Unit 8: Applications of Integration
Calculus AB · Unit 8 · Paper 3

Applications of Integration 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 39 terms and is the same for everyone, so a teacher can assign “Unit 8, 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

When the amount is greatest

2

Volume by cross sections, general form

3

In minus out

4

Rectangle cross section with a stated ratio

5

Vertical slices mean top minus bottom

6

Semicircle on diameter s

7

Mean Value Theorem for integrals

8

Integrating with respect to y

9

Limits come from intersections

10

Net Change Theorem

11

Volume by disks

12

Area is never negative

Short answer 1. Define or explain: Area between two curves

3 pts

Short answer 2. Define or explain: Volume by known cross sections

3 pts

Short answer 3. Define or explain: Volume of revolution about a horizontal line

3 pts

Short answer 4. Define or explain: Perpendicular to which axis

3 pts

Free response

9 pts

A particle moves along the x-axis with velocity v(t) = t² − 4t + 3 meters per second for 0 ≤ t ≤ 4 seconds. At time t = 0 the particle is at position x = 2 meters.

Find all times in the interval at which the particle is at rest, and find the intervals on which it is moving to the right.

Find the position of the particle at time t = 4.

Find the total distance traveled by the particle over the interval [0, 4].