Study Guide
Learning Objectives
- Construct tables and graphs for parametric functions (4.1.A.1).
- Use f(t) = (x(t), y(t)) notation (4.1.A.2).
- Generate tables by evaluating at ti in domain (4.1.A.3).
- Sketch by connecting points in increasing t (4.1.A.4).
- Interpret restricted domain start/end points (4.1.A.5).
Course scope only (Unit 4 additional topic; not on the AP Exam).
Suggested Practice Sequence
1. Evaluate x(t), y(t) at integer t values. 2. Organize tables with columns t, x, y. 3. Plot (x, y) and connect in rising t. 4. Mark start/end for restricted domains. 5. Check with technology when available.
Classroom / Check-In Moves
- "t, then x, then y" table chant.
- Number points 1,2,3 in time order on the sketch.
- Domain interval written before graphing.
Misconception Watch-List
- Graphing (t, x) or (t, y) as the plane path.
- Wrong connection order between points.
- Forgetting domain limits visible segment.
- Treating t as the vertical coordinate in the xy-plane.
Vocabulary to Own
- parameter; parametric equations
- x(t); y(t); f(t) = (x(t), y(t))
- domain of t; start/end point
- increasing t direction
Materials Map
- Practice: tables, graphs, domain
- Word: motion/path contexts
- Mixed / multi-*: light preview 4.2
- Review & practice test: construct fluency
- Interactive: parameter/table/graph checks