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Basic Mathematics Question Paper

Basic Mathematics

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
INSTITUTE OF OPEN LEARNING (IOL)
UNIVERSITY EXAMINATIONS 2008/2009
EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE

SMA102: BASIC MATHEMATICS

DATE: MONDAY 10TH AUGUST, 2009
TIME: 8.00 A.M –10.00 A.M
INSTRUCTIONS:
Answer Question ONE and any other TWO questions
QUESTION ONE
a) If
3 2
x - 6x + 8 = 0 has roots a and ß , find the equation whose roots are
1
1

and

[5 Marks]
a
ß
b)
Without using tables or calculator find the values of
(i)
Cos 3360 0

[2 marks]
(ii)
Cosec (-840 0 )

[2 marks]
(iii)
Tan 750 0

[2 marks]
(iv)
Cot(-30 0 )

[2 marks]

c)
Solve the equation log
x 16
log 5

[4 Marks]
5
x

c)
One of the factors of the cubic polynomial
2 3
x + 3 2
x + ax + b is (x-2). When the polynomial is divided by (x-1),
a remainder of –5 results.

Find a and b, and hence factorize the polynomial completely. [6 Marks]
d)
Solve the following equation for 0
0
0 = s = 90

[4 Marks]
3 tan 2 x –2 tan x –2 = 0
1- 3i
f)
Express the complex number
in the Cartesian form a+ b i
1+ 3i

Cartesian form a + bi

[2 marks]
g)
Find the number of permutations of the letters of PARALLEL
[1 mark]

Page 1 of 3

QUESTION TWO
a)
Find the general solution to the equation
3
sin
s - 2cos2s =3

[7 marks]
1+ Cos?
b) Prove
that
= C
?
2
0t

[5 marks]
1- Cos ?
2
e)
By using De Moivre’s theorem or otherwise prove that
3tan?
?
3
- tan
tan
3
? =

[8 marks]
2
1- 3tan ?
QUESTION THREE
a)
State the Remainder theorem.

[1marks]
1+ x
b)
Expand
as a serious of ascending
1- x
1

Power of x upto and including the term in 2
x . BY substituting x =
find and
10
approximation
for 11

[ 11 m
arks]
c)
Factorize the following as far as possible 3
x - 5 2
x + 2x + 8
[4 marks]
c)
Express the function
2
- x -2 x + 2 in the form
a(x - p)2 + .
q Hence obtain the greatest value of
2
- x -2 x +2
[4 marks]

QUESTION FOUR
a) Given
that
x = 3sin? + sin 5 and
y = 3Cos? + Cos ?
5

i)
Show that 2
2
x + y
= 10 + 6 Cos 4 ?

[5 marks]

ii)
Obtain the greatest and the least values of 2
2
x + y
[6 marks]

iii)
Solve the equation 2
2
x + y =13

[4 marks]

b)
Express 3 - i
in the form r(Cos? + isin? )
Hence obtain
12
( 3 - i )

[5 marks]
QUESTION FIVE
a) Given that log x + 2log y = ,
4 show the xy = 16. Hence solve for x and y the
2
4
simultaneous equations log x + y =
10 (
) 1

Page 2 of 3

log x + 2log y = 4 [
12
marks]
2
4
b) Obtain the three roots of i, where i = -1

[6 marks]
c) In how many ways can five boys be chosen from a class of 20 boys if the class
captain
has
to
be
included.
[2
marks]

Page 3 of 3

Basic Mathematics Question Paper

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