College Board
Reasoning from Tabular Data
Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...
CK-12 Foundation
Antiderivative: Piecing it Together
Build a function backwards. Given a graph of the derivative of a function, pupils piece together a graph of the original function, the antiderivative. Learners use their graphs and the graphs of the derivatives to answer questions about...
CK-12 Foundation
Constant, Identity, and Power Rules: Power Rule
Learn to gain power in finding derivatives. The resource introduces the power rule. Using the sliders in the interactive, pupils create polynomial functions and find their derivatives. Given the derivative of a polynomial, learners...
CK-12 Foundation
Chain Rule
Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...
CK-12 Foundation
Higher Order Derivatives—Acceleration and Jerk
Accelerate your class through finding the second derivative. Using a bank of equations, pupils determine the equations for distance, velocity, and acceleration and their associated function notations. With the equations, learners answer...
CK-12 Foundation
Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...
CK-12 Foundation
Slope of a Tangent Line: Slope of the Tangent and Secant Lines
Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...
CK-12 Foundation
Tangent Line Approximation: Estimating Square Roots
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
CK-12 Foundation
Derivatives of Trigonometric Functions: Derivative of sin(x)
Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...
CK-12 Foundation
Differential Equations Representing Growth and Decay: Rice Legend
The legend of a wise man who asks a king for rice as a reward presents a context to study exponential solutions to differential equations. Pupils move quantities of rice to a chessboard and calculate the amount of rice for each day. To...
CK-12 Foundation
Logarithmic Differentiation: Graphing the Derivative of a Logarithm
Log the values of the derivative of a logarithm. The interactive plots the derivative of the natural logarithm. Learners first determine the derivative of natural logarithm and the general logarithm. Using the formulas for the...
Mathematics Vision Project
Quadratic Equations
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
University of North Texas
Math Exam 1 Review
Perfect as a review guide, this worksheet provides a range of questions focusing on functions. Topics include composing functions, transformations, domains, and polynomials. Also included are corresponding worksheets focusing on other...
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson begins with looking at limits of simple linear and rational functions, and leads to the definition of the derivative....
CK-12 Foundation
Evaluate Limits Using Graphs and Tables: Where Is That Limit?
Limits are made easy through graphs and tables. An easy-to-use interactive lets users change a function on a coordinate plane. They relate graphs and tables to the limit at a specific value.
CK-12 Foundation
Evaluate Limits Using Graphs and Tables: Evaluate the Limits
Discontinuities in the graph? No worries. Pupils investigate the limit of a function given graphically using an interactive. The graph has removable and jump discontinuities.
CK-12 Foundation
One-Sided Limit Type: One-Sided Limits
Not everything that's one-sided is bad. A slider interactive aids learners in investigating one-sided limits from graphs. A set of challenge questions assesses their understanding of the relationship between one- and two-sided limits.
CK-12 Foundation
One-Sided Limit Type: Limit Notation and Graphs
A one-sided limit is no less important than a two-sided limit. Young mathematicians use an interactive to match limit notation to graphs. The exercise requires interpreting how one-sided limits connect to features of graphs.
CK-12 Foundation
Infinite Limit Type: Properties of Limits
Limits can provide some valuable information about graphs. A slider interactive lets learners see the behavior of a graph around asymptotes. They investigate relationships between limits and asymptotes.
CK-12 Foundation
Infinite Limit Type: Evaluating Limits of Rational Functions
Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...
CK-12 Foundation
Infinite Limit Type: Asymptotes and End Behavior Question
There are an infinite number of reasons to use the resource. Scholars drag vertical and horizontal lines to the graph of a rational function to identify all asymptotes. They investigate the connection between asymptotes and limits to...
CK-12 Foundation
Identify Functions and the Vertical Line Test: The Vertical Line Test
There's no easier test than the vertical line test. Learners drag a vertical line across the graphs of several relations in an interactive. They answer a set of challenge questions that focus on whether the graphs represent functions.
CK-12 Foundation
Zeroes and Intercepts of Polynomials: Function Intercepts
There is zero reason not to use the resource. Given a graph with a polynomial function and a linear function, scholars move the line in an interactive. To wrap up the lesson, they note how zeros and intersection points change.
CK-12 Foundation
Restricted Domain and Range: Restricted Circle Radius and Area
There's no restriction to how much your class can learn about domain and range. Users of an interactive adjust the radius of a circle to see its effects on the area. They note how restrictions in the domain (radius) relate to...