Unit 1: Limits & Continuity
Calculus BC · Unit 1 · Paper 2

Limits & Continuity 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 22 terms and is the same for everyone, so a teacher can assign “Unit 1, 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

Removable vs jump discontinuity

2

Recheck the form after each L'Hôpital step

3

Comparing growth rates

4

Special trig limits

5

Intermediate Value Theorem

6

Why a table cannot prove a limit

7

Indeterminate forms requiring rewriting

8

One-sided limits and existence

9

Continuity of a composition

10

L'Hôpital's Rule conditions

11

Three conditions for continuity at a

12

Squeeze theorem

Short answer 1. Define or explain: Growth hierarchy for limits

3 pts

Short answer 2. Define or explain: Oscillation as a failure mode

3 pts

Short answer 3. Define or explain: Limit at infinity by degree

3 pts

Short answer 4. Define or explain: Repeated application of L'Hôpital

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.

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.