This is the second lesson in a seven-lesson unit on Parametrics, Polars, and Vectors
for students enrolled in AP Calculus BC or Calculus 2.
Every lesson includes
✎ A set of Guided Student Notes
✎ A daily homework assignment
✎ Two forms of a daily homework quiz or exit ticket
✎ Teachers also have the benefit of a fully-editable SMART Board® Lesson
for presentation and discussion.
★ Find the slope of a tangent line to a parametric curve
★ Find the arc length of a parametrically-defined curve
★ Solve problems involving planar motion, velocity, and speed
★ Use technology to find arc length of a parametrically-defined curve
College Board® Learning Objectives:
★ LO2.1C Calculate derivatives
★ LO 3.3B (b) Evaluate definite integrals
★ EK2.1C7(BC) Methods for calculating derivatives can be extended to parametric functions
★ LO 2.3C Solve problems involving planar motion
★ EK 2.3C4 (BC) Derivatives can be used to determine velocity, speed, and acceleration for a particle moving along curves given by parametric or vector-valued functions
★ LO 3.4C Apply definite integrals to problems involving motion
★ EK 3.4C2 (BC): The definite integral can be used to determine displacement, distance, and position of a particle moving along a curve given by parametric or vector valued- functions
★ EK 3.4D3 (BC): The length of a planar curve defined by a function or by a parametrically defined curve can be calculated using a definite integral.
The unit includes the following topics:
1. Parametric Equations and Plane Curves
2. Parametric Equations and Calculus
3. Polar Coordinates and Graphs
4. Area and Arc Length in Polar Coordinates
5. Vectors in the Plane
6. Vector-Valued Functions
7. Velocity and Acceleration of Vector Functions
The SMART Board lesson can be used in many ways.
Teachers can display the presentation using the following:
* SMART Board®
* Airliner Wireless Slate
* SMART Notebook for IPAD App
* Through the SMART Notebook Express ®
* Promethean Boards©
* Other APPS available for Tablets
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