AP Calculus BC Unit 7 practice questions: Differential Equations
8 original multiple-choice questions on AP Calc BC Unit 7, differential equations. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
dy/dx = x + y with y(0) = 1. Using Euler's method with one step of size 0.1, what is the approximation of y(0.1)?
Question 2 of 8
A population satisfies dP/dt = 0.2P(1 − P/500). At what population is it growing fastest?
Question 3 of 8
For the logistic model dP/dt = 0.2P(1 − P/500) with P(0) = 50, what is lim (t→∞) P(t)?
Question 4 of 8
Solve dy/dx = 2xy with y(0) = 3.
Question 5 of 8
Which function is a general solution of dy/dx = y?
Question 6 of 8
In the slope field for dy/dx = xy, what is the slope at the point (1, 2)?
Question 7 of 8
A population grows by dP/dt = kP and doubles every 5 years. What is k?
Question 8 of 8
dy/dx = y with y(0) = 1. Using Euler's method with two steps of size 0.5, what is the estimate for y(1)?
Key ideas in Unit 7
- A differential equation relates a function to its derivatives; a slope field shows dy/dx at points in the plane.
- Separation of variables: get all y on one side and all x on the other, integrate, then use the initial condition to find the constant.
- Exponential growth dy/dt = ky has solution y = y₀e^(kt).
- Euler's method (BC) steps along tangent lines: yₙ₊₁ = yₙ + h·(dy/dx at the current point).
- Logistic growth (BC), dP/dt = kP(1 − P/L), approaches the carrying capacity L and grows fastest at P = L/2.
More AP Calc BC practice
← Unit 6: Integration and Accumulation of Change
Unit 8: Applications of Integration →
The full AP Calculus BC practice test, all units
Studying from your own notes? Turn them into a practice quiz, a study guide or flashcards.