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Math 100: Mathematics Question Paper
Math 100: Mathematics
Course:Mathemetics
Institution: Kenya Methodist University question papers
Exam Year:2008
KENYA METHODIST UNIVERSITY
END OF FIRST TRIMESTER 2008 EXAMINATION
FACULTY : BUSINESS AND MANAGEMENT STUDIES
DEPARTMENT : BUSINESS ADMINISTRATION
COURSE CODE : MATH 100
COURSE TITLE : MATHEMATICS
TIME : 3 HOURS
INSTRUCTION
• Answer Question ONE and THREE other Questions
Question 1
a) Given that ? is the set of positive integers less than 100 and the set A and B are subsets of ?. A is the set of multiples of 2 and B is the set of multiples of 7
i) List the members of A, B, AnB, A B. (2marks)
ii) Write down the values of n(A), n(B), n(A B) and verify that n(A B) = n(A) + n(B) – N(AnB). (3marks)
iii) List down A1 and B1, A1nB1, A1 B1. (2marks)
b) i) List the members of the set of real numbers for which the expression
1 does not exist.
(x-1) (x-2) (x-3) (1mark)
ii) Explain the term function, image of a function and the domain of a function.
(3marks)
iii) The domain of the function f(x) = x2+1 is R. Find its range. (2marks)
C) Solve for x given:
i) Log?2 ¼ = x (3marks)
ii) ½ log (x+1) = -2 (3marks)
d) i) Using an example of matrix A and B, what does the phrase “matrix multiplication is not communicative “ mean? (1mark)
ii) Find the inverse of the matrix M where M = and hence solve the matrix equation MX = C, in which X = and C = (5marks)
Question 2
a) i) Derive the quadratic formula by solving the equation ax2 + bx +c = 0 where a, b and c are constants. (4marks)
b) Find the inverse of the function:
f(x) = x3 + 1 (3marks)
c) i) Determine fog and gof given that f(x) = 3x – 4, g(x) = x3 (4marks)
ii) Given that f(x) = x3 - x
find f(-2), f(-1), f(0), f(1),
Hence sketch the function f(x) = x3 – x and determine whether its even, odd or neither. (4marks)
Question 3
a) Solve for x in the equation
2x2 + 7x – 15 = 0 (3marks)
b) Solve the following system of equation using row operation method.
X – 2y + 3z = 9
-x + 3y – z = -6
2x – 5y + 5z = 17 (8marks)
c) Solve the system below by elimination
x + 2y = 4
x – 2y = 1 (4marks)
Question 4
a) Find the sum of the first eight terms of the geometrical progression
2 + 6 + 18 + … (4marks)
b) The second term of an arithmetical progression is three times the seventh, and the ninth term is 1. Find the first term, the common difference and which is the first term less than 0. (4marks)
c) How many terms of the Arithmetic progression 15 + 13 + 11 + … are required to make a total of -36. (3marks)
d) If Sn = 121? , r = ? tn = ? Find a and n. (4marks)
Question 5
a) 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. (2marks)
ii) The annual rate of interest that the bank paid (2marks)
b) A computer whose marked price is sh.40,000 is sold at sh.56,000 in hire purchase terms.
i) Kioki bought the computer on hire purchase terms. He paid a deposit of 25% of the hire purchase price and cleared the balance by equal monthly installments of sh.2,625. Calculate the number of installments. (3marks)
ii) Had Kioki bought the computer on cash price terms, he would have been allowed a discount of 12 ½ % on marked price. Calculate the difference between the cash price and hire purchase price and express it as a percentage of the cash price.
(3marks)
c) If $ 1,700 is invested at 7.8% compound quarterly, find the amount compounded at the end of 10 years in Ksh. Give 1$ - Ksh.72.00
(5marks)
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