Montgomery College
Department of Mathematics
Rockville Campus
Sample Midterm Exam
Instructions:
The questions below should give you a good idea about the Midterm Exam. Please read
each question carefully. You will be expected to show appropriate work to r
Montgomery College
Department of Mathematics
Rockville Campus
Sample Test #2: Answer Key
1.
dy
dx
1
4x 14x 2 4 4 tan 1 4x.
cosx 2y1 2y . Substitute x 0, y 0 to obtain y 1 .
2
So y 1 x.
2
2. x. 2yy 1. y 2
3.
g x
1
x
1. g x 0 if
3x 2 8x
4.
dy
dx
5.
y 2x
MA 181 FINAL EXAM REVIEW
Page 1
REVISED Fall 2009
I.
CLEARLY AND COMPLETELY STATE
1.
The definition of continuity of a function f ( x ) at x = a and how to use this definition in
a problem.
2.
The formal definition of f (x ) , the derivative of a function
Montgomery College
Department of Mathematics
Rockville Campus
Sample Midterm: Answer Key
1. Using x values close to 0, we find that lim x 0
2. lim x 1
3. lim x 2
x1 3x1
x1
1
x2
x1 3x1
x1
lim x 1
4
x 2 4
lim x2
1
x2
6 x 1
x
x1 3x1
x1 3x1
1. 79.
lim x 1
Montgomery College
Department of Mathematics
Rockville Campus
Sample Test #3: Answer Key
1.
f x xe x 2 x so f x e x x 2 4x 2.
Make a table of signs for f x:
2 2
2 2
x
f x
.
It shows that f has inflection points at 2 2 and 2 2 .
2.
Let x be the distance be
Montgomery College
Department of Mathematics
Rockville Campus
Sample Test #1: Answer Key
1. Using x values close to 1, we find that lim x 1 fx . 7071
h1 3 1
h
2. lim h0
3. lim x 2
1
x2
lim h0
4
x 2 4
h 3 3h 2 3h
h
lim x2
1
x2
3.
1.
4
4. Answers vary.
Montgomery College
Department of Mathematics
Rockville Campus
Sample Test #3
Instructions:
Test #3, the third online test, will have 8 multiple-choice questions plus 1 bonus question.
You will need to carefully solve each problem before selecting what you
Montgomery College
Department of Mathematics
Rockville Campus
Sample Test #1
Instructions:
Test #1, the first online test, will have 12 multiple-choice questions. You will need to
carefully solve each problem before selecting what you believe is the corre
Montgomery College
Department of Mathematics
Rockville Campus
Sample Test #2
Instructions:
Test #2, the second online test, will have 8 multiple-choice questions plus 1 bonus
question. You will need to carefully solve each problem before selecting what yo