AP Calculus AB Unit 4 — Contextual Applications of Differentiation Practice Test
AP Calculus AB Unit 4 — Contextual Applications of Differentiation Practice Test
Quiz Summary
0 of 19 questions completed
Questions:
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
Information
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
Results
Results
0 of 19 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

Categories
 Not categorized 0%
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 Answered
 Review

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.)
CorrectIncorrect 
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?
CorrectIncorrect 
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?
CorrectIncorrect 
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.
CorrectIncorrect 
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 .
CorrectIncorrect 
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?
CorrectIncorrect 
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
CorrectIncorrect 
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?
CorrectIncorrect 
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?
CorrectIncorrect 
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?
CorrectIncorrect 
Question 12 of 19
12. Question
The differentiable functions and are related by the following equation:
Also, . Find when .
CorrectIncorrect 
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)?
CorrectIncorrect 
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)?
CorrectIncorrect 
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)?
CorrectIncorrect 
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) ?
CorrectIncorrect 
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 ?
CorrectIncorrect 
Question 18 of 19
18. Question
CorrectIncorrect 
Question 19 of 19
19. Question
CorrectIncorrect