Unit 4: Contextual Applications
Calculus AB · Unit 4 · Paper 3

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 3” 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

Units of a definite integral

2

Total distance

3

Increasing at a decreasing rate

4

Related rates: one equation, one unknown rate

5

Marginal cost as a derivative

6

Displacement vs total distance

7

Changing direction test

8

Related rates with a cone or sphere

9

Related rates procedure

10

Cone volume relation

11

Position from velocity

12

The rate is decreasing

Short answer 1. Define or explain: Linearization formula

3 pts

Short answer 2. Define or explain: Units of a derivative

3 pts

Short answer 3. Define or explain: Particle at rest vs changing direction

3 pts

Short answer 4. Define or explain: Rate versus change versus amount

3 pts

Free response

9 pts

NO CALCULATOR. A particle moves along the x-axis so that its velocity at time t, for 0 ≤ t ≤ 5, is given by v(t) = t² − 6t + 8. At time t = 0 the particle is at position x = 2.

A. Find all intervals of time in 0 ≤ t ≤ 5 during which the particle is moving to the left. Justify your answer.

B. Find the acceleration of the particle at time t = 1. Is the speed of the particle increasing or decreasing at t = 1? Give a reason for your answer.

C. Find the total distance traveled by the particle over the interval 0 ≤ t ≤ 5.

D. Find the position of the particle at time t = 5.