Students engage in a lesson that is about finding the differentials of an equation. They practice computing the differential and apply them to obtaining the approximations for cube roots. The lesson includes examples for the teacher to...

Recycle, reuse, and rearrange! Young scholars learn to rearrange formulas to highlight a variable of interest. They then use their new formulas to make calculations.

Predict the year that college costs will double in your state using linear modeling. The first part of this two-part project based learning activity asks young mathematicians to use data from the College Board. They graph the data,...

Combine algebraic and geometric strategies to find solutions. The task asks learners to find the coordinates of a third vertex of a triangle to create a triangle with a specific area. The project is a set of seven problems that...

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...

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...

Don't give your classes the third degree when working with polynomials! Teach them to recognize the successive differences and identify the degree of the polynomial. The lesson leads learners through a process to develop an understanding...

The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors. 

Win the war of the worlds! Scholars solve a variety of problems related to an alien invasion. They determine where spaceships have landed on a coordinate map, devise a plan to avoid the aliens, observe the aliens, and break a code to...

Gain an upper hand in preparation for the exam. Teachers and pupils use six released questions to gain an understanding of the AP® Calculus exam. By answering the questions, scholars see how different concept of the course show up on the...

Get the most out of released items. Teachers use the included materials to learn about test-takers' performance on released free-response questions. Pupils respond to the questions and compare their responses to sample scored responses...

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...

The AP® exam is not just about the calculations. By reviewing the free-response questions from 2008, teachers and pupils see that several items require justifications and explanations to gain full credit. The chief reader even points out...

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...

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...

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...

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...

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...

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...

Developing fluency with basic addition and subtraction is fundamental to the success of all young mathematicians. This four-day lesson series begins with learners using ten-frames and hundreds charts to recognize patterns when adding and...

Class members create a table of the number of chords that can be drawn given the number of points on a circle. Pupils analyze the data created, find a function to fit to it, and use the function to make further predictions.

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...

Take a peek into the exam. Released items from the Calculus AB exam provide pupils insight into how questions appear on the exam. The six questions range from finding the area under a curve and the volume of the revolution to working...

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...