Interactive
CK-12 Foundation

Derivatives of Trigonometric Functions: Derivative of sin(x)

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Logarithmic Differentiation: Graphing the Derivative of a Logarithm

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima

For Students 11th - Higher Ed
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...
Interactive
Curated OER

Graphing of Functions Using First and Second Derivatives

For Students 11th - 12th
In this calculus learning exercise, students solve problems using the first and second derivatives. They define the behavior of the function based on the derivative. There are 11 questions with an answer key.
Interactive
CK-12 Foundation

Higher Order Derivatives—Acceleration and Jerk

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Constant, Identity, and Power Rules: Power Rule

For Students 11th - Higher Ed
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...
Interactive
Curated OER

Review of Calculus BC I

For Students 10th - 12th
In this review worksheet, students match a function to the proper description.  they identify the domain of a function.  Students determine the slope of an inverse function.  They find the derivative of given...
Interactive
CK-12 Foundation

Antiderivative: Piecing it Together

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Chain Rule

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Slope of a Tangent Line: Slope of the Tangent and Secant Lines

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Tangent Line Approximation: Estimating Square Roots

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Average and Instantaneous Rates of Change

For Students 11th - Higher Ed
How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...
Interactive
Curated OER

Twenty-Eight Multiple Choice No Calculator Allowed AP Calculus BC Practice Exam

For Students 12th - Higher Ed
In this AP Calculus BC practice exam, students solve twenty-eight multiple choice problems without the use of a calculator.  This worksheet should be completed in fifty-five minutes.
Interactive
Curated OER

Implicit Differentiation Problems

For Students 9th - 10th
In this calculus worksheet, students perform implicit differentiation to take the derivative. They solve function explicitly of x. They differentiate between implicitly and explicitly. There are 16 problems with an answer key.
Interactive
Curated OER

The Method of U-Substitution

For Students 9th - 10th
In this calculus instructional activity, students solve problems using U-Substitution. They find antiderivatives  using indefinite integrals. There are 18 questions with an answer key.
Interactive
Curated OER

Product Rule

For Students 9th - 10th
In this calculus worksheet, students find the derivative of a function. They use the product rule to to differentiate each problem. There are 21 problems with an answer key.
Interactive
Curated OER

Differentiation Using the Chain Rule

For Students 10th - 12th
In this calculus worksheet, students solve problems using differentiation and the chain rules. They take the derivatives of equations using specific equations. There are 21 problems with an answer key.
Interactive
Curated OER

Word Problems

For Students 10th - 11th
In this calculus worksheet, learners use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Interactive
Curated OER

The Limit Definition of a Definite Integral

For Students 11th - 12th
In this calculus worksheet, students calculate the derivative and integral of different functions. They use interval to mark the beginning and end of their calculations. There are 15 questions with an answer key.
Interactive
Curated OER

The Method of Integration by Partial Fractions

For Students 9th - 10th
For this calculus worksheet, students solve problems using integration by partial fractions. They add fractions to get a common denominator, then take the derivative. There are 20 questions with an answer key.
Interactive
Curated OER

Review of Calculus

For Students 12th
In this calculus worksheet, 12th graders solve problems that cover a variety of topics, including limits, derivatives, integrals, and problem solving.  The one page interactive worksheet contains forty-eight questions and is self...
Interactive
Curated OER

Review of Calculus BC II

For Students 11th - 12th
In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series.  The one page...
Interactive
CK-12 Foundation

Related Rates of Car Speeds

For Students 11th - Higher Ed
Speed up your pupils' understanding of derivatives. Two cars travel in perpendicular distances to each other. With the aid of the interactive, learners visualize the situation. Pupils use the derivative to calculate the instantaneous...
Interactive
CK-12 Foundation

Absolute Versus Local Extrema

For Students 11th - Higher Ed
Get the class to take an extreme look at functions. The interactive presents a function on a closed interval with a movable tangent line. Using the given function, pupils determine the extrema, critical points, and points of...