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85 resources with the concept area under a curve

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2001 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
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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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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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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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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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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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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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1998 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Take a peek into the exam. Released items from the Calculus AB exam provide pupils insight into how questions appear on the exam. The six questions range from finding the area under a curve and the volume of the revolution to working...
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14:56
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Area under a Graph

For Students 8th - 12th Standards
What? The calculation of area is a linear distance? A short video shows how to use the areas of simple polygons to estimate the area under a graph. Pupils divide the area under a curve into figures to easier calculate the area. Given...
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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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7:43
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Calculus, What Is It Good For?

For Students 11th - Higher Ed
Explore the meaning of differentiation and integration. A video lesson describes in detail what differentiating and integrating an equation means using the momentum and kinetic energy formulas. Progressing from a linear to a quadratic...
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InteGreat!

For Students 11th - Higher Ed
Take a great look at integration! Young scholars use an interactive to learn how to integrate a function. Learners input a function and view the integral as well as see a graphical representation.
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Normal Distribution

For Students 6th - 12th Standards
Does the size of the bin matter? The resource allows pupils to explore the relationship between the normal curve and histograms. Learners view histograms compared to a normal curve with a set standard deviation. Using the interactive,...
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Overlapping Gaussians

For Students 9th - 12th Standards
Adjust the overlap to compare probabilities. Using sliders, learners adjust the shape of two Gaussian curves. The interactive calculates the area of the left tail for one curve and the right tail for the other. Pupils set the interactive...
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Area Between Curves: Income and Expenses

For Students 11th - Higher Ed
Use the area of polygons to calculate the area between curves. Pupils calculate areas under income and expense curves by filling the space with squares and right triangles. Using that information, they determine the profit related to the...
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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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Properties of Definite Integrals

For Students 11th - Higher Ed
Close your eyes and visualize a definite integral. An interactive provides a visualization of a function and definite integral on a closed interval. Pupils move one point of the interval in either the positive or negative direction....
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Area Sums: Estimation with Rectangles

For Students 11th - Higher Ed
The more rectangles, the better the estimate. Using the interactive, pupils explore estimating the area under a curve using left-hand sums. Learners respond to challenge questions on how to get better estimates using the same technique.
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Properties of a Normal Distribution: Uniform Distributions

For Students 9th - 12th Standards
There's nothing normal about an extraordinary resource. Scholars change the dimensions of a normal distribution using a slider interactive. Determining the area under the graph gives probabilities for different situations.
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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...
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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...