AP®︎ Calculus BC: Unit 3 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Unit 3 of AP Calculus BC – Differentiation: Composite, Implicit, and Inverse Functions.
Questions List
Unit 3 (All Topics)
Question 1 Topic 3.1Easy
Let . If , which of the following could be and ?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus BC 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 3: Differentiation: Composite, Implicit, and Inverse Functions
Use chain rule, implicit differentiation, inverses, and higher-order derivatives.
Topic 3.1: The Chain Rule
Learning Objective: FUN-3.C
Calculate derivatives of compositions of differentiable functions.
Essential Knowledge: FUN-3.C.1
The chain rule provides a way to differentiate composite functions.
Topic 3.2: Implicit Differentiation
Learning Objective: FUN-3.D
Calculate derivatives of implicitly defined functions.
Essential Knowledge: FUN-3.D.1
The chain rule is the basis for implicit differentiation.
Topic 3.3: Differentiating Inverse Functions
Learning Objective: FUN-3.E
Calculate derivatives of inverse and inverse trigonometric functions.
Essential Knowledge: FUN-3.E.1
The chain rule and definition of an inverse function can be used to find the derivative of an inverse function, provided the derivative exists.
Topic 3.4: Differentiating Inverse Trigonometric Functions
Learning Objective: FUN-3.E
Calculate derivatives of inverse and inverse trigonometric functions.
Essential Knowledge: FUN-3.E.2
The chain rule applied with the definition of an inverse function, or the formula for the derivative of an inverse function, can be used to find the derivatives of inverse trigonometric functions.
Topic 3.5: Selecting Procedures for Calculating Derivatives
Topic 3.6: Calculating Higher - Order Derivatives
Learning Objective: FUN-3.F
Determine higher order derivatives of a function.
Essential Knowledge: FUN-3.F.1
Differentiating f′ produces the second derivative f′′, provided the derivative of f′ exists; repeating this process produces higher-order derivatives of f.
Essential Knowledge: FUN-3.F.2
Higher-order derivatives are represented with a variety of notations. For y = f(x), notations for the second derivative include d^2y/dx^2, f''(x), and y''. Higher-order derivatives can be denoted d^n y/dx^n or f^(n)(x).
