Chris Evans Math

This packet contains 18 multi-part questions modeled after past AP Calculus free response questions. This document can be used as an AP exam review packet or split up and used throughout the course (which is what I intended in writing the problems). The packet covers most all of the content in AP Calculus AB. I also sell these same problems divided up into four units (differentiation, applications of differentiation, integration, differential equations and applications of integration).

Excellent for inclusion during the Applications of Differentiation Unit or AP Test Prep! This packet contains 5 multi-part free response questions. These questions were modeled after past AP exam questions. The questions focus on applications of differentiation, including extrema, concavity, horizontal and vertical tangent lines, kinematics, and the Mean Value Theorem.

Excellent for inclusion during the Integration Unit or AP Test Prep! This packet contains 4 multi-part free response questions. These questions were modeled after past AP exam questions. The questions focus on integration, including Riemann sums, trapezoidal approximations, net change, total distance, accumulation functions, and the average value of a function over a given interval.

Excellent for inclusion during the Differentiation Unit or AP Test Prep! This packet contains 5 multi-part free response questions. These questions were mostly modeled after past AP exam questions. The questions focus on differentiation, including tangent lines, rates of change, continuity, implicit differentiation, and related rates. Answer key is included.

Excellent for inclusion during the Differential Equations/Applications of Integration Unit or AP Test Prep! This packet contains 4 multi-part free response questions. These questions were modeled after past AP exam questions. The questions focus on slope fields, integration using separation of variables, areas between curves, volumes of solids of revolutions, and volumes of solids with known cross sections.

The 2011 Indianapolis 500 had an unexpected ending. This activity provides students with information about the last lap of the top three finishers, including their position relative to one another when the last lap started and their approximate speeds at various times during the last lap. Students can work in groups and use their understanding of integration to predict in which order the cars finish. A link is included to show them the footage of the last lap of the race once they have made thei

This activity presents students with a piece-wise defined function that models a portion of the roller coaster "The Racer". Students are then introduced to the concepts of concavity and points of inflection. The activity walks them through graphing a sketch of the derivative function and then asks them to make connections between concavity and points of inflection and the graph of the first derivative. The intent is to get them to see for themselves the need for the second derivative.

This activity introduces students to the concept of evaluating the slope of a tangent line to a curve. Students are asked to draw in several tangent lines at various points to the graphs of y=x^2 and y=sin(x). They then use their algebra knowledge to approximate the slope of the tangent lines they have drawn, and make conjectures about the slope equation (derivative). I have students complete this before introducing the limit definition of the derivative.

Students use the limit definition of the derivative to identify the pattern that is the Power Rule for Differentiation.

This activity has students explore the derivatives of e^x and a^x as well as the antiderivative of 1/x. They use their graphing calculator to evaluate slopes at various points and then their knowledge of graphs of functions to make conjectures about these derivatives and antiderivatives. Students are then provided with some practice problems to attempt to apply what they have learned.