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Bcu 102 Foundations Of Mathematics Question Paper
Bcu 102 Foundations Of Mathematics
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
ORDINARY EXAMINATION FOR THE BACHELOR OF BUSINESS
INFORMATION TECHNOLOGY
BCU 102 FOUNDATIONS OF MATHEMATICS
DATE: AUGUST, 2014
TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other TWO
QUESTION ONE (30 MARKS)
a) Define the following terms
i)
Real numbers
ii)
Rational numbers
(1 Mark)
(1 Mark)
b) Simplify
i)
24
8x
ii)
3
3 6
216
(3 Marks)
294
3x 2
(3 Marks)
6x 4
c) i. Explain clearly what is a logarithm
(1 Marks)
ii) Solve the equation log 2 x 2 3 log 2 8 10
(3 Marks)
d) i. State the difference between finite and infinite series
(2 Marks)
ii) The yearly depreciation of a certain machine is 25% of its value at the beginning
of the year. If the original cost of the machine is $20, 000, what is its value
after 6 years?
(3 Marks)
e) i) Define permutations and combinations of r objects from n objects.
(2 Marks)
ii) 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?
(2 Marks)
4
3
2
f) The expression px qx 3 x 2 x 3 has a remainder x 1 when divided by
x2
3x 2 .Find the values of p and q .
g) Solve the equation for values of
2
2 cos
3 cos
(5 Marks)
0
0
from 0 to 360 inclusive
1 0
(4 Marks)
1
QUESTION TWO (20 MARKS
a) i) State the remainder theorem and factor theorem
Given that f ( x)
ii)
2x
3
3x
2
(2 Marks)
32 x 15 .Find the remainder when f (x) is
divided by 2x 1 , using long division. Is 2x 1 a factor of f (x) ?
(5 Marks)
iii) Solve the equation 2 x
b) Given the function f ( x)
3
2
3x 32x 15 0
2 x 2 12 x 23
(5 Marks)
i) Express f (x) in standard form
( 5 Marks)
ii) State the minimum value , vertex, and line of symmetry of f (x)
( 3 Marks)
QUESTION THREE (20 MARKS)
a) i) State the difference between a sequence and a series
( 2 Marks)
ii) The first term of an AP is -12,and the last term is 40.If the sum of the progression
is 196,find the number of terms and the common difference.
(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.
c) Use series to express the repeated decimal into a fraction 2.69
(4 Marks)
(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)
QUESTION FOUR (20 MARKS)
a) Simplify 16 3 4 n
853n
b) Solve the equation 2 x 2
c)
i).
4n
1
( 5 Marks)
6x 3 0
( 5 Marks)
State the main difference between common logarithms and natural
logarithms.
ii)
(2 Marks)
Determine log 7 83 .64
d) Without using calculator, simplify
(3 Marks)
15!
15!
11!4! 12!3!
2
( 5 Marks)
QUESTION FIVE (20 MARKS)
1 tan 30 0
1 tan 30 0
b) Eliminate from the following equations
x 4 sec , y 9 tan
a) Express in surds form and rationalize
( 5 Marks)
(5 Marks)
3
5
and sin B
,where A and B is acute angles, find the exact value of
13
5
(5 Marks)
sin( A B)
3
d) Prove that sin 3 A 3 sin A 4 sin A
(5 Marks)
c) If sin A
3
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