Math 211
Exam 1
Fall 2016
1. Determine, for vectors u = i + 2j k, v = i + j + k, w = i + k
(a) (10 points) A unit vector in the direction u + 2v 3w
(b) (10 points) The triple product u (v w)
2. Given the points P (1, 1, 1), Q(2, 1, 3) and R(3, 1, 1) in sp
Math 211
Exam 1
Fall 2016
1. Determine, for vectors u = i + 2j k, v = i + j + k, w = i + k
(a) (10 points) A unit vector in the direction u + 2v 3w
(b) (10 points) The triple product u (v w)
2. Given the points P (1, 1, 1), Q(2, 1, 3) and R(3, 1, 1) in sp
MATH 110, Linear Algebra, Fall 2013
Solutions to Homework #1.
Chapter 1.
1.
a
1
(a ib)
a ib
b
= 2
=
= 2
+i 2
2
(a + ib)
(a + ib)(a ib)
a +b
a +b
a + b2
3. Recall that v = (1)v. Thus (v) = (1)(1)v) = (1)(1)v = (1)v = v.
4. Suppose av = 0 but a = 0. Then v
(12 points) De_ne each of the following sets where X and Y are sets in
the universe U:
(a) X [ Y : The union of the sets X and Y , denoted X [ Y , is given
by
X [ Y := fz 2 U j z 2 X or z 2 Y g:
(b) P(X): The power set of the set X, denoted P(X), is the s
Math 108 - Pretest
Do not use calculators, books, notes, or help from others. Give yourself one hour of undistracted time to solve all problems.
1. Evaluate the following. Show every step. Do not use calculators. Do not use decimals.
32
(a) 5(2 (3) =
(b)5
Math 108 - Self Assessment Exercises
1
8.1 - Systems of Equations
Review problems
1. A box has the volume of 12 cubic inches. If the width of the box is 4 in, and the length is 9 in,
what is its height?
2. A circle has a circumference of 40 in. Find the r
Math 108 - Self Assessment
5.4 - Graphs of Sine and Cosine
Review Problems
1. Simplify the following:
2
39
5
(a)
(b)
1
2
4
2. Use transformations of graphs (translation, reflection, stretch, compresssion) to sketch the graphs of
the following:
(a) y = (x
Math 108 - Self Assessment
5.2 - Right Triangle Trigonometry
Review Problems
1. Find the hypotenuse of a right triangle whose legs are 3 and 7.
2. Find the leg of a right triangle whose other leg is 8 and the hypotenuse is 9.
Basic Knowledge
3. Find the f
Math 108 - Self Assessment Exercises
1
4.1 and 4.2 - Exponential functions
Review problems
1. Operations on exponents. Simplify. Write answers with only p ositive exponents.
(2x3 y)4
(a)
(b) (16x4 y 8 )3/4
1 )3
(2xy
Basic knowledge
2. Given function f (x)
Math 108 - Self Assessment Exercises
1
2.7 - Transformations of Functions
Review problems
1. Graphs of functions. Sketch the graph of each function. Label intercepts and asymptotes (if
any).
(a) y = x
(b) y = x2
(c) y = x3
(d) y = |x|
(e) y = 1
(f ) y = x
PRACTICE PROBLEMS IN ALGEBRA, TRIGONOMETRY,
AND ANALYTIC GEOMETRY
The accompanying problems from the subjects covered on the Mathematics Placement
Examination can be used by students to identify subject areas that need attention in
preparation for the exa
Math 131
Final Exam
December 19, 2011
Name: (Print)
Student ID:
Instructors Name:
Signature*:
Your signature above arms that this examination is completed in
accordance with the NJIT academic Integrity Code.
Problem
Score
1
2
3
4
5
6
7
8
9
10
Total
1
Writ
Math 131 Exam 2, November 16, 2011
Read each problem carefully and show ALL your work. No calculators.
1.
(16 pts) A ball is thrown upward into the air at time t 0 seconds. Its height in feet above
the ground is given by h(t ) 16t 2 64t 80 .
a. Find the v
Math 131 Exam 1, Oct. 26, 2011
Read each problem carefully and show ALL your work. No calculators.
You may NOT use methods more advanced than those taught in this course up to this point
in the semester.
1.
(12 points) Evaluate the following limits. If th
Math 656 March 10, 2011
Midterm Examination
This is a closed-book exam; neither notes nor calculators are allowed. Explain your work
Note: points add up to 108. You only need 100 points.
1) (14pts) Derive the expression for sinh1 z (arcsinh z) using the d
Math 656 March 10, 2011
Midterm Examination Solutions
1) (14pts) Derive the expression for sinh1 z (arcsinh z) using the definition of sinh w in terms of
exponentials, and use it to find all values of sinh1(2i). Plot these values as points in the complex
Math 656 FINAL EXAM May 11, 2010
This is a closed-book exam; neither notes nor electronic devices are allowed. Please explain all work.
1) (20pts) Categorize all zeros and singularities of the following functions, find two lowest-order non-zero
terms in t
Math 665 FINAL EXAM May 13, 2010
1) Categorize all zeros and singularities of the following functions, find two lowest-order non-zero terms in the
Laurent or Taylor series of f(z) near the given point zo, and state the region on which the corresponding
ex
Math 656 * Homework 20
Due Thursday April 21, 2011
dx
1 x
1. Calculate
6
Integrand has 3 simple poles in upper half-plane:
3 i
;i
z1,2,3 (1)1/6 (ei i 2 k )1/6 cfw_ei /6 , i, ei 5 /6
2
Method 1 Closing via semi-circle CR in the upper half-plane:
dx
dz
Math 656 * Homework 19
Due Monday April 18, 2011
1. Calculate the following improper integrals:
+
(c)
x
0
dx
(assume a > 0, otherwise intergal does not converge)
5
+ a5
Close the contour along the boundary of circular sector with angle 2 / 5 :
C = Cx + C