AP Calculus AB · Free-response questions 2018

6 questions, each with its course unit and the official scoring guidelines.

Official paper (PDF) · Questions All AP Calc AB papers→

Question 1

Open answer

$Question 1 — 1. People enter a line for an escalator at a rate modeled by the function r given by r o f t equal s, 44 ti m es o p e n pa renthesis, t over 100, close parenthesis, cubed, times open parenthesis, 1 minus the fraction t…$

Source: College Board — AP Calculus AB, Free-response questions, 2018

Question 2

Open answer

Question 2 — 2. A particle moves along the x-axis with velocity given by v of t equals, t h e f ra ct ion w ith numerator 10 times the sine of open parenthesis, 0.4 times t squared, close parenthesis, and denominator t squared,…

Source: College Board — AP Calculus AB, Free-response questions, 2018

Question 3

Open answer

Question 3 — 3. The graph of the continuous function g, the derivative of the function f, is shown above. The function g is piecewise linear for ne ga tive 5 l es s t h an or e qu a l to x , less tha n 3 and g of x equals, 2 times…

Source: College Board — AP Calculus AB, Free-response questions, 2018

Question 4

Open answer

Question 4 — The figure presents a 2 row table with 5 columns of data. The heading for row 1 is “t, in years,” and the heading for row 2 is “H of t, in meters.” The data in the table are as follows. Column 1. t is 2. H of t is 1.5.…

Source: College Board — AP Calculus AB, Free-response questions, 2018

Question 5

Open answer

Question 5 — 5. Let f be the function defined by x . (a) Find the average rate of change of f on the interval 0 le s s than or equal to x, less than or equal to pi . (b) What is the slope of the line tangent to the graph of f at x e…

Source: College Board — AP Calculus AB, Free-response questions, 2018

Question 6

Open answer

Question 6 — 6. Consider the differential equation ) the d e ri v a t i v e of y with respect to x equals, one third x, times open parenthesis, y minus 2, close parenthesis, squared . (a) A slope field for the given differential…

Source: College Board — AP Calculus AB, Free-response questions, 2018

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