UR Calculus Placement Self-Assessment Exam

GOAL: The purpose of this exam is to help you decide which calculus class to take first. If you have taken a class in calculus but are not sure whether to enroll in MATH 211 (Calculus I) or MATH 212 (Calculus II), this is the place to start.

NOTE: We ask for an email address in order to send you a copy of your exam, which you may want to share with your advisor. However, the results are not directly used by the department. Ultimately you will are free to enroll in whichever course you think is best for your needs. Note that this exam can not be used to obtain course credit for Calculus I.

PREPARATION: It is a good idea to review Calculus I before the exam. The topics of the exam are:

1) Function properties

2) Finding derivatives using derivative rules, including power functions, exponential functions, ln x, sin x, cos x, tan x, sec x, csc x, cot x

3) Calculating tangent slopes

4) Finding tangent lines

5) Understanding what the derivative means

6) Limits (including Lâ€™Hopitals rule)

7) Calculating basic antiderivatives

8) Interpreting graphs of functions and derivatives

ADDITIONAL RESOURCES: Do not use a calculator, textbook, notes or any other aid while working on the exams. You may find it useful to have scrap paper and a pencil available.

TIME LIMIT: Use as much time as you need.

RESULTS: After you have submitted the exam for grading, you will see your result on each question. Your total score, along with the appropriate placement advice for that score, will be at the bottom of the page.

01-05 points: You appear to have substantial gaps in your Calculus knowledge. We recommend

that you enroll in Math 211.

06-10 points: You appear to have some major gaps in your Calculus knowledge. We do not

recommend enrolling in Math 212 unless you plan to spend substantial time

studying Calculus 1 topics before the semester

11-15 points: You appear to have a solid base for your Calculus knowledge; you may just need

to fill some minor gaps before taking Calculus 2. We recommend spending time

studying topics missed on the assessment exam and enrolling in Math 212.

16-20 points: You are very well prepared for Calculus 2. We recommend enrolling in Math 212.

QUESTIONS: Contact Dr. Hoke at khoke@richmond.edu

PLEASE USE YOUR UNIVERSITY OF RICHMOND EMAIL ADDRESS IN THE FORM BELOW

Email address *

Question 1 *

1 point

Only (i)

(i) and (ii)

Only (iii)

(i), (ii), and (iii)

Question 2 *

1 point

(1)

(2)

(3)

(4)

Question 3 *

1 point

(1)

(2)

(3)

(4)

Question 4 *

1 point

(1)

(2)

(3)

(4)

Question 5 *

1 point

(1)

(2)

(3)

(4)

(5)

Question 6 *

1 point

(1)

(2)

(3)

(4)

Question 7 *

1 point

0

1

-1

Unknown

Question 8 *

1 point

(1)

(2)

(3)

(4)

Question 9 *

1 point

Nothing

It is always increasing

It is always positive

Question 10 *

1 point

Infinity

Negative infinity

0

1

Question 11 *

1 point

Infinity

Negative infinity

0

1

Question 12 *

1 point

Infinity

Negative infinity

0

1

Question 13 *

1 point

converges to c1/c3

converges to c2/c4

converges to 0

converges, but the exact value cannot be determined

diverges

Question 14 *

1 point

(1)

(2)

(3)

(4)

Question 15 *

1 point

(1)

(2)

(3)

(4)

(5)

Question 16 *

1 point

(1)

(2)

(3)

(4)

(5)

Question 17

1 point

-90

30

90

340

The remaining questions refer to the graph below. It represents the velocity (not position) of two particles moving along a straight line. Both particles start at exactly the same position at time t = 0. Positive velocity indicates a particle moving to the right, while negative velocity means it is moving to the left.

Question 18 *

1 point

A

B

They wind up at the same location

It is impossible to tell

Question 19 *

1 point

A

B

Both particles switch directions at some point

Neither particle switched direction

Question 20 *

1 point

At time t = 0, Particle B is traveling leftward and its speed gradually increases until it reaches a maximum at t = 1.5. Then the particle continually slows down until it stops at about t = 2.8 and starts moving with increasing speed in the rightward direction.

At time t = 0, Particle B is traveling leftward and its speed gradually decreases until it reaches its lowest value at t = 1.5. From t = 1.5 until t = 3, the particle is traveling in the rightward direction and gradually gaining more and more speed.

At time t = 0, Particle B is several units to the left of the starting position. It slowly moves farther left until t = 1.5 when it switches direction and begins moving back toward the starting location. It passes the starting location at about t = 2.8 and continues moving to the right, ending a short distance to the right of starting position at time t = 3.