# DIT 107 MATHEMATICS FOR SCIENCE.

UNIVERSITY EXAMINATIONS: 2015/2016
EXAMINATION FOR THE DIPLOMA IN BUSINESS/ INFORMATION
TECHNOLOGY
DIT 107 MATHEMATICS FOR SCIENCE
DATE: AUGUST 2016 TIME: 1½HOURS

QUESTION ONE
a) The sums of the 5th and 13th terms of an Arithmetic Progress are 21 and 37 respectively.
Determine:
i) The 40th term. (3 Marks)
ii) The sum of the 29th term. (3 Marks)
b) For the sequence -2, ½, -1/8 ……
Find:
i) The sum to the 18th term. (4 Marks)
ii) The sum to infinity. (4 Marks)
c) The expression x
3 + ax − 2x − 4 divisible exactly by(x + 1). Find
the value of a and the remainder when the expression in divided by
(x + 2). (6 Marks)
QUESTION TWO
a) Simplify the following expressions by rationalization

QUESTION THREE
a) i) Using the long division method, find the remainder when the function

ii) Using the remainder theorem, confirm your solution in b (i) above. (5 Marks)
iii) From your result in a) i), state whether (x + 1) in a factor of f (x) (1 Mark)
b) Convert the recurring decimal 0.72 to its simplest fraction

QUESTION FOUR
a) By using the appropriate formula method, determine the roots to the quadratic function

ii) Expand the following expression using the binomial theorem

QUESTION FIVE
a) State any three measurements of statistical variation (4 Marks)
b) Distinguish between
i) Qualitative and quantitative variables (2 Marks)
ii) Discrete and continuous data. (2 Marks)
c) Find the mean, the mode and the median for the following grouped
data distribution

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