**UNIVERSITY EXAMINATIONS 2017/2018**

**ORDINARY EXAMINATION FOR BACHELOR OF SCIENCE IN **

**INFORMATION TECHNOLOGY **

**BIT1110 MATHEMATICS FOR SCIENCE**

**BCU 102: FOUNDATIONS OF MATHEMATICS**

**BCT 1103: MATHEMATICS FOR ENGINEERS**

**BAC 1103: COMPUTING MATHEMATICS**

**(DAY/EVENING)**

**DATE: APRIL, 2018 TIME: 2 HOURS**

**INSTRUCTIONS: Answer question ONE and Any other TWO questions**

**QUESTION ONE: 30 MARKS (COMPULSORY)**

a) Answer the following questions

i. State the remainder theorem

c) Four men and their wives sit on a bench. In how many ways can they be arranged if

i. There is no restriction 3 Marks

ii. Each man sits next to his wife 3 Marks

a) Find the third, tenth, twenty-first and nth terms of the A.P. with first term being 6 and

common difference 5. 4 Marks

d) Evaluate 2 sin 15o cos 15o 3 Marks

e) If you deposit KES 5000 into an account paying 6% annual interest compounded monthly,

how long until there is KES 8000 in the account? 4 Marks

f) Proof that 2 sin 0=1

2 Marks

**QUESTION TWO: 20 MARKS**

**QUESTION THREE: 20 MARKS**

**QUESTION FOUR: 20 MARKS**

a) In an AP, the 13th term is 27, and the 10th term is three times the second term. Find the first

term, the common difference and the sum of the first ten terms 5 Marks

b) Find the third, tenth, twenty-first and nth terms of the G.P. which begins 3+6+…….

5 Marks

c) Triangle PQR, r = 5.75 and the sizes of angles P and Q are 42o

and 65o

respectively.

Calculate the length of PR 5Marks

d) In triangle PQR, QR = 3.5, RP = 4 and PQ = 5. Calculate the size of angle P and hence the

area of the triangle 5 Marks

**QUESTION FIVE: 20 MARKS**

a) On the graph paper provided plot the following graphs

a) Write 40 X 39 X 38 X 37 in factorial notation 3Marks

b) How many even numbers, greater than 2000, can be formed with the digits 1, 2, 4, 8, if each

digit may be used only once in each number? Explain your arguments. 4 Marks

c) Giving their forms, define the following terms 3 Marks

i. Irrational number

ii. Quadratic equation

iii. Polynomial expression