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AP Test Prep
College Board

2000 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How are concepts divided? Pupils use the AP® Calculus free-response questions to see how the exam addresses concepts. The concepts are divided into those that use calculators and others that do not. Calculator items require finding...
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AP Test Prep
College Board

1999 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Get a 20/20 view of the exam. Free-response questions from the 1999 Calculus BC exam provide an insight to the exams. Pupils review the questions to see how topics show up on the test. Topics range from particle motion along a function,...
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AP Test Prep
College Board

1998 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Provide a test run. Pupils use the questions to practice taking the free-response section of the AP® Calculus BC exam. Teachers see the different ways questions appear on the exam to prepare individuals for whatever comes their way on...
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AP Test Prep
College Board

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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AP Test Prep
College Board

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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AP Test Prep
College Board

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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AP Test Prep
College Board

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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AP Test Prep
College Board

2000 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Gain an upper hand in preparation for the exam. Teachers and pupils use six released questions to gain an understanding of the AP® Calculus exam. By answering the questions, scholars see how different concept of the course show up on the...
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AP Test Prep
College Board

1999 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Gain an understanding of the test before taking your own. Scholars develop an understanding of how calculus concepts appear on the AP® exam. The six released questions come from across the curriculum and include particle movement and...
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AP Test Prep
College Board

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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AP Test Prep
College Board

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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Lesson Plan
Project Maths

Integral Calculus

For Teachers 10th - Higher Ed
From derivatives to antiderivatives and back again. Building on the second lesson of the three-part series covering functions, learners explore the concept of an antiderivative. They connect the concept to the graph of the function and...
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Interactive
CK-12 Foundation

Trapezoidal and Midpoint Approximations: Area of a Skirt

For Students 11th - Higher Ed
When are trapezoids better than rectangles? Using trapezoids pupils approximate the area of fabric defined by a function. Just like with rectangles, learners realize the more trapezoids the more accurate the approximation. Scholars use...
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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...
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Lesson Plan
West Contra Costa Unified School District

Indefinite Integrals

For Teachers 11th - Higher Ed Standards
The inverse of matter is anti-matter, so the inverse of a derivative is an antiderivative. The lesson introduces antiderivatives and indefinite integrals to the class along with the notation for integrals. Groups work together to find...
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Handout
Curated OER

Math Handbook: Calculus

For Students 10th - 12th
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...
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Lesson Plan
Curated OER

Worksheet 34 - Antiderivatives

For Teachers Higher Ed
In this antiderivative worksheet, students compute antiderivatives, as well as definite and indefinite integrals. This one-page worksheet contains approximately six multi-step problems.
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Lesson Plan
Curated OER

Worksheet 31 - Doman & Range

For Teachers Higher Ed
In this function worksheet, students determine the domain and range of given functions. They use trigonometric ratios to determine if a statement is true or false. Students differentiate equations. In this one-page worksheet, students...
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Lesson Plan
Curated OER

Computing Indefinite Integrals

For Teachers 11th - Higher Ed
Provide your students with a framework for introducing indefinite integrals. It takes into account a learner’s prior knowledge of slope fields and definite integrals and uses the notion of an antiderivative to give them an intuitive...
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Lesson Plan
Curated OER

Euler Encore 1

For Teachers 11th - 12th
In this math worksheet, learners use Euler's Method to solve differential equations. They are given an equation to graph (y'). Students sketch that equation as well as the related equation (y). They find the area of given rectangles and...
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Lesson Plan
Curated OER

What is an Antiderivative? Slope Fields

For Teachers 10th - 12th
Students take the derivative of a function. For this calculus lesson, students define slope fields and what they are used for. They relate slope fields to the real world.
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Worksheet
Curated OER

Worksheet 8 - Double Integrals

For Students Higher Ed
For this double integral worksheet, students compute the antiderivatives, explore the order of integration, and determine the double integrals of given functions. They sketch the volume of a solid represented by double integrals. This...
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Worksheet
Curated OER

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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Worksheet
Curated OER

Trig Identities and Antiderivatives

For Students 11th - Higher Ed
In this math learning exercise, students practice solving the problems that are related to the concepts of identities and antiderivatives.