Mean Value Theorem Teacher Resources

Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...

Differentiate between calculus concepts. The beginning of a helpful calculus resource begins with a short review of functions and moves right into limits to define derivatives. The six-chapter resource continues with applications of...

Does the exam look pupils expected? Released free-response questions from the AP® Calculus BC exam allow teachers and pupils to see and practice with actual exam questions. Three of the questions come from the AB portion of the course...

Develop an awareness of the exam. Pupils and teachers use the six release free-response questions to see how the exam covers topics. The questions are divided among calculator and non-calculator items. Scholars see the importance of...

Differentiate between the exams. Using the Q&A document, teachers compare the free-response questions that BC test-takers see to those that AB test-takers see. The pupils see which questions come from AB content and also those that...

Get a free peek into a calculus exam. Released free-response items from the AP® Calculus AB exam provide teachers and pupils examples of how topics may appear. The six questions cover topics such as growth rates, volumes of rotations,...

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...

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...

Be integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...

Give AP Calculus classes the opportunity to check the accuracy of their calculations! A calculus activity involves the collection of data, the application of mathematics, and the analysis of the accuracy of results. Young mathematicians...

The AP® exam is not just about the calculations. By reviewing the free-response questions from 2008, teachers and pupils see that several items require justifications and explanations to gain full credit. The chief reader even points out...

The test is not all about skills. The six free-response questions contain two real-world application problems. Those items deal with populations and velocities. The other four questions ask pupils to show their knowledge of calculus...

How would those items score? The resource provides pupils an opportunity to answer actual free-response questions and determine their scores. Items from the AP® Calculus AB exam from the 2008 administration demonstrate how topics appear...

What do the questions look like? Six free-response questions provide pupils with knowledge of how calculus topics appear on the AP® Calculus exam. The questions involve calculator and non-calculator problems by providing mathematical and...

Half are real-world. The 2011 AP® Calculus AB free-response questions let pupils and teachers see how content appears on the exam. Half of the questions contain real-world context, and four items do not allow calculators. Real-world...

Let them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...

This is integral to the test. Pupils realize that every question in the released free-response items from the 2008 AP® Calculus exam Form B requires integration. By reviewing the additional resources, scholars learn how important it is...

Take another look at the exam. A set of questions is a different form for the 2004 AP® Calculus BC free-response question section. The questions are evenly split into calculator and non-calculator sections. Pupils use their knowledge of...

In this integral formula, students explore how theorems are derived. They write proofs supporting Cauchy's Inequality, Liouville's Theorem, the Fundamental Theorem of Algebra, Gauss' Mean Value Theorem and Cauchy's Residue Theorem. ...

In this differentiation learning exercise, students differentiate functions, sketch graphs of functions, determine the area of inscribed polygons, and use the Mean Value Theorem for functions and intervals. This four-page learning...

Young scholars read an article to explain the reasoning behind theorems. In this calculus lesson, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they...

If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...

Students investigate the average value of a function given different interval values. In this calculus lesson, students explore word problems and apply their knowledge of average value to find the answer. They apply previous knowledge to...

In this calculus worksheet, students calculate the derivative, find the invertible given the derivative and review basic concepts for their AP calculus exam. There are 17 questions.