AP Calculus AB · Free-response questions 2015

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

$Question 1 — 1. The rate at which rainwater flows into a drainpipe is modeled by the function R, where R o f t e qu a l s 2 0 s i n e open parenthesis, the fraction t squared over 35, close parenthesis cubic feet per hour, t is…$

Source: College Board — AP Calculus AB, Free-response questions, 2015

Question 2

Open answer

Question 2 — 2. Let f and g be the functions defined by f o f x equals 1 plus x plus e superscript x squared minus 2 x e and g o f x equals x superscript 4, minus 6 point five x squared, plus 6 x, plus 2. Let R and S be the two…

Source: College Board — AP Calculus AB, Free-response questions, 2015

Question 3

Open answer

Question 3 — t, open parenthesis minutes close parenthesis 0 12 20 24 40 v o f t, open parenthesis meters per minute close parenthesis 0 200 240 negative 220 150 3. Johanna jogs along a straight path. For0 le s s than or equal to t,…

Source: College Board — AP Calculus AB, Free-response questions, 2015

Question 4

Open answer

Question 4 — 4. Consider the differential equation t he d er i v ative of y with respect to x, equals 2 x minus y.. (a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated. The…

Source: College Board — AP Calculus AB, Free-response questions, 2015

Question 5

Open answer

Question 5 — 5. The figure above shows the graph of , the derivative of a twice-differentiable function f, on the interval o p en bracket negative three comma four close bracket. . The graph of f prime has horizontal tangents at x…

Source: College Board — AP Calculus AB, Free-response questions, 2015

Question 6

Open answer

$Question 6 — 6. Consider the curve given by the equation y c ub ed minus x y equals 2. . It can be shown that t h e d er i v a tive of y with respect to x, equals the fraction with numerator y and denominator 3 y squared minus x. .…$

Source: College Board — AP Calculus AB, Free-response questions, 2015

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