Unit 6: Integration & Accumulation
Calculus AB · Unit 6 · Paper 2

Integration & Accumulation 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 17 terms and is the same for everyone, so a teacher can assign “Unit 6, 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

Definite integral as a limit of Riemann sums

2

Trapezoidal rule

3

Riemann sum from a table

4

Splitting an integral at a sign change

5

Net change theorem

6

Fundamental Theorem of Calculus part 1

7

Common antiderivatives

8

Choosing u in a substitution

9

Over- or underestimate justification

10

Riemann sums

11

Properties of definite integrals

12

Interpreting an integral in context

Short answer 1. Define or explain: Accumulation function analysis

3 pts

Short answer 2. Define or explain: Fundamental Theorem of Calculus part 2

3 pts

Short answer 3. Define or explain: Accumulation function

3 pts

Short answer 4. Define or explain: u-substitution

3 pts

Free response

9 pts

This course has no free-response prompt tagged to this unit, so one from elsewhere in the course is used. It is still worth writing — the skill transfers.

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].