Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 24, 25, 26 · 7 college lessons
Parametric Curves & Vector-Valued Motion
How do parameters and vectors represent orientation, motion, tangent behavior, curvature evidence, area, and length beyond single-valued graphs?
Pathways
Lesson 01 · Week 24
Parametric Representation, Elimination & Orientation
Reading a curve as coordinated functions of a parameter.
Lesson 02 · Week 24First Derivatives & Tangent Lines
Computing dy/dx from parameter derivatives.
Lesson 03 · Week 24Second Derivatives & Concavity
Differentiating dy/dx with respect to t and dividing by dx/dt.
Lesson 04 · Week 25Area from Parametric Curves
Accumulating y dx with orientation.
Lesson 05 · Week 25Parametric Arc Length
Integrating speed along a parametric curve.
Lesson 06 · Week 26Vector-Valued Position, Velocity & Acceleration
Differentiating vectors componentwise.
Lesson 07 · Week 26Projectile, Cycloid & Trajectory Modelling
Connecting equations, parameter bounds, and physical interpretation.