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Study Guide

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Learning Objectives

  • Associate linear transformations with matrices (4.13.A.1).
  • Build A from unit/basis vector images (4.13.A.2).
  • Use rotation matrix [[cos,-sin],[sin,cos]] (4.13.A.3).
  • Interpret |det(A)| as area dilation magnitude (4.13.A.4).
  • Compose transformations; matrix product rule (4.13.B.1, 4.13.B.2).
  • Find inverse transformation via A^-1 (4.13.C.1, 4.13.C.2).
  • Identify/describe from graphical and verbal info (2.A, 3.A).

Course scope only (Unit 4 additional topic; not on the AP Exam).

Suggested Practice Sequence

1. Build A from basis images. 2. Recognize rotation and scaling matrices. 3. Compute |det| and interpret dilation. 4. Compose two transformations (matrix product). 5. Find and verify inverse transformation.

Classroom / Check-In Moves

  • Where do i-hat and j-hat go?
  • What does |det| tell about area?
  • Does order matter for AB?

Misconception Watch-List

  • Wrong rotation matrix signs.
  • Treating composition as addition.
  • Assuming inverse always exists without det check.

Vocabulary to Own

  • transformation matrix; composition
  • rotation; dilation; inverse transformation
  • basis images; |det(A)|

Materials Map

  • Practice: association, rotation, composition, inverse
  • Word: geometric transformation contexts
  • Mixed / multi-*: combine with 4.11-4.12
  • Review and practice test: matrices-as-functions fluency
  • Interactive: rotation, composition, inverse checks

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

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