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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) Find the inverse of
3 1 8 -1 0 2 4 4 -5 (6 Marks) b) Let ?? ?? = ??2 - 5?? + 6. Obtain the coordinates of the vertex and state whether it is a maximum or minimum. (3 Marks) c) Evaluate lim???1 ??2-1 ??2-3??+2 . (2 Marks) d) Solve by elimination method the system of linear equations ?? + 12?? + 3?? = 120 2?? + ?? + 2?? = 80 4?? + 3?? + 6?? = 219 (5 Marks) e) Solve 3?? + 4?? = 7 ?? + 2?? = 2 by finding the inverse of the matrix ?? = 3 4 1 2 . (3 Marks) f) A manufacturer determines that when x hundred units of a particular commodity are produced, the profit will be ??(??) = 4000(15 - ??)(?? - 2) shillings. i. Find ??'(??) (2 Marks) ii. Find where ??'(??) = 0 (2 Marks) g) By giving an example in each case, explain the difference between a sequence and a series. (4 Marks) h) Evaluate ? ? ? ? 2 1 2 23 dx x (3 Marks)
2
QUESTION TWO (20 MARKS)
a) Let ?? = 1,2,3,4,5,6,7,8,9,10 where U denotes the universal set and ?? = 1,2,3,5 and ?? = {2,4,6,8}. Find: i. A'' (1 Mark) ii. ?? ? ?? ' (2 Marks) iii. ??' n ??' (3 Marks) b) In a G.P the sum of the terms is 224 and the last term is 128. Find the number of terms if the common ratio is 2. (4 Marks) c) A new employee earns a basic salary of 7,200 p.a and receives annual increments of $350. Determine the employee’s salary in the 9th year and calculate the total amount she will have received in the first 12 years. (5 Marks) d) The value of a machine originally valued at kshs. 3,000 depreciates at 15% p.a. the machine is sold when its value is less than ksh. 550, after how many years is it sold? (5 Marks)
QUESTION THREE (20 MARKS)
a) Let ?? =
2 3 -1 0 2 4 -2 5 6 . Find ?? . (3 Marks) b) Given that ?? = 4 2 3 2 , ?? = 3 2 -1 1 6 2 . Find AB and ???? ??. (3 Marks) c) Differentiate: i. ?? = ??2 - 6?? + 5 3 (3 Marks) ii. ?? = ??2??3 ??2 + ?? + 2 (3 Marks) iii. ?? = ??2 2-?? (3 Marks) d) A manager estimates that when x thousand people are employed at her firm, the profit will be P(x) million shillings; where ?? ?? = -??2 + 6??. What level of employment maximizes profit? What is the maximum profit? (5 Marks)
QUESTION FOUR (20 MARKS)
a) Let ?? ?? = 4-3?? 4-11??
and ?? ?? = 6?? 1-10??
.
Find: i. ?????? ?? (3 Marks) ii. ?????? ?? (3 Marks) b) A company receives $45 for each unit of output sold. It has a variable cost of $25 per item and a fixed cost of $1600. What is its profit if it sells 200 items? (3 Marks) c) Evaluate the integral ? 3?? + 2 4 ????. (3 Marks) d) Solve the system of equations by matrix method ?? + 3?? + 2?? = 3 2?? + 4?? + 2?? = 8 ?? + 2?? - ?? = 10 (8 Marks)
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QUESTION FIVE (20 MARKS)
a) Sketch the graph of ?? ?? = 2?? ?????? - 3 = ?? = 3. (4 Marks) b) Suppose that the amount, A(t) of a certain radioactive substance present at time t is given by A(t)=1000e-0.1t 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) c) Solve the inequalities and illustrate your solution on a number line 3?? + 4 < 25 = 8?? - 7 . (3 Marks) d) Obtain the stationary points of the function ?? ?? = 2??3 - 3??2 - 12?? - 7 and use the second derivative test to classify them. (6 Marks) e) Given the universal set ?? = ??,??,??,??,??,??,?? ?????? ?????? ???????? ?? = ??,??,?? ,?? = ??,??,?? , Represent ?? ? ?? in a Venn diagram. (3 Marks)
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