# 2019ap Calculus

AP Calculus AB Scoring Guidelines from the 2019 Exam Administration Keywords scoring guidelines; 2019 AP exam administration; teacher resources; exam resources; exam practice; exam scoring information; exam preparation; course preparation; AP Scoring Guidelines from the 2019 Exam Administration; £½? 2019 AP Calculus AB & BC Free Response Question #1. Read this document to make sure you are ready! 2020 AP Testing Guide.pdf. Friday: TAKE THE DAY OFF!

### Questions And Worked Solutions For AP Calculus AB 2019

AP Calculus AB 2019 Free Response Question 1
Rate in, rate out problem. Integral of a rate; average value of a function

1. Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(πt/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4 + 20.1t2. Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0).
(a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5)? Give youranswer to the nearest whole number.
(b) What is the average number of fish that leave the lake per hour over the 5-hour period frommidnight (t = 0) to 5 A.M. (t = 5)?
(c) At what time t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake? Justify your answer.
(d) Is the rate of change in the number of fish in the lake increasing or decreasing at 5 A.M. (t = 5)? Explainyour reasoning.

AP Calculus AB 2019 Free Response Question 2
2. The velocity of a particle, P, moving along the x-axis is given by the differentiable function Vp, where Vp(t) is measured in meters per hour and t is measured in hours. Selected values of Vp(t) are shown in the tableabove. Particle P is at the origin at time t = 0.
(a) Justify why there must be at least one time t, for 0.3 ≤ t ≤ 2.8, at which VP'(t), the acceleration ofparticle P, equals 0 meters per hour per hour.
(b) Use a trapezoidal sum with the three subintervals [0, 0.3], [0.3, 1.7], and [1.7, 2.8] to approximate thevalue of .
(c) A second particle, Q, also moves along the x-axis so that its velocity for 0 ≤ t ≤ 4 is given bymeters per hour. Find the time interval during which the velocity of particle Q is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is at least 60 meters per hour.
(d) At time t = 0, particle Q is at position x = −90. Using the result from part (b) and the function VQ frompart (c), approximate the distance between particles P and Q at time t = 2.8.

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AP Calculus AB 2019 Free Response Question 3
3. The continuous function f is defined on the closed interval −6 ≤ x ≤ 5. The figure above shows a portion ofthe graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3). It isknown that the point (3, 3 −√5 ) is on the graph of f.

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AP Calculus AB 2019 Free Response Question 4
4. A cylindrical barrel with a diameter of 2 feet contains collected rainwater, as shown in the figure above. Thewater drains out through a valve (not shown) at the bottom of the barrel. The rate of change of the height h ofthe water in the barrel with respect to time t is modeled bydh/dt = -1/10 √, where h is measured in feet and t is measured in seconds. (The volume V of a cylinder with radius r and height h is V = πr2«/sup>h.)
(a) Find the rate of change of the volume of water in the barrel with respect to time when the height of thewater is 4 feet. Indicate units of measure.
(b) When the height of the water is 3 feet, is the rate of change of the height of the water with respect to timeincreasing or decreasing? Explain your reasoning.
(c) At time t = 0 seconds, the height of the water is 5 feet. Use separation of variables to find an expressionfor h in terms of t.

AP Calculus AB 2019 Free Response Question 5
5. Let R be the region enclosed by the graphs of g(x)) = −2 + 3 + cos(π/2 x) and h(x) = 6 - 2(x - 1)2, they-axis, and the vertical line x = 2, as shown in the figure above.
(a) Find the area of R.
(b) Region R is the base of a solid. For the solid, at each x the cross section perpendicular to the x-axis hasarea A(x) = 1/(x + 3). Find the volume of the solid.
(c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R isrotated about the horizontal line y = 6.

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## 2019 Ap Calculus Ab

AP Calculus AB 2019 Free Response Question 6
6. Functions f, g, and h are twice-differentiable functions with g(2) = h(2) = 4. The line y = 4 + 2/3 (x - 2) is tangent to both the graph of g at x = 2 and the graph of h at x = 2.
(a) Find h'(2).
(b) Let a be the function given by a(x) = 3x3h(x). Write an expression for a'(x). Find a'(2).
(d) It is known that g(x) ≤ h(x) for 1 < x < 3. Let k be a function satisfying g(x) ≤ k(x) ≤ h(x) for1 < x < 3. Is k continuous at x = 2? Justify your answer.

## 2019 Ap Calculus Bc Frq

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. Other documents virejected scriptures study.

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### Chapter 4

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