Calculus AB · Unit 1 · Paper 1

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 1 Paper 2 Paper 3

Each paper is built from this unit’s 19 terms and is the same for everyone, so a teacher can assign “Unit 1, 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

Limits at infinity of rational functions

Continuity on an interval

Extreme Value Theorem

Infinite limit vs limit at infinity

Indeterminate form 0/0

Limits involving absolute value

Horizontal asymptote

Squeeze theorem

Limit of a piecewise function at a boundary

Special trig limits

Intermediate Value Theorem

Continuity of piecewise functions

Short answer 1. Define or explain: Vertical asymptote

3 pts

Short answer 2. Define or explain: Evaluating a limit algebraically

3 pts

Short answer 3. Define or explain: Limit definition informally

3 pts

Short answer 4. Define or explain: Removable discontinuity

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.

Let R be the region in the first quadrant bounded by the graphs of y = √x and y = x/2.

Find the area of R.

Find the volume of the solid generated when R is revolved about the x-axis.

The region R is the base of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of this solid.