Midterm Solutions
March 2003
56:238 Evolutionary Computation
Problem 1 (7%)
a)
b) Compute a unit vector u in the direction of v.
c) Are vectors v and w orthogonal?
Solution
a)
b)
c) Yes, because the p
Midterm 2 Solutions
Loyola University Chicago
Math 161-002, Fall 2014
Name (print):
Signature:
Please do not start working until instructed to do so.
You have 75 minutes.
You must show your work to re
1.
2.
3.
4.
5.
Math 118 Practice 2nd Midterm Solutions
What are the maximum and minimum values of the function f (x) = x3 3x + 1 on the interval
[0, 3], and where do they occur?
Check endpoints and cr
CSE 311: Foundations of Computing I
Midterm Practice Questions Solutions
Logic
(a) Show that the expression (p q) (p r) is a contingency.
Solution:
Under the assignment p = T, q = T, r = T, (p q) (p r
Math 52 Sample Midterm Solutions
1. This is just a straight computation using Gauss-Jordan elimination. The
final answer is:
x1 =
30 67x4
;
33
x2 =
9 + 8x4
;
11
x3 =
324 + 475x4
.
99
Here x4 is the fr
Midterm Solutions
Math 154 - Introduction to Combinatorics
The exam has five questions for five points each
This exam is graded out of 20 points
Grade in increments of 0.5 points.
Question 1.
[5]
Prov
MA 526 Midterm
Fall 2016
Solutions
Name:
Question Points Score
1
15
2
10
3
15
4
15
5
15
Total:
70
MA 526
Solutions
Midterm, Page 1 of 5
1. Let I be the ideal hx2 y 2 , xy 2 x, y 3 yi C[x, y].
(a) (5 p
Math 430 Practice Midterm Solutions
1. (a) A group is a set G with an operation : G G G so that
i. There is an identity element 1 G so that 1 g = g 1 = g for all g G,
ii. for each g G there is an inve
Midterm Exam 1 Review (Solutions)
Math 251, Winter 16, Gedeon
Midterm Exam 1 is scheduled for Monday, January 25th, at 3:00pm (in class). Remember that
calculators are not allowed for this exam. The f
MAT 145 : Midterm Solutions
Michael Williams
Each problem is worth 15 points.
1. Let X be the set cfw_a, b, c, d with the topology TX = cfw_, X, cfw_a, cfw_b, cfw_a, b, and
let Y be the (same) set cfw
Math 23: Differential Equations
(Winter 2017)
Midterm Exam Solutions
1. [20 points] TRUE or FALSE? You do not need to justify your answer.
(a) [3 points] Critical points or equilibrium points for a fi
Name:
Prof. Alexandru Suciu
MATH 3150
Real Analysis
Spring 2011
Midterm Exam
Instructions: Write your name in the space provided. Calculators are permitted, but no notes
are allowed. Each problem is w
ASEN 6367
Advanced Finite Element Methods Spring 2017
Midterm Exam 1
Solutions
QUESTION 1. 30 pts = 5 pts per item.
(a) d x is the infinitesimal change in the independent variable x, whereas dy = y d
Math 105A Summer 2017 Midterm Solutions Sketched
Aaron Chen
July 2017
Problem 1
(a) Define Machine Epsilon.
(b) List the following in order of increasing computational cost by number of operations.
i.
Solutions to Midterm Exam
1. Solve the following initial-value problems:
(a) y 0 = 3y, y(0) = 2.
SOLUTION: y = 2e3x
(b) y 0 = y 2 , y(0) = 1.
SOLUTION: y 2 y 0 = 1, y 1 = x+c. The initial data then im
Math 103. Practice 1st Midterm. Solutions
Problem 1 Consider the line through (2, 7) and (3, 5).
1. Find an equation for that line.
12x + 5y 11 = 0 or y =
12
11
x+
5
5
2. Find the x and y intercepts.
Midterm Solutions
May 12, 2017
Problem 1
First we compute Df and Dg at generic points:
u
e 0
z
0
x
Df
= v u Dg
=
0 z 2 2yz
(u,v)
(x,y,z)
1 2
Next we use the chain rule and the fact that g(0, 1, 2)
1
COS 226
Algorithms and Data Structures
Fall 2011
Midterm Solutions
1. Union find.
(a) Impossible: has a cycle 0-1, 1-2, 2-3, and 3-0 in the parent-link representation.
(b) Impossible: the nodes 1, 2
CS 100
Introduction to Computer Science
Midterm Sample Solutions
The answers below are shown in blue.
1. Convert the following numbers from binary to decimal.
a. 1110
8 + 4 + 2 = 14
b. 1010
8 + 2 = 10
ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY
ECE-278: Digital Logic Design
Fall 2016
Solutions - Midterm Exam
(October 13th @ 5:30 pm)
Presentation and clarity are very important
MAT 511: PRACTICE MIDTERM SOLUTIONS
TU, OCT 11, 2016
Your name:
(please print)
This is a practice midterm. It is longer and the actual one to give you more practice.
No books or notes other than the h
Auctions, Matching,
and Mechanisms
Slides courtesy of Jon Levin
From Econ 136: Market Design
http:/web.stanford.edu/~jdlevin/teaching.html
1
Selling a single good
Seller has a single good that she wan
Lecture Notes 3: Game Theory
Stanford University
Econ 51: Economic Analysis II
Spring 2006
Prof. Christopher R. Makler
1.
Introduction to Strategic Interaction and Cournot Duopoly
1.1
Strategic (or No
Lecture Notes 2: Public Economics
Stanford University
Econ 51: Economic Analysis II
Spring 2006
Prof. Christopher R. Makler
1.
Externalities
1.1
Consumption Externalities: The Edgeworth Box
Lets start
Lecture Notes 4: The Economics of Information
Stanford University
Econ 51: Economic Analysis II
Spring 2006
Prof. Christopher R. Makler
1.
Introduction to the Economics of Information
1. Information i
Lecture 12: Dynamic Games of Complete Information
Econ 51 - Stanford University
February 21, 2017
1
Introduction: Extensive Form Games
The elements of a strategic (normal) form game were players, stra
Lecture 5: Externalities
Christopher R. Makler
Econ 51 - Stanford University
1
The Coase Theorem
[Note: this is the improved version of what we did in class.]
The book has a fine treatment of this. Ho
Lecture 8: Pricing Strategies with Market Power
Christopher R. Makler
Econ 51 - Stanford University
These lecture notes illustrate the mathematical examples from lecture.
Lets think about a monopolist
Lecture 2: General Equilibrium in an Exchange Economy
Christopher R. Makler
Econ 51 - Stanford University
1
From Endowments to Allocations
The simplest economy to consider has two people (Alison and B