MATH U101 · Tutorial practice · §11.4–11.5, §13.1–13.4, §14.1–14.2
Tutorial Practice Drill
Fresh problems in the same sixteen pattern families as Tutorial Sheets 2–5 — polar symmetry, limaçon area, polar arc length, lens areas, velocity–acceleration angles, tangent lines, vector integrals, initial-value problems, the arc-length parameter, T/κ/N for a helix, osculating circles, domain/level-curve descriptions, two-variable limits by known patterns, two-path non-existence proofs, squeezes, and continuity questions. Six per sheet, randomized every visit, self-marking, with the method on every answer.
Same pattern families as Sheets 2–5; the sheets themselves stay yours to solve. The tutorial companion holds the originals with hints and collapsed solutions; this page serves the same patterns in new clothes so you can recognise them without a hint. Learn first: polar lesson · vector functions lesson · several-variables lesson.
For each problem, before any algebra, write the family name from the key below (e.g. "IVP: integrate twice"). Then solve on paper, reveal, and check the family and the answer; for any miss open "see the method". Untick families you've mastered to focus the sheet. Exact forms (surds, multiples of π) earn the mark — a decimal is given only as a check.