Curated OER
Filling The Urn
Learners calculate the area under a curve. In this calculus lesson,students calculate the area by integrating the equation. They calculate the volume of cylindrical shapes created between graphs.
Curated OER
Easy Bias-Covered Curves
Students watch a demonstration on how to make easy-bias covered curves. Using that information, they practice making their own with different types of materials. They share their creations with the class to end the lesson plan.
Curated OER
Area Under A Curve
Students investigate the concept of finding the areas under curves while examining the graphing for inscribed and circumscribed rectangles. Finally, students compute the area under the curve by using the left-hand endpoints. The examples...
Curated OER
Area Between Two Curves
Students engage in a lesson that is concerned with the concept of computing the area between 2 curves with respect to the x and y axis. They concentrate on using positive and negative intervals and find the curve while determining the...
Curated OER
Lesson #94 Exact Area Under A Curve
Students examine diagrams to determine the exact area under a curve. Using given formulas, they identify the area of the curve using the x and y-axis, as well as rectangles. As a class, students sing a song called "Failing My Calculus"...
Curated OER
Area Between Two Curves
Students investigate the concept area that is found between two curves. They find the area in the top and bottom curve and then examine the differences. The examples can be used for direct instruction and to provide a guide for helping...
Curated OER
Lesson #94 Exact Area Under a Curve
Students research Riemann Sums. In this area lesson students listen to a lecture on finding the area under a curve. Links to a song about Riemann Sums, and a song titled "Failing My Calculus" are included.
Curated OER
The Curved House - Endless House Project
Students analyze the art and architecture projects of Frederick Kiesler. For this architecture analysis lesson, students read and study images the endless house project. Students complete discussion activities and questions for...
College Board
2010 AP® Calculus BC Free-Response Questions Form B
Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...
Flipped Math
Calculus AB/BC - Approximating Areas with Riemann Sums
There are several ways to estimate the area if the curve does not create nice geometric figures. The presenter introduces the idea of using areas of rectangles to estimate the area under the curve. Pupils use four types of Riemann Sums,...
College Board
2009 AP® Calculus BC Free-Response Questions Form B
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...
College Board
1998 AP® Calculus AB Free-Response Questions
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...
College Board
2006 AP® Calculus BC Free-Response Questions
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...
College Board
2015 AP® Microeconomics Free-Response Questions
Two sandwich shops must decide whether it's to their benefit to set pricing together. What happens when the government also intervenes with a price subsidy? Learners consider these questions as they tackle prompts from College Board....
College Board
2004 AP® Microeconomics Free-Response Questions
All goods have a social cost. A set of questions considers how to best calculate the impact the production of goods has on society. Other practice problems from College Board consider supply-and-demand curves and the impact of licensing...
College Board
2003 AP® Microeconomics Free-Response Questions
A company producing smoke alarms has a monopoly. However, what factors influence its profit and production? A series of prompts from College Board asks learners to consider the impact. Other practice problems include examining what...
College Board
2004 AP® Microeconomics Free-Response Questions Form B
A company enjoys a monopoly. What happens to its profits when another firm introduces a similar product? Learners consider the case using questions from College Board. Other prompts include the effects of sales taxes and supply and...
College Board
2003 AP® Microeconomics Free-Response Questions Form B
How are monopolies and competitive firms similar and different? Scholars consider the question using authentic College Board materials. Other prompts consider supply and demand curves and the relationship between wages and output.
College Board
2003 AP® Calculus AB Free-Response Questions Form B
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...
College Board
2008 AP® Calculus AB Free-Response Questions Form B
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...
College Board
2007 AP® Calculus AB Free-Response Questions Form B
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...
College Board
2011 AP® Calculus BC Free-Response Questions Form B
Take a second look. Form B of the AP® Calculus BC free-response questions allow pupils and teachers to see another set of items. The six questions expand the set of items from the 2011 free-response questions. Form B items include a...
College Board
2007 AP® Calculus BC Free-Response Questions Form B
There is just a single real-world problem. Released free-response items from the 2007 AP® Calculus BC Form B contains only one real-world question. The question involves rate of change of wind chill scenario. The mathematical problems...
College Board
2003 AP® Calculus BC Free-Response Questions Form B
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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