A fly's path through a room, a planet's orbit, a spiral, a rose — some curves can't be written as a single function of x. This unit gives you three new languages for motion and shape: parametric, vector, and polar.
Let a parameter t drive both x and y. Find the slope, the concavity, and the arc length of a curve that's traced out over time.
Position, velocity, and acceleration, one derivative apart. Differentiate component-wise, then solve motion: speed, displacement, distance.
Trade x and y for radius and angle. Watch roses, cardioids, and spirals sweep into being as θ turns — and find slopes in polar form.
Area isn't ∫y dx here — it's a fan of pie slices, ½∫r² dθ. Find the area of one region, or the area trapped between two polar curves.
Multiple-choice with deep explanations and a weak-spot tracker, plus full 9-point free-response — the parametric/vector motion problem and the polar-area problem, the two question types Unit 9 always brings to the exam.
Start practicing →Go in order. Parametric sets up the idea of a parameter driving a curve; Vectors is the same idea in motion language; then Polar graphing and Polar area build the other coordinate system from the ground up. Each tool animates the thing the textbook only describes.
Drill the two things that lose points: the parametric motion problem (displacement vs. distance) and polar area (½∫r², and finding the right limits). The cheat sheet has every formula and the "which setup?" logic on one printable page.