Get premium membership and access revision papers, questions with answers as well as video lessons.
Mathematics For Science Question Paper
Mathematics For Science
Course:Bachelor Of Science
Institution: Kenyatta University question papers
Exam Year:2009
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FRIST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE
SMA 100:
MATHEMATICS FOR SCIENCE
=================================================================
DATE: MONDAY 28TH DECEMBER 2009
TIME: 8.00 A.M. – 10.00 A.M.
INSTRUCTIONS
Answer Question ONE and any other Two Questions.
Question One (30 marks)
a)
Find the values of a and b if the expression 2x3 – 15x2 + ax +b is divisible both by
(x-4)
and
by
2x-1.
(5
marks)
b)
Find the sum of the first n terms of the sequence { 1/2, 1/4, 1/8, …}. (4 marks)
c)
How many three digit numbers can be made from the integers 2, 3, 4, 5, 6 if
i)
each
integer
is
used
only
once (2
marks)
ii)
there is no restriction on the number of times each integer can be used?
(2 marks)
1
d)
Find the exact value of Log
.
(3 marks)
3 27
e)
Solve the equation 2cos2 ? - sin? = ,
1 where 0 = ? = p
2 .
(6
marks)
Page 1 of 4
f)
A student’s assessment consists of three tests, of which he must pass at least two to
continue with the course. He estimates that the probabilities of passing the tests are
0.7, 0.8 and 0.9 respectively. Calculate the probability that he will be able to stay
on the course.
(8 marks)
Question Two (20 marks)
a)
Establish the identity
1- sin?
cos?
=
(5 marks)
cos?
1+ sin?
b)
Solve the following trigonometric equations.
i)
3 cos? + 3 = 2 sin2 ? ,
0 = ? = p
2
(5
marks)
ii)
Cos 2? + 3 = 5 cos ? ,
0 = ? = p
2
(5
marks)
4
p
12
3p
c)
If sin a = ,
< a < p and sin ß =
, p < ß <
,
5
2
5
2
find the exact value of sin(a + ß ) .
(5 marks)
Question Three (20 marks)
a) Given
that
log2x + 2 log 4 y = 4, show that xy = 16. Hence solve for x and y given
that
log 10 (x+y) = 1
log2 x + 2 log 4 y = 4
(8 marks)
b)
Solve for x by completing the square of 2x2 – 3x -1 = 0.
(5 marks)
c)
Find the values of a and b, if f(x) = x3 + 2x2 + ax + b is divisible by both x-2 and 2x
– 1.
(4 marks)
Page 2 of 4
log 1 log 1
d)
Simplify
a 8
a 27
(3 marks)
log 1 log 9
a 4
a
Question Four
(20 marks)
a)
Consider a population of 1000 people and assume 500 of them are male and the rest
are female. It is found that the probability of a member of the population, chosen at
random, suffering from colour blindness is 0.03. However, given that the person
chosen is male, the probability of his being colour blind is 0.05.
Let C, C1, M, F represent colour blind , not colour blind, male and Female
respectively. Find
i)
P(C M)
(3 marks)
ii)
P(C1 F)
(3 marks)
iii)
P(C1 M)
(3 marks)
b)
The projected population distribution of a certain country for the year 2025 is given
as
follows:
Age group (years)
Frequency(thousands)
0-14 9928
15-29 9953
30-44 10075
45-59 9808
60-74 8989
75-89 4289
90-99 469
Calculate the mean and standard deviation of the age of the population.
(6
marks)
Page 3 of 4
d)
A union contract specifies that each worker will receive a 5% pay increase each year
for the next 30 years. One worker is paid ksh. 20,000 the fist year. What is this
person’s total lifetime salary over a 30 year period?
(5 marks)
Question Five (20 marks)
a)
Find the fourth term in the expansion of (3x +2y)7 .
(5
marks)
b)
A School club has 213 members of whom 7 are boys and 6 are girls. In how many
different ways can a committee of 5 be selected if
i)
the committee comprises of 2 boys and 3 girls.
(2 marks)
ii)
the committee has at least one girl.
(3 marks)
iii)
The committee must include 1 boy who is the chairman and one girl who is
the
secretary
of
the
club.
(4
marks)
c) The
function
f(x) = 0.022x2 – 0.4x +60.07
Models women’s earnings as a percentage of men’s x years after 1960. in which year
was this percentage at a minimum. What was the percentage for that year?
(5 marks)
Page 4 of 4
More Question Papers
Popular Exams
Return to Question Papers