What is important from the instruction? Using the questions, pupils and teachers see how the AP® Computer Science exam addresses topics. Scholars realize the importance of the case studies from the course. The released questions range...

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...

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...

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...

This is integral to the test. Pupils realize that every question in the released free-response items from the 2008 AP® Calculus exam Form B requires integration. By reviewing the additional resources, scholars learn how important it is...

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...

Go a little deeper. Learners use the released 2006 AP® Calculus BC free-response questions to review for the BC test, which covers content from Calculus AB and Calculus BC. Topics include volumes of revolution, particle motion,...

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...

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...

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...

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...

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...

Ready to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...

Local linearity isn't the first thing that comes to mind to start off an AP® Calculus course. A scholarly article discusses one possible beginning to the AP® Calculus course: investigating and introducing derivatives through activities...

All's fair in math and war. Scholars examine the Battle of Trafalgar using calculus. They set up and solve a system of differential equations to determine the number of ships remaining in each fleet over time.

Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...

No need to go to extreme lengths to find resources on extrema. The central focus of an AP® curriculum module is on critical points and extrema, and how to cover these concepts throughout the course. A set of three worksheets helps assess...

Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...

How does one factor in the social costs of a product? What factors influence price? Learners consider the question and others using authentic College Board materials. Other questions examine profits and competition in the market and the...

Imports often affect the production of domestic goods. Scholars consider the variables in this situation with a scaffolded prompt from College Board. Other items examine factors in production and compare the production advantage between...

Monopolies may have an advantage in some markets, but what are they? A scaffolded problem set examines the effects monopolies have on a market. Other authentic College Board problems examine labor markets and how a variety of factors...

The government catches a firm in the act of polluting. What will happen to the company's profits? Learners consider the question and others using authentic College Board materials. Other problem sets examine wages and labor and price...

Inventors with patents have a distinct advantage in the market. But what happens when the patent expires? A series of questions from College Board asks learners to consider the effects of a patent expiration. Other practice prompts...

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.