**MAASAI MARA UNIVERSITYREGULAR UNIVERSITY EXAMINATIONS 2013/2014 ACADEMIC YEAR**

**FIRST YEAR FIRST SEMESTERSCHOOL OF BUSINESS AND ECONOMICS**

**CERTIFICATE IN BUSINESS MANAGEMENTCOURSE CODE: CBM 02**

**COURSE TITLE: BUSINESS MATHEMATICSDATE:23RD APRIL 2014 TIME: 9.00AM – 11.30AM**

**INSTRUCTIONS TO CANDIDATES**

**Question ONE is compulsory**

**Answer any other THREE questions**

This paper consists of 3 printed pages. Please turn over.Question one (25 marks)

a) Compute the slope of the straight line segment that connects the points ( 3,2) and ( 7,4) and draw a sketch of the straight line ( 6 marks)

b) Use the Venn diagram to find

i) Union of set

ii) Intersection of sets

iii) Set difference

Of Set A = ( a,b,c,d,f), Set B= ( b, f, e g,h) and set C = ( b, f, g, j, k, l) ( 8 marks)

c) Define the term matrix (2 marks)

d) What is the chance of rolling a 1 or 2 on a six-sided? (3 marks)

e) Suppose an amount of sh 1500 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly for 6 year. Find the amount by the end of the 6th year.

( 6 marks)

**QUESTION TWO ( 15 marks)**

a) Solve the following simultaneous equations

2x + 3y – z = 6

–x – y – z = 9

x + y + 6z = 0 ( 10 marks)

b) Given that the following two matrices are equal, find the value of x and y

( 5 marks)

**QUESTION THREE ( 15 marks)**

a) A and B were partners who agreed to share their profits based on their capital contributions. In that year their business made a profit of Kshs. 60,000.

i) How much did each partner get if their capital contributions were Kshs. 420,000 and Kshs. 380,000 respectively and a 5% interest allowance was made? ( 6 marks)

ii) In the second year, they agreed to admit partner C. However, they agreed on a new profit sharing ratio of A: ½, B: ¼ , C: ¼. In that year C got a profit share of Kshs.15,000. How much will each of the others get? 6 marks)

**QUESTION FOUR ( 15 marks)**

a) Explain the meaning of the following term as used in set theory.

a) Null sets

b) Disjoint sets (4 marks)

b) The probability that a man now aged 65 years will be alive on 2023 is 5/8 , while the probability that his wife now aged 63 will be alive in 2023 is 5/6.

i) The probability that only the wife will be alive in 2023. (4 marks)

ii) The probability that at least one of them will be alive in 2023. (4 marks)

iii) The probability that only the husband will be alive in 2023. (3 marks)

**QUESTION FIVE ( 15 marks)**

Esau wants to take a loan of Kshs. 3,000,000 to buy a van for his transport business. The bank gives him three options. Either:

i) take the loan at a simple interest of 18% payable in 6 years ( 4 marks)

ii) take the loan at an interest of 12% compounded monthly payable in 6 years ( 4 marks)

iii)Take the loan at an interest of 9% compounded quarterly payable in 8 years.

( 4 marks)

Determine how much he will pay in each option and advice him which one to take. ( 3 marks)