Additional Exercises before Midterm 1
1. Let S be the statement:
Every integer that is a multiple of 3 is an even number.
Complete the following sentences.
(a) S is a false
(TRUE or FALSE) statement.
(b) The converse of the statement S is:
every interger
Review Guide for Midterm 1
Friday, February 3, 2017, 5:30 6:50 p.m.
Location and exam room splits
1E1 (Arts Building) : Last names starting with A K
N1001 (Science Building): Last names starting with L S
N1002 (Science Building): Last names starting with
MA121 Mock Test 1
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the midterm based solely on the topics covered by the mock
test! Go back through
Solutions of Additional Exercises before Midterm 1 (Part 2)
2 Given simple statements:
p : The integer n = 3k, where k Z;
q : The integer n = 2m, where m Z.
(a) Write the logical compound statement that underlies the mathematical statement S of
Problem 1
Winter 2017
MA121 Recommended Problems
(Part 1)
The following exercises are assigned from the course package:
B. Secord, S.J. Stack, D.C. Vaughan, T. Balfour and P. Zhang: Logic and Algebra, The 3rd Edition
(Winter 2017)
1.2
1.4
1.5
1.6
#1(a, c, d, f, h,
MA121 Mock Test 1
Answers
(Full Solutions will NOT be posted;
use the MACs drop-in help centre if you have any questions.)
* Please remember that the mock test was meant as a means of providing an extra set of practice
questions and basis for a review cla
Hanyu Deng
Assignment Assignment 4 F16 due 10/12/2016 at 11:59pm EDT
MA121 F16
2. (1 pt)
Let the universe of discourse for each variable be the set of
real numbers. Determine if each statement is True (T ) or False
No odd integer can be expressed as the s
Hanyu Deng
Assignment Assignment 8 F16 due 11/10/2016 at 11:59pm EST
1. (1 pt) Prove the following using the definition of
n+3
n+2
n+2
k = k1 + k .
(correct)
n
k .
Correct Answers:
Proof:
RS =
n+2
n+2
k1 + k =
MA121 F16
? = ? = ? = ? = ? = ? = LS
Q.E.D.
1
Hanyu Deng
Assignment Assignment 3 F16 due 10/05/2016 at 11:59pm EDT
1. (1 pt) If x > 4 then x2 + 3x + 9 > 29.
Proof:
x > 4, so x2 > .
x > 4, so 3x > .
+ > , which implies
Hence
Therefore, x2 + 3x + 9 > 29.
+
+
>
A. (2s + 1)(2r + 1)
G. 2(2rs)
B. n = 2r
H.
Hanyu Deng
Assignment Assignment 9 F16 due 11/17/2016 at 11:59pm EST
MA121 F16
Thus n3 n = 3(9q3 + 9q2 r + 3qr2 q + k), and so ? .
1. (1 pt) Use the Euclidean Algorithm to determine each of
the following:
a) gcd(96, 120) =
b) gcd(37800, 132) =
c) gcd(6300
Hanyu Deng
Assignment Assignment 10 F16 due 11/24/2016 at 11:59pm EST
1. (1 pt) Let a = 130 and b = 50.
(a) Using the Euclidean Algorithm, find GCD(130, 50).
130 = ( )( )+
= ( )( )+
= ( )( )+
= ( )( )+
GCD(130, 50) =
.
(b) By using the Euclidean Algorithm
Hanyu Deng
Assignment Assignment 2 F16 due 09/28/2016 at 11:59pm EDT
3. (1 pt) Determine whether the following statements are
equivalent. Choose True if they are equivalent or False if not.
1. (1 pt)
Enter T for each true proposition, F for each false pro
Hanyu Deng
Assignment Assignment 5 F16 due 10/20/2016 at 11:59pm EDT
1. (1 pt) Prove the following statement using mathematical
induction.
If n N, then 8n 3n is divisible by 5.
Proof by Induction:
? ? ? ? ? ? ? ? ? ? ? ? ? ?
Q.E.D.
I
L
C
A
N
D
B
H
F
J
M
2
Hanyu Deng
Assignment Assignment 12 F16 due 12/08/2016 at 11:59pm EST
MA121 F16
(incorrect)
1. (1 pt) Let u = 4cis and w = 7cis . Evaluate the follow6
4
ing expression, stating your answer in polar form, such that the
argument satisfies 0 < 2.
uw2 =
cis .
Hanyu Deng
Assignment Assignment 7 F16 due 11/04/2016 at 12:59am EDT
MA121 F16
3. (1 pt) A pianist plans to play 5 different pieces at a
recital. In how many ways can she arrange these pieces in the
program?
1. (1 pt) Determine if each of the following fu
Hanyu Deng
Assignment Assignment 1 F16 due 09/21/2016 at 11:59pm EDT
MA121 F16
Answer(s) submitted:
1. (1 pt) Suppose that A = cfw_2, 4, 6, B = cfw_2, 6,C = cfw_4, 6
and D = cfw_4, 6, 8.
(incorrect)
Correct Answers:
For each of the following, state which,
Fall Term, 2016
First Name:
Surname:
Section: A
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
MA 122 Introductory Linear Algebra
Midterm September 29, 2016
SOLUTIONS
Instructors:
Time Allowed: 80 minutes
Total Value: 90 marks
Number of Pages: 6 plus cover
Winter Term, 2017
Name:
Last (Family) Name:
Section:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 121 Introduction to Mathematical Proofs
Midterm 1 February 3, 2017
Instructors:
Dr. P. Zhang: Section C - 10:00 am (BA110)
Dr. R. Rundle: Section
MA170 Mock Final Exam
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the exam based solely on the topics covered by the mock
test! Go back through
MA122 Mock Final Exam
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the exam based solely on the topics covered by the mock
test! Go back through
MA121 Midterm 2 Page 1 of 4
Student Number:
cfw_I0 marks] 1. Consider the following data among 110 students in the MA121 class:
30 students are also taking MA122
35 students are also taking MA103
20 students are taking both MA122 and MA103
(a) Fill the
Fall Term, 2014
Name: 5!; ( Wk: 5
Section:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 122 Introductory Linear Algebra
Midterm October 22, 2014
Instructors:
Section A n 1:30 pm MWF -. S. Bauman
Section B 4:00 pm TR S. Bauman
Section C w 8:30
MA170 Mock Exam
Answers
(Full Solutions will NOT be posted;
use the MACs drop-in help centre if you have any questions.)
* Please remember that the mock test was meant as a means of providing an extra set of practice
questions and basis for a review class
MA104 Mock Final Exam
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the exam based solely on the topics covered by the mock
test! Go back through
Chapter 2
Investing and Financing Decisions
and the Statement of Financial
Position
Chapter Overview
Overview of accounting concepts Conceptual Framework.
Business activities (transactions) affecting:
Types of transactions:
Balance Sheet (Ch. 2)
Income St
Additional Exercises for Sections 4.1 and 4.2
SOLUTIONS
1. (a) Find all complex numbers z such that |z| = 3 and z + z = 0.
Solution. Let z = a + bi. The identity z + z = 0 implies that 2a = (a + bi) + (a bi) = 0. So
a = 0.
|z| = a2 + b2 = 02 + b2 = |b| =
[10 marks] 1. Consider the following data among 110 students in the MA121 class:
30 students are also taking MA122
35 students are also taking MA103
20 students are taking both MA122 and MA103
(a) Fill the blanks:
Let U be the set that consists of student
Questions from an earlier final paper of MA121
1. Let a, b be integers and n be a positive integer. Let d = gcd(a, b).
Given simple statements
p:
n|a ;
q:
n|b ;
r:
d|n .
(a) Use the simple statements p, q and r to compose a quantified
statement in proposi