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Mathematics For Science Question Paper
Mathematics For Science
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2012
UNIVERSITY EXAMINATIONS: 2011/2012
YEAR 1 EXAMINATION FOR THE BACHELOR OF SCIENCE IN
INFORMATION TECHNOLOGY
BIT 1110 MATHEMATICS FOR SCIENCE
DATE: APRIL 2012 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE
a) Derive the quadratic formula. (5 Marks)
b) Factorize completely the expression 45a2 – 20b2 and hence or otherwise find its value when a = 5
and b = 3. (5 Marks)
c) Evaluate ( ) ( )
2
3 1 1
2 4 8 16 81
27
- ? ? × ÷ ? ?
? ?
(5 Marks)
d) What is the remainder when f (x) = x3 + 2x2 - 9x -13 is divided by x -3 . (5 Marks)
e) The 6th term of an AP is -23 and the 10th term is -35. Find the first term, the common difference, and
the sum of the first 15 terms of the series. (10 Marks)
QUESTION TWO
a) The first, the third and the seventh terms of an increasing arithmetic progression are three
consecutive terms of a geometric progression. If the first term of the arithmetic progression is 10,
find the common difference of the arithmetic progression. (5 Marks)
b) At the beginning of every year, a lady deposited Ksh 10 000 in a financial institution which paid
compound interest at the rate of 20% p.a. She stopped further deposits after three years. The money
remained invested in the institution for a further eight years.
i) How much money did she have at the end of the first three years? (5 Marks)
ii)How much interest did the money generate in the entire period (5 Marks)
2
c) lf
x2 2 x 3 +2 and y= 3 2 find the value of y .
x
+
= - (5 Marks)
QUESTION THREE
a) Rice costs x Kshs for one kilogram. When rice costs Kshs (x -2) for one kilogram, Sindani found
that he can buy 3 Kg more for 1000 kshs. Form an equation in x and solve it to find the original
price of one kilogram of rice. (Give your answer to the nearest 5 cents. (6 Marks)
b) Without using the calculator, find the value of
10 10 10 log 96 + log 12.5- log 12 (4 Marks)
c) Given that log 3 = 0.4771 and log5=0.6990 , evaluate the following without using a calculator:
log135
log 1125
(6 Marks)
d) Solve the equation:
52x+1 = 32-x (4 Marks)
QUESTION FOUR
a) Find two values of ? between 0o and3600 such that Sin ? =0.5 (4 Marks)
b) If 1800 < x < 3600 and cos x= -5
13
, find without using tables, the exact values of sin x and tan x.
(6 Marks)
c) ABC is a triangle whose base BC=35cm. The point X on BC is such that BX=21cm,
AX= 16cm and angle AXB= 600. Calculate
i) the length of AB (3 Marks)
ii)the length of AC (3 Marks)
iii) the size of angle BAC (4 Marks)
QUESTION FIVE
a) In how many ways can a class of 20 children be split into two groups of 8 and 12 respectively if
there are twins in the class who must not be separated? (6 Marks)
b) Determine the probability of having your birthday on a Sunday. (2 Marks)
c) Using the binomial expansion of (1- 2x)10, find the value of 0.9810 correct to five decimal places.`
(6 Marks)
d) Solve for x in the equation 32x-3 ÷ 8x+4 = 64 ÷ 2x (6 Marks)
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