DEPARTMENT OF MATHEMATICS
Math 190 Final Exam
FALL 2007
Instructions
Answer any ten questions from Part I. Pages 3 to 14
Answer any ten questions from Part II. Pages 15 to 26
This exam contains one question per page show your work beneath the question, th
The City College of New York
Department of Mathematics
Math 20100 Final Exam Spring 2009
Instructions: No electronic device of any sort may be used during this exam. Please show all
work in the space provided following each question. The time for the exam
203 Fall 2008 Group Final Solutions
1a: Take cross products of the normal to get the direction of the line:
Cross@82, - 1, 1<, 81, 0, - 3<D
83, 7, 1<
Then parameterize the line using the point and the direction to get:
x = 4 + 3 t , y = -7 t , z = -3 + t
final07sols.nb
M203 Fall 2007 Exam solutions
Q1a: find a normal to the plane by taking cross product of two vectors in the plane.
vector along line: <2,3,4> point on line: (1,2,3), displacement vector from line to point:
<1,2,3>-<1,2,0>= <0,0,3> Cross pro
1
MATH 203 Final Exam
May 18, 2009
Instructions: Complete every question in Part I (Questions 1-7.) Complete three of
the ve questions in Part II (Questions 8-12). Each question is worth 10 points.
No calculators or other electronic devices may be used du
Department of Mathematics
Math 203
The City College of New York
Final Exam
Spring 2008
No calculators permitted. Answers may be left in terms of radicals, , e, etc and do not
need to be simplied unless stated otherwise. Each question is worth 10 points.
P
1
MATH 203 Final Exam
May 23, 2007
PART I: Answer all parts of Questions 1-8 (points as indicated).
z
Question 1 (8 points) Given the two lines x 2 = y = z + 1 and x + 2 = y 1 = 10
3
4
5
6
8
(a) Are they parallel? Explain.
(b) Find an equation of the plan
Department of Mathematics
Math 20300
The City College of NY
Spring 2006
Final Exam
No calculators permitted. Answers may be left in terms of radicals, !, e, etc. and do not
need to be simplified unless stated otherwise. Show all work.
Part I. Answer all 7
MATH 203
FINAL EXAMINATION
SPRING 2005
PART I: Answer ALL questions in this part (10 points each)
Show all work and simplify all answers. NO CALCULATORS!
x2 y 2 z 2
1. (a) Sketch the graph of
+
+
= 1. Also graph the traces of this graph in the xy 4
4
64
a
MATH 203 Final Exam
December 19, 2007
PART I: Answer all parts of Questions 1-7. Each question is worth 10 points
Question 1 a) Find an equation of the plane that contains both the line
x 1 = y 2 = z 3 and the point (1, 2, 0).
2
3
4
b) Find parametric equ
Course Learning Outcomes
1. model spatial problems with vectors, lines, planes, curves and surfaces in threedimensional space
a,b,c
2. use dierentiation to compute tangent lines and tangent planes
a,b,c
3. use dierentiation for multivariate functions to n
Department of Mathematics
Math 19500 Final Examination May, 2007
The City College of CUNY
Instructions
Please show all your work in this booklet.
Answer any ten questions from Part I.
Answer any ten questions from Part II.
This exam contains one question
Department of Mathematics
The City College of New York
Math 19000 Final Examination Spring 2007
Instructions: Show all work in this booklet.
You may use a scientic calculator.
Answer 10 questions in Part I and 10 questions in Part II.
Each question is wor
COURSE LEARNING OUTCOMES
DEPARTMENT:
Mathematics
COURSE #: 17300
COURSE TITLE: Introduction to Probability and
Statristics
CATEGORY: Introductory
TERM OFFERED: Spring 2007
PRE-REQUISITES: Placement by the math dept.
HOURS/CREDITS: 4 hrs/wk; 4 credits
DATE
College Algebra and Trigonometry
by
Carl Stitz, Ph.D.
Lakeland Community College
Jeff Zeager, Ph.D.
Lorain County Community College
August 26, 2010
ii
Acknowledgements
The authors are indebted to the many people who support this project. From Lakeland Com