Unit I. Analysis of Graphs
Videocasts- 1 Section B: Review Time (unitedstreaming)
The Candy-Coated World of Calculus,Program 1: Calculus Basics. Section B is reviews functions and function behavior (Student Login: hcpss_student, Password: student).
Unit II. Limits of Functions (including one-sided limits)
Unit III. Asymptotic Behavior
Unit IV. Continuity as a Property of Functions
Tutorials- 1 Intermediate Value Theorem
This link contains an animated introduction to the Intermediate Value Theorem. Videocasts- 2 Continuity
This website contains RealMedia lessons of worked problems on continuity. - 3 Section F: Continuity (DE streaming)
The Candy-Coated World of Calculus, Program 3: Derivatives. Part 2 Section F discusses continuity (Student Login: hcpss_student, Password: student).
Unit V. Concept of the Derivative
Unit VI. Computing Derivatives
Games- 1 Derivative Pong
Play Pong with functions and their derivatives: return the correct derivatives, let the incorrect derivatives pass.
- 2 Surfin' Powers of x
Graph different functions. If you enter the right derivative, Surfin' Sinefeld will surf the tangent line.
Quizzes and Tests- 3 Derivatives Review
This link contains an interactive derivatives matching quiz for Product Rule, Quotient Rule, and Implicit Differentiation, and offers correctly worked solutions.
- 4 Devious Derivatives Quiz
Tutorials- 5 Chain Rule
This link contains an animated proof of the chain rule and examples of using the chain rule to calculate various derivatives.
- 6 Derivative Rules Sheet with Proofs
The user can see derivatives for the given functions and can see in-depth proofs for most of the derivatives. Videocasts- 7 Differentiation Rules
This link contains RealMedia lessons on differentiation rules. - 8 Differentiation Rules
This website contains RealMedia lessons differentiation rules for elementary functions. - 9 Implicit Differentiation
This link contains RealMedia lessons of worked problems on Implicit Differentiation. - 10 Section C: Rules to Lessen the Work (DE streaming)
The Candy-Coated World of Calculus, Program 4: Work-Saving Rules. Section C shows how to find the derivative of elementary functions (Student Login: hcpss_student, Password: student). - 11 Section E: The Chain Rule (DE streaming)
The Candy-Coated World of Calculus, Program 5: Finding Derivatives. Section E discusses how to use the Chain Rule (Student Login: hcpss_student, Password: student).
Unit VII. The Derivative at a Point
Activities- 1 Slope of a Curve at a Point
This activity requires students to use Geometer’s Sketchpad to investigate what it means for a curve to have slope. They will create a function which determines the slope of a curve f(x) at every point along the curve. - 2 Slopes of Tangents
This activity requires students to use Geometer’s Sketchpad to explore the relationship between the slopes of secant lines and the slope of tangent lines, and will express this relationship as a limit statement. They will use the results of their exploration to construct the tangent line to the curve. eTools- 3 Average Rates of Change and Derivatives
This link allows students to use an applet to investigate average rates of change and derivatives with several different functions. Tutorials- 4 Derivative of Absolute Value Function at Vertex
This link uses the definition of derivative to prove that the absolute value function is not differentiable at x = 0. Videocasts- 5 Linear Approximations
This link contains RealMedia lessons on derivatives as the best linear approximations to functions.
- 6 Slopes of Tangent Lines
This link contains RealMedia lessons defining slope of tangent line as limit of slopes of secant lines with examples of finding slope of tangent lines.
