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QUEENS UNIVERSITY FINAL EXAMINATION
FACULTY OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 126 ANDREW MCBACHERN
December 18, 2015
INSTRUCTIONS TO STUDENTS:
This examina
MATH 111 April Exam Preparation Solutions
MATH 111 FINAL EXAMINATION PREPARATION SOLUTIONS
page 1 of 34 pages
APR 2015
1. This is a multi-part question with short answer parts.
1 2
(a) For the matrix A =
find the eigenvalues and for each of these find a
MATH 111 Midyear exam preparation Dec. 2013
MATH 111
page 1
MIDYEAR EXAM PREPARATION
DEC 2013
1. For this question, only the answer will be marked. 2 marks for each
3 2
(a) Find the inverse of the matrix
.
2 1
3 2 1 a
(b) Calculate the matrix product
Math 111 2013-14
Assignment 8 Solutions
Due ThursdayMarch 6, 2014
1. By calculating the first few cases, find a simple expression for the sum:
Sn = 11! + 22! + 33! + nn! .
[Hint: they grow like factorials so calculate the quantities 1!, 2!, 3!, 4!, 5!, 6!
Math 111 2013-14
Assignment 6 Solutions
Due Thursday Jan 23, 2014
1. Find a formula for the nth term of the sequence defined by the third-order recursion
tn+2 = 3tn+1 + 6tn 8tn1
with initial values t0 = 3, t1 = t2 = 6 . Check that your answer works for t3
Math 111 2013-14
Assignment 7 Solutions
Due Thursday Feb 6, 2014
1. Find the solution to the dynamical system:
xn 1 1 2 1 xn
y 2 1 1 y
n 1
n
zn 1 3 0 1 zn
x0 0
y 1
0
z0 0
Note that you already found the eigenvalues and the eigenvectors in A
Math 111
Assignment 3
1. The (u, v, y) data points at the right have been observed:
It is desired to fit a regression model of the form
y = u + v.
Find the least squares value of = . Calculate and display
the residual vector and use it to check your a
Math 111
Assignment 9
Due Thursday March 20 2014
1. Consider a population in which individuals progress through three
stages: juvenile X, subadult Y and adult Z. Suppose that each year
juveniles survive with probability p and become subadults, subadults
s
Math 111
Assignment 4
Due Thursday Nov. 14, 2013
1. This problem concerns the code based on the 31-hat game. Here the message should be decomposed
into blocks of length 315 = 26. Suppose that one of the blocks in the starting message has eight 0s
followed
Math 111 2013-14
Assignment 7
Due Thursday Feb 6, 2014
1. Find the solution to the dynamical system:
xn 1 1 2 1 xn
y 2 1 1 y
n 1
n
zn 1 3 0 1 zn
x0 0
y 1
0
z0 0
Note that you already found the eigenvalues and the eigenvectors in Assign 6. T
Math 111
Assignment 10
Due Thursday April 3rd 2014
1. Find the nine 9th roots of 512i. Those that can be expressed simply in terms of a square root
should be rewritten that way. Display these roots on a complex plane diagram.
2. Calculate ( 3 i )100. Expr
Math 111 2013-14
Assignment 6
Due Thursday Jan 23, 2014
Dont forget! To get marks for this, you must put at the top of page 1, a score between 0 and 10 which is
a composite estimate of the quality of your work and the effort you put into the assignment. Y
Math 111 2013-14
Assignment 8
Due ThursdayMarch 6, 2014
k
1
2
3
4
5
6
1. By calculating the first few cases, find a simple expression for the sum:
Sn = 11! + 22! + 33! + nn! .
[Hint: they grow like factorials so calculate the quantities 1!, 2!, 3!, 4!, 5!
Math 111
Assignment 1
Due Thursday Sept. 26 2013
1. Consider the system: Au = k where A = [p q r]:
3
1 2 r u
2 1 4 v = k .
2
1 1 1 w
In terms of the two unknown parameters r and k, how many solutions [u, v, w] does the system
have? This is similar
Math 111 2013-14
Assignment 5
Due Thursday Nov. 28, 2013
1. Decompose the transformation pictured below as
(a) a rotation about the origin followed by a translation
(b) a translation followed by a rotation about the origin
(c) a rotation about a point dif
Math 111 2013-14
Assignment 2
Due Thursday Oct. 10.
1. Find an equation in normal form ax + by + cz = d for the plane P that passes through the point
(1, 0, 1) and contains the line (x, y, z) = (1t, t, 2).
2. Find the shortest distance between the lines (
Camille Pennell
Assignment Week 02 due 09/23/2016 at 09:04pm EDT
MATH 126
y-intercept:
Problem 1. 1. (1 point) Solve x2 2x = 24 by factoring,
completing the square, or the quadratic formula. If there is more
than one correct answer, enter your answers as
Joshua Yale
Assignment Practice for April Final due 04/10/2017 at 08:59am EDT
Problem 4. 4. (1 point) Evaluate the definite integral.
Problem 1. 1. (1 point) Use the Table of Integrals in the
back of your textbook to evaluate the integral.
Z
MATH 126
Z 12
MATH 111 Complete Notes
Winter 2017
Chapter 5
Games and State Transitions
6
5
4
1
2
3
50 Series
51 Board Games
52 Reproduction
53 Complex Numbers
54 Complex Systems
MATH 111 Chapter 5C 2016-17 (revised March2017)
1
50C Series
Series: general concepts
An i
Math 111
Assignment 5 Solutions
Due Tuesday Nov. 17, 2016
1. The linear transformation T: R 2 R 2 is pictured at the right.
The starting box is a square with sides x=1 and y=1. The
image is a parallelogram with corners at (2, 3/2), (0, 3/2),
(2, 3/2), (0,
Math 111 2016-17
Assignment 8 Solutions
Due Thursday Feb 9, 2017
1. Find the solution to the dynamical system:
xn 1 1 2 1 xn
y 2 1 1 y
n 1
n
zn 1 3 0 1 zn
x0 0
y 1
0
z0 0
Note that you already found the eigenvalues and the eigenvectors in A
Math 111 2016-17
Assignment 7 Solutions
Due Thursday Jan 26, 2017
The last two questions were hard! Kudos to those who managed to get them.
1. Find a formula for the nth term of the sequence defined by the third-order recursion
tn+2 = tn+1 + 10tn + 8tn1
w
Math 111 2016-17
Assignment 9 Solutions
Due Thursday March 9, 2017
1. By calculating the first few cases, find a simple expression for the sum:
Sn = 11! + 22! + 33! + nn! .
[Hint: they grow like factorials so calculate the quantities 1!, 2!, 3!, 4!, 5!, 6
_
NAME: LAST
FIRST
Math 111
_
Student #
Test 5 Solutions
March 2 2017
There are 4 questions worth a total of 20 marks.
1. [9 marks] The sequence xn is tabulated at the right. It follows the rule that
each term is the sum of the previous two. We are intere
Page 1 of 4 pages
MATH 111 Test 4 Solutions Feb 2 2017
_
NAME: LAST
Math 111
FIRST
_
Student #
Test 4 Solutions
Feb 2 2017
There are 4 questions on 4 pages each worth 5 marks. Answer in the space provided. If you
need extra space advise the marker where t
Geometric interpretation of the product.
(a) What happens in the diagram when we multiply two complex
numbers z and w? Write them in polar form. Use r and s for their
moduli and (theta) and (phi) for their arguments:
z = r(cos + isin)
w = s(cos + isin)
Th