Calculus AB · Unit 8 · Paper 1

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 1 Paper 2 Paper 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 1” 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

Net Change Theorem

Semicircle on diameter s

Average value formula

Area is never negative

Average value of a function

MVT for integrals

Horizontal slices mean right minus left

Volume by known cross sections

Limits come from intersections

Cross-section area formulas

Keep decimals until the end

When the amount is greatest

Short answer 1. Define or explain: Washers with a shifted axis

3 pts

Short answer 2. Define or explain: Washer inner and outer radii

3 pts

Short answer 3. Define or explain: Area between two curves

3 pts

Short answer 4. Define or explain: Volume by washers

3 pts

Free response

9 pts

A particle moves along the x-axis with velocity v(t) = t² − 6t + 8 for 0 ≤ t ≤ 5, and its position at time t = 0 is s(0) = 2.

Find all times in the open interval (0, 5) at which the particle changes direction. Justify your answer.

Find the displacement of the particle over the interval [0, 5].

Find the total distance traveled by the particle over the interval [0, 5].