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Study Guide

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Learning Objectives

  • Describe when distance from origin increases/decreases (3.15.A.1-A.2).
  • Identify relative extrema as closest/farthest points (3.15.A.3).
  • Compute and interpret average rate of change of r (3.15.A.4-A.5).

Suggested Practice Sequence

1. Learn the four sign/monotonicity distance rules. 2. Practice relative extrema on simple polar graphs. 3. Compute (Delta r)/(Delta theta) from tables. 4. Interpret ROC as radius change per radian. 5. Estimate r within an interval using average ROC.

Classroom / Check-In Moves

  • "Sign of r?" then "increasing or decreasing?"
  • Two-point ROC quick calculation.
  • Extremum: "What changed— increasing to decreasing?"

Misconception Watch-List

  • Using Delta theta / Delta r instead of Delta r / Delta theta.
  • Treating decreasing theta as automatically decreasing distance.
  • Missing |r| logic for negative r.
  • Calling endpoint automatically an extremum without monotonic switch.

Vocabulary to Own

  • average rate of change; Delta r; Delta theta
  • distance from origin; relative extremum
  • increasing/decreasing r
  • estimate within interval

Materials Map

  • Practice: trends, ROC, extrema, estimates
  • Word: radar/orbit contexts
  • Mixed / multi-*: link 3.14 graphs
  • Review & practice test: ROC fluency
  • Interactive: trend and ROC checks

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