AP®︎ Calculus AB: Unit 7 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Unit 7 of AP Calculus AB – Differential Equations.
Questions List
Unit 7 (All Topics)
Question 1 Topic 7.1Easy
Which of the following is a differential equation?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus AB Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Unit 7: Differential Equations
Solve separable differential equations and model exponential growth with slope fields.
Topic 7.1: Modeling Situations with Differential Equations
Learning Objective: FUN-7.A
Interpret verbal statements of problems as differential equations involving a derivative expression.
Essential Knowledge: FUN-7.A.1
Differential equations relate a function of an independent variable and the function’s derivatives.
Topic 7.2: Verifying Solutions for Differential Equations
Learning Objective: FUN-7.B
Verify solutions to differential equations.
Essential Knowledge: FUN-7.B.1
Derivatives can be used to verify that a function is a solution to a given differential equation.
Essential Knowledge: FUN-7.B.2
There may be infinitely many general solutions to a differential equation.
Topic 7.3: Sketching Slope Fields
Learning Objective: FUN-7.C
Estimate solutions to differential equations.
Essential Knowledge: FUN-7.C.1
A slope field is a graphical representation of a differential equation on a finite set of points in the plane.
Essential Knowledge: FUN-7.C.2
Slope fields provide information about the behavior of solutions to first-order differential equations.
Topic 7.4: Reasoning Using Slope Fields
Learning Objective: FUN-7.C
Estimate solutions to differential equations.
Essential Knowledge: FUN-7.C.3
Solutions to differential equations are functions or families of functions.
Topic 7.6: Finding General Solutions Using Separation of Variables
Learning Objective: FUN-7.D
Determine general solutions to differential equations.
Essential Knowledge: FUN-7.D.1
Some differential equations can be solved by separation of variables.
Essential Knowledge: FUN-7.D.2
Antidifferentiation can be used to find general solutions to differential equations.
Topic 7.7: Finding Particular Solutions Using Initial Conditions and Separation of Variables
Learning Objective: FUN-7.E
Determine particular solutions to differential equations.
Essential Knowledge: FUN-7.E.1
A general solution may describe infinitely many solutions to a differential equation. There is only one particular solution passing through a given point.
Essential Knowledge: FUN-7.E.2
The function F defined by F(x) = y(a) + ∫_a^x f(t, y(t)) dt is a particular solution to the differential equation dy/dx = f(x, y), satisfying F(a) = y(a).
Essential Knowledge: FUN-7.E.3
Solutions to differential equations may be subject to domain restrictions.
Topic 7.8: Exponential Models with Differential Equations
Learning Objective: FUN-7.F
Interpret the meaning of a differential equation and its variables in context.
Essential Knowledge: FUN-7.F.1
Specific applications of finding general and particular solutions to differential equations include motion along a line and exponential growth and decay.
Essential Knowledge: FUN-7.F.2
The model for exponential growth and decay that arises from the statement “The rate of change of a quantity is proportional to the size of the quantity” is dy/dt = ky.
Learning Objective: FUN-7.G
Determine general and particular solutions for problems involving differential equations in context.
Essential Knowledge: FUN-7.G.1
The exponential growth and decay model, dy/dt = ky, with initial condition y = y0 when t = 0, has solutions of the form y = y0 e^{kt}.
