Study Guide

Learning Objectives

• Express parametric position as vector-valued p(t) (4.9.A.1).
• Compute |p(t)| as distance from origin (4.9.A.1).
• Use vector-valued v(t) for velocity, direction, and speed (4.9.A.2).
• Support conclusions with logical rationale or data (3.C).

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

Suggested Practice Sequence

1. Write p(t) = <x(t), y(t)> from parametric equations. 2. Evaluate p(t0) and compute |p(t0)|. 3. Interpret |p(t)| as distance from origin. 4. Analyze v(t) component signs for direction. 5. Compute |v(t)| as speed and justify claims (3.C).

Classroom / Check-In Moves

• "Position vector or velocity vector?"
• "Distance from origin uses |p(t)|."
• "What data supports that direction?"

Misconception Watch-List

• Using position magnitude as speed.
• Ignoring i,j equivalence with component pairs.
• Direction claims without sign/table evidence.
• Treating vector-valued function as scalar speed only.

Vocabulary to Own

• vector-valued function; position vector; velocity vector
• p(t); v(t); |p(t)|; |v(t)|
• speed; distance from origin
• component signs; rationale

Materials Map

• Practice: p(t), v(t), magnitudes, direction
• Word: particle motion contexts
• Mixed / multi-*: combine 4.1-4.3, 4.8, 4.9
• Review & practice test: vector-valued fluency
• Interactive: magnitude and direction checks