Unit 9 includes all the topics listed in the title. These are BC only topics (CED – 2019 p. 163 – 176). These topics account for about 11 – 12% of questions on the BC exam.
Comments on Prerequisites: In BC Calculus the work with parametric, vector, and polar equations is somewhat limited. I always hoped that students had studied these topics in detail in their precalculus classes and had more precalculus knowledge and experience with them than is required for the BC exam. This will help them in calculus, so see that they are included in your precalculus classes.
Topics 9.1 – 9.3 Parametric Equations
Topic 9.1: Defining and Differentiation Parametric Equations. Finding dy/dx in terms of dy/dt and dx/dt
Topic 9.2: Second Derivatives of Parametric Equations. Finding the second derivative. See Implicit Differentiation of Parametric Equations this discusses the second derivative.
Topic 9.3: Finding Arc Lengths of Curves Given by Parametric Equations.
Topics 9.4 – 9.6 Vector-Valued Functions and Motion in the plane
Topic 9.4 : Defining and Differentiating Vector-Valued Functions. Finding the second derivative. See this A Vector’s Derivatives which includes a note on second derivatives.
Topic 9.5: Integrating Vector-Valued Functions
Topic 9.6: Solving Motion Problems Using Parametric and Vector-Valued Functions. Position, Velocity, acceleration, speed, total distance traveled, and displacement extended to motion in the plane.
Topics 9.7 – 9.9 Polar Equation and Area in Polar Form.
Topic 9.7: Defining Polar Coordinate and Differentiation in Polar Form. The derivatives and their meaning.
Topic 9.8: Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
Topic 9.9: Finding the Area of the Region Bounded by Two Polar Curves. Students should know how to find the intersections of polar curves to use for the limits of integration.
The suggested time for Unit 9 is about 10 – 11 BC classes of 40 – 50-minutes, this includes time for testing etc.
Previous posts on these topics:
Parametric and Vector Equations
Implicit Differentiation of Parametric Equations
Adapting 2012 BC 2 (A parametric equation question)
Polar Equations for AP Calculus
Visualizing Unit 9 Desmos Demonstrations for Polar, Vector and Parametric Curves