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Bbm 112 Question Paper

Bbm 112

Course:Bachelor Of Business Management

Institution: Mount Kenya University question papers

Exam Year:2012

UNIVERSITY EXAMINATION 2012/2013
SCHOOL OF BUSINESS AND PUBLIC MANAGEMENT
DEPARTMENT OF ACCOUNTING & FINANCE
REGULAR
UNIT CODE: BBM 112
UNIT TITLE: FOUNDATION MATHEMATICS
DECEMBER 2012 MAIN EXAM TIME: 2HRS
Instructions:Answer question ONE (COMPULSORY) and any other TWO
questions
Question one
a) Express
7
21
in the form kv7
(2marks)
b) Express 8-1/3 as an exact fraction in its simplest form
(2marks)
c) Evaluate S
=
=
+
30
10
(7 2 )
r
r
r
(4marks)
d) Solve the inequality(i) x2 +3x >10 (3marks)
(ii)Find the set of values of x which satisfy both of the following inequalities:
(3marks)
3x -2 < x +3
x2 +3x >10
e) f(x) = (vx+3)2 +(1 -3vx)2Show that f(x) can be written in the form ax + b
where a and b are integers to be found.
(3marks)
A geometric series has first term a and common ratio r where r > 1.The sum of the first
n terms of the series is denoted by Sn.Given that S4= 10x S2,
f) Find the value of r. (5marks)
Given also that S3= 26,
g) Find the value of a, (3marks)
h) Show that S6= 728.
(2 marks)
i) Find the interest on Ksh 743400 for
4
3
8 years at the rate of %
2
1
2 interest per
annum
(3 marks
Question Two
Given that y = 2x find expressions in terms of y for
a) 2x+2
b) 23-x
(4marks)
c) Show that using the substitution y = 2x the equation 2x+2 + 23-x =33 can be
rewritten as
4y2 + 33y + 8 = 0(2marks)
Hence solve the equation 2x+2 + 23-x=33
(4marks)
d) Expand (1 + 3x)8in ascending powers of x up to and including the term in x3.
You should simplify each coefficient in your expansion.
(4marks)
e) Use your series, together with a suitable value of x which you should state, to
estimate the value of (1.003)8, giving your answer to 8 significant figures.
(3marks)
f) In a school, there are 20 teachers who teach Mathematics or Physics. Of these
12 teach Mathematics and 4 teach Physics and Mathematics. Draws are Venn
diagram and state how many teach Physics.
(3marks)
Question Three
Given that t = log3x, find expressions in terms of t for
i.
2
3 log x
ii. x 9 log (4marks)
(b) Hence, or otherwise, find to 3 significant figures the value of x such that
2
3 log x - x 9 log = 4
(3marks)
A geometric series has first term a and common ratio r where r > 1.
The sum of the first n terms of the series is denoted by Sn.
Given that S4= 10x S2,
(c) Find the value of r. (5marks)
Given also that S3= 26,
(d) Find the value of a, (3marks)
(e) Show that S6= 728.
(2 marks)
(f) Find the value of the determinant
8 4 15
3 6 10
2 5 7
(3marks)
Question Four
f (x) = 4x - 3x2 - x3
a) Fully factorise f (x) = 4x - 3x2 - x3
(3marks)
b) Sketch the curve y = f(x), showing the coordinates of any points of intersection
with the coordinate axes. (3marks)
c) A geometric series has first term 1200. Its sum to infinity is 960.
i. Show that the common ratio of the series is
4
1 -
(3marks)
ii.
Find, to 3 decimal places, the differences between the ninth and tenth terms of
the series.
(3marks)
iii. Write down an expression for the sum of the first n terms of the series
(2marks)
iv. Prove that the sum of the first n terms of the series is 960(1 + 0.25n)
(2marks)
d) Solve the simultaneous equations x+y =9 and
2
1 1 1 + =
x y
(4marks)
Question Five
The first three terms of arithmetic are p, 5p -8 and 3p +8 respectively.
a) Show that p = 4
(2marks)
b) Find the value of the 40th term of his series
(3marks)
c) Prove that the sum of the first n terms of this series is a perfect square
(3marks)
d) Find the market equilibrium price and the quantity if the demand equation is p-
3q =22 and the supply equation q2 +2p +4q =100 where p is the price and q is
the quantity of the commodity. Find the total revenue at market equilibrium
price. (4marks)
e) A person buys 20kgs, of rice, 10kgs of Ata, 5kgs of pasta, 4kgs of sugar and
2kgs of salt for a month. Rice cost Ksh 80 per Kg, Ata costs Ksh 75 per Kg, pasta
costs Ksh 175 per Kg, sugar costs Ksh 105 per Kg and salt costs Ksh 40 per Kg.
using Matrix Multiplication, find the amount of money spent by the person.
(3marks)
f) f(x) = x3 -19x -30
i. Show that (x +2) is a factor of f(x)
(2marks)
ii. Factorise f(x) completely
(3marks)

Bbm 112 Question Paper

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