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

Mean Value Theorem for integrals

Rectangle cross section with a stated ratio

Average value formula

Area is never negative

Average value of a function

MVT for integrals

Switch variables before splitting

Cross-section area formulas

More than two intersections

Choosing the variable of integration

Volume by cross sections, general form

When the amount is greatest

Short answer 1. Define or explain: Interpreting average value

3 pts

Short answer 2. Define or explain: Net change from a rate in an applied context

3 pts

Short answer 3. Define or explain: Integrating with respect to y

3 pts

Short answer 4. Define or explain: Volume by known cross sections

3 pts

Free response

9 pts

CALCULATOR PERMITTED. Let R be the region in the first and second quadrants bounded above by the graph of y = 4 − x² and below by the graph of y = x + 2.

A. Find the x-coordinates of the points where the two graphs intersect, and find the area of region R.

B. Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of the solid.

C. Find the volume of the solid generated when region R is rotated about the horizontal line y = −2.

D. Write, but do not evaluate, an integral expression that gives the perimeter of region R.