# BIT 1110, BCU 102, BAC 1103, BCT 1103   MATHEMATICS FOR SCIENCE, FOUNDATION MATHS, COMPUTING MATHS, MATHS FOR ENGINEERS.

UNIVERSITY EXAMINATIONS: 2018/2019
ORDINARY EXAMINATION FOR BSc. IT, BBIT, BAC, BSD, BISF
BIT 1110, BCU 102, BAC 1103, BCT 1103: MATHEMATICS FOR SCIENCE,
FOUNDATION MATHS, COMPUTING MATHS, MATHS FOR ENGINEERS
(DAY/EVENING)
DATE: AUGUST, 2019 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and Any other two questions

QUESTION ONE
(a) Eight boys and two girls sit on a bench. If the girls may sit neither at the ends nor together, in
how many ways can they be arranged? [5 Marks]
(b) In how many ways can a committee of nine be formed from ten men and their wives if no
husband serves on it with his wife [5 Marks]
(c) The expression ??
2 + ?? + ? is divisible by ? − 1, has a remainder 2 when divided by
? + 1 and a remainder of 8 when divided by ? − 2 . Find the values of ?, ? ??? ? [5 Marks]
(d) Rationalize the denominators

iv) Solve the equation: 1 + cos θ = 2 sin2θ for all values of θ between 0° and 360° [1 Mark]
Total [30 Marks]
QUESTION TWO
(a) Write down the first four terms of the expansions of the following in ascending powers of x

(d) A man travelling along a straight level road in the direction of 053º observes a pylon on a
bearing of 037 º. 800m further along the road the bearing of the pylon is 296 º. Calculate the distance
of the pylon from the road [4 Marks]
(e) A circle of radius r is drawn with its centre on the circumference of another circle of radius r.
show that the area common to both circles is

[4 Marks]
Total [20 Marks]
QUESTION THREE
(a) The roots of the equation 2x

QUESTION FOUR
a) Prove by induction that 1

QUESTION FIVE
(a) If S = sinθ, Simplify:

Total [20 Marks]

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