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...
College Board
2002 AP® Calculus AB Free-Response Questions
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...
College Board
2004 AP® Calculus BC Free-Response Questions
Given a set of questions, pupils realize the way the Calculus BC free-response exam asks questions. The items include both contextual and non-contextual questions. Both types are split into the calculator and non-calculator sections for...
College Board
2003 AP® Calculus BC Free-Response Questions
There are shaded areas, particles, polar equations, oh my! Teachers use the materials to see how their pupils compare to the AP® Calculus BC exam expectations. Scholars use the released items to practice on several BC topics and become...
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
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
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
2005 AP® Calculus AB Free-Response Questions Form B
Grab a peak inside the test. The 2005 free-response questions from the AP® Calculus exam allow learners to see how topics appear on the tests. Topics cover differential equations, bounded areas, particle motion, and slopes of tangent lines.
College Board
2012 AP® Calculus BC Free-Response Questions
Get better prepared. Individuals use the six released AP® Calculus BC free-response questions to practice for the actual exam. The questions contain two calculator items and four non-calculator items. Topics include particle movement,...
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
2002 AP® Calculus AB Free-Response Questions Form B
Become better at the test concepts. An educational resource presents six free-response questions from the AP® Calculus AB exam. Pupils use the items to practice the content, which contains concepts ranging from particle motion to ships...
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
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
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
2010 AP® Calculus BC Free-Response Questions
What do a zoo, snow, and a moving particle have in common? The six free-response items from the 2010 AP® Calculus BC exam allow teachers and pupils see how items may show up in context. Three of the questions are from only the BC portion...
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
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
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
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
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...
CK-12 Foundation
Trapezoidal and Midpoint Approximations: Area of a Skirt
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...
Curated OER
Riemann Sums
Mathematicians use their calculators to investigate Riemann sums. Your learners will explore the relationship between the limit of two Riemann sums and the definite integral of the function.
Texas Instruments
Quartic Regions
Young scholars explore quartic functions in this calculus lesson. They investigate an application of derivatives and definite integrals, then explore the question of which of the "three bumps" of a quartic is the largest.
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