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Dbit 302 Fundamentals Of Management Mathematics Question Paper
Dbit 302 Fundamentals Of Management Mathematics
Course:Diploma In Business Information Technology
Institution: Kca University question papers
Exam Year:2012
UNIVERSITY EXAMINATIONS: 2011/2012
EXAMINATION FOR THE DIPLOMA IN BUSINESS INFORMATION
TECHNOLOGY
DBIT 302 FUNDAMENTALS OF MANAGEMENT MATHEMATICS
DATE: MARCH, 2012 TIME: 1½ HOURS
INSTRUCTIONS: Answer Any Three Questions
QUESTION ONE
a) Explain the following terms and use a venn diagram to demonstrate their meaning.
i. union of sets
ii. complement of a set
iii. intersection of sets (3 Marks)
b) A credit union has issued a 3 year loan of Kshs.5, 000. Simple interest is charged at rate of 10 per
cent per year. The principal plus interest is to be repaid at the end of the third year. Compute the
interest for the 3 year period. What amount will be repaid at the end of the third year. (3 Marks)
c) Simplify the following without using tables (6 Marks)
i. log8 + log12.5
ii. log40 – log4
iii.
log3
log 27
d) Solve the following equations by completing the square (6 Marks)
i. x2 + 4x - 5 = 0
ii. 2x2 = 14x - 9
e) A firm which produces a single product is interested in determining the function that expresses
2
annual total cost y as a function of the number of units produced x. Accountants indicates that
fixed expenditures each year are $20,000. They also have estimated that raw materials costs for
each unit produced are $4.50 and labour costs per unit are $2.50 in the assembly department,
$1.70 in the finishing room and $1.30 in the packaging and shipping department. Determine the
total cost function. (2 Marks)
QUESTION TWO
a) Kibet is employed at a pharmaceutical company on a salary of Ksh. 35,000 and an annual increment
of Ksh 2,000 that is his salary increases with Kshs. 2,000 per month after completing every year .
Use arithmetic sequence to determine how long it will take for his salary to rise to Kshs. 57,000 per
month. (5 Marks)
b) In a survey of 50 students at KCAU it was found that 36 are in Diploma Programme, 20 have
laptops and only 3 are neither Diploma students nor have computers. With the help of a Venn
diagram or otherwise find how many students
i. Are in diploma and have laptops (3 Marks)
ii. Have a laptop but not in Diploma programme (1 Mark)
c) i) What is a function? (1 Mark)
ii) Define the domain and range of a function (2 Marks)
d) Briefly explain the following properties of a function (3 Marks)
i. surjective property
ii. Injection property
iii. Bijective property
e) The first term and the 11th term of an arithmetic sequence are 3 and 153. Calculate the common
difference and the 21st term. (5 Marks)
QUESTION THREE
a) Given the equations f(x) = 2x+4 and g(x) = 3x2 , then determine
i. fg(x)
ii. gf(x) (4 Marks)
b) Find the inverse of the following function f(x) =
2
2 4
-
-
x
x (2 Marks)
c) Solve the following quadratic equations by (6 Marks)
3
i. Factorization
3x = 2x2 - 2
ii. By use of formula
4x2 – x – 3 = 0
d) Suppose that Kshs. 1,000 is invested in a savings bank which earns interest at rate of 8 per cent
per year compounded annually. If all interest is left in the account what will the account balance
be after 10 years? (3 Marks)
e) Tom who operates a travel and tour company is contemplating the purchase of another vehicle.
The estimated cost of a new vehicle is Kshs. 800,000 and the estimated average operating cost is
Kshs 0.65 per mile.
i. Determine mathematical function which represent total cost C of owning and operating the
vehicle in terms of number of miles X is driven. (2 Marks)
ii. What are projected total costs if the car is driven 50,000 miles during its life time.
(3 Marks)
QUESTION FOUR
a) Given the functional relationship
t = g(v)
= v2 + v – 10
Determine the output of the following (6 Marks)
i. g(0)
ii. g(-5)
iii. g(x + y)
b) A long term investment of Kshs. 250,000 has been made by a small company. The interest rate is
12 per cent per year and interest is compounded quarterly, if all interest is reinvested at the same
rate of interest, what will the value of the investment be after 8 years? (4 Marks)
c) Solve the following quadratic equation graphically (3 Marks)
y = x2 + 5x + 6 for 0= x = 5
d) Solve for x in the following equations
i. 10x+5 – 8 = 60 (4 Marks)
ii. ex = 80 (3 Marks)
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QUESTION FIVE
a) Given U = {1, 2, 3, 4, …, 12}
A = {1, 4, 6, 8}; B = {1, 2, 3, 7}; C = {5, 9, 10, 11, 12}
Find the following
i. AnB ii) (A?B)nC iii) An c (5 Marks)
b) In a group of 40 friends, 24 drinks Sprite, 18 drinks Fanta and 38 drinks either Sprite or Fanta.
Find how many friends drink both brands of Soda. (3 Marks)
c) Find the range and domain of
i. y = x2 + 4x + 4 (3 Marks)
ii. y =
4 3
3 3
2 + +
+
x x
x (3 Marks)
d) Solve the following simultaneous equations (6 Marks)
i. By substitution
x + y = 24
2x – y = -6
ii. By elimination
2x – 5y = 1
3x + 5y = 14
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