BCREV - AP Calculus Exam Review: Free Response Lesson
AP Calculus Exam Review: Free Response
Reviewing the types of problems that appear in the free-response sections, accompanied by an explanation of their solutions, will serve you well on the exam. Selected problems from released versions of the free-response sections of several recent AP exams are presented for your review.
2008 Problem 1
The presentation below illustrates how to find the area of a region bounded by two intersecting curves (Problem 1a).
Problems 1b, 1c, and 1d are the focus of the next three videos. A graphing calculator is required for 1b, and finding the volume of a solid by using cross sections is addressed in 1c. Finding the volume of water in a pond using cross sections is the problem to be solved in 1d.
2008 Problem 2
This four-part problem targets rate of change, extrema, and integration in a practical situation. Problem 2a involves finding the rate of change from a table and 2b requires the use of the Trapezoidal Rule. Problem 2c involves relative maxima/minima.
Problem 2d applies numerical integration using a graphing calculator in a practical setting.
2011 Problem 1
Velocity and acceleration for a moving particle are featured in this problem. Determining if the speed is increasing or decreasing is the focus of Problem 1a below.
Finding the slope of a tangent to the path of the particle at a given time is the focus of Problem 1b, and finding the total distance traveled over a given interval is the topic of Problem 1c. Problem 1d is concerned with finding the particle's position at a given time.
2011 Problem 3
The presentation in Problem 3a below focuses on writing the equation of a tangent line of a function, while part b determines the area of the function.
The next presentation illustrates how to write an equation to find the volume of a solid generated by revolving a region about the y - axis (Problem 3c)
2011 Problem 4
This problem provides a graph rather than an explicit equation of a piecewise function from which computations related to the derivative, absolute maximum, inflection point, average value of the graphed function, and the Mean Value Theorem are expected. View the four presentations below.
2011 Problem 6
Please take down important notes, such as formulas, and attempt the practice examples on your own before viewing the solutions!
Free-Response Questions, Solutions, and Scoring Guidelines
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