CK-12 Foundation
Area Between Curves: Income and Expenses
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...
Houston Area Calculus Teachers
Area and Volume
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created from the...
Flipped Math
Calculus AB/BC - The Fundamental Theorem of Calculus and Definite Integrals
Learning about definite integrals is fundamental to any calculus course. The eighth of 16 parts in Unit 6 - Integration focuses on the Fundamental Theorem of Calculus. Scholars first see how to find antiderivatives, then discover how to...
Curated OER
A.P. Calculus Integration Test
In this A.P. Calculus worksheet, learners complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others are...
Curated OER
Area of Curve
In this calculus activity, students calculate the area of a curve bounded between two regions. There are 2 questions asking for the area and length of a curve.
Curated OER
Area Between Two Curves
Twelfth graders identify and find the area between two curves. In this calculus lesson, 12th graders decide what the best way is to find the shaded area between two curves using examples from previous lessons. They relate areas between...
Curated OER
Finding the Area Under A Curve with Random Probability
Students explore the concept of area under a curve. In this area under a curve lesson plan, students find the area under a curve using the Monte Carlo method using random points and probability. Students calculate the area under the same...
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...
College Board
2002 AP® Calculus BC Free-Response Questions
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...
College Board
2003 AP® Calculus AB Free-Response Questions
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...
College Board
2005 AP® Calculus BC Free-Response Questions
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...
Curated OER
AP Calculus Practice Exam BC Version: Part B
In this calculus worksheet, students solve 17 multiple choice problems. Students find limits, summations, and derivatives of functions. Students find the area of an enclosed region between two curves.
Curated OER
Areas Between the Curves
In this algebra worksheet, students solve and complete 12 problems involving sine, cosine, area and function.
Curated OER
The Fundamental Theorem of Calculus and Area Under the Curve
Twelfth graders review the fundamental theorem of calculus and solve for the area under the curve. In this calculus lesson plan, 12th graders differentiate between the area under the curve and the definite integral as it related to the...
Curated OER
The Region Between Two Curves
Learners find the area of a region between two curves. They integrate functions such as sin(x) and cos(x) on a given interval and find the area bounded by the two functions. Pupils use their TI-89 to aid them in finding the bounded...
Curated OER
Calculus Review Worksheet
In this calculus worksheet, students determine the area of a region bounded by the given curves. The two page worksheet contains three problems. Answers are not provided.
Curated OER
Test on Chapter 7
Students review integrals and how they apply to solving equations. In this calculus lesson, students assess their knowledge of area between two curves, arc length, finding the volume using disk, washer and shell method. This assignment...
Curated OER
AP Calculus Practice Exam
In this Calculus worksheet, 12th graders are provided with practice problems for their exam. Topics covered include limits, derivatives, area bounded by a curve, minimization of cost, and the volume of a solid of revolution. The four...
Curated OER
Seventeen Multiple Choice Calculator AP Calculus BC Practice Test
In this AP Calculus BC worksheet, students answer seventeen multiple choice questions with the use of a calculator. The questions are a fifty minutes times practice test for the AP exam.
Curated OER
AP Calculus Practice Exam BC Version- Section I -Part B
In this AP Calculus Practice Exam worksheet, students solve seventeen multiple-choice questions using a graphing calculator. This BC practice test is designed to be finished in fifty minutes.
Curated OER
A.P. Calculus Practice Exam BC Version Section I Part B
In this AP Calculus practice test worksheet, students prepare for the BC version on the test by solving seventeen multiple-choice questions using a calculator. The test should be timed and 50 minutes in length.
Curated OER
Calculus Test
In this calculus learning exercise, learners integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.
Curated OER
Filling The Urn
Students calculate the area under a curve. For this calculus lesson,students calculate the area by integrating the equation. They calculate the volume of cylindrical shapes created between graphs.
Curated OER
Definite Integral
Learners investigate the intervals represented by a function in this calculus activity. They decide what interval of the function will be positive, negative or zero. They are then given graphs of functions and asked to analyze it.