MATH 114 Sample Final Exam 2
1. Consider the line that is tangent to the cycloid given by the parametric equations x = sin , y = 1 cos , at = . At what point (0, y) does this line meet the y-axis? (a) (0,1) (b) (0, 2 1) (c) (0, 0) (d) (0, 2) (e) (0, 2 1)
MATH 114 - Assignment 8 Solutions
Due Monday November 17th
B1. Determine whether each set is a basis for R3 .
1
5
0
1
(b) Since the set 3 , 0 , 1 , 0 has 4 vectors and the dimension of R3 is
1
1
0
3
3, this set cannot be linearly independent and hence
MATH 114 - Assignment 4 Solutions
Due Tuesday October 14th
From PROBLEMS 2.2 - Homework Problems (p. 89-90):
B1 Find the RREF and rank of the following matrices:
2 3
1 0
(a) The RREF of 3 1 is 0 1; rank = 2.
3 2
0 0
2 4 8
1 0 2
(c) The RREF of 1 1 3
MATH 114 - Assignment 3
Due Monday October 6th at 4pm (in the dropboxes)
Please hand in the following problems (from Introduction to Linear Algebra for Science and
Engineering, Second Edition):
From PROBLEMS 1.5 - Homework Problems (p. 58):
4
6
(2)(6
Math 114, MAKEUP FINAL EXAM
January 15, 2003
INSTRUCTIONS
OFFICIAL USE ONLY
INSTRUCTIONS: 1. Please complete the information requested below. There are 14 multiple choice problems and 6 open answer problems. No partial credit will be given on the multiple
Math 114: Final Exam
May 4, 2012
Instructions:
1. Please sign your name and indicate the name of your instructor and your teaching
assistant:
A. Your Name:
B. Your Instructor:
C. Your Teaching Assistant:
2. This exam is 2 hours long and there are 16 quest
MATH 114, FINAL EXAM MAY 7th 2009, 12-2PM Name: klasdjSolutionsadfsdfgdsfgsdfgkjjhsdaf Penn ID number: klasdjjhsdfsdaf
Signature: klasdjSolutionsadfsdfgdsfgsdfgkjjhsdaf Circle the name of your instructor:
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1. The
Math 114: Final Exam
May 9, 2008
Instructions:
1. Please sign your name and indicate the name of your instructor and your teaching assistant: A. Your Name: B. Your Instructor: C. Your Teaching Assistant:
2. This exam is 2 hours long and there are 20 quest
Math 114 Spring 2011 Final Exam
1. The set of points equidistant from the points (2, 1, 1) and (4, 3, 5) is a plane.
What is the equation of this plane?
(A) 3x + y 2z = 0
(B) 2x + 4y 6z = 6
(C) x + 2y 3z = 11
(D) 2x + 14y + 10z = 15
(E) 6x + 2y 4z = 5
(F)
Final Exam - December 14, 2006 Math 114
Name: Instructor: Teaching Assistant: Recitation Day/Time:
There are nine questions on this examination. Some have multiple parts. It is important to show your work and justify each statement. You will receive parti
Calculus II (Math 114) Fall 2006
The Makeup Final Exam
There are nine questions on this examination. Some have multiple parts. It is important to show your work and justify each statement. You will receive partial credit for substantial progress towards t
MATH 114 Sample Final Exam 1
1. A curve is given in parametric form by x = et the point (1,0) is (a) y = 3 x + 2
3 2
2 1
, y = t3 + 1. Its tangent line at
2 3
(b) y = x + 1
(c) y = 2 x 3
(d) y = x 1
(e) y = 0
2. The arc length of the curve given in polar
MATH 114 - Assignment 5 Solutions
Due Monday October 20th
From PROBLEMS 3.2 - Homework Problems (p. 142 - 143):
B1 Let A =
1 4 2
and let fA be the corresponding matrix mapping.
5 3 1
(a) Since A is 2 3, the domain of fA is R3 and the codomain is R2 .
3