Unit 4: Contextual Applications
Calculus AB · Unit 4 · Paper 2

Contextual Applications unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 40 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 2” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 36 min 33 points0/17 attempted
1

Position from velocity

2

Average velocity versus instantaneous

3

Related rates with a cone or sphere

4

Position needs an initial condition

5

Units of a definite integral

6

Particle at rest vs changing direction

7

Speed is not a derivative

8

Cone volume relation

9

Sphere volume and surface area

10

Common related-rates error

11

Rectilinear motion

12

Linearization formula

Short answer 1. Define or explain: Decreasing at a decreasing rate

3 pts

Short answer 2. Define or explain: Related rates procedure

3 pts

Short answer 3. Define or explain: Rate versus change versus amount

3 pts

Short answer 4. Define or explain: The rate is decreasing

3 pts

Free response

9 pts

Water flows into an inverted right circular cone-shaped tank at a constant rate of 3 cubic meters per minute. The tank has height 10 m and top radius 5 m, so the water-surface radius r and the water depth h always satisfy r = h/2.

Show that the volume of water in the tank is V = (π/12)h³.

Find the rate at which the depth of the water is rising at the instant when h = 4 m. Include units.

Find the rate at which the radius of the water surface is increasing at that same instant. Include units.