TWO PRACTICE MIDTERMS
MATT
1. Practice Midterm 1
Problem 1. Find the area enclosed between the curves y = x2 and y = x2/3 .
Problem 2. Evaluate
y = x.
RR
D (x + y
4 )dA
where D is bounded by y =
5
x and
R 2 R lnx 1
Problem 3. We want to compute 1 0 x(y+1)
Math32B Discussion Section Notes
Jiayin Guo
April 18, 2014
It is a growing note for Math32B. It is designed to be a supplement of what I said in
the discuss session. Thus all the answer will be provided but only some problems will be
given detailed soluti
Math 32B
Practice Final
1. Write down Greenes theorem including all hypothesis and its conclusion. Write down
the denitions of any terms which appear in the theorem.
Solution: See page 1009 in your textbook. Important terms to know are boundary
orientatio
MATH 32B, Section 3 - Practice Midterm One
Name:
Student ID Number:
Instructions:
This is a practice exam for the first midterm examination in MATH 32B. You should
follow the following rules when preparing with this midterm:
1. This exam is meant to be 50
Math 32A Practice Midterm 1
February 5th, 2014
Your name:
Your SID:
There are four problems on this exam, each worth ten points. You have
fifty minutes. Good luck!
1
Problem 1: Consider vectors v = h12, 3, 4i and u = h1, 2, 2i. Find
the projection of u on
Statistics 10
Introduction to Statistical Reasoning
Fall 2013
Instructor: Nathan Langholz
Room and time: MWF 9:00 - 9:50A BUNCHE 1209B
Office: 9432 Boelter Hall
Office Hours: Monday and Wednesday 2:30 to 4:00 or by appointment
Email: [email protected]
Final Exam Sample
Math 32B/2, Spring 2014
This is a collection of problems that would not be unreasonable for a real final exam.
WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample
exam does not guarantee its inclusi
MATH 31B LECTURE 1 AND 3
PRACTICE MIDTERM
1
2
MATH 31B LECTURE 1 AND 3 PRACTICE MIDTERM
Problem 1. (Multiple choice, 10 pts) Evaluate the improper integral
Z 1
1
dx
1 x
Indicate your answer in the box below:
(a) 1; (b) 0; (c) 1; (d) integral diverges; (e)
Midterm Exam 2 Sample
Math 32B/2, Spring 2014
This is a collection of problems that would not be unreasonable for a real midterm exam.
WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample
exam does not guarantee its i
Midterm Exam 1 Sample
Math 32B/2, Spring 2014
This is a collection of problems that would not be unreasonable for a real midterm exam.
WARNING: the inclusion (or exclusion) of a certain topic or type of problem on this sample
exam does not guarantee its i
M IDTERM 1
April 24, 2002
Instructions.
Please show your work. You will receive little or no credit for an answer
not accompanied by appropriate explanations, even if the answer is correct.
If you have a question about a particular problem, please raise y
‘H Willlll
Read all of the following information before starting the ex
0 Check your eiram to make sure all pages are present.
. NO CALCULATORSh—ﬁ
0 Show all work, clearly and in order, if you want to get full credit. I reserve the right to
take off p
lVlIDTERM 1
Math 32B. Lecture 3 (‘2 pm)
Name:
University ID:
Circle your TA’s name:
Josh Keneda Matt Stoffregen Stephanie Lewkiewicz
I certify that all of the work on this exam is my own.
Signature
Directions: The exam has ﬁve questions. No outside
.
-_._.
-_._-
z
r
MATH 32B Midterm I, Fall 2010
I
Names J:.
'
~
,.'
T
TA's Name and Section Number:
10
Qu,nn
fll (J.vf#r'~"'
Problem . (4
Find the trip . egral f f fE zdxdydz. Here E is the solid bounded by the
planes x = 0, y = 0, Z = and 2x + 2y + Z = 2
32B Midterm 1 Solutions
1. Question 1
R x=1 R y=1
4
(a) Compute the following integral: x=0 y=x2/3 xey dydx.
Solution. We change the order of integration to compute the integral as follows:
Z y=1
Z y=1 Z x=y3/2
Z x=1 Z y=1
3/2
4
y4
y4
ey dy
(1/2)[x2 ]x=y
Math 32B, Summer 2016
Sample problems for Midterm
Exercise 1: Let D beRRthe region bounded by the coordinate axes and the line 2x + 3y = 12. Set up the
integral D f (x, y)dA as an iterated integral in the order dxdy and in the order dydx.
2
2
2
2
Exercise
MATH 32B
FIRST MIDTERM EXAMINATION
January, 26th 2009
Please show your work. You will receive little or no credit for a correct answer to a
problem which is not accompanied by sufficient explanations. If you have a question about
any particular problem, p
Math 32B, Lecture 4
Multivariable Calculus
Sample Final Exam
Instructions: You have three hours to complete the exam. There are ten problems, worth a
total of one hundred points. You may not use any books, notes, or calculators. Show all your
Work; partia
Math 32B, Lecture 4
Multivariable Calculus
Sample Final Exam
Instructions: You have three hours to complete the exam. There are ten problems, worth a
total of one hundred points. You may not use any books, notes, or calculators. Show all your
work; partia
1. (10 pts) Suppose a wire is wound along a cone in such a way that its
path is described by
~r(t) = ht2 , t cos t, t sin ti,
1t4
If the charge density (per unit length) along the wire is given by
y2 + z2
(x, y, z) = ,
x
find the total charge in the wire.
W. Conley
Math 32B, Lecture 1
Wed, Nov 18, 2015
Midterm 2
Last Name:
First Name:
Student ID:
Signature:
Section:
Tuesday:
Thursday:
1A
1B
TA: Zach Norwood
1C
1D
TA: Eric Auld
1E
1F
TA: Trent Hinkle
Instructions: Do not open this exam until instructed to d
W. Conley
Math 32B, Lecture 1
Mon, Oct 26, 2015
Midterm 1
Last Name:
First Name:
Student ID:
Signature:
Section:
Tuesday:
Thursday:
1A
1B
TA: Zach Norwood
1C
1D
TA: Eric Auld
1E
1F
TA: Trent Hinkle
Instructions: Do not open this exam until instructed to d
6m
and 0 S :1: S Electric charge has accumulated on this surface so that
TM, A urns/1&5,
. E
1. (10 pomts) Lets:F 8 be the part of the cone x = 2x/y2 + 22 Where g 2 0
\ , ; j,
5 a /‘ y
2n"
at
ta
/
its charge density (per unit area) at each point is
What
W. Conley
Math 32B, Lecture 3
Fri, Apr 25, 2014
Midterm 1
Last Name:
First Name:
Student ID:
Signature:
Section:
Tuesday:
Thursday:
3A
3B
TA: Ioannis Lagkas-Nikolos
3C
3D
TA: Fei Xie
3E
3F
TA: Sangchul Lee
Instructions: Do not open this exam until instruc
1. (10 points) Consider the curve C parametrized by
rot):(t~2)i+(t2—5)j+m/t—1k, 23t<5.
Compute the line integral / F - dr Where
C
1+ :32, zsin(yz) + 2xy,1n(1 + £132) + ysin(yz)>.
5 w,
F(w,y,z) = <y2 +
k W,
/ \ ' I , /
I x I x V 2/ l V LY /,yr17)/Tf* ,_
1. (10 points) Compute the following, in any way you like. (Hint: Draw a
picture!)
\/§ m g «4:;
/ / 3,12 dy dx + / /
' 7
9/1 ”2/ f ‘
\ ’1‘ 5 W 43 an 5);];
1‘ 51mm; m.
k it” ‘ 3 ‘ I ‘
C29 «m
y2dydm+f / y dydm
_\/§ -—:1;
\1r
k
fry/)1 /7(Qﬂ/g(~/:W/Jxﬂ/ﬂ
1. (10 pts) Suppose a Wire is wound along a cone in such a way that its
path is described by
77(16): (t2,tcost,tsint>, 1 < t < 4
If the Charge density (per unit length) along the Wire is given by
y2+z2
pt’ww): ﬂ ,
find the total Charge in the Wire.
WW “
Part 1: Short Answer Problems (Worth 48%)
For full credit you need to show all your work. .
1. [12%] Refer to the ﬁgure below. The vertical distance between points A and B
represents a tax in the market.
051152253354455 9man
a. Find the Ber-unitﬂrden of