Parametric curves and orientation

Explore parametric curves as moving points whose coordinates share a parameter. This precalculus practice set develops coordinate substitution, tables of positions, graph orientation and repeated traversal. Compare paths that look alike but move in different directions or reach the same point at different times.

The questions progress from direct evaluation to graphical interpretation and counterexamples about motion. Both single-select and multiselect formats provide worked explanations and checks. Use ordered samples and elementary trigonometry; derivatives and calculus-based speed formulas are not required. Each question supplies its own equations and parameter interval.