Cycloids and alternative traversals

Study cycloids through the geometry of a point on a rolling wheel. This precalculus extension practice connects wheel radius, rotation angle, horizontal advance and height, using exact parameter samples and a plotted arch. Compare a rolling-point path with the path of the wheel centre and examine alternative traversals.

Ten focused single-select and multiselect questions progress from geometric interpretation to changes of parameter and reversal. Detailed explanations use tabulation, arc length and elementary trigonometry rather than derivatives. Assume rolling without slipping on a horizontal line whenever a wheel model is stated. No calculus knowledge is needed.