AP Calculus AB Unit 4 — Contextual Applications of Differentiation Practice Test
AP Calculus AB Unit 4 — Contextual Applications of Differentiation Practice Test
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Question 1 of 19
1. Question
A particle is moving in a straight path with a constant initial velocity. The particle is then subjected to a force causing a timedependent acceleration given as a function of time: a(t)=(a+b) t After 10 seconds, the particle has a velocity equal to k meterspersecond. Find the initial velocity in terms of the constants k , a , and b Units are all in S.I. (meters, seconds, meterspersecond, etc.)
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Question 2 of 19
2. Question
The position of a particle as a function of time is given below: At what values of t does the particle change direction?
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Question 3 of 19
3. Question
A gun sends a bullet straight up with a launch velocity of 220 ft/s. It reaches a height of s=220 t−16 t ^{2} after t seconds. What is its velocity 500 ft into the air?
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Question 4 of 19
4. Question
A right triangle has sides of length x and y which are both increasing in length over time such that: x ( t )=2 t y ( t )=4 t ^{2} Find the rate at which the angle θ opposite y ( t ) is changing with respect to time.
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Question 5 of 19
5. Question
A tank is being filled with a liquid. The function V gives the volume of liquid in the tank, in liters, after t minutes. What is the best interpretation for the following statement? The value of the derivative at V at t =1 is equal to 2 .
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Question 6 of 19
6. Question
A weight that is attached to the end of a spring is pulled and then released. The function H gives its height, in centimeters, after t seconds. What is the best interpretation for the following statement?
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Question 7 of 19
7. Question
A weight that is attached to the end of a spring is pulled and then released. The function H gives its height, in centimeters, after t seconds. What is the best interpretation for the following statement? H ‘ (0)=3
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Question 8 of 19
8. Question
An object is moving along a line. The following graph gives the object’s velocity over time Which point on the graph is neither speeding up nor slowing down?
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Question 9 of 19
9. Question
Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views t days after Nora uploaded the video:V (t)=100⋅ e ^{0.4 t }What is the instantaneous rate of change of the number of views 4 days after the video was uploaded?
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Question 10 of 19
10. Question
Consider the following problem:
The radius r (t) of the base of a cylinder is increasing at a rate of 1 meter per hour and the height h(t ) of the cylinder is decreasing at a rate of 4 meters per hour. At a certain instant t _{0} , the base radius is 5 meters and the height is 8 meters. What is the rate of change of the volume V (t) of the cylinder at that instant?CorrectIncorrect 
Question 11 of 19
11. Question
Tom was given this problem: The side s (t) of a square is decreasing at a rate of 2 kilometres per hour. At a certain instant t 0 , the side is 9 kilometres. What is the rate of change of the area A (t ) of the square at that instant? Which equation should Tom use to solve the problem?
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Question 12 of 19
12. Question
The differentiable functions and are related by the following equation:
Also, . Find when .
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Question 13 of 19
13. Question
The radius of a circle is decreasing at a rate of 6.5 meters per minute. At a certain instant, the radius is 12 meters. What is the rate of change of the area of the circle at that instant (in square meters per minute)?
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Question 14 of 19
14. Question
One diagonal of a rhombus is decreasing at a rate of 7 centimeters per minute and the other diagonal of the rhombus is increasing at a rate of 10 centimetersper minute. At a certain instant, the decreasing diagonal is 4 centimeters and the increasing diagonal is 6 centimeters. What is the rate of change of the area of the rhombus at that instant (in square centimeters per minute)?
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Question 15 of 19
15. Question
The surface area of a sphere is increasing at a rate of hour. At a certain instant, the surface area is 36 π 14 π square meters per square meters. What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)?
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Question 16 of 19
16. Question
The local linear approximation to the function g at x=6 is y=−3 x+ 4 . What is the value of g ( 6 ) + g ‘ (6) ?
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Question 17 of 19
17. Question
Let f be a differentiable function with f ( 2 )=−3 and f ‘ ( 2 )=−4 . What is the f (1.9) value of the approximation of using the function’s local linear approximation at x=2 ?
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Question 18 of 19
18. Question
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Question 19 of 19
19. Question
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