**KCA UNIVERSITY**

**FACULTY OF COMPUTING AND INFORMATION MANAGEMENT**

**BACHELOR OF SCIENCE IN TECHNOLOGY **

**BACHELOR OF BUSINESS INFORMATION TECHNOLOGY**

**BACHELOR OF APPLIED COMPUTING **

**BACHELOR OF INFORMATION AND COMMUNICATION TECHNOLOGY **

**BIT 1110: MATHEMATICS FOR SCIENCE EXAMINATION**

**BCU 102: FOUNDATION OF MATHEMATICS **

**BAC 1103: COMPUTING MATHEMATICS**

**BCT 1103: MATHEMATICS FOR ENGINEERS **

**FULLTIME/PARTTIME/DISTANCE LEARNING**

**DATE: DECEMBER 2018 TIME: 2 HOURS**

**Instructions: Answer Question One and Any Other Two Questions**

**QUESTION 1: 30 MARKS (COMPULSORY)**

**QUESTION 2: 20 MARKS**

a) The sum of the second and fourth terms of an AP is 15, and the sum of the fifth and the sixth

terms is 25. Find the first term and the common difference 4 Marks

b) The first term of a GP is 16 and the fifth term is 9. What is the value of the seventh term?

4 Marks

**QUESTION 4: 20 MARKS**

a) 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

b) Write down the sum and product of the root in the following equation 3×2 + 9x + 7 = 0

**QUESTION 5: 20 MARKS**

a) Find the sum of the following series 𝟑 + 𝟓 + 𝟕 … … . + (𝟐𝒏 + 𝟏) 4 Marks

b) Expand (2-x)6

in ascending powers of x. Taking x = 0.002, and using the first three terms of

the expansion, find the value of (1.998)6 as accurately as you can. Examine the fourth term of

the expansion to find how many places of decimals your answer is correct. 4 Marks

b) Write 40 X 39 X 38 X 37 in factorial notation 2 Marks

c) How many ways can the letters of the word BISIEGE be arranged 4 Marks

b) Answer the following questions

i. State the remainder theorem 1 Mark

ii. Using the long division method divide x

5

– 4x

3 + 2x + 3 by x – 1 2 Marks

iii. Using the remainder theorem confirm indeed that the remainder of x

5

– 4×3 + 2x + 3

divided by x – 1 is indeed 2