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AP Calculus BC Exam Questions – AP Central | College Board
Download free-response questions from past AP Calculus BC exams, along with scoring guidelines, sample responses from exam takers, and scoring distributions.
Calculus BC 2023 Free-Response Questions CALCULUS BC SECTION II, Part A Time—30 minutes
CALCULUS BC FREE-RESPONSE QUESTIONS . 5. Consider the family of functions . 1 . fx ()= x . 2 . −2. x + k, where . k . is a constant. (a) Find the value of . k, for . k > 0, such that the slope of the line tangent to the graph of . f . at . x = 0 equals 6. (b) For . k = −8, find the value of . fx d ∫. 1 . x. 0 . (c) For . k = 1, find the ...
Free Response Questions Louis A. Talman, Ph.D. Emeritus Professor of Mathematics Metropolitan State University of Denver May 19, 2024 We use the symbol \˘" to mean \is approximately equal to" throughout this document. 1. (a) Reading from the given table, we nd C(3) = 85 and C(7) = 69. We are to take the
2006 CALCULUS AB FREE-RESPONSE QUESTIONS Graph of f The graph of the function f shown above consists of six line segments. Let g be the function given by g(x) = f (t) dt. (a) Find g(4), g'(4), and g" (4). (b) Does g have a relative minimum, a relative maximum, or neither at x = 1 ? Justify your answer.
Values of W t at selected times t for the first 20 minutes are given in the table above. (a) Use the data in the table to estimate W 12 . Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem. (b) Use the data in the table to evaluate t dt .
Use a left Riemann sum with the four subintervals indicated by the table to estimate the total amount of water removed from the tank during the 8 hours. Is this an overestimate or an underestimate of the total amount of water removed? Give a reason for your answer.
Find the average rate of change of A t over the interval 0 t 30 . Indicate units of measure. Find the value of A 15 . Using correct units, interpret the meaning of the value in the context of the problem.
Free Response Questions Louis A. Talman, Ph.D. Emeritus Professor of Mathematics Metropolitan State University of Denver May xx, 2023 1. (a) The integral Z 135 60 f(t)dtgives, in gallons, the amount of gas pumped into the gas tank during the time interval 60 t 135. This amount is given by Z 135 60 f(t)dt˘f(90) 30 + f(120) 30 + f(135) 15 (1)
AP Calculus BC Free Response - AP Practice Exams
Test prep resources for you AP Calculus BC free response questions. Prior year questions, video solutions, and FRQ practice problems for AP Calc.