BSc (Hons) Computer Science with Network
Security
BSc (Hons) Business Information Systems
Cohort: BCNS/11B/FT & BIS/11/FT
Special Resit Examinations for September
2014
MODULE: FUNDAMENTAL MATHEMATICS
MODULE CODE: MATH1106
Duration: 2 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 do not carry equal marks.
5.
Show all your workings.
6.
Total marks 100.
This question paper contains 4 questions and 3 pages.
Page 1 of 3
Fundamental Mathematics (MATH1106)
SITE/September Resit
ANSWER ALL QUESTIONS
QUESTION 1: (25 MARKS)
(a) Simplify
i) i318
(2 Marks)
ii) i-1139
(4 Marks)
(b) Find the square root of 3+4i.
(10 Marks)
(c) Express 3+4i in polar form.
(3 Marks)
(d) Using De Moivre’s Theorem prove that
(6 Marks)
(cos 3 +isin3 )5/(cos2 +isin2 )4 = cos7 +isin7 .
QUESTION 2: (25 MARKS)
(a) Convert the decimal number 134 to base 2 (binary).
(3 Marks)
(b) Convert the decimal number 1024 to base 8 (Octal).
(3 Marks)
(c) Convert the decimal number 4096 to base 16 (Hexadecimal).
(3 Marks)
(d) Convert (101101110)2 to base 10.
(4 Marks)
(e) Convert (562107)8 to base 10.
(4 Marks)
(f) Convert (FD10AC)16 to base 10.
(4 Marks)
(g) Convert 0.6875 to binary.
(4 Marks)
QUESTION 3: (40 MARKS)
(a) Implement the NOT, AND, OR and NOR functions using only NAND gates.
(6 Marks)
(b) Implement the NOT, OR, AND and NAND functions using only NOR gates.
(6 Marks)
(c) Design a logic circuit, using NAND gates having not more than three inputs for
the given boolean expression Z = A’ + B’ + C + D’
(5 Marks)
(d) Given the boolean expression T = (P + Q’)(R’ + S), use a truth table to list all
possible values of T.
(6 Marks)
Page 2 of 3
Fundamental Mathematics (MATH1106)
SITE/September Resit
(e) Without using the Karnaugh map, simplify the expression
(5 Marks)
(f) Simplify the expression D = X’YZ’ +X’Y’Z +XYZ’ +XY’Z using the Karnaugh
map.
(5 Marks)
(g) Prove
i) x+xy+yz=(x+y)(x+z)
(3 Marks)
ii)
(4 Marks)
(x+y)(x’+z)(y+z)=(x+y)(x’+z)
QUESTION 4: (10 MARKS)
(a) Compute
2
3
i2j2
i=0
j=0
(5 Marks)
(b) Solve
4x+3
2
1
X
3
4
2x-1
1
-1
= 0.
(5 Marks)
****END OF QUESTION PAPER***
Page 3 of 3
Fundamental Mathematics (MATH1106)
SITE/September Resit