# computational mathematics, Formulas and forms for Mathematics. Masinde Muliro University of Science and Technology

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UNIVERSITY REGULAR EXAMINATIONS

2013 /2014 ACADEMIC YEAR

SEMESTER EXAMINATIONS

(MAIN EXAMINATION)

FOR THE DIPLOMA IN INFORMATION TECHNOLOGY

COURSE CODE: DIT 063:

COURSE TITLE: BASIC MATHS EXAMS

DATE: 20TH AUGUST, 2014 TIME: 9:00A.M.-11:00A.M.

_____________________________________________________________________________

INSTRUCTIONS TO CANDIDATES:

Attempt question ONE (1) and ANY TWO (2) other questions from section B.

KIBABII UNIVERSITY COLLEGE (A Constituent College of MasindeMuliro University of Science Technology)P.O. Box 1699-50200 Bungoma, KenyaTel. 020-2028660/0708-085934/0734-831729E-mail: [email protected]

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QUESTIONS

Instructions to candidates: Answer all questions in section A

SECTION A (24mks) and SECTION B (36mks)

QUESTION # 1

(a) Find the value of X that satisfy the equation below:

X2-5x+6=0 (3mks)

(b) (i) show that x0=1 (3mks)

(iii) Find the values of (32)2/5 (2mks)

(ii) Given that log2=0.3010 (3mks)

Log3=0.4771

Find log 72

(c) (i) Find the next three terms of :1,3,5,7,_,_,_,

(6mks)

(d) The cost of the land in the year 2013 was 5,000,000.00.At the end of each year, the land

value increases by 2%.What will be the value of the land by the end of the year 2015.

(4mks)

(e) Evaluate:

5P3 (3mks)

SETCION B (36mks)

QUESTION # 2

(a) The 20th term of an arithmetic sequence is 60 and the 16th term is 20.Find the first term

and the common difference. (5mks)

(b) The first term of a G.P. is x+1.If the third term of the same sequence is (x+1) (x2-2x+1)

Show that the second term is x2 -1. (5mks)

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(c) The 2nd, 4th and 7th terms of an A.P. are the first three consecutive terms of a G.P., if the

common difference of the AP is 2. (8mks)

Find:

i) the common ratio

ii) The sum of the first eight terms of the G.P.

QUESTION # 3

(a) Find the value of x in

152x-6 =32x-6 (6mks)

(b) 22x+3(2x)-4=0 (6mks)

(c) There are two competing financial institutions A and B.A offers a simple interest services

to the clients and B offers a compound interest services to the clients given that the rates

for the two institutions are the same. Lilian and Evans decided to deposit 10,000 each, in

institution A and institution B respectively at the rate of 8% p.a. Find the difference in

their accounts (6mks)

QUESTION # 4

(a) Find the x-intercept for the graph of each function given below:

(i) f(x)=x2+2x-3 (3mks)

(ii) g(x)=x2+2x-1 (3mks)

(b) Given that COSβ=4 /5 find:

(i) cos2β+sin2β (4mks)

(ii) cos2β+tanβ/4sinβ (2mks)

(c) Convert the following :

(i) 3/5πc to degrees (2mks)

(ii) 720₀ to radians (2mks)

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QUESTION # 5

(a) John has 8 friends. In how many ways can he invite one or more of them to a dinner

(4mks)

(b) (i)How many different signals can be made by 5 flags from 8 flags of different colors?

(6mks)

(c) Show that :

(i) a0=1 (4mks)

(ii) find the values of X in 9(2x-4)=6(2x-4) (4mks)

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