Chapter 6 Metabolism: Energy and Enzymes
Multiple Choice Questions
1. If enzymes could not be used during a reaction, which of the following could be added
to a system to make the reaction occur faster?
A) substrate
B) energy, possibly in the form of heat
Chapter 5 Membrane Structure and Function
Multiple Choice Questions
1. Which of the following is the reason plants wilt on a hot summer day?
A) loss of water
B) lack of turgor pressure
C) heat weakens the plant cell walls
D) both loss of water and therefo
Chapter 43
Student: _
1. All but which of these animals are likely to undergo parthenogenesis?
A. humans
B. flatworms
C. fish
D. lizards
2. Semen contains alkaline secretions for what purpose?
A. Sperm swim better under basic conditions.
B. The female vag
Introduction to Abstract Mathematics
Fall 2013
Assignment 1.1
Due September 6
Exercise 1. Consider Example 2 in the paper by Gale and Shapley that we discussed in
class today.
a. Explain why there are a total of 24 possible sets of marriages.
b. Choose an
Introduction to Abstract Mathematics
Fall 2013
Assignment 3.1
Due September 20
Exercise 1.Express the following statements symbolically, and determine if they are true
or false. You may assume that the universe of discourse is R.
a. For all x 1/4, there i
Introduction to Abstract Mathematics
Fall 2013
Assignment 2.2
Due September 13
Exercise 1. Use a proof by contradiction to show that if n = 2k + 1 for some integer k ,
then n is odd. [Note: While intuitively obvious, this fact does require some kind of pr
Introduction to Abstract Mathematics
Fall 2013
Assignment 2.1
Due September 13
Exercise 1. Let P and Q be statements. Verify the following logical equivalences by either
constructing a truth table or by using established equivalences.
a. P P P P P
=
=
b.
Introduction to Abstract Mathematics
Fall 2013
Assignment 1.2
Due September 6
Exercise 1. Determine the prime constituents of each of the following statements, and use
this to express these statements symbolically.
a. If I am tired or hungry, then I canno
Introduction to Abstract Mathematics
Fall 2013
Assignment 3.2
Due September 20
Exercise 1. Conjecture and prove a formula for the sum of the rst n Fibonacci numbers.
Exercise 2. For n 1, the nth harmonic number is dened to be
n
Hn =
k=1
Prove that for all
Introduction to Abstract Mathematics
Fall 2013
Assignment 4.1
Due September 27
Exercise 1. Let Fn denote the nth Fibonacci number (where, as in class, we set F0 = 0 and
F1 = 1). Prove that for all n 0,
n
n
1+ 5
1
1 5
.
Fn =
2
2
5
Exercise 2.[The Division
Introduction to Abstract Mathematics
Fall 2013
Assignment 5.3
Due October 4
Exercise 1. For each pair (a, b), nd gcd(a, b) as well as x and y so that xa + yb = gcd(a, b).
a. (14, 23)
b. (130, 150)
c. (34, 144)
Exercise 2. Let a, b, c Z. Prove that if a|c,
Introduction to Abstract Mathematics
Fall 2013
Assignment 5.2
Due October 4
Exercise 1. Let a, b, c Z. Prove that if c|a and c|b, then c|xa + yb for every x, y Z.
Exercise 2. Let m, n Z. Prove that if m|n and m|n + 1, then m = 1.
Exercise 3. Show that the
Introduction to Abstract Mathematics
Fall 2013
Exercise 1. In this exercise we will provide another proof that
for the sake of contradiction that 2 is rational.
a. Let p, q N with p/q =
Assignment 5.1
Due October 4
2 is irrational. Assume
2. Show that 0 <
Introduction to Abstract Mathematics
Fall 2013
Assignment 4.2
Due September 27
Exercise 1. Given integers n and k , with 0 k n, the (n, k ) binomial coecient is
n
k
=
n!
,
k !(n k )!
where we dene 0! = 1.
a. Prove that if 1 k n 1, then
n1
n1
+
k1
k
=
n
.
Introduction to Abstract Mathematics
Fall 2013
Assignment 4.3
Due September 27
Exercise 1. What amounts of money can be formed using only $2 and $5 bills? Be sure to
prove your answer is correct!
Exercise 2. Consider an instance of the stable marriage pro
Math 2321 Spring 2009
Calculus III
First Midterm Exam
Friday, February 6
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. You must justify all of your answers to receive credit. Notatio
Math 2321 Spring 2009
Calculus III
Final Exam
Saturday, May 9
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. Except on multiple choice questions, you must justify all of your answers
Math 2321 Spring 2009
Calculus III
Third Midterm Exam
Monday, April 6
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. Except on multiple choice questions, you must justify all of your
Math 2321 Spring 2009
Calculus III
Second Midterm Exam
Wednesday, March 4
Your name (please print):
Instructions: This is a closed book, closed notes exam. Use of calculators is not
permitted. Except on multiple choice questions, you must justify all of y
Calculus III
Spring 2010
Exam 1
Practice Problems
Exercise 1. Consider the following four planes:
P1
P2
P3
P4
:
:
:
:
4x 2y + 2z = 4
5x + 2z = 5
x 4y + 3z = 1
6x + 3y 3z = 6
Which are parallel? Are any of them identical? For those pairs that are not paral
Calculus III
Spring 2010
Exam 3 Practice Problems
Problem 1. Evaluate the following integrals.
xy dA where R is the region bounded by the curves x = y 2 and y = x 2.
a.
R
1
1
b.
1
c.
y
2
yex
dx dy [Hint: Reverse the order of integration.]
x3
x dA where R
Calculus III
Spring 2010
Exam 2
Practice Problems
Exercise 1. Verify that the function z = ln(ex + ey ) satises the partial dierential equation
2z 2z
x2 y 2
2z
xy
2
= 0.
Exercise 2. Explain why the function f (x, y ) = x + e4y is dierentiable at the poi
Calculus I
Fall 2009
Final Exam
Practice Problems 1
Exercise 1. Evaluate the following limits, if they exist.
a.
d.
lim
x0
lim
x
3+x
x
3
x2 + x + 1 + x
Exercise 2. Find
b.
e.
lim e1/x
c.
t2 4
t2 t3 8
f.
x0
lim
lim (2x + |x 3|)
x3
sin
0 + tan
lim
dy
.
dx
Calculus I
Fall 2009
Exam 1
Practice Problems
Exercise 1. Find a formula for a function f whose graph passes through (0, 0), has vertical
asymptotes x = 1 and x = 2 and has horizontal asymptote y = 3.
Exercise 2. Find the limit.
x 2x + 8
b. lim
x 4
x3 4x2
Calculus I
Fall 2007
Exam 1 Practice Problems
1. Find equations for the two lines tangent to the curve
y=
x1
x+1
that have slope 2.
2
2. Let f (x) = ex . Show that there is a c in [0, 1] for which f (c) = 1/2. [Hint: Apply
the Intermediate Value Theorem t
Calculus I
Spring 2008
Exam 1 Practice Problems
1. The function
tan z
sin 2z
is not dened, and therefore not continuous, at z = 0. Is the discontinuity removable?
q (z ) =
2. If f (x) = x3 x2 + x, use the Intermediate Value Property to show that there is
Calculus I
Fall 2009
Final Exam
Practice Problems 2
Exercise 1. Evaluate the integral.
9
a.
1
d.
1
u 2u 2
du
u
2
y (y + 1) dy
b.
5
c.
x
dx
1 + x4
f.
0
1
csc2 x
dx
1 + cot x
e.
0
x
Exercise 2. Find the derivative of y =
1
h0 h
1x
x
2+h
Exercise 3. Find lim
Calculus I
Spring 2008
Final assignment
Instructions: The following exercises constitute the essay portion of the nal exam for Math
1311. You should write up your solutions neatly and carefully, paying particular attention
to explanation of your work in W
Calculus I
Fall 2009
Exam 3
Practice Problems
Exercise 1. A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the
building. What is the length of the shortest ladder that will reach from the ground over the
fence to the wall of t