Curated OER
Riemann Rectangle Errors
High schoolers calculate the area under a curve. In this calculus instructional activity, students integrate the function to find the area under the curve. They use the Ti to create a visual of the graph.
Curated OER
Riemann Sums
Students calculate the area under a curve. In this calculus lesson, students use Riemann Sums to find the area under a curve. They apply the boundaries of intervals as they solve for each area.
College Board
2009 AP® Calculus AB Free-Response Questions Form B
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,...
College Board
2006 AP® Calculus AB Free-Response Questions Form B
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...
College Board
2011 AP® Calculus BC Free-Response Questions
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...
College Board
2004 AP® Calculus AB Free-Response Questions Form B
The test is not all about skills. The six free-response questions contain two real-world application problems. Those items deal with populations and velocities. The other four questions ask pupils to show their knowledge of calculus...
College Board
2010 AP® Calculus AB Free-Response Questions Form B
Most say that practice makes perfect. Scholars use the released free-response questions to practice for the AP® Calculus AB exam. Each question comes with several parts and either do or do not allow calculators. Items include topics such...
College Board
2011 AP® Calculus AB Free-Response Questions Form B
Half are real-world. The 2011 AP® Calculus AB free-response questions let pupils and teachers see how content appears on the exam. Half of the questions contain real-world context, and four items do not allow calculators. Real-world...
College Board
2004 AP® Calculus BC Free-Response Questions Form B
Take another look at the exam. A set of questions is a different form for the 2004 AP® Calculus BC free-response question section. The questions are evenly split into calculator and non-calculator sections. Pupils use their knowledge of...
College Board
2002 AP® Calculus BC Free-Response Questions Form B
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...
College Board
2005 AP® Calculus BC Free-Response Questions Form B
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...
Shodor Education Foundation
InteGreat!
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.
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...
CK-12 Foundation
Properties of Definite Integrals
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....
College Board
2004 AP® Calculus AB Free-Response Questions
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...
College Board
2001 AP® Calculus AB Free-Response Questions
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...
College Board
2005 AP® Calculus AB Free-Response Questions
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...
College Board
1999 AP® Calculus AB Free-Response Questions
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...
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
1998 AP® Calculus BC Free-Response Questions
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...
College Board
1999 AP® Calculus BC Free-Response Questions
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,...
College Board
2001 AP® Calculus BC Free-Response Questions
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...
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
2000 AP® Calculus BC Free-Response Questions
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...