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68 resources with the concept fundamental theorem of calculus

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Other Resource Types (68)
38 Items in Collection
Lesson Planet

AP Calculus AB

For Students 11th - 12th
Prepare high school mathematicians for the AP Calculus AB exam with a collection of 38 videos that can be used to introduce the topics or as a review. The videos focus on two processes; differentiating a function and integrating a...
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2009 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2007 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2006 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Develop more than just a topical approach to the exam. The six free-response questions from 2006 reveal how the AP exam assesses topics. By using the questions, pupils practice topics such as velocity, sketch slope fields, solving...
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2015 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How will the exam ask this question? The free-response questions from the 2015 AP Calculus BC exam demonstrate how questions appear on the test. Using the questions, pupils gain experience answering similar inquiries to what they see on...
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2016 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
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2018 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
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2016 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2015 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2014 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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....
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2013 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2012 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2011 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2014 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
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2017 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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 the...
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2018 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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.
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2010 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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 to...
2 In 2 Collections
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Quadratic Equations

For Teachers 10th - 12th Standards
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...
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Calculus AB/BC - The Fundamental Theorem of Calculus and Accumulation Functions

For Students 10th - 12th
New ReviewConnect integrals with differentiation. The beginning of the video introduces the definition of an accumulation function. Scholars learn about the relationship between integrals and derivatives. Using what is commonly known as Part Two...
4:49
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Fundamental Theorem of Calculus Part 2

For Students 11th - Higher Ed
Use the Fundamental Theorem, not just look at it. Learners watch as the video walks viewers through finding the definite integral of a trigonometric function. The presenter provides helpful suggestions as she evaluates the example...
11:57
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Part 1 of the Dreaded Fundamental Theorem of Calculus!

For Students 11th - Higher Ed
Use the Fundamental Theorem of Calculus to find a derivative. With an example, pupils observe how being to derive a formula to help determine the derivative of any given integral. The video derives the formula using the first part of the...
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2005 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Let's put it in context. Pupils use the AP® Calculus BC free-response questions to practice for the exam. Five of the six released items deal with mathematical problems, with one using a real-world situation. Learners use differentiation...
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2003 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
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...
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2002 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
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...
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2012 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Get better prepared. Individuals use the six released AP® Calculus BC free-response questions to practice for the actual exam. The questions contain two calculator items and four non-calculator items. Topics include particle movement,...
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2011 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
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2005 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Grab a peak inside the test. The 2005 free-response questions from the AP® Calculus exam allow learners to see how topics appear on the tests. Topics cover differential equations, bounded areas, particle motion, and slopes of tangent lines.
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2002 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Become better at the test concepts. An educational resource presents six free-response questions from the AP® Calculus AB exam. Pupils use the items to practice the content, which contains concepts ranging from particle motion to ships...
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2009 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
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,...
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2006 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
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...
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2003 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
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...
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Calculus Volume 2

For Students 11th - Higher Ed
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....
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Calculus Volume 1

For Students 11th - Higher Ed
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...
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Fundamental Theorem of Calculus

For Teachers 10th - 12th
Does it make more sense to teach the Second Fundamental Theorem of Calculus before the First Fundamental Theorem of Calculus? An AP® Calculus curriculum module explores the interesting question. A set of five worksheets first looks at...
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The Fundamental Theorem of Calculus

For Teachers 10th - 12th
Knowledge of definite integrals is fundamental to the understanding of calculus. Instructors of an AP® Calculus course consult a comprehensive guide to the Fundamental Theorem of Calculus. The document provides teaching suggestions and...
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Functions Defined by Integrals

For Teachers 10th - 12th
Functions defined by integrals need to be carefully integrated into the course. An AP® Calculus curriculum module discusses functions defined by integrals. It explains several reasons why pupils have difficulty with the concept and...
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2006 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Move along with the review. Teachers and scholars use the six released free-response questions to review for their upcoming AP® exam. Questions from the 2006 exam contain problems dealing with cars, objects moving along a curve, and...
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2005 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
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2004 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Given a set of questions, pupils realize the way the Calculus BC free-response exam asks questions. The items include both contextual and non-contextual questions. Both types are split into the calculator and non-calculator sections for...
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2003 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
There are shaded areas, particles, polar equations, oh my! Teachers use the materials to see how their pupils compare to the AP® Calculus BC exam expectations. Scholars use the released items to practice on several BC topics and become...
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2002 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Where do the questions come from? Individuals examine released items and see the topics included. Teachers use the materials to see the distribution between strictly BC content and that which is shared with AB. The 2002 Calculus BC is...
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2008 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2005 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
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...
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2003 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Take a free look. Released free-response questions from the 2003 AP® Calculus AB exam show how questions cover different topics. Pupils and teachers review the topics of bounded regions, particle movement, rates, relationships between...
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2002 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Peek behind the curtain. Using a helpful resource, teachers and pupils see the way concepts appear on the AP® Calculus exam. Scholars use the questions to prepare for their own exams, gaining quality practice before test day. Questions...
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2004 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Develop a deeper understanding of calculus. The released item and support materials allows teachers and pupils to dig deeper into calculus topics. Scholars use the commentary and descriptions of the items to gain a better understanding...
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2001 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Take a closer look at the exam. Released items from the 2001 Calculus AB exam allow teachers and pupils to view how the exam presents questions. Scholars use the questions to prepare for the test and compare their responses to the...
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Vectors: A Curriculum Module for AP® Calculus BC

For Students 10th - 12th
It is all in a matter of time. The model curriculum module uses parametric equations and vectors to solve problems dealing with particle motion along a curve. At the beginning of the lesson, the unit reviews parametric equations and...
13:50
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Newton and Leibniz: Crash Course History of Science #17

For Students 9th - 12th Standards
The scientific revolution went out with a bang, thanks to some impressive intellectuals! Newton's and Leibniz's noteworthy discoveries unfold in the 17th installment in a lengthy History of Science series. Viewers witness the birth of...
20:46
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Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8

For Students 11th - Higher Ed
Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance helps...
17:05
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Essence of Calculus, Chapter 1

For Students 11th - Higher Ed
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...
12:39
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What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9

For Students 11th - Higher Ed
It seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.
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Total Cost to Produce the Turbo Blender

For Students 11th - Higher Ed
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. They...
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Lake Pollution

For Students 11th - Higher Ed
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.
1 In 1 Collection 1:47
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The Second Fundamental Theorem of Calculus

For Students 11th - Higher Ed
How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to evaluate a definite...
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Historical Reflections on the Fundamental Theorem Of (Integral) Calculus

For Teachers 11th - 12th
Highlight the process of mathematical discovery for your classes. This lesson examines the development of the Fundamental Theorem of Calculus over time. Understanding the history of the theorem helps create a better understanding of the...
1 In 1 Collection
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Fundamental Theorems of Mathematics

For Teachers 9th - Higher Ed
There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are true. 
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The Fundamental Theorems of Calculus

For Teachers 11th - Higher Ed
Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The...
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Study Guide for the Advanced Placement Calculus AB Examination

For Teachers 11th - 12th Standards
Is this going to be on the test? A calculus study guide provides an organized list of important topics and a few examples with answers. The topics include elementary functions, limits, differential calculus, and integral calculus,...
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Accumulation Functions

For Teachers 12th
Twelfth graders explore functions defined by a definite integral.  In this Calculus instructional activity, 12th graders investigate accumulation functions in which a variable is a limit of integration.  The instructional activity is...
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The Area Function

For Teachers 11th - 12th
Learners explore the concept of area under a curve.  In this area under a curve instructional activity, students find integrals of various functions.  Learners use their Ti-Nspire to graph functions and find the area under the curve...
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Seeing Is Believing

For Teachers 11th - Higher Ed
Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
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Why We Use Theorem In Calculus

For Teachers 11th - Higher Ed
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...
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Nine Definite Integrals and Fundamental Theorem Of Calculus Problems

For Students 11th - Higher Ed
In this definite integral worksheet, student find the value of five definite integrals.  Student then explain why a definite integral inequality holds true.  Finally, students are given the graph of a functions and asked to determine...
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Introduction to Slope Fields

For Teachers 11th - 12th
Pupils plot slope fields. In this introduction to slope fields lesson plan, students plot 12 slope fields for given differential equations.
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Challenge Sheet 2: Evaluate Functions

For Students Higher Ed
For this function worksheet, students evaluate integrals using the fundamental theorem of calculus. They identify the maxima and minima on intervals. This one-page worksheet contains seven problems.
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Basic Calculus II: Fundamental Theorem of Calculus

For Students Higher Ed
In this fundamental theorem worksheet, students find the antiderivative of a function. This two page worksheet contains five multi-step problems.
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Linear Systems

For Students Higher Ed
In this linear systems worksheet, 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 the column...