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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 SECOND TRIMESTER 2008 EXAMINATIONS

FACULTY : BUSINESS AND MANAGEMENT STUDIES
DEPARTEMENT : BUSINESS ADMINISTRATION
COURSE CODE : MATH 100
COURSE TITLE : MATHEMATICS
TIME : 2 HOURS

INSTRUCTIONS:
Answer any THREE Questions in Section A and any TWO Questions in Section B

Question 1
(a) Define:
(i) Commutative Law of Multiplication
(ii) Associative Law of Addition
(iii) Associative Law of Multiplication
(iv) Distributive Law of Multiplication over Addition
Also give one example for each. (4 marks)

(b) The function is given by

find the values of and (2 marks)

(c) Solve following given equations for either x or b (as the case may be)
(i) (ii)
(iii) (iv) (4 marks)

Question 2

(a) (i) Evaluate
12!
2! 9!
(ii) Write in factorial form (4 marks)

(b) Find number of terms in this progression
-13, -10, -7, -------,56 (3 marks)

(c) (i) if

2x 3 -x 1 6 2
= +

1 0 1 0 0 0

find the value of x

(ii) evaluate determinant

4 5 (3 marks)

3 8

Question 3
(a) Kamau borrows Ksh. 5000/- for 8 months at 1% simple interest per month. How much interest is paid? (4 marks)

(b) Find the value of k for which the equation

has equal roots. Also verify your solution. (5 marks)

SECTION B
Question 4
(a) Using the completing square method solve the equation
(5 marks)

(b) Solve the quadratic inequality
(5marks)

(c) Solve for x

(i)

(ii) (5 marks)

(d) Factorise and solve for x
(5 marks)

Question 5
(a) Given

Evaluate
(i) (ii) (6 marks)

(b) Find the equation of the line passing through ( -2 , 3 ) and ( 4 , - 5 ). (3 marks)

(c) Given

,
and

Find
(i) (ii) (iii) (iv) (v) (5 marks)

(d) The marked price of a gas cooker is Ksh.9000/-. A dealer charges 20% more under hire purchase. If the deposit is Ksh. 600/- calculate the amount monthly instalments if there are 12 equal instalments. (5 marks)

(e) Given
and

(6 marks)

,
Question 6
(a) Draw the graph of
(4 marks)

(b) Find the sum of the positive even integers less than 100. (6 marks)

(c) The third term of a geometric sequence is 9 and 6th term is 243.
Find the first term and the common ratio. (6 marks)

(d) From a pack of playing cards , the Ace, King, Queen and Ten of spades are taken. In how many ways can three of these five cards be placed in a row from left to right.
(4 marks)

(e) If are the roots of general quadratic equation

then show that
(4 marks)

Question 7
(a) Sum of the squares of three consecutive positive integers is 1208.
Form the equation and find the numbers. (7 marks)

(b) State which of the following matrix multiplication no meaning and simplify the others

(i) (ii)

1 2 4 5 5 1 2
0 3 6 0 4

(iii) (iv)

5 6 3 5 6
2 3
0 4 4 0 4

(8 marks)

(c) Sum of two numbers is50 and three fifths of the lager number is 11 more than two thirds of the smaller number. Form the equation and find the numbers. (7 marks)

(d) Simplify
(3 marks)

Math 100: Mathematics Question Paper

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