BSc(Hons.) Business Information Systems
Cohort: BIS/11/FT
Resit Examinations for 2013 – 2014 /
Semester 2
MODULE: FUNDAMENTAL MATHEMATICS
MODULE CODE: MATH1106
Duration: 2 ½ Hours
Instructions to Candidates:
1.
Answer all questions.
2.
Questions may be answered in any order but your answers must
show the question number clearly.
3.
Always start a new question on a fresh page.
4.
All questions carry equal marks.
5.
Total marks 100.
This question paper contains 4 questions and 3 pages.
Page 1 of 3
Fundamental Mathematics (MATH1106)
SITE/VK 2013-2014 S2
ANSWER ALL QUESTIONS
QUESTION 1: (25 MARKS)
(a) Simplify
i) i39
(2 Marks)
ii) i-149
(4 Marks)
(b) Find the square root of -6+8i.
(10 Marks)
(c) Express 3+i in polar form.
(3 Marks)
(d) Using De Moivre’s Theorem prove
(6 Marks)
(cos 3 +isin3 )6/(cos2 +isin2 )5 = cos8 +isin8
QUESTION 2: (25 MARKS)
(a) By showing all your workings, convert the decimal number 34 to
i) Base 2 (binary)
(3 Marks)
ii) Base 8 (Octal)
(3 Marks)
iii) Base 16 (Hexadecimal)
(3 Marks)
(b) By showing all you workings, convert
i) (1001101110)2 to base 10.
(4 Marks)
ii) (2107)8 to base 10.
(4 Marks)
iii) (10AC)16 to base 10.
(4 Marks)
(c) Convert 0.6875 to binary.
(4 Marks)
QUESTION 3: (25 MARKS)
(a) Prove
i) x+xy+yz=(x+y)(x+z)
(3 Marks)
ii) (x+y)(x’+z)(y+z)=(x+y)(x’+z)
(4 Marks)
Page 2 of 3
Fundamental Mathematics (MATH1106)
SITE/VK 2013-2014 S2
(b) Simplify the Boolean expression ABC+A’B’C+A’BC+ABC’+A’B’C’ without
using Karnaugh Map.
(5 Marks)
(c) Using Karnaugh Map simplify the Boolean expression
F=w’x’y’z’+w’x’y’z+w’x’yz’+w’xy’z’+w’xy’z+w’xyz’+wx’y’z’+wx’y’z+wxy’z’+wxy’z
+wxyz’
(5 Marks)
(d) Given the Boolean function F=x’y+xy’
i) Implement F using AND, OR and NOT gates.
(3 Marks)
ii) Implement F using only NAND and NOT gates.
(5 Marks)
QUESTION 4: (25 MARKS)
(a) Compute
2
3
i3j2
i=0
j=0
(5 Marks)
(b) Solve
2x+3
1
1
x
3
3
x-1
1
-1
=0
(7 Marks)
(c) Using Gaussian Elimination Method solve the following equations
x1 + x2 + x3 =4
x1 + 2x2 + 3x3 = 9
2x1 + 3x2 + x3 = 7
(13 Marks)
****END OF QUESTION PAPER***
Page 3 of 3
Fundamental Mathematics (MATH1106)
SITE/VK 2013-2014 S2