Parametric Functions
Unit 4 is not assessed on the AP exam; schools include it based on local requirements, and everything here still builds directly toward calculus. A parametric function assigns each parameter value t a full point (x(t), y(t)), so the graph is a journey: it has a shape, and also a start, a direction of travel, and an extent that the t interval controls.
The mistakes are information-loss mistakes: eliminating the parameter and reporting the whole x-y curve when the journey only covers a clipped piece of it, forgetting that elimination erases direction and starting point, and assuming a path has exactly one parametrization when reversing, rescaling, and shifting all produce equally valid ones. The lesson drills the recover-the-journey discipline.
The work
3 ways in · any order
Lesson
Parametric Functions
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A parameter drives both coordinates, so the graph is a journey with direction and extent. The lesson tables and traces parametric curves, eliminates the parameter without losing the path, and rebuilds journeys at new speeds and directions. Ten scenarios close it out.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 4.1 misconceptions: parameter elimination that silently overstates the traced path, and the assumption that a curve owns exactly one parametrization. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.