Bit 1110 Mathematics For Science Question Paper
Bit 1110 Mathematics For Science
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2014
1
UNIVERSITY EXAMINATIONS: 2013/2014
ORDINARY EXAMINATION FOR THE BACHELOR OF SCIENCE
IN INFORMATION TECHNOLOGY
BIT 1110 MATHEMATICS FOR SCIENCE
DATE: APRIL, 2014 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other TWO
QUESTION ONE
a) Define the following terms
i. Rational numbers (1 Mark)
ii. Irrational numbers (1 Mark)
b) Simplify
i.
2 5 3
10 6
(3 Marks)
ii.
a b
a b ab
2
2 2
9
12 3
(3 Marks)
c) i. Explain clearly what is a logarithm (1 Mark)
iii. Solve the equation log 2 2log 9 3 3 3 x (3 Marks)
d) i. State the difference between sequence and a series (2 Marks)
iv. A contest will have five cash prizes totaling 5,000,andtherewillbea100 difference of between successive prizes. Find the first prize.
(3 Marks)
e) i. Define permutations and combinations of r objects from n objects
(2 Marks)
ii. The manager of a supermarket has been supplied with 6 products, but
2
there are 4 available display slots for the products. Determine the number
of ways the manager can arrange the products given that repetition is not
allowed. (2 Marks)
f) i. If x 3 and x 2 factors of a polynomial
9 6 4 3 2 x ax x bx .Find the values of a and b . (4 Marks)
ii. Solve the equation for values of from 0 0 to 0 360 inclusive
4cot 39 24cosec 2
(5 Marks)
QUESTION TWO
a) i. State the remainder theorem (2 Marks)
iii. Given that ( ) 2 7 5 3 2 f x x x .Find the remainder when f (x) is
divided by 2x 3 , using long division. (4 Marks)
b) Let f(x) be a polynomial such that when f(x) is divided by x 9 the remainder is
99 and when f(x) is divided by x 99 the remainder is 19 find the remainder
when f(x) is divided by x 9 x 99 . (6 Marks)
c) Show that x 2 is a factor of ( ) 7 6 3 f x x x .use this fact to factorize the
expression 7 6 3 x x .Hence solve the equation 7 6 0 3 x x . (8 Marks)
QUESTION THREE
a) i. State the difference between finite and infinite sequence (2 Marks)
ii. The arithmetic sequence has first term 5 and common difference 2.How
many terms of this sequence must be added to get 2,700? (5 Marks)
b) The purchase value of an office computer is 12,500.Itsannualdepreciationis
1875.Find the value of the computer after 8 years. (4 Marks)
c) Use series to express the repeated decimal into a fraction 2.1125 (5 Marks)
d) The second and the fifth terms of a geometric sequence are 10 and 1250,
respectively.Is 31,250 a term of this sequence? If so, which term is it? (4 Marks)
3
QUESTION FOUR
a) Simplify 2
1
3 3 6 4 7 4 6 16
25
1
8x y x y x y (4 Marks)
b) Solve the equation log 6 log 2 5 0 2 x x (7 Marks)
c) Given the function ( ) 5 30 49 2 f x x x
i. Express f (x) in standard form (6 Marks)
ii. Find the minimum value of f (x) (3 Marks)
QUESTION FIVE
a) Express in standard form and rationalize 0
0
1 sin 45
1 sin 45
(5 Marks)
b) Eliminate from the following equations
x 1 cos , y 1 sin (5 Marks)
c) If
5
3
sin A and
17
15
cosB ,where A is obtuse and B is acute, find the exact
value of sin(A B) (5 Marks)
d) Prove that cos3A 4cos A 3cosA 3 (5 Marks)
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