Solutions to Midterm 1a MA 225 B1 Spring 2011
Question 1
(i) b c is a vector, so we can take its dot product with a. Since the dot product of two vectors is
a scalar, this quantity is a scalar.
(ii) B
Calc I & II review MA 225 B1 Spring 2011
The purpose of these exercises is to emphasize that you are expected to know the material from
Calculus I and II, and to highlight concepts that I feel are par
MA 225 PRACTICE FINAL SOLUTIONS
1. (12 points) Answer the following questions about 3D vector geometry.
(a) (3 pts) Find a vector which is normal to the plane 2x 3z = 1.
Solution: Copying the coeffici
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MA 225 PRACTICE FINAL
1. (12 points) Answer the following questions about 3D vector geometry.
(a) (3 pts) Find a vector which is normal to the plane 2x 3z = 1.
(b) (3 pts) Find the angle between the v
FINAL EXAM
Math 21a, Spring 03
Name:
Start by printing your name in the above box and
check your section in the box to the left.
Try to answer each question on the same page as
the question is asked
SOLUTIONS Practice Midterm 1 MA 225 Fall 2016
Question 1 Let
u = h2, 1, 3i,
v = h4, 5, 0i,
w = h1, 1, 4i
be vectors in R3 . For each of the following, if the quantity makes sense, compute it. If it do
MA 225 PRACTICE MIDTERM I
1. (10 points)
Find the area of the triangle with vertices (0, 0, 0), (1, 0, 1) and (0, 1, 1).
2. (10 points)
(a) (4 pts)
Find the equation of a line passing through (1, 2, 3
Solutions - Midterm 1a - MA 225 - Fall 2016
Question 1 Let
u = h5, 2, 1i,
v = h1, 0, 3i,
w = h2, 3, 4i
be vectors in R3 . For each of the following, if the quantity makes sense, compute it. If it does
MA 225 PRACTICE MIDTERM II
1. (10RRR
points) Let D be the region in space bounded by the surface x2 + y 2 = 9 and the planes z = 0 and z = 1.
Find
z 2 dV . Sketch D (3 pts), set up an appropriate iter
Practice Midterm 1 MA 225 Fall 2016
Name:
BU ID:
Discussion section (circle one):
B2: W 9-10,
B3: W 2-3,
B4: W 1-2,
B5: Th 830-930,
B6: Th 930-1030
Instructions: Please write clearly and show all work
Exam 1 Solutions
1. (20 points) Write the equation of the plane that passes through the three points
(3, 2, 1), (0, 2, 1), and (2, 0, 2). For full credit, you must check your answer
by plugging in the
Solutions to Quiz 3 MA 225 B2 and B3 Spring 2011
Question 1 A parameterization of the line is
r(t) = (1 t) 0, 2, 3 + t 1, 6, 4 = t, 2 + 4t, 3 + t ,
Thus,
1
f (r(t)|r (t)|dt =
f (x, y, z )ds =
C
0
1
18
Quiz 1 MA 225 B2 Spring 2011
Instructor: Margaret Beck
TF:
Man-Ho Ho
Date:
February 2, 2011
Name:
BU ID:
Score: 1.
(out of 24)
2.
(out of 14)
3.
(out of 42)
4.
(out of 20)
Total:
(out of 100)
Instruct
Quiz 3 MA 225 B2 Spring 2011
Instructor: Margaret Beck
TF:
Man-Ho Ho
Date:
April 27, 2011
Name:
BU ID:
Score: 1.
(out of 20)
2.
(out of 20)
3.
(out of 20)
4.
(out of 20)
5.
(out of 20)
Total:
(out of
Solutions to Quiz 2 MA 225 B2 Spring 2011
Question 1 If we test the approach to the origin along a line of the form y = mx, we nd
5mx4
5m
=
,
4 ) x4
(1 + 3m
(1 + 3m4 )
which is dierent for dierent val
Quiz 2 MA 225 B2 Spring 2011
Instructor: Margaret Beck
TF:
Man-Ho Ho
Date:
March 9, 2011
Name:
BU ID:
Score: 1.
(out of 20)
2.
(out of 20)
3.
(out of 45)
4.
(out of 15)
Total:
(out of 100)
Instruction
Midterm 2a MA 225 B1 Spring 2011
Instructor: Margaret Beck
TF:
Man-Ho Ho
Date:
March 31, 2011
Name:
BU ID:
Score: 1.
(out of 10)
2.
(out of 10)
3.
(out of 10)
4.
(out of 10)
5.
(out of 10)
6.
(out of
Solutions to Midterm 2a MA 225 B1 Spring 2011
Question 1 Dierentiating both sides of the equation with respect to y , we obtain
z + yzy = zy /(x + z ).
Solving this equation for zy , we nd
z
z (x + z
Midterm 1a MA 225 B1 Spring 2011
Instructor: Margaret Beck
TF:
Man-Ho Ho
Date:
February 15, 2011
Name:
BU ID:
Score: 1.
(out of 10)
2.
(out of 10)
3.
(out of 10)
4.
(out of 10)
5.
(out of 20)
6.
(out
Solutions to Calc I & II review MA 225 B1 Spring 2011
If you got (m)any of these wrong, dont worry! It has been at least a month since you took Calc II,
and longer since you had Calc I. Just be aware
Solutions to Quiz 1 MA 225 B2 Spring 2011
Question 1
(i) 5, 22, 7
(ii) 1
(iii) 1, 2, 7
(iv) They are not orthogonal, because their dot product is nonzero. They are not parallel, because
their cross pr
Exam 3
Answer each question on a separate sheet of paper. Write on the front and back of
the sheet of paper if you need the space.
No calculators or phones or anything like that.
One sheet (front a
Exam 3
Answer each question on a separate sheet of paper. Write on the front and back of
the sheet of paper if you need the space.
No calculators or phones or anything like that.
One sheet (front a
Exam 1
Answer each question on a separate sheet of paper. Write on the front and back of
the sheet of paper if you need the space.
No calculators or phones or anything like that.
No notes or books.
Academic conduct statement [3 points] Please write out the statement I am aware that this
exam, like any exam, is governed by the Boston University academic conduct code.
Please print your name:
Pleas