Study Guide
Learning Objectives
- Interpret f(t) = (x(t), y(t)) as planar position at time t (4.2.A.1).
- Find horizontal extrema from max/min of x(t) (4.2.A.2).
- Find vertical extrema from max/min of y(t) (4.2.A.2).
- Relate zeros of x(t) to y-intercepts and zeros of y(t) to x-intercepts (4.2.A.3).
Course scope only (Unit 4 additional topic; not on the AP Exam).
Suggested Practice Sequence
1. Evaluate position at several t values. 2. Scan x(t) for minimum and maximum on the domain. 3. Scan y(t) for minimum and maximum on the domain. 4. Solve x(t)=0 and y(t)=0 within the domain. 5. Mark intercepts and extrema on the motion graph.
Classroom / Check-In Moves
- "Position first: where at t = ...?"
- Separate x-extreme and y-extreme questions.
- Intercept prompts: "Which function equals zero?"
Misconception Watch-List
- Using y = f(x) instead of parametric position.
- Mixing up which zero gives which intercept.
- Finding extrema outside the given t-domain.
- Assuming one t-value gives both horizontal and vertical extrema.
Vocabulary to Own
- planar motion; particle position
- horizontal extrema; vertical extrema
- x-intercept; y-intercept
- x(t); y(t); domain of t
Materials Map
- Practice: position, extrema, intercepts
- Word: motion contexts (robot, projectile setup)
- Mixed / multi-*: combine 4.1 tables with 4.2 features
- Review & practice test: position fluency
- Interactive: intercept/extrema checks