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...

Pupils learn how to find the derivative of a function by applying the definition using limits. Learners understand that the derivative provides the slope of the tangent line and use that information to find the equation of the tangent...

It seems like it should be about three. Pupils learn to get an estimate of the derivative of a function at a point by using the derivative functionality of their graphing calculators. They take that information to determine the equation...

Don't go off on a tangent while writing equations of tangent lines! Scholars determine the equations for tangent lines to circles. They attempt both concrete and abstract examples, such as a tangent line to the unit circle through...

Tie up everything in one differentiable bow. Pupils work through 20 problems to review the concepts from the unit. The problems range from finding the average rate of change to finding the derivatives of various functions that require...

Use derivatives to find equations of lines. Pupils learn more rules to use as shortcuts to find derivatives. Using the rules, they find the equations of the tangent line and the normal line at a given point. Scholars then apply the new...

Twelfth graders recognize the use of the slope of the secant line and connect it with the graph of the secant line, as the secant line approaches the tangent line. They also recognize the two forms of the slope formula used and practice...

Providing both review and practice problems, this worksheet prompts students to answer five questions having to do with slope, tangents lines, graphing, the Squeeze Theorem, differentiable functions and derivatives. This activity could...

Frolic through a field of slopes. Learners watch a video describing slope fields and how to create one. Scholars use given slope fields to determine the equation of a tangent line and the possible differential equation. Pupils continue...

No need to be exact every time. Pupils watch an engaging video on approximating function values. They see how to write the equation of a tangent line, use it to calculate approximations, and then determine whether it is an overestimate...

Derive tangent lines through derivatives. Scholars use an app to graph functions and investigate derivatives and tangent lines. The interactive automatically graphs a tangent line at a specified point and can also produce tables of values.

The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils...

Differentiate everyone's knowledge. Pupils work through nine review questions to highlight key concepts from Unit 7. Items range from finding slope fields and reasoning with them to finding general and particular solutions of...

In this limit of slopes worksheet, students compute the limit of slopes, find the slope of the secant line, and determine the slope of the tangent line. This one-page worksheet contains five multi-step problems.

In this limits worksheets, students graph tangent lines and determine the slope of a secant line. This one-page worksheet contains six multi-step problems.

What do a zoo, snow, and a moving particle have in common? The six free-response items from the 2010 AP® Calculus BC exam allow teachers and pupils see how items may show up in context. Three of the questions are from only the BC portion...

Take an abbreviated look at the exam. Class members review released items to prepare for the BC exam. The released questions are the six free-response questions from the 2001 exam. Three of the items have context, while the other three...

Find a solution in the field. An informative video presentation shows pupils how to use the information from a slope field to sketch the graph of a particular solution to a differential equation. Individuals learn how to determine the...

Get a better grasp of the intended content. The six free-response questions provide insight into the purpose of the AP® Calculus content. Two questions have real-world context while the remaining are void of context. The items range from...

In this calculus overview activity, learners: find the equation of a tangent line, curve sketch, and find limits.  Students should have covered continuity as well.

Get the most out of released items. Teachers use the included materials to learn about test-takers' performance on released free-response questions. Pupils respond to the questions and compare their responses to sample scored responses...

In this inverse functions activity, students solve and complete 3 sets of different problems. First, they find the expression and simplify. Then, students find the value of a given variable when it is the inverse in the function. They...

Though the items may be older, they still provide information. Released free-response items from the 2002 AP® Calculus BC exam provide teachers and pupils with information about how topics appear on the exam. Questions come from the AB...

An exam divides the six free-response questions into calculator use and no calculator use items. The non-calculator items are conceptual in nature and test whether pupils understand the calculus concepts. Scholars explain their answers...