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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, and there will be a
$100 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.Its annual depreciation is $
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)

Bit 1110 Mathematics For Science Question Paper

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