Math Placement Exam, 1
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MATH PLACEMENT EXAM
NO CALCULATORS
PLEASE CIRCLE YOUR ANSWERS AND WRITE YOUR NAME ON EVERY
PAGE!
Part I: Algebra, Geometry and Logic
1. Evaluate or simplify each of the f
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University of Chicago
Math 203-31,51
Fall 2017
EXAM 2 SOLUTIONS
1. (12 points) True or False. Only answers are needed. Place answers in the grid above
Let (X, d) and (Y, d ) be metric spaces
(a) If f
University of Chicago
Math 203-31,51
Fall 2017
EXAM 2 OUTLINE
General information
(1) Section 31: Exam is Friday, December 8, 10:30-12:30 in Rosenwald Hall 015
(2) Section 51: Exam is Thursday, Decemb
Homework 1
(due on Thursday, Jan 19, 2018) When solving the problems below as well as future
homework problems, please give detailed derivations and arguments in order to receive
credit. In your solut
Calculus Placement Exam
Harris School of Public Policy
September 20, 2010
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Calculus Placement Exam
Harris School of Public Policy
September 19, 2011
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Calculus Placement Exam
Harris School of Public Policy
September 24, 2012
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Calculus Placement Exam
Harris School of Public Policy
September 23, 2013
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Part II. Calculus
1. Consider the function
y = (5 x)1/3
a. What is the domain of the function?
b. What is the image of the function?
c. What is f(x) at x = 13?
d. What is f(x)?
e. What is f(x) at x =
Calculus Placement Exam
Harris School of Public Policy
September 24, 2007
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Calculus Placement Exam
Harris School of Public Policy
September 17, 2007
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Calculus Placement Exam
Harris School of Public Policy
September 22, 2008
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
Calculus Placement Exam
Harris School of Public Policy
September 21, 2009
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue book
University of Chicago
Math 203-31,51
Fall 2017
Homework 6: Due November 6
Note: indicates problems that wont be graded but you are encouraged to do for your own
understanding
1. Let X = (7, 2) cfw_1 c
University of Chicago
Math 203-31,51
Fall 2017
Homework 4: Due October 23
Note: indicates problems that wont be graded but you are encouraged to do for your own
understanding
1. Let k k be a norm on
University of Chicago
Math 203-31,51
Fall 2017
Homework 5: Due October 30
Note: indicates problems that wont be graded but you are encouraged to do for your own
understanding
1. 3.3.12
2. 3.3.22
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[email protected]
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University of Chicago
Math 203-31,51
Fall 2017
Homework 1: Due October 02
Note:
If its been a while since youve taken a proof-based course you might review elementary
proof techniques: induction, con
University of Chicago
Math 203-31,51
Fall 2017
Homework 2: Due October 09
Note:
All numbered problems from Boller and Sally.
indicates problems that wont be graded but you are encouraged to do for y
University of Chicago
Math 203-31,51
Fall 2017
Homework3: Due October 16
Note: indicates problems that wont be graded but you are encouraged to do for your own
understanding
1. Let K R be a compact se
University of Chicago
Math 203-31,51
Fall 2017
Homework 7: Due November 13
Note: indicates problems that wont be graded but you are encouraged to do for your own
understanding
1. Show that the followi
University of Chicago
Math 203-31,51
Fall 2017
Homework 9: Due November 29
1. 3.7.11
2. 3.8.3
(Some obvious polynomials work for (i)
3. Let X be a compact metric space and let A denote the set of all
University of Chicago
Math 203-31,51
Fall 2017
Homework 8: Due November 20
Note: indicates problems that wont be graded but you are encouraged to do for your own
understanding
1. Let X be a set and le
University of Chicago
Math 203-31,51
Fall 2017
EXAM 2 OUTLINE
Format
(1) True or false questions. Focus on definitions, examples, counter-examples, statements of
theorems
(2) Short answers: computatio
University of Chicago
Math 203-31,51
Fall 2017
EXAM 1 OUTLINE
Format
(1) True or false questions. Focus on definitions, examples, counter-examples, statements
of theorems
(2) Short answers: computatio
University of Chicago
Math 203-31,51
Fall 2017
EXAM 1
1. (12 points) True or False. Only answers are needed. Place answers in the grid above
(a) Recall the construction of R as equivalence classes of