Fall, 2002
Hour Exam 1
Name :
Scores :
/100
Please carefully read each problem, follow the exact instructions and show your work in detail.
1. (6pts) Vectors ! and ! are given below. Sketch the vector ! " 3! and ! ! 2!.
u
v
u
v
u
v
2. (16pts) Consider vec
Disclaimer: This practice exam is representative of problems that could appear on your exam,
but it does not cover all eligible topics. While some problems on the actual exam may be similar,
you should not expect that all exam problems are represented on
Math 231, Fall 2013
Exam 1
NAME: _
PLEASE PRINT
You have 50 minutes to complete this exam. No notes or
calculators are allowed. Show all work. Unsupported or illegible
answers will receive no credit. There are a total of 50 points on
this exam.
A page of
Math 231, Fall 2013
1.) [16 points] Given the vectors
v
a = i + 4k ,
Exam 1 Key
v
b = 3i 2 j + k
v
a.) Find the unit vector in the same direction as vector a .
v v
b.) Compute a b .
v
v
c.) Compute the angle between vectors a and b .
v
v
d.) Compute the s
Math 231 Practice Exam 1 Key
1.) [15 points] Given the vectors
v
a = 3i + 4 j k ,
v
v
g.) Compute the vector projection of a onto b .
v
b = 2j+k
1
2.) [10 points] An ant walks on a sideways slinky with position at time t specified by
x = 8 + sin 3t , y =
Math 231 Practice Exam 2 Key
1.) [10 points] Consider the function f ( x, y, z ) = x 2 y + cos(3xz) at the point (1,2,3).
a.) What is direction of maximum increase?
b.) What is the direction of maximum decrease?
c.) Find the rate of change of f(x,y,z) in
Fall, 2002
Hour Exam 4
Solutions
Please carefully read each problem, follow the exact instructions and show your work in detail.
Part I - Dont use a calculator.
1. (15pts) Evaluate the integral.
a. ! ! !2xy ! y 2 "dA where R "
R
1
!x, y " | " 1 # x # 1, 0
Fall, 2002
Hour Exam 2
Name :
Scores :
/100
Please carefully read each problem, follow the exact instructions and show your work in detail.
Part I - Dont use a calculator.
1. (6pts) Find the domain and range of the function f!x, y " !
4 ! x 2 ! 4y 2 " 0 #
Fall, 2002
Hour Exam 2
Solutions
Please carefully read each problem, follow the exact instructions and show your work in detail.
1. (10pts) Identify and then sketch the graph of the curve C traced out by !t " where
r
r
!a " !t " "# 2, 4 cos t, 3 sin t $,
Fall, 2002
Hour Exam 1
- Solutions
Please carefully read each problem, follow the exact instructions and how your work in detail.
1. (6pts) Vectors ! and ! are given below. Sketch the vector ! " 3! and ! ! 2!.
u
v
u
v
u
v
2. (16pts) Consider vectors ! #$
Fall, 2002
Hour Exam 2
Name :
Scores :
/100
Please carefully read each problem, follow the exact instructions and show your work in detail.
Part I - Dont use a calculator.
1. (6pts) Find the domain and range of the function f!x, y " !
4 ! x 2 ! 4y 2 .
2.
Fall, 2002
Hour Exam 2
Name :
Scores :
/100
Please carefully read each problem, follow the exact instructions and show your work in detail.
1. (10pts) Identify and then sketch the graph of the curve C traced out by !t " where
r
r
!a " !t " "# 2, 4 cos t,
Disclaimer: This practice exam is representative of problems that could appear on your exam,
but it does not cover all eligible topics. While some problems on the actual exam may be similar,
you should not expect that all exam problems are represented on