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Bbm 112/Sbc 112 Question Paper
Bbm 112/Sbc 112
Course:Bachelor Of Business Management
Institution: Mount Kenya University question papers
Exam Year:2012
UNIVERSITY EXAMINATION 2011/2012
SCHOOL OF BUSINESS AND PUBLIC MANAGEMENT
DEPARTMENT OF MANAGEMENT
VIRTUAL CAMPUS
UNIT CODE: BBM 112/SBC 112 UNIT TITLE: FOUNDATION MATHEMATICS
DATE: MAY 2012 MAIN EXAM TIME: 2HRS
ANSWER QUESTION ONE AND ANY OTHER TWO QUESTIONS
SECTION A (30 MARKS)
Question 1
(a) Solve the equations below
i. 9x – (4x -3) = 11 + 2(2x-7) (2.5 marks)
ii -
x +5 = 14 (2.5 marks)
(b) Given the following sub-set of real numbers
{-8, -7, -v6, 2,
, 0, v2, 3 ,5}
From the subset above list a set of the numbers that are
(i) Natural numbers (1 Marks)
(ii) Integers (2 marks)
(ii) Rational numbers (2 marks)
(c) i. Given two sets A and B,
A = {2, 4, 6, 8, 10, 12, 14}
B = {2, 3, 6, 9, 12, 14}
Find
1. A union B i.e. A?B (2 marks)
2. A intersection B i.e. A? B (2 marks)
ii. Give the universal set e = {1, 2, 3, 4, 5, 6, 7}, and B= {3, 4, 6} find B complement. (1 mark)
(d) For the function f(x) = 3x2 + 2x – 3, evaluate
i. f(4) (1 marks)
ii. f (k) (1 marks)
iii. f (k + m) (3 marks)
(e) Simplify the following
i. 220 ÷ 215 (1 marks)
ii. 4
X 2xy3z2 (2 marks)
iii. Log10 0.00001 (2 marks)
(f) i. A and B are two matrices
A=
2 5 6
4 1 3
8 2 2
B=
1 3 7
2 1 0
3 0 1
Compute A-B (3 marks)
ii. y= 4x
-3
+ 5x-2+ 2x+10 (2 marks)
SECTION B
Question 2
(a) Evaluate !
!!
(4 marks)
(b) Given the following matrix B=
2 1 3
4 0 3
1 3 5
, find determinant of B (4 marks)
(c) Solve the following system of linear equation using either elimination method or substitution
method.
2x - 3y = -7
3x + y = -5 (5 marks)
(d) Use matrix method to solve the following pair of simultaneous equation.
3x + 2y = 2
4x – y = 5 (7 marks)
Question 3
(a) i. y=(3x5+8x)(x2+ 3x) (4 marks)
(b) Compute the following
(2 + 5)
dx (5 marks)
(c) Given the following marginal revenue (MR) function, derive the corresponding total revenue
(TR) function.
MR=25 -3Q2 TR=0 when Q=0 (4 marks)
(d) Find the area under the curve of the following function between x = 2 and x = 5
y = 2 +3x (4 marks)
(e) Find the gradient of the curve y=x3 + 5x+3 at the point (3, 15) (3 marks)
Question 4
(a) Given U={1,2,3,4,5,6,7,8,9,10,11} which is a universal set and A, B, C, D, as its subset,
illustrate on a Venn diagram the sets
A = {2, 4, 8}
B = {1,3,5,9}
C = {3,4,5,6}
D = {4,5,6,7}
Illustrate on a Venn diagram the sets
i. A?B (2 marks)
ii. C? D (2 marks)
(b) In an Olympic games, 74 countries won gold medals, 88 won silver medals, 108 won bronze
medals, 60 won both gold and silver medals, 66 won both gold and bronze medals, 72 won silver
and bronze medals and 56 won gold, silver and bronze medals.
i. Represent this information using Venn diagram. (4 marks)
ii. Using information in Venn diagram
1. Find how many countries Won only gold medals (1.5 marks)
2. Find how many countries Won only silver medals (1.5 marks)
3. Find how many countries Won gold and silver medals but no bronze medals
(1.5 marks)
4. Find how many countries Won silver and bronze medals but no gold medals
(1.5 marks)
(c) Given the following equation solve for x
x2-2x-8=0 (3 marks)
(d) Sketch the graph of the function f(x) = 2x+3 (3 marks)
Question 5
( a) The products P and Q are to be processed using two machines, A and B. Each unit of P
requires 6 hours in machine A and 2 hours in machine B while each unit of Q requires 5
hours A and 3 hours in B. If the number of hours available in A and in B, are 36 hours and 18
hours respectively. Express the following information in matrix form. (4 marks)
(b) Find
of the function, y = !
" (6 marks)
(c) find the derivative of y =
+ v (2 marks)
(d) P and Q are two matrices
P=
2 1
3 2
4 3
Q=$1 2
3 2
%
Are the two matrices conformable for multiplication in the order PQ and QP? If they are,
find product of matrices. (3 marks)
(e) If f and g are functions from the set of integers define by f(x) = 2x+3 and g(x) = 3x + 2.
What is the composition of?
i. f and g i.e. find (fog)x ( 2.5 marks)
ii. g and f i.e. find (gof)x (2.5 marks
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