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
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
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
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
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
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
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
Globalisation Supplementary Notes
1. Illustrating effects of trade creation and trade diversion
Country A signs FTA with country B buys from B, not from member C
DWL drops (shaded area): a + b gain t
Policies to Control Inflation
Identify
Contractionary
MP
Explain
Lower MS rise in i/r cost of borrowing
increases reduces I + C purchased with loans
fall in AD GPL falls
Contractionary
FP
Reduce G, i
Macroeconomic Aims, Issues and Policies (Part II) Notes
1. Conflicts of Economic Aims
- Economic growth and low inflation
Especially at full employment because pressures on SS-side will cause GPL to
Macroeconomic Aims, Issues and Policies (Part I) Notes
1. Key Economic Goals
- Efficiency in resource allocation: right mix of goods and services produced at the lowest
possible COP
- Equitable income
Macroeconomic Aims, Issues and Policies (Part III) Notes
1. Definition of Monetary Policy
- Central banks policy regarding MS
- In some small open economies, central banks may choose to anchor monetar
Chapter S1: Probability
1. Properties involving Probabilities
P ( A B ) P( A) P( B) P ( A B)
P ( A B ) P( A) P( B | A)
*Not in MF15
Tips:
- Draw Venn diagram to see better
- The only two properties yo
J1 Topics
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
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25
26
Title
Chapter 1: Scarcity, Choice and Opportunity Cost
Explain two ways in which an economy might move from a point w
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