Fundamental Theorem of Calculus Teacher Resources

Students explore the Fundamental Theorem of Calculus and apply the properties of definite integrals to solving equations. As a class, they explore formulas to use in evaluating integral yields in regions above and below the x-axis....

Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...

Students plot slope fields. In this introduction to slope fields lesson, students plot 12 slope fields for given differential equations.

In this math worksheet, students give examples of functions that will satisfy given conditions. Students tell the tabulations for a given function. Students use the definition of a derivative to compute the inverse of a function. they...

In this linear systems instructional activity, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to...

Dive into the essence of calculus. The first installment of an 11-part playlist introduces the video series by looking at the area of a circle and the area under curves. The narrator explains how to look at calculus as taking a hard...

Explain the timing of a lake cleanup to the EPA using calculus. A project-based learning opportunity has learners compare rate functions to compute a total change. Their solutions explain the time needed to rid a lake of pollutants.

Delve into the middle of calculus. The resource is the second eBook of three that covers the complete calculus content. Seven chapters begin with integrals and different methods of integration before moving on to differential equations....

Class members blend their knowledge of functions and problem-solving skills to provide business advice to the Turbo Blender manufacturers. Through a project-based approach, learners examine marginal cost data to produce a function....

Pupils interact with six released questions from the 2018 AP Calculus AB exam. Teachers use the additional materials to determine where the class is in terms of readiness for the exam to help provide additional instruction as needed.

Don't just rely on the textbook. Released items from the AP Calculus BC provide pupils and teachers insight on how topics appear on the exam. The six items are divided into calculator and non-calculator sets with half of them also...

Grow your knowledge of Calculus AB. Items released from the 2007 AP® Calculus AB exam provide information to teachers about the importance of particular topics. Pupils use the questions to gain an understanding of ways the exam assesses...

Pupils use the six released free-response questions from an AP Calculus BC exam to prepare for their own exam. The questions cover a range of topics from the BC curriculum, with half of the items coming strictly from AB material and...

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...

Using the common errors and test taker responses, it's easy for teachers to see where to pinpoint instruction throughout the AP Calculus course. Pupils, using the released items, develop an understanding of how future exams assess the...

What is the important stuff? The free-response questions from the 2013 Calculus AB exam highlight the topics in calculus assessed that year. Items provide pupils the opportunity to experience questions similar to what they will see on...

Is this going to be on the test? The resource contains the AP Calculus AB free-response questions that were on the 2010 test. Pupils use the six questions to prepare for their tests. Teachers use the included response resources...

How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...

How will the topics be assessed? Using the six released items from the Calculus AB test, pupils see how the exam assesses content from the course. With the additional materials covering test taker's responses and scoring keys, teachers...

Give classes a sneak peek at an upcoming test. Scholars work released items from the AP Calculus AB test to prepare for their own exams. The resource consists of six items, two graphing calculator items, and four non-calculator items....

What's on the test? Released items provide insight into the AP Calculus test. The six items are split into two groups, two calculator items and four non-calculator items. Resources allow teachers to see what kinds of answers test takers...

So this is the real test? The resource provides the free-response questions from the 2011 AP Calculus AB exam. The six questions are split into two sections, calculator and non-calculator items. Several resources give teachers...

The split is 50-50. Released free-response questions from the 2016 AP Calculus BC show that half the questions are from the AB portion of the course and the others are from the BC portion. Teachers and pupils use the items to prepare and...

What was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...