AP Calculus BC Unit 7 — Differential Equations Practice Test
AP Calculus BC Unit 7 — Differential Equations Practice Test
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Question 1 of 19
1. Question
A radioactive material decays at a rate of change proportional to the current amount, Q, of the radioactive material. Which equation describes this relationship?
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Question 2 of 19
2. Question
is a solution to the above equation?
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Question 3 of 19
3. Question
Which differential equation generates the slope field?
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Question 4 of 19
4. Question
What is the general solution to the differential equation that generated the slope field?
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Question 5 of 19
5. Question
Kajal tried to solve the differential equation. This is his work Is Kajal’s work correct? If not, what is her mistake?
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Question 6 of 19
6. Question
Can this differential equation be solved using separation of variables?
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Question 7 of 19
7. Question
We are given that f ( 1.5 ) =4 and a table of values of the derivative f ‘ . Use Euler’s method with a stepsize of 1 to approximate f (4.5)
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Question 8 of 19
8. Question
and f ( 2 )=12 . Find f (−1).
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Question 9 of 19
9. Question
And y ( 2 )=3 . What is t When Y=6 . Choose all answers that apply.
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Question 10 of 19
10. Question
, y=1 And when T= 4, Solve the equation.
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Question 11 of 19
11. Question
The amount of medication in Rory’s bloodstream decreases at a rate that is proportional at any time to the amount of the medication in the bloodstream at that time. Rory takes 150 milligrams of medication initially. The amount of medication is halved every 13 hours. How many milligrams of the medication are in Rory’s bloodstream after 8 hours?
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Question 12 of 19
12. Question
Which graph could be a solution to the logistic differential equation
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Question 13 of 19
13. Question
The Population p(t) of worms in a compost pile after t years satisfies the logistic differential equation where the initial population is 18 worms What is the population when it’s growing the fastest?
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Question 14 of 19
14. Question
Solve the separable differential equation with the condition y ( 0 )=4 .
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Question 15 of 19
15. Question
Let y=f(x) be the solution to be differential Equation , with initial condition f ( 1 )=2 . What is the approximation for f ( 0 ) obtained by using Euler’s Method with two steps of equal length starting at x=1 ?
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Question 16 of 19
16. Question
The solution of the differential equation contains the point (3,−2) . Using Euler’s Method with ∆ x=−0.3 to approximate y when x=2.7 gives….
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Question 17 of 19
17. Question
The table above shows values of f ‘ (x) , the derivative of a function f , for selected values of x . If f (−0.2 )=1 , what is the approximation for f (0.4) obtained by using Euler’s method with step size of 0.2 starting at x=−0.2 ?
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Question 18 of 19
18. Question
What is the general solution to the differential equation that generated the slope field?
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Question 19 of 19
19. Question
and y (−1 )=1 . What is x , When y=2,
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