
? ?
y y
y y
(3 Marks)
(b) If log10 2 = 0.301 and log10 3 = 0.477. Find the logarithms of the following numbers without using tables or calculators (i) 6 (2 Marks) (ii) 20 (2 Marks) (iii)2 ¼ (2 Marks) (iv) 21 2 (2 Marks)
(c) If the third and 15th terms of an A.P are 2 and -34 respectively, what are the first five terms of the A.P. (3 Marks)
(d) Find the 8th term of the G.P. 16, 8, 4… (3 Marks)
3
(e) Solve the quadratic equation (i) 2??2 + 9?? + 7 = 3 (3 Marks)
(ii) 6??2 + 3?? = 0 (2 Marks)
QUESTION THREE – (20 MARKS)
(a) Draw the graph of the following quadratic equation for the given range of x. state the line of symmetry and the maximum or minimum value of the function -3 = ?? = 4 ?? = 2??2 - ?? - 15 (5 Marks)
(b) A company produces two products i.e. Product M and N. The cost of making 20 units of product M and 15 units of product N is Sh.750. The cost of making 10 units of product M and 13 units of product N is Sh.400. the company makes a profit of 25% and 30% on each unit of the products M and N respectively. Required: (i) Express the above cost of making one unit of products M and N in for simultaneous equation. (2 Marks) (ii) Calculate cost of making one unit of product M and product N. (3 Marks) (iii)Calculate the selling price of one unit. (2 Marks) (c) A firm rents its premises and rental agreement provides for regular annual increase of Sh.2,650. If the rent in the first year is Sh.8500. What is the rent in the 15th year? (3 Marks) (d) A firm buys a power press for Sh.42,500 which is expected to last for 20 years and to have a scrap value of Sh.7500. if depreciation is on the straight line method how much should be provided for in each year. (6 Marks)
QUESTION FOUR – (20 MARKS)
(a) Discuss the meaning of Venn diagram and the uses of Venn diagrams. (5 Marks) (b) The main daily newspapers in Nyika areas; the National, the new Era and the citizen. The management of one of the dailies is concerned about the low sales volume of their paper in a recent survey of 100 families in Yoruba town. The numbers that read the various newspapers were found to be as follows:
4
Newspaper Number of Readers The citizen 28 Citizen and New Era 8 The New Era 30 Citizen and National 10 The National 42 New Era and National 5 ALL the three papers 3
Required: (i) Put the above information in a Venn diagram (well labelled). (3 Marks) (ii) Determine the number of families who did not read any of the three news papers. (5 Marks) (iii)Mrembo Beauty advertising firm in Yoruba want to know which Newspaper they should advertise in so that they can reach the largest audience. Advice the company. (2 Marks) (c) Given that log?? = ??,log?? = ?? ??????log?? = ??. Find ? ?3 42 log log z yx (4 Marks)
(d) In a certain factory money was being paid. A received
8 1
of the total amount, B received
3 2
of the total amount. Out of the remaining amount C, D, E received the amount in the
ratio 2:3:4. If E received Sh.800, how much did each get? (6 Marks)
QUESTION FIVE – (20 MARKS)
(a) Differentiate w.r.t x the following polynomials: (i) ?? = ??4 + 5 (2 Marks)
(ii) ?? = ??3 + 5??2 (2 Marks)
(iii)?? = 5?? + 7 3??2 + 5 (3 Marks)
(iv) 5 3 24 x x y ? ? (3 Marks)
5
(b) Integrate the following functions w.r.t x (i) 3 4x dx dy ? (1 Mark)
(ii) 4 1232 23 ? ??? x xx dx dy
(2 Marks)
(c) A firm’s demand function is given by x P 2 100 ?? and its cost function is 300020 ?? xC . Determine the optimum level of output for profit maximization. (4 Marks) (d) A producer wants to increase his sales. To do so he must lower the price. His total sales (R) from sales of output x is give by the expression ? ? xxR ?? 148 . His production costs are Sh.1000 fixed and Sh.36 per unit and the total cost; ?? = 1000 + 36?? Required: (i) The output that would maximize revenue. (2 Marks) (ii) The maximum total revenue (1 Mark) (iii)The profit '??' in terms of the number of units (2 Marks) (iv) The output to maximize profit (5 Marks)
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