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Dit 107 Mathematics For Science Question Paper

Dit 107 Mathematics For Science

Course:Diploma In Information Technology

Institution: Kca University question papers

Exam Year:2014

UNIVERSITY EXAMINATIONS: 2013/2014
ORDINARY EXAMINATION FOR THE DIPLOMA IN
INFORMATION TECHNOLOGY
DIT 107 MATHEMATICS FOR SCIENCE
DATE: AUGUST, 2014
TIME: 11/2HOURS
INSTRUCTIONS: Answer Any Three Questions
QUESTION ONE
1
x4
a) Solve for x in the equation:
b) Given that W
5
x2
4
(4 Marks)
0
nB x , find the value of
x
when W
n 0.001296.
4300 , B 11900 ,
(4 Marks)
c) Three numbers n 2 , n
and n 3 are consecutive terms of a geometrical
progression. Determine:
i. value of n
ii. common ratio
iii. sum of the first 10 terms
(6 Marks)
2
d) Simplify the expression
x 5y
x
1
3
y
1
2
15
5
(2 Marks)
3
log 49 log 343
e) Simplify without using tables or calculators
1
log 2401
2
3 log 7
(4 Marks)
1
QUESTION TWO
a) The first term of an arithmetical progression is
12 , and the last term is 40 .If the
sum of the progression is 196 , determine the:
i. number of terms (2 Marks)
ii. common difference (4 Marks)
b) Solve the indicial equations
i. 2x
1
ii. 22x
51
2x
2x
c) Given that sin A
(4 Marks)
12
(6 Marks)
0
5
and cosB
13
4
, where A and B are acute, determine
5
without using a calculator, the value of cos A B .
(4 Marks)
QUESTION THREE
a) Find the sixth term in the binomial expansion of 3 x 3 y
y
10
when x
1
.
3
(5 Marks)
14
b) If
7
1
and
2
14
2
7
2
p 7
q 2 , find the values of p and q where p and
q are rational numbers.
(4 Marks)
c) A mixed hockey team containing 5 men and 6 women is to be chosen from 7
men and 9 women. In how many ways can this be done?
d) Find the remainder when f x
4x5
x3
x2
(6 Marks)
3 is divided by 2x 1 using
long division.
(5 Marks)
QUESTION FOUR
a) Solve the following equation:
b) If 3x 1 is a factor of 6 x 3
equation 6 x 3
ax 2
x 2
log 2 x log x 2
2.5
(6 Marks)
ax 2 x 2 , find the value of a and hence solve the
0. (8 Marks)
c) If the sum to infinity of a geometrical progression with a positive common ratio
is 9 and the sum of the first two terms is 15 , find the common ratio.
2
(6 Marks)
QUESTION FIVE
a) Convert the following recurring decimals 0. 6 5 by applying sum to infinity of a
G.P.
(4 Marks)
2 log a x log a x 1
b) Evaluate
log a x 2 .
(4 Marks)
c) Simplify the following:
1
i.
81 4 9
1
32 27
ii.
1
2
2
3
9t 2 25 a 2
6t 2 19 at 15 a 2
(6 Marks)
d) Solve the equation e 2 x
5e x
6
0
3
(6 Marks)

Dit 107 Mathematics For Science Question Paper

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