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...

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...

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,...

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...

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...

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...

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...

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...

It's time to put analytical applications to work. Learners use the eight questions of the mid-Unit 5 review to refresh their memories of the key points. Pupils apply what they have learned to use the Mean Value Theorem, find extrema...

Time to put it all together in one sheet—well five. Pupils review all the topics presented in the resources for Analytical Applications of Differentiation. The five pages summarize the concepts with explanations and examples.

Find deeper meaning in graphs. Pupils use the knowledge gained from the previous sections in the unit to sketch graphs of a function's derivative. Learners also see how to sketch a graph of a function given the graph of its derivatives....

Move beyond setting up equations. Pupils continue with optimization problems and use their knowledge of derivatives to find solutions. They watch as the video uses equations from previous examples and find solutions to answer specific...

Let's finish a functional review. Pupils work through 31 items to review the concepts learned in Unit 8. Scholars determine whether a mapping is a function and identify the domain and range. Using function notation, individuals then...

Create a graphical description. Pupils watch a video presentation starting with vocabulary on properties of a graph of a function and then use the vocabulary to find key features of graphs of a function. Scholars use three graphs in the...

Quadratics need no introduction, but here is one anyway. Learners watch a video that introduces them to quadratics. The pupils learn what a quadratic is, its key features, and how to sketch a graph of the parabola it defines. Then, they...

Do some interpretive modeling. Class members watch three examples of interpreting key features of a graph of a quadratic to find solutions to a real-world problem. Learners review how to find the key features on a graph using technology...

Take a look in the window. Pupils watch a presentation to discover how to graph a polynomial using a graphing calculator and using the window to find the extrema. Scholars use their knowledge from previous lessons to gain a rough idea of...

Build up a polynomial. Learners use printed cards to create polynomials. Using a graphing utility, pupils make comparisons between the polynomials they built. To further cement the concept, they build upon their algebraic vocabulary as...

Of course, calculus can help you build the largest box possible. Scholars play a digital game to gain familiarity with situations where optimization would be appropriate. After gaining a solid conceptual understanding of optimization,...

Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...

In this differentiation worksheet, students solve and complete 8 various types of problems. First, they differentiate each of the equations listed. Then, students find an equation of the tangent to the curve at a given point. They also...

In this properties of parabolas activity, students identify the vertex and the minimum and maximum value of each parabola. They graph parabolas on a coordinate plane. This four-page activity contains 14 problems. Answers are provided on...

Students investigate maxima and minima by finding the shortest distance. In this calculus lesson plan, students calculate the shortest distance a bug travels to get to the other side of the tv. They analyze their findings discussing...

In this algebra worksheet, students find the maxima and the minima of the parabola. They calculate the maximum and minimum area and apply the formulas of polygons to help them solve equations. There are 8 questions with an answer key.