Exam Strategy
Calculus BC · AP · Infinite Sequences and Series
CED focus
Integral Test for Convergence
This topic is assessed on the AP Exam.
Multiple-choice tips
- Decide if the item is net change, total area, or volume before integrating.
- Name the convergence test before picking an MC answer.
- Eliminate endpoint errors on interval-of-convergence choices.
- On Taylor MC, match degree or center to the stem.
- Distinguish nth-term test (divergence only) from convergence claims.
Free-response tips
- State integrand meaning and units; show FTC or Riemann setup explicitly.
- State the test and verify its hypotheses for series convergence.
- Show ratio/root steps for radius; test endpoints separately.
- Write a Taylor polynomial with labeled center and degree.
- Bound error with a remainder when accuracy is asked.
Common traps
- Wrong limits or missing π in volume setups
- Concluding convergence from nth-term test alone
- Forgetting to test interval endpoints
- Using a Taylor polynomial of wrong degree
Quick checklist
- [ ] Can name and apply one convergence test correctly
- [ ] Can find a Taylor polynomial about a given center
- [ ] Can state what a remainder bound guarantees