Basic Mathematics For Environmental Sciences Question Paper

Basic Mathematics For Environmental Sciences

Course:Bachelor Of Environmental Studies

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ENVIRONMENTAL SCIENCE (RESOURCE CONSERVATION)

ERC 102:
BASIC MATHEMATICS FOR ENVIRONMENTAL SCIENCES

DATE: Thursday, 24th December, 2009

TIME: 8.00 a.m. – 10.00 a.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer question ONE and any other FOUR.
Question One
? 2
4 - 6?
? 4 ?
? 4
6
0 ?
?
?
?
?
a)
Given the matrices A=
B =
?
?
?
?
? 1
3
7 ? and C =?- 2?
?- 2 5 - 3?
?
?
?
?
?- 3 2 - 5?
? 8 ?
Find:
i)
AB
ii)
2CTB
(6 marks)
4
b) Evaluate ? (2x3 -4x2 +5) dx

(4 marks)
2
2x
3
c)
Solve the following
=

(4 marks)
7 + 2x
x -3

Page 1 of 3

d)
The table shows the ages of people who attended a seminar
Ages
Cumulative
frequency
20---24 2
25---29 6
30---34 19
35---39 37
40---44 66
45---49 87
50---54 102
55---59 110
Calculate:
i)
Mean
and
standard
deviation
(9
marks)
ii)
Coefficient
of
variation (2
marks)

Question Two
a)
Explain any two properties of determinants giving an example in each case.

(4 marks)
b)
Using the inverse/Cofactor method solve the following system of equations.
2x + 2 y + z =5

3x - 2 y + 2z =18

(11 marks)
x + 4y - z = - 5

Question Three
a)
Differentiate the following:
4 2
x +5x -7
i) y =

(4 marks)
2x +1
ii)
y =( 4
6x +5) (
3
12x )

(4 marks)
b)
Using the intercept/vertex method sketch the function f (x)=- 3x +13x +10

(7 marks)

Page 2 of 3

Question Four
a)
Using graphical method Maximize 500x + 250y
8x + 2y = 400
Subject
to
2x + y =120

(5 marks)
x, y =0
b)
The table shows the daily wages of workers in a factory
Wages
(Ksh.)
No.
of
workers
100---200
6
200---300
9
300---400
13
400---600
18

600---800

25
800---1000
14
1000---1200
10
1200---1500
5
i)
Calculate
the
median
wage
(3
marks)

ii)
Labour law requires that the minimum daily wage to be Ksh. 500. Find
percentage of workers who earned above this wage.
(3 marks)
iii)
Calculate the range of wages between which 80% of workers lie.
(4 marks)

Question Five
a)
There were 120 people in a café one morning 46 ordered cocoa, 65 ordered milk,
19 ordered milk and tea, 22 ordered cocoa and milk, 13 ordered cocoa only, 4
ordered all three items and 7 ordered none of the above.
i)
Show this information in a Venn diagram.

(4 marks)
ii)
Find number of people who ordered tea.

(2 marks)
iii)
Find number of people who ordered one item only.
(2 marks)
b) i) Differentiate
y =(2x + 4x - )5
3
2 (4
marks)
? 2
5 3
4
-4
?
ii)
Evaluate
? x + x 2 -12x + 6 dx
?
?

(3
marks)
? 5
3
?

Page 3 of 3

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