Question 1
(a) A given number in base x can be converted to any other base y. According to the expansion method, if abc.de is any given number in base x, then
write its value in base 10. [3]
(b) Convert the following numbers using number system conversions, show
your answer in details: [6]
i. (723)8 to hexa decimal system
ii. (0.ABDF )16to decimal system iii.Convert 0.375 to binary system
iv. Which digits from (0,1,2,3,4,5) are not allowed in Quinary system (base 5) representation.
v. (11010.1011)2 to hexadecimal.
vi. (257)10 to the binary system.
(c) Consider the binary number 10.0011 [4] i.Convert the above number to the decimal system
ii. What are the place values of the digits 1 in the number 0.00112
iii. what is the sum of (1+1+1+1) in binary system iv.calculate 101 divided by 10 using long division.
(d) Which one is the correct representation of a binary number from the following? [2]
i. 1101
ii. (214)2
iii. (0000)2
iv. (11)2
Question 2
(a) Is an = 3n+2 a general term of a sequence? Why? [2]
n−4
(b) Which term of the sequence with general term 3n−1 is 7 ? [2]
5n+7 12
(c) An arithmetic sequence has its 4th term equal to 18 and its 12th term equal to 50. Find its 99th term. [4]
(d) State whether the following sequences are arithmetic, geometric or not any of them. Find the common ratio if it is a geometric sequence and find the common difference d if it is an arithmetic sequence. Then, find the
next two terms. [6]
i. −3, 3, −3, 3
ii. bn = n2 + 3
iii. −1 , −5 , −7
2 6 6
(e) Consider the geometric sequence (bn) with b1 = 1 and q = 3. Is 243 a
term of this sequence? [3]
(f) The nineteenth term of a sequence is -52, and the fourth term is -7. The difference between consecutive terms in the sequence is constant. Find
the 201st term. [3]
(g) Show whether the following sequence is convergent or divergent.
limn→∞(n−1 ) [2]
(h) Is the following numbers 1,-4,9,-16,... represent a sequence, if so, find a formula for the nth term of the sequence.
(i) Show by mathematical induction that for all positive integers n,
1 + 1 + ... + 1 = 1 − 1
(j) Find the remainder when 3123 is divided by 7. [2]
Question 3
(a) State whether the following statements are false or true, explain your answer: [6]
i. Given any integers a, b, c and any positive integer n
If a ≡ b (mod n) and b ≡ c(mod n), then a ≡ c(mod n). ii.Suppose a ≡ b(mod n) and c ≡ d(mod n),then
a + c ≡ b + c(mod n).
iii. 7x ≡ 12(mod 7).
(b) Find the least positive value of x such that:
71 ≡ x (mod 8) [3]
(c) Calculate the multiplicative inverse of 168 in modulo 83. [3]
(d) Calculate the inverse of 4 modulo 15. Show your steps. [3]
Question 4
(a) A triangle has sides a = 2 and b = 3 and angle C = 60.
Find [4]
i. the length of side c.
ii. Find the sine of angle B using sine rules.
(b) If we have a triangle which has one of its side c = 2 and angles A = π/4
and B = π/3. Workout the length a of the side opposite A. [4]
(c) XY Z is a right angled triangle with Y = 90◦. Given that y = 85, sin X = 77 ,
find z, Cos(Z) and the angle of Z. [6]
(d) Let g be a function with its domain (0, ∞), defined by g(x) = 1 . [6]
i. Sketch the graph of g.
ii. Is g continuous at other points of its domain?
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
