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Hbc 2110: Management Mathematics I Question Paper
Hbc 2110: Management Mathematics I
Course:Bachelor Commerce
Institution: Dedan Kimathi University Of Technology question papers
Exam Year:2013
KIMATHI UNIVERSITY COLLEGE OF TECHNOLOGY
UNIVERSITY EXAMINATION 2012/2013
EXAMINATION FOR BACHELOR OF COMMERCE
HBC 2110: MANAGEMENT MATHEMATICS I
DATE APRIL 2013 TIME: 2HRS
Instructions: Answer questions ONE and Any other TWO questions.
Question One (COMPULSORY)
a) Consider the universal set T and its subsets A, B and C presented below:
T = [a, b, c, d, e, f]
A = [a, d]
B = [b, c, f]
C = [a, c, e, f]
Find:
i) A ? B (1marks)
ii) A ? C (1marks)
iii) B ? C (1marks)
iv) A ? B ? C (2marks)
b) Solve without using tables.
i) Log3 (27)(81) (2marks)
ii) Log5 (125/625) (2marks)
c) Using suitable examples defined the following terms:
i) Dependent variable (2marks)
ii) Independent variable (1marks)
iii) Range (1mark)
d) At what rate percent will $4,000 yield $1324 compound interest in 3 years?
(3marks)
e) A certain sum of money is put out at compound interest for 4 years at 5 percent per
year. The interest for third year is greater than that of second year by $12.50. Find the
total interest for the four years and also the original sum. (4marks)
f) Sh. 5,000,000 is invested at 8% p.a. find the amount after 2 years if the interest is
compounded continuously. (3marks)
g) A company sets aside a sum of $5,000 annually for 10 years to pay off a debenture issue
of $60,000. If the sinking fund is accumulated at 5% p. a. compound interest, find the
surplus after the full redemption of the debenture issue. (4marks)
h) Solve the following simultaneous equations using substitution technique:
2x – 3y = 8
3x + 4y = -5 (3marks)
Question Two
a) Find the future amount of annuity of $40,000 payable at the end of each quarter for 6
years at 8% p. a. compounded quarterly. (5marks)
b) Which is better investment, 8% p. a. compounded half-yearly or 7.5% p. a. compounded
continuously? (5marks)
c) The third term of a G.P is 18 and the 7th term is 1458. Find the first term and the
common ratio. (5marks)
d) A field is 10 meters longer than it is wide. The area is 7200 m2 . What is the width?
(5marks)
Question three
a) In a certain population, the annual birth and death rates per 1000 are 39.4 and 19.4
respectively. Find the number of years in which the population will be doubled.
(5marks)
b) A machine is depreciated in such a way that the value of the machine at the end of any
year is 90% of its value at the beginning of the year. The cost of the machine was
$12,000 and it was sold eventually as waste metal for $200. Find the number of years
during which the machine was in use. (5marks)
c) A house sells for $50,000 down and 10 semi-annual payments of $5,000 each, the first
due 3 years hence. Find the cash price of the house, if money is worth 6% p. a.
compounded semi-annually. (5marks)
d) Comprehensive Book publishers Limited are planning to produce a new text book in life
skills. The fixed costs are Sh. 3,300,000 and the variable costs are Sh. 312.50 per
textbook. The wholesale price will be Sh. 437.50 per textbook. How many textbooks
must Comprehensive Book Publishers publish and sell in order to break-even?
(5marks)
Question Four
a) In an A.P the thirteenth term is 27 and the seventh term is three times the second term.
Find the first term, the common difference and the sum of the first ten terms.
(6marks)
b) Calculate the future amount of an annuity immediate of $2,000 per annum for 20 years,
the rate of interest being 13.5% p. a. (4marks)
c) Dehan invested equal amounts one at 6% simple interest and the other at 5%
compound interest. If the former earns $437.50 more as interest at the end of 2 years,
find the total amount invested. (5marks)
d) Solve the equations y + 2x = 3 and x2 + y2 = 2 (5marks)
Question Five
a) Solve the equation 2m2 – 5m -3 = 0 (3marks)
b) Two adjacent sides of a rectangle are of lengths (x+4) cm and (x+6) cm. the area of the
rectangle is equal to twice the area of the square whose side is x. what are the
dimensions of the rectangle? (5marks)
c) A researcher in Kisumu City has randomly interviewed individuals in the city centre. The
following are the data he collected: 40 of those interviewed are Christians; 25 were
Kenyans; 10 were Kenyan Christians; 35 were neither Kenyan nor Christians. Using Venn
diagram, find the following:
(i) The number of Christians non-Kenyans.
(ii) The number of Kenyan non-Christians.
(iii) The total number of individuals interviewed. (5marks)
d) Broadway has the capacity to produce three types of cookies X, Y and Z using
ingredients P, Q and R. the recipe for each unit of cake is given as follows:
X – 20, 15 and 40 grams of P, Q and R respectively
Y – 12, 36 and 16 grams of P, Q and R respectively
Z – 30, 15 and 40 grams of P, Q and R respectively
If 130, 225 and 200 units of P, Q and R respectively must be used. Formulate a set of
simultaneous equations and solve them such that they would indicate the number of
units of each cookie to produce in order to utilize completely the available ingredients.
(7marks)
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