AP Calculus BC (GT) Student Resources

Quarter 2

Quarter 2

UNIT V: Parametric Equations and Polar Coordinate System

- Activities
- 1 Parametric, Vector, Polar and 3-D functions

In this TI activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions. - 2 Parametric, Polar, and 3-D Functions

In this TI activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions. - 3 Parametric, Vector, Polar and 3-D functions

In this TI activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions. eTools - 4 Area Inside a Polar Curve

Interactive applet that allows the user to visualize sweeping out the area inside a polar curve. - 5 Famous Polar Curves

List of applets that allow the user to explore famous polar curves. - 6 Graphing Cycloids (Applet: Cycloids)

By adjusting the length of the radius, the user can produce the graphs of various types of cycloids. - 7 Parametric Equations in Three Dimensions

Graphs a path in three-dimensions. - 8 Plotting Polar Points (Applet: Polar Coordinates)

This applet allows the user to drag a point in the polar coordinate system and note the changes to r, theta, x, and y. The coordinate grid lines may be turned on or off. Reviews - 9 Polar Coordinates and Graphing

AP-style problems. Teacher Support - 10 The Cycloid Family
- 11 Larson 6th Edition, Section 9.2
- 12 Larson 6th Edition, Section 9.2
- 13 Larson 6th Edition, Section 9.2

D - 14 Larson 6th Edition, Section 9.3
- 15 Larson 6th Edition, Section 9.3
- 16 Larson 6th Edition, Section 9.4
- 17 Larson 6th Edition, Section 9.4
- 18 Larson 6th Edition, Section 9.4
- 19 Larson 6th Edition, Section 9.4
- 20 Larson 6th Edition, Section 9.5
- 21 Larson 6th Edition, Section 9.5
- 22 Pearson 3rd Edition, Section 10.1
- 23 Pearson 3rd Edition, Section 10.1
- 24 Pearson 3rd Edition, Section 10.1
- 25 Pearson 3rd Edition, Section 10.1
- 26 Pearson 3rd Edition, Section 10.1
- 27 Pearson 3rd Edition, Section 10.3
- 28 Pearson 3rd Edition, Section 10.3
- 29 Pearson 3rd Edition, Section 10.3
- 30 Pearson 3rd Edition, Section 10.3
- 31 Parametric Derivatives

This is a tutorial fro finding parametric derivatives. - 32 Parametric Integrals

This tutorial demonstrates how to evaluate parametric integrals. - 33 Polar Coordinates

The first segment of this online tutorial provides an introduction to polar coordinates. - 34 Polar Coordinates (Calculus Book II, Chapter 5, Section 2)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 35 Polar Graphs

Section 3 of this link provides an online tutorial for sketching polar graphs. - 36 Polar Integrals

This tutorial demonstrates how to evaluate polar integrals. - 37 Sketching Polar Curves (Calculus Book II, Chapter 5, Section 2, Module 3)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.

UNIT VI: Vectors

- eTools
- 1 Graphical Respresentation of Cross Product

This applet allows the user to drag a vector in a plane and view the resulting cross product vector. - 2 Graphing Vectors in Three Dimensions

This applet allows the user to enter coordinates to create vectors, and the "boxes" created by the endpoints. - 3 Interactive Gallery of Quadric Surfaces

This online resource provides an interactive gallery of quadric surfaces. - 4 Linear Combinations in 3-D

This link contains an applet that allows the user to insert vectors and graph linear combinations. - 5 Relations between Cartesian, Cylindrical, and Spherical Coordinates

This online resource explains how to convert between cartesian, cylindrical, and spherical coordinates. Reviews - 6 Converting Coordinates

This link reviews how to change cylindrical coordinates into rectangular coordinates. - 7 Shortest Distances

This link reviews shortest distances between a point and a plane. - 8 Surfaces of Revolution

This link contains equations for surfaces of revolution and 3-D graphs. Text - 9 Larson 6th Edition, Section 10.1
- 10 Larson 6th Edition, Section 10.1
- 11 Larson 6th Edition, Section 10.1
- 12 Larson 6th Edition, Section 10.2
- 13 Larson 6th Edition, Section 10.2
- 14 Larson 6th Edition, Section 10.2
- 15 Larson 6th Edition, Section 10.3
- 16 Larson 6th Edition, Section 10.3

- 17 Larson 6th Edition, Section 10.3
- 18 Larson 6th Edition, Section 10.3
- 19 Larson 6th Edition, Section 10.4
- 20 Larson 6th Edition, Section 10.5
- 21 Larson 6th Edition, Section 10.5
- 22 Larson 6th Edition, Section 10.5
- 23 Larson 6th Edition, Section 10.6
- 24 Larson 6th Edition, Section 10.6
- 25 Larson 6th Edition, Section 10.7
- 26 Larson 6th Edition, Section 10.7
- 27 Pearson 3rd Edition, Section 10.2
- 28 Pearson 3rd Edition, Section 11.1
- 29 Pearson 3rd Edition, Section 11.1
- 30 Pearson 3rd Edition, Section 11.1
- 31 Pearson 3rd Edition, Section 11.1
- 32 Pearson 3rd Edition, Section 11.1
- 33 Pearson 3rd Edition, Section 11.2

- 34 Pearson 3rd Edition, Section 11.2
- 35 Pearson 3rd Edition, Section 11.2
- 36 Pearson 3rd Edition, Section 11.2
- 37 Pearson 3rd Edition, Section 11.3
- 38 Pearson 3rd Edition, Section 11.4
- 39 Pearson 3rd Edition, Section 11.4
- 40 Pearson 3rd Edition, Section 11.4
- 41 Pearson 3rd Edition, Section 11.5
- 42 Pearson 3rd Edition, Section 11.5, 14.6

- 43 Pearson 3rd Edition, Section 11.5, 14.6
- 44 Pearson 3rd Edition, Section 11.6
- 45 Cross Product (Calculus Book III, Chapter 2, Section 4)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 46 Dot Product (Calculus Book III, Chapter 2, Sections 2-3)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 47 Dot Product (Calculus Book III, Chapter 2, Sections 2-3)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 48 Equations of Lines in Space (Calculus Book III, Chapter 2, Section 5, Module 1)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 49 Equations of Planes (Calculus Book III, Chapter 2, Section 5, Module 2)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 50 Introduction to Vectors

This link provides an online tutorial introduction to vectors. - 51 Orthogonal Vectors (Calculus Book III, Chapter 2, Section 2, Module 5)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 52 Unit Vectors

This link provides an online tutorial for an introduction to unit vectors. - 53 Vector Projection (Calculus Book III, Chapter 2, Section 2, Module 4)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems. - 54 Vectors (Calculus Book III, Chapter 2, Section 1)

Tutorial includes extensive notes (if you click on the Help button) and step-by-step interactive problems.