Infinite Sequences and Series BC only
Fifteen topics on sums with no last term. A series converges when its partial sums settle, which is the only definition there is, and terms shrinking to zero is necessary and never sufficient. Most of the unit is tests that decide convergence without computing it: the integral test, whose value is not the sum, the p-series threshold at p > 1 strictly, two comparison pairings that conclude nothing, the alternating test with two conditions, and the ratio test whose value of 1 is no information at all. Then approximation: a Taylor polynomial built on a centre, two error bounds that answer the same question by different means, and an interval of convergence whose endpoints the ratio test cannot see.
Key forms For every problem in this unit
60 open-ended problems.
Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.
Switch to All, work through some cards, and tag them as Got it or Revisit.
Test the unit.
Twenty mixed items drawn from across all 15 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from. AB students are served only the AB items; BC students get the whole unit.
Check what stuck.
Units 1 through 10, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 45-question section, your choice. Even coverage means this is a retention check rather than a score estimate.