Math 100: Mathematics Question Paper
Math 100: Mathematics
Course:Mathemetics
Institution: Kenya Methodist University question papers
Exam Year:2008
KENYA METHODIST UNIVERSITY
END OF SECOND TRIMESTER 2008 EXAMINATIONS
FACULTY : BUSINESS AND MANAGEMENT STUDIES
DEPARTEMENT : BUSINESS ADMINISTRATION
COURSE CODE : MATH 100
COURSE TITLE : MATHEMATICS
TIME : 2 HOURS
INSTRUCTIONS:
• Answer Question ONE (Compulsory) and any other TWO Questions
Question 1
(a) (i) Give two examples of set of numbers that are real numbers. (2 marks)
(ii) Define a rational number (1 mark)
(b) Given that S is the set of positive integers less than 50 and the set A and B are subset of S. A is the set of multiples of 2 and B is the set of multiples of 5.
(i) List the members of A,B, AnB, AUB (2 marks)
(ii) Write down the values of n(A),n(B),n(AUB),n(AnB) and verify that n(AUB = n(A)+n(B) - n(AnB) (2 marks)
(c) (i) Given that a, b, c e R, state the axiom of additive inverse and associative axiom for multiplication. (2 marks)
(ii) Find the values of x for which the following expression does not exist.
2x+5
x²-x-6 (2 marks)
(d) (i) Explain the term function, image of a function and the domain of a function.
(3 marks)
(ii) Given that f(x) = v(x+3) and g(x) = v (16 - x²). Find
(f+g) x and Dom (f+g) x (3 marks)
(e) Find y if log2 y – 2 =log2 92 (3 marks)
(f) (i) Find the inverse of the matrix M where M = 3 2
5 4
and hence solve the matrix equation
MX=C, in which X = x and C = 1
y 3 (5 marks)
Question 2
(a) A man wished to save shs.200,000 in 4 years time. Find the sum of money he has to deposit now at 12% p.a. interest compounded semi – annually to realize his goal
(4 marks)
(b) A sewing machine valued at sh.25,000 can be bought by cash at a discount of 10% or by installments whereby a deposit of sh.3000 is paid followed by 15 monthly installments of sh.1500 each. Find:
(i) The cash price of the machine (1 mark)
(ii) The hire purchase price of the machine (2 marks)
(iii) The carrying charge (3 marks)
(c) A certain sum of money is deposited in a bank that pays simple interest at a certain rate. After 3 years, the total amount of money in the account is sh.358, 400.The interest earned each year is sh.12,800. Calculate:
(i) The amount of money which was deposited (2 marks)
(ii) The annual rate of interest that the bank paid (3 marks)
Question 3
(a) Derive the Quadratic formula by solving the equation
ax² +bx+c=0 where a, b, and c are constants (4 marks)
(b) Find the inverse of the function
f(x)=v(2x-3)
(c) (i) Determine fog and gof,given that
f(x)= x-1 g(x) = 1/x
x+1 (4 marks)
(ii) Given that f(x) = x²+1,find f(-2) , f(-1) , f(0) , f(1), f(2) , hence sketch the function
f(x) =x²+1 and determine whether its even , odd or neither (4 marks)
Question 4
(a) (i) Graph the function f(x) = x²-4x+3 for x to be the integers in the interval
[-1,5 ] (3 marks)
(ii) Using the graph above solve for x in
x²- 4x + 3 = 3 (1mark)
x²- 4x = 0
(b) Solve the following system of equation using row operation method
X – 3z = -2
3x + y + z = 5
2x +2y + z = 4 (6 marks)
(c) Solve the system of equation below by elimination
3x + 2y = 10
2x + 5y = 3 (3 marks)
Question 5
(a) Find the sum of the first eight terms of the geometrical progression
2 + 6 + 18 + ………….. (4 marks)
(b) The second term of an arithmetical progression is three times the seventh, and the ninth term is 1. Find the first term and the common difference (4 marks)
(c) How many terms of the Arithmetic progression 15 +13 + 11 +…………. are required to make a total of – 36 (3 marks)
(d) If Sn =121? , r = ?, Tn = ?. Find a and n (4 marks)
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