Math 107: Calculus II, Spring 2015: Midterm Exam II Monday, April Give your name, TA and section number:
|
|
- Hope Morris
- 5 years ago
- Views:
Transcription
1 Math 7: Calculus II, Spring 25: Midterm Exam II Monda, April 3 25 Give our name, TA and section number: Name: TA: Section number:. There are 5 questions for a total of points. The value of each part of each question is stated. 2. Do not open our booklet until told to begin. The exam will be 5 minutes long. 3. You ma not use phones, calculators, books, notes or an other paper. Write all our answers on this booklet. If ou need more space, ou can use the back of the pages. 4. Unless specified otherwise, ou must show ALL our working and explain our answers clearl to obtain full credit! 5. Read the questions carefull! Make sure ou understand what each question asks of ou. Please read the following statement and then sign and date it: I agree to complete this exam without unauthorized assistance from an person, materials, or device. Signature: Date: Question Points Score Total: i
2 . Let X be a discrete random variable with range {,, 2, 3, 4} and probabilit mass function P (X ) 9, P (X ) 2 9, P (X 2) 3 9, P (X 3) 2 9, P (X 4) 9. For the following questions, carr out the computations and leave our answer as an irreducible fraction. (a) (2 points) Find E(X) and var(x). Show all our work! E(X) 4 k P (X k) k var(x) (k 2) 2 P (X k) k ( 2) ( ) (b) (8 points) Find P ( X 3). Show all our work! P ( X 3) P (X ) + P (X 2) + P (X 3) Alternativel, ou could do P ( X 3) P (X ) (X 4) (c) ( points) We measure X four times independentl. What is the probabilit that X 2 for exactl two of the four measurements? Show all our work! We have 4 trials (the 4 measurements), and we can think of the outcome X 2 as success and X 2 as failure. There are ( 4 2) was of getting 2 success in 4 trials, the probabilit of each success is P (X 2) 3 9 3, and the probabilit of failure is P (X 2) Thus the probabilit of getting X 2 exactl 2 out of 4 times is: ( ) 4 ( 2 3 )2 ( ) NOTE: This question was the same as the one in the practice slides, just with different numbers.
3 2. Suppose that a continuous random variable X has distribution function { e x for x > ; f(x) otherwise. (a) (5 points) Find P (X 5). Show all our work! P (X 5) 5 f(x)dx dx + 5 e x dx ( e x ) 5 e 5. (b) (5 points) Find E(X). Show all our work! since f(x) for x. Thus, E(X) E(X) lim b b xe x dx xe x dx xe x dx lim b ( xe x e x ) b B L Hopital, Also, lim b ( be b e b + ) lim b be b lim b e b. lim b be b lim b b e b lim b e b. lim b e b, so E(X). NOTE: This question was also in the practice slides, with e 2x instead of e x, and it was part of a long homework question ou had to solve where ou had e ax for a parameter a. 2
4 3. (2 points) The following pictures, in some order, denote the image of the vector v transformations given b the matrices. ( ) A ; A 2 ( ) ; A 3 ( ) ; A 4 ( ) ( ) 4 under the Match the pictures with the corresponding matrix b writing A i for the correct value of i in the line next to the picture. You do not have to show an work. I am sorr, I don t have the pictures. (a) A 2, because ( ( ) 4 ) ( ) 4 (b) A 4, because ( ( ) ( 4 ) 4) (c) A 3, because ( ( ) ( 4 ) 4) (d) A, because ( ( ) ( 4 4 ) ) 3
5 4. (8 points) Find the general solution to the differential equation d ( ). dx Show all our work! You will be graded on the completeness and qualit of our solution. First note that the constant functions (x) and (x) satisf the differential equation, therefore the are solutions. Now, assume that (x),, then we can divide b ( ) to get (x)( (x)) (x). Integrating we get, Now we can use the substitution of variables (x)( (x)) (x)dx dx. (x), d (x)dx, to get ( ) dx. NOTE: You did not lose points if ou didn t write out the substitution explicitl and separated variables to get ( ) dx. However, if ou wrote ( ) dx. that is a crucial mistake that shows profound misunderstanding. Alex was ver generous in grading that, and didn t subtract nearl as man points as I would have. If ou have written that, please think about it carefull. dx dx means (x), the derivative of, which is a function of x. You cannot split up the dx and multipl b it - that s not a number and that makes no sense. I know some high school books sa that, but I told ou that s dumming down the procedure for obtaining the answer and ou should not bu that. Please think carefull about how we derived the separation of variables we are using. I was sad to see some students still write that. We use partial fraction decomposition to compute d d ( ) + d ln ln + C, for C an arbitrar real constant Thus ln ln x + C for C an arbitrar real constant. So, ln x + C 4
6 for C an arbitrar real constant. So, ec e x for C an arbitrar real constant (so e C can range through all positive real numbers). So, i.e., ±ec e x, Cex, for C an arbitrar non-zero constant (since ±e C ranges through all nonzero real numbers as C ranges through all the real numbers.) Now we have to solve for : ( )Ce x ( + Ce x ) Ce x, so the general solution of our differential equation is (x) Cex, for an C, and the constant functions (x) and (x). + Cex NOTE: This is just a particular case of the logistics equation, with all constants being equal to. NOTE: It was important to not forget the trivial solutions. I emphasized that in class even when we had an initial value condition - we alwas checked the constant solutions first that we disregard when we separate variables (if we had an initial constraint that the didn t satisf, we dismissed them.) Also, that s wh I put the question on the review slides where the solution turned out to be precisel the constant solution. 5
7 5. Let A ( ) 3. 2 (a) (5 points) State the definition of what it means for a scalar λ to be an eigenvalue of A. A scalar λ is an eigenvalue of A if there exists a nonzero vector v such that Av λv. NOTE: That s it. That s all ou had to write. NONZERO is the essential part of this definition. If ou don t sa that, then Av λv is triviall satisfied b the zero vector for an real number λ, so an real number would be an eigenvalue. I stressed this over and over again in class. (b) (5 points) Find the eigenvalues of A (start from the definition, carr out and explain all the steps in our argument.) Show all our work! You will be graded on the completeness and qualit of our solution. ( x A scalar λ is an eigenvalue of A if there exists a nonzero vector such that Av λv. ) Now Av λv Av λv Av λiv (A λi)v [( ) ( )] ( ) 3 x λ 2 ( ( ) ( 3 λ x 2 λ) ) ( ) Thus ( ) λ ( is ) an eigenvalue if and onl if the last equation has a nonzero solution, i.e., if there is x which satisfies it. ( ) 3 λ This equation has a nonzero solution if and onl if the matrix 2 ( ) λ x if the inverse existed, then we could multipl b it on both sides to get be the unique ( solution. ) 3 λ The matrix 2 λ we get so is NOT invertible ( ) and that would ( ) 3 λ is not invertible if and onl if det. Solving this, 2 λ (3 λ)( λ) 2, λ 3 or. NOTE: The essential part was to realize that we need a NONZERO solution to ( ( ) ( 3 λ x, 2 λ) ) 6
8 and to know that that onl happens if the coefficient matrix is not invertible, and that is wh we need its determinant to be. Unless ou explicitl said these things, our solution is not complete. NOTE: When ou distribute and pull out v from Av λiv, ou need to keep it on the right: (A λi)v. Note that ( ) ( ) x 3 2 is not even defined!! And also, it s not true that (A B)C CA CB, even if the multiplications are defined! What is true is that (A B)C AC BC, but we don t have that AC CA or BC CB. 7
Math 106: Calculus I, Spring 2018: Midterm Exam II Monday, April Give your name, TA and section number:
Math 106: Calculus I, Spring 2018: Midterm Exam II Monday, April 6 2018 Give your name, TA and section number: Name: TA: Section number: 1. There are 6 questions for a total of 100 points. The value of
More informationMATH LECTURE NOTES FIRST ORDER SEPARABLE DIFFERENTIAL EQUATIONS OVERVIEW
MATH 234 - LECTURE NOTES FIRST ORDER SEPARABLE DIFFERENTIAL EQUATIONS OVERVIEW Now will will begin with the process of learning how to solve differential equations. We will learn different techniques for
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER AND RECITATION INSTRUCTOR:
MA66 EXAM II SPRING 09 MARCH 5, 09 TEST NUMBER INSTRUCTIONS:. Do not open the exam booklet until you are instructed to do so.. Before you open the booklet fill in the information below and use a # pencil
More informationMA 262, Spring 2018, Midterm 1 Version 01 (Green)
MA 262, Spring 2018, Midterm 1 Version 01 (Green) INSTRUCTIONS 1. Switch off your phone upon entering the exam room. 2. Do not open the exam booklet until you are instructed to do so. 3. Before you open
More informationMath 369 Exam #1 Practice Problems
Math 69 Exam # Practice Problems Find the set of solutions of the following sstem of linear equations Show enough work to make our steps clear x + + z + 4w x 4z 6w x + 5 + 7z + w Answer: We solve b forming
More informationExam 3. Math Spring 2015 April 8, 2015 Name: } {{ } (from xkcd) Read all of the following information before starting the exam:
Exam 3 Math 2 - Spring 205 April 8, 205 Name: } {{ } by writing my name I pledge to abide by the Emory College Honor Code (from xkcd) Read all of the following information before starting the exam: For
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER RECITATION INSTRUCTOR:
MA262 FINAL EXAM SPRING 2016 MAY 2, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More informationUniversity of Connecticut Department of Mathematics
University of Connecticut Department of Mathematics Math 1131 Sample Exam 2 Fall 2014 Name: Instructor Name: Section: TA Name: Discussion Section: This sample exam is just a guide to prepare for the actual
More informationMath 290, Midterm II-key
Math 290, Midterm II-key Name (Print): (first) Signature: (last) The following rules apply: There are a total of 20 points on this 50 minutes exam. This contains 7 pages (including this cover page) and
More informationMA EXAM 3 INSTRUCTIONS VERSION 01 April 14, Section # and recitation time
MA 16600 EXAM 3 INSTRUCTIONS VERSION 01 April 14, 2015 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More informationCollege of Sciences PHYS 101 General Physics 1 F a l l S e m e s t e r Midterm1 Exam October 26, 2015 Monday, 19:00-21:00. Please read.
Name: Surname: Number: K O Ç U N I V E R S I T Y College of Sciences PHYS 101 General Phsics 1 F a l l S e m e s t e r 0 1 5 Midterm1 Exam October 6, 015 Monda, 19:00-1:00 Please read. Count to make sure
More informationf x = x x 4. Find the critical numbers of f, showing all of the
MTH 5 Winter Term 011 Test 1 - Calculator Portion Name You may hold onto this portion of the test and work on it some more after you have completed the no calculator portion of the test. On this portion
More informationExam 3 review for Math 1190
Exam 3 review for Math 9 Be sure to be familiar with the following : Extreme Value Theorem Optimization The antiderivative u-substitution as a method for finding antiderivatives Reimann sums (e.g. L 6
More informationUniversity of Connecticut Department of Mathematics
University of Connecticut Department of Mathematics Math 1131 Sample Exam 2 Fall 2015 Name: Instructor Name: Section: TA Name: Discussion Section: This sample exam is just a guide to prepare for the actual
More informationMath 162: Calculus IIA
Math 162: Calculus IIA Final Exam December 15, 2015 NAME (please print legibly): Your University ID Number: Your University email Indicate your instructor with a check in the box: JJ Lee Doug Ravenel Timur
More informationProblem # Max points possible Actual score Total 100
MIDTERM 1-18.01 - FALL 2014. Name: Email: Please put a check by your recitation section. Instructor Time B.Yang MW 10 M. Hoyois MW 11 M. Hoyois MW 12 X. Sun MW 1 R. Chang MW 2 Problem # Max points possible
More informationMATH 1553-C MIDTERM EXAMINATION 3
MATH 553-C MIDTERM EXAMINATION 3 Name GT Email @gatech.edu Please read all instructions carefully before beginning. Please leave your GT ID card on your desk until your TA scans your exam. Each problem
More informationSpring /11/2009
MA 123 Elementary Calculus SECOND MIDTERM Spring 2009 03/11/2009 Name: Sec.: Do not remove this answer page you will return the whole exam. You will be allowed two hours to complete this test. No books
More informationName: Math 1120, Final. December 12, Net id: PLACE AN X IN THE BOX TO INDICATE YOUR SECTION
Math 1120, Final December 12, 2017 Name: Net id: PLACE AN X IN THE BOX TO INDICATE YOUR SECTION Ian Lizarraga MWF 8:00 8:50 Ian Lizarraga MWF 9:05 9:55 Swee Hong Chan MWF 12:20 1:10 Teddy Einstein MWF
More informationMATH 223 FINAL EXAM APRIL, 2005
MATH 223 FINAL EXAM APRIL, 2005 Instructions: (a) There are 10 problems in this exam. Each problem is worth five points, divided equally among parts. (b) Full credit is given to complete work only. Simply
More informationMA 262, Fall 2017, Final Version 01(Green)
INSTRUCTIONS MA 262, Fall 2017, Final Version 01(Green) (1) Switch off your phone upon entering the exam room. (2) Do not open the exam booklet until you are instructed to do so. (3) Before you open the
More informationUniversity of Connecticut Department of Mathematics
University of Connecticut Department of Mathematics Math 1131 Sample Exam 1 Fall 2013 Name: This sample exam is just a guide to prepare for the actual exam. Questions on the actual exam may or may not
More informationMATH 1553 PRACTICE MIDTERM 3 (VERSION B)
MATH 1553 PRACTICE MIDTERM 3 (VERSION B) Name Section 1 2 3 4 5 Total Please read all instructions carefully before beginning. Each problem is worth 10 points. The maximum score on this exam is 50 points.
More informationFinal Exam Practice Problems Part II: Sequences and Series Math 1C: Calculus III
Name : c Jeffrey A. Anderson Class Number:. Final Exam Practice Problems Part II: Sequences and Series Math C: Calculus III What are the rules of this exam? PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO
More informationPractice Questions for Final
Math 39 Practice Questions for Final June. 8th 4 Name : 8. Continuous Probability Models You should know Continuous Random Variables Discrete Probability Distributions Expected Value of Discrete Random
More informationProblem # Max points possible Actual score Total 120
FINAL EXAMINATION - MATH 2121, FALL 2017. Name: ID#: Email: Lecture & Tutorial: Problem # Max points possible Actual score 1 15 2 15 3 10 4 15 5 15 6 15 7 10 8 10 9 15 Total 120 You have 180 minutes to
More informationFinal. for Math 308, Winter This exam contains 7 questions for a total of 100 points in 15 pages.
Final for Math 308, Winter 208 NAME (last - first): Do not open this exam until you are told to begin. You will have 0 minutes for the exam. This exam contains 7 questions for a total of 00 points in 5
More informationMA FINAL EXAM Green December 16, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 600 FINAL EXAM Green December 6, 205 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. Be sure the paper you are looking at right
More informationMATH 1207 R02 MIDTERM EXAM 2 SOLUTION
MATH 7 R MIDTERM EXAM SOLUTION FALL 6 - MOON Name: Write your answer neatly and show steps. Except calculators, any electronic devices including laptops and cell phones are not allowed. () (5 pts) Find
More informationMA162 EXAM III SPRING 2017 APRIL 11, 2017 TEST NUMBER 01 INSTRUCTIONS:
MA62 EXAM III SPRING 207 APRIL, 207 TEST NUMBER 0 INSTRUCTIONS:. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and use a #
More informationNAME: MA Sample Final Exam. Record all your answers on the answer sheet provided. The answer sheet is the only thing that will be graded.
NAME: MA 300 Sample Final Exam PUID: INSTRUCTIONS There are 5 problems on 4 pages. Record all your answers on the answer sheet provided. The answer sheet is the only thing that will be graded. No books
More informationMA EXAM 3 INSTRUCTIONS VERSION 01 April 17, Section # and recitation time
MA 16600 EXAM 3 INSTRUCTIONS VERSION 01 April 17, 2014 Your name Student ID # Your TA s name Section # and recitation time 1. You must use a #2 pencil on the scantron sheet (answer sheet). 2. Check that
More informationMath 180 Written Homework Assignment #10 Due Tuesday, December 2nd at the beginning of your discussion class.
Math 18 Written Homework Assignment #1 Due Tuesday, December 2nd at the beginning of your discussion class. Directions. You are welcome to work on the following problems with other MATH 18 students, but
More informationTest 3, Linear Algebra
Test 3, Linear Algebra Dr. Adam Graham-Squire, Fall 2017 Name: I pledge that I have neither given nor received any unauthorized assistance on this exam. (signature) DIRECTIONS 1. Don t panic. 2. Show all
More information- - - - - - - - - - - - - - - - - - DISCLAIMER - - - - - - - - - - - - - - - - - - General Information: This is a midterm from a previous semester. This means: This midterm contains problems that are of
More informationSpring 2017 Midterm 1 04/26/2017
Math 2B Spring 2017 Midterm 1 04/26/2017 Time Limit: 50 Minutes Name (Print): Student ID This exam contains 10 pages (including this cover page) and 5 problems. Check to see if any pages are missing. Enter
More information1. In this problem, if the statement is always true, circle T; otherwise, circle F.
Math 1553, Extra Practice for Midterm 3 (sections 45-65) Solutions 1 In this problem, if the statement is always true, circle T; otherwise, circle F a) T F If A is a square matrix and the homogeneous equation
More informationMATH 153 FIRST MIDTERM EXAM
NAME: Solutions MATH 53 FIRST MIDTERM EXAM October 2, 2005. Do not open this exam until you are told to begin. 2. This exam has pages including this cover. There are 8 questions. 3. Write your name on
More informationTurn off all cell phones, pagers, radios, mp3 players, and other similar devices.
Math 25 B and C Midterm 2 Palmieri, Autumn 26 Your Name Your Signature Student ID # TA s Name and quiz section (circle): Cady Cruz Jacobs BA CB BB BC CA CC Turn off all cell phones, pagers, radios, mp3
More informationSpring 2016 Exam 1 without number 13.
MARK BOX problem points 0 5-9 45 without number 3. (Topic of number 3 is not on our Exam this semester.) Solutions on homepage (under previous exams). 0 0 0 NAME: 2 0 3 0 PIN: % 00 INSTRUCTIONS On Problem
More informationMath 1132 Practice Exam 1 Spring 2016
University of Connecticut Department of Mathematics Math 32 Practice Exam Spring 206 Name: Instructor Name: TA Name: Section: Discussion Section: Read This First! Please read each question carefully. Show
More informationMA EXAM 1 Green February 8, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 16100 EXAM 1 Green February 8, 2016 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME 1. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. Be sure the paper you are looking at right
More informationWithout fully opening the exam, check that you have pages 1 through 12.
Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through 2. Show all your work on the standard response
More informationMA 113 Calculus I Fall 2017 Exam 1 Tuesday, 19 September Multiple Choice Answers. Question
MA 113 Calculus I Fall 2017 Exam 1 Tuesday, 19 September 2017 Name: Section: Last 4 digits of student ID #: This exam has 12 multiple choice questions (five points each) and 4 free response questions (ten
More informationMath 42: Fall 2015 Midterm 2 November 3, 2015
Math 4: Fall 5 Midterm November 3, 5 NAME: Solutions Time: 8 minutes For each problem, you should write down all of your work carefully and legibly to receive full credit When asked to justify your answer,
More informationMath 115 Final Exam April 24, 2017
On my honor, as a student, I have neither given nor received unauthorized aid on this academic work. Initials: Do not write in this area Your Initials Only: Math 5 Final Exam April 2, 207 Your U-M ID #
More informationMath 54 Homework 3 Solutions 9/
Math 54 Homework 3 Solutions 9/4.8.8.2 0 0 3 3 0 0 3 6 2 9 3 0 0 3 0 0 3 a a/3 0 0 3 b b/3. c c/3 0 0 3.8.8 The number of rows of a matrix is the size (dimension) of the space it maps to; the number of
More informationMath 116 Second Midterm November 13, 2017
On my honor, as a student, I have neither given nor received unauthorized aid on this academic work. Initials: Do not write in this area Your Initials Only: Math 6 Second Midterm November 3, 7 Your U-M
More informationMA FINAL EXAM Green May 5, You must use a #2 pencil on the mark sense sheet (answer sheet).
MA 600 FINAL EXAM Green May 5, 06 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a # pencil on the mark sense sheet (answer sheet).. Be sure the paper you are looking at right now is GREEN!
More informationFall 2015 Exam 3 PIN: 17
MARK BOX problem points 0 10 1 10 2-6 50 7 15 8a/8b 15 NAME: PIN: 17 KEY-e-poo % 100 INSTRUCTIONS On Problem 0, fill in the blanks and boxes. As you know, if you do not make at least half of the points
More informationMath 2930 Worksheet Equilibria and Stability
Math 2930 Worksheet Equilibria and Stabilit Week 3 September 7, 2017 Question 1. (a) Let C be the temperature (in Fahrenheit) of a cup of coffee that is cooling off to room temperature. Which of the following
More informationFirst Midterm Exam. You are responsible for upholding the University of Maryland Honor Code while taking this exam.
Econ300 Spring 014 First Midterm Exam version W This exam consists of 5 multiple choice questions. The maximum duration of the exam is 50 minutes. 1. In the spaces provided on the scantron, write your
More informationLinear algebra and differential equations (Math 54): Lecture 10
Linear algebra and differential equations (Math 54): Lecture 10 Vivek Shende February 24, 2016 Hello and welcome to class! As you may have observed, your usual professor isn t here today. He ll be back
More informationFall 2016 Exam 1 HAND IN PART NAME: PIN:
HAND IN PART MARK BOX problem points 0 15 1-12 60 13 10 14 15 NAME: PIN: % 100 INSTRUCTIONS This exam comes in two parts. (1) HAND IN PART. Hand in only this part. (2) STATEMENT OF MULTIPLE CHOICE PROBLEMS.
More informationEigenvalues and Eigenvectors, More Direction Fields and Systems of ODEs
Eigenvalues and Eigenvectors, More Direction Fields and Systems of ODEs First let us speak a bit about eigenvalues. Defn. An eigenvalue λ of an nxn matrix A means a scalar (perhaps a complex number) such
More informationWithout fully opening the exam, check that you have pages 1 through 12.
MTH 33 Exam 2 April th, 208 Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through 2. Show all
More informationMATH 220 CALCULUS I SPRING 2018, MIDTERM I FEB 16, 2018
MATH 220 CALCULUS I SPRING 2018, MIDTERM I FEB 16, 2018 DEPARTMENT OF MATHEMATICS UNIVERSITY OF PITTSBURGH NAME: ID NUMBER: (1) Do not open this exam until you are told to begin. (2) This exam has 12 pages
More informationMath 308 Spring Midterm Answers May 6, 2013
Math 38 Spring Midterm Answers May 6, 23 Instructions. Part A consists of questions that require a short answer. There is no partial credit and no need to show your work. In Part A you get 2 points per
More informationMathematics Page 1 of 9 Student-No.:
Mathematics 5-95 Page of 9 Student-No.: Midterm Duration: 8 minutes This test has 7 questions on 9 pages, for a total of 7 points. Question 7 is a bonus question. Read all the questions carefully before
More informationFinal exam (practice) UCLA: Math 31B, Spring 2017
Instructor: Noah White Date: Final exam (practice) UCLA: Math 31B, Spring 2017 This exam has 8 questions, for a total of 80 points. Please print your working and answers neatly. Write your solutions in
More informationMath 2114 Common Final Exam May 13, 2015 Form A
Math 4 Common Final Exam May 3, 5 Form A Instructions: Using a # pencil only, write your name and your instructor s name in the blanks provided. Write your student ID number and your CRN in the blanks
More informationLast/Family Name First/Given Name Seat # Exam # Failure to follow the instructions below will constitute a breach of the Honor Code:
Math 21, Winter 2018 Schaeffer/Solis Midterm Exam 2 (February 28th, 2018) Last/Family Name First/Given Name Seat # Exam # Failure to follow the instructions below will constitute a breach of the Honor
More informationSpring 2018 Exam 1 MARK BOX HAND IN PART NAME: PIN:
problem MARK BOX points HAND IN PART - 65=x5 4 5 5 6 NAME: PIN: % INSTRUCTIONS This exam comes in two parts. () HAND IN PART. Hand in only this part. () STATEMENT OF MULTIPLE CHOICE PROBLEMS. Do not hand
More informationMTH 133 Solutions to Exam 2 April 19, Without fully opening the exam, check that you have pages 1 through 12.
MTH 33 Solutions to Exam 2 April 9, 207 Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through
More informationMath 221 Midterm Fall 2017 Section 104 Dijana Kreso
The University of British Columbia Midterm October 5, 017 Group B Math 1: Matrix Algebra Section 104 (Dijana Kreso) Last Name: Student Number: First Name: Section: Format: 50 min long exam. Total: 5 marks.
More informationMAT 127: Calculus C, Fall 2010 Solutions to Midterm I
MAT 7: Calculus C, Fall 00 Solutions to Midterm I Problem (0pts) Consider the four differential equations for = (): (a) = ( + ) (b) = ( + ) (c) = e + (d) = e. Each of the four diagrams below shows a solution
More informationWithout fully opening the exam, check that you have pages 1 through 11.
MTH 33 Solutions to Final Exam May, 8 Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show
More informationProblems and results for the ninth week Mathematics A3 for Civil Engineering students
Problems and results for the ninth week Mathematics A3 for Civil Engineering students. Production line I of a factor works 0% of time, while production line II works 70% of time, independentl of each other.
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER AND RECITATION INSTRUCTOR:
MA166 EXAM I SPRING 2019 FEBRUARY 5, 2019 TEST NUMBER 22 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More informationSummer Session Practice Final Exam
Math 2F Summer Session 25 Practice Final Exam Time Limit: Hours Name (Print): Teaching Assistant This exam contains pages (including this cover page) and 9 problems. Check to see if any pages are missing.
More informationMatrices related to linear transformations
Math 4326 Fall 207 Matrices related to linear transformations We have encountered several ways in which matrices relate to linear transformations. In this note, I summarize the important facts and formulas
More informationMath 308 Midterm November 6, 2009
Math 308 Midterm November 6, 2009 We will write A 1,..., A n for the columns of an m n matrix A. If x R n, we will write x = (x 1,..., x n ). he null space and range of a matrix A are denoted by N (A)
More informationMath 164-1: Optimization Instructor: Alpár R. Mészáros
Math 164-1: Optimization Instructor: Alpár R. Mészáros First Midterm, April 20, 2016 Name (use a pen): Student ID (use a pen): Signature (use a pen): Rules: Duration of the exam: 50 minutes. By writing
More informationMTH 133 Solutions to Exam 2 November 15, Without fully opening the exam, check that you have pages 1 through 13.
MTH 33 Solutions to Exam 2 November 5, 207 Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through
More informationMA 113 Calculus I Fall 2015 Exam 3 Tuesday, 17 November Multiple Choice Answers. Question
MA 11 Calculus I Fall 2015 Exam Tuesday, 17 November 2015 Name: Section: Last 4 digits of student ID #: This exam has ten multiple choice questions (five points each) and five free response questions (ten
More informationGive your answers in exact form, except as noted in particular problems.
Math 125 Final Examination Spring 2010 Your Name Your Signature Student ID # Quiz Section Professor s Name TA s Name This exam is closed book. You may use one 8 2 1 11 sheet of handwritten notes (both
More informationCalculators, computers and related devices are not permitted.
ACM 95b/100b Midterm Exam February 6, 2004 Due February 10, 2004 ACM 95b/100b 3pm in Firestone 307 E. Sterl Phinney (2 pts) Include grading section number The honor code is in effect. Please follow all
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER RECITATION INSTRUCTOR:
MA262 EXAM I SPRING 2016 FEBRUARY 25, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More informationMath 113 (Calculus 2) Exam 4
Math 3 (Calculus ) Exam 4 November 0 November, 009 Sections 0, 3 7 Name Student ID Section Instructor In some cases a series may be seen to converge or diverge for more than one reason. For such problems
More informationMATH 33A LECTURE 3 PRACTICE MIDTERM I
MATH A LECTURE PRACTICE MIDTERM I Please note: Show your work Correct answers not accompanied by sufficent explanations will receive little or no credit (except on multiple-choice problems) Please call
More informationECE580 Fall 2015 Solution to Midterm Exam 1 October 23, Please leave fractions as fractions, but simplify them, etc.
ECE580 Fall 2015 Solution to Midterm Exam 1 October 23, 2015 1 Name: Solution Score: /100 This exam is closed-book. You must show ALL of your work for full credit. Please read the questions carefully.
More informationMTH 132 Solutions to Exam 2 Nov. 23rd 2015
Name: Section: Instructor: READ THE FOLLOWING INSTRUCTIONS. Do not open your exam until told to do so. No calculators, cell phones or any other electronic devices can be used on this exam. Clear your desk
More informationMath Makeup Exam - 3/14/2018
Math 22 - Makeup Exam - 3/4/28 Name: Section: The following rules apply: This is a closed-book exam. You may not use any books or notes on this exam. For free response questions, you must show all work.
More informationECE302 Exam 2 Version A April 21, You must show ALL of your work for full credit. Please leave fractions as fractions, but simplify them, etc.
ECE32 Exam 2 Version A April 21, 214 1 Name: Solution Score: /1 This exam is closed-book. You must show ALL of your work for full credit. Please read the questions carefully. Please check your answers
More informationProblem Out of Score Problem Out of Score Total 45
Midterm Exam #1 Math 11, Section 5 January 3, 15 Duration: 5 minutes Name: Student Number: Do not open this test until instructed to do so! This exam should have 8 pages, including this cover sheet. No
More informationMath 111, Introduction to the Calculus, Fall 2011 Midterm I Practice Exam 1 Solutions
Math 111, Introduction to the Calculus, Fall 2011 Midterm I Practice Exam 1 Solutions For each question, there is a model solution (showing you the level of detail I expect on the exam) and then below
More informationUniversity of Ottawa
University of Ottawa Department of Mathematics and Statistics MAT 1302B : Mathematical Methods II Professor: Hadi Salmasian First Midterm Exam Version A February 3, 2017 Surname First Name Student # DGD
More informationMath 1131 Final Exam Review Spring 2013
University of Connecticut Department of Mathematics Math 1131 Final Exam Review Spring 2013 Name: Instructor Name: TA Name: 4 th February 2010 Section: Discussion Section: Read This First! Please read
More informationMath 116 First Midterm October 9, 2017
On m honor, as a student, I have neither given nor received unauthorized aid on this academic work. Initials: Do not write in this area Your Initials Onl: Math 116 First Midterm October 9, 217 Your U-M
More informationTest 2 - Answer Key Version A
MATH 8 Student s Printed Name: Instructor: CUID: Section: Fall 27 8., 8.2,. -.4 Instructions: You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook,
More informationMTH 133 Exam 2 November 16th, Without fully opening the exam, check that you have pages 1 through 12.
Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through 2. Show all your work on the standard response
More informationMath 115 Final Exam. December 11, 2008
Math 5 Final Exam December, 28 Name: EXAM SOLUTIONS Instructor: Section:. Do not open this exam until you are told to do so. 2. This exam has 8 pages including this cover. There are 9 problems. Note that
More informationz-test, t-test Kenneth A. Ribet Math 10A November 28, 2017
Math 10A November 28, 2017 Welcome back, Bears! This is the last week of classes. RRR Week December 4 8: This class will meet in this room on December 5, 7 for structured reviews by T. Zhu and crew. Final
More informationStatistics 100A Homework 5 Solutions
Chapter 5 Statistics 1A Homework 5 Solutions Ryan Rosario 1. Let X be a random variable with probability density function a What is the value of c? fx { c1 x 1 < x < 1 otherwise We know that for fx to
More informationMath 320, spring 2011 before the first midterm
Math 320, spring 2011 before the first midterm Typical Exam Problems 1 Consider the linear system of equations 2x 1 + 3x 2 2x 3 + x 4 = y 1 x 1 + 3x 2 2x 3 + 2x 4 = y 2 x 1 + 2x 3 x 4 = y 3 where x 1,,
More informationMTH 133 Solutions to Exam 1 Feb. 25th 2015
MTH 133 Solutions to Exam 1 Feb. 5th 15 Name: Section: Recitation Instructor: READ THE FOLLOWING INSTRUCTIONS. Do not open your exam until told to do so. No calculators, cell phones or any other electronic
More informationPage Points Score Total: 100
Math 1130 Spring 2019 Sample Midterm 2a 2/28/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 10 pages (including this cover page) and 9 problems. Check to see if any
More informationUniversity of Ottawa
University of Ottawa Department of Mathematics and Statistics MAT 1302A: Mathematical Methods II Instructor: Hadi Salmasian Final Exam April 2016 Surname First Name Seat # Instructions: (a) You have 3
More informationMath 152 Second Midterm March 20, 2012
Math 52 Second Midterm March 20, 202 Name: EXAM SOLUTIONS Instructor: Jose Gonzalez Section: 202 Student ID: Exam prepared by Jose Gonzalez. Do not open this exam until you are told to do so. 2. SPECIAL
More informationMTH 132 Solutions to Exam 2 Apr. 13th 2015
MTH 13 Solutions to Exam Apr. 13th 015 Name: Section: Instructor: READ THE FOLLOWING INSTRUCTIONS. Do not open your exam until told to do so. No calculators, cell phones or any other electronic devices
More information