Study Guide

Learning Objectives

• Describe direction from increasing/decreasing x(t) and y(t) (4.3.A.1).
• Recognize direction can change with t (4.3.A.2).
• Compare parametrizations of the same curve (4.3.A.3).
• Compute average rates and secant slope from their ratio (4.3.A.4).

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

Suggested Practice Sequence

1. Pick an interval; sign-check changes in x(t) and y(t). 2. State right/left and up/down direction separately. 3. Compare direction on two subintervals. 4. Compute average ROC for x and y on [t1, t2]. 5. Form secant slope and justify with data (3.C).

Classroom / Check-In Moves

• "x up? y down? Say both before one arrow."
• Table two t-values; compute Delta x, Delta y, Delta t.
• Pair-share: same curve, two parametrizations.

Misconception Watch-List

• Using instantaneous derivative language when only average ROC is required.
• Reversing right/left or up/down sign rules.
• Computing slope as Delta t / Delta x.
• Assuming direction at one t applies for all t.

Vocabulary to Own

• direction of motion; increasing/decreasing component
• average rate of change; secant slope
• parametrization; traversal direction
• interval [t1, t2]

Materials Map

• Practice: direction, rates, parametrizations
• Word: motion contexts with direction/rate questions
• Mixed / multi-*: combine 4.1-4.2 with 4.3
• Review & practice test: direction/rate fluency
• Interactive: direction and average-rate checks