AP Calculus BC · Unit 9
Parametric Equations, Polar Coordinates, and Vector-Valued Functions
In short
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions in AP Calculus BC covers 9 topics: Defining and Differentiating Parametric Equations, Second Derivatives of Parametric Equations, Finding Arc Lengths of Curves Given by Parametric Equations, Defining and Differentiating Vector-Valued Functions and 5 more. Open each one for what you need to know, a self-check list and how it is tested on the exam.
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What is in Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions?
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
9.1 Defining and Differentiating Parametric Equations
- I can calculate the derivative dy/dx of a parametrically defined curve by dividing dy/dt by dx/dt, and use it to find the slope of the tangent line.
9.2 Second Derivatives of Parametric Equations
- I can calculate the second derivative of a parametric function by dividing the derivative of dy/dx with respect to t by dx/dt.
9.3 Finding Arc Lengths of Curves Given by Parametric Equations
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
- I can use the definite integral of the velocity vector to find a particle's displacement and position, and the definite integral of speed to find the total distance traveled over an interval of time.
9.7 Defining Polar Coordinates and Differentiating in Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
9.9 Finding the Area of the Region Bounded by Two Polar Curves
Parametric Equations, Polar Coordinates, and Vector-Valued Functions: common questions
What is in Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions?
It covers 9 topics: 9.1 Defining and Differentiating Parametric Equations; 9.2 Second Derivatives of Parametric Equations; 9.3 Finding Arc Lengths of Curves Given by Parametric Equations; 9.4 Defining and Differentiating Vector-Valued Functions; 9.5 Integrating Vector-Valued Functions; 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions; 9.7 Defining Polar Coordinates and Differentiating in Polar Form; 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve; 9.9 Finding the Area of the Region Bounded by Two Polar Curves.
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