AP CALCULUS FREE RESPONSE QUESTIONS PDF

Integral of a rate; average value of a function 1. Give your answer to the nearest whole number. Justify your answer. Explain your reasoning.

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You can use a calculator. Find total entering. Finding the absolute minimum on a closed interval. People enter a line for an escalator at a rate modeled by the function r given by where r t is measured in people per second and t is measured in seconds.

As people get on the escalator, they exit the line at a constant rate of 0. To the nearest whole number, find the number of people in line at this time. Justify your answer. Given velocity. Find derivative at a point, acceleration, using calculator.

Distinguish between displacement and distance traveled. Find when velocity is equal to that of a second particle. Interpret the meaning of each integral in the context of the problem. At what time t are the two particles moving with the same velocity? Using the FTC and a graph geometrically. Using the FTC and a function. Finding an antiderivative. Using the first derivative to find where a function is increasing and concave up. Finding and justifying points of inflection. The graph of the continuous function g, the derivative f, is shown above.

Give a reason for your answer. Approximating a derivative at a point. Trapezoidal Rule to approximate average value. Related rates problem using a new function 4. The height of a tree at time t is given by a twice-differentiable function H, where H t is measured in meters and t is measured in years. Selected values of H t are given in the table above. When the tree is 50 meters tall, the diameter of the base of the tree is increasing at a rate of 0. According to this model, what is the rate of change of the height of the tree with respect to time, in meters per year, at the time when the tree is 50 meters tall?

Find average rate of change. Slope of tangent line using product rule. Absolute minimum using Candidates Test. You should definitely review the Unit Circle since trig values came up a lot during the exam. Find the value of or state that it does not exist.

Sketch the solution curve that passes through the point 0, 2 , and sketch the solution curve that passes through the point 1, 0. Use your equation to approximate f 0. Show Step-by-step Solutions Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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You can use a calculator. Find total entering. Finding the absolute minimum on a closed interval. People enter a line for an escalator at a rate modeled by the function r given by where r t is measured in people per second and t is measured in seconds.

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AP Calculus practice questions

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