AP®︎ Calculus AB: Unit 4 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Unit 4 of AP Calculus AB – Contextual Applications of Differentiation.
Questions List
Unit 4 (All Topics)
Question 1 Topic 4.1Easy
is the height, in centimeters, of a tomato plant days after it is planted, and . Which of the following is the best interpretation of ?
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 4: Contextual Applications of Differentiation
Apply derivatives to real-world scenarios involving rates, motion, and L'Hospital's Rule.
Topic 4.1: Interpreting the Meaning of the Derivative in Context
Learning Objective: CHA-3.A
Interpret the meaning of a derivative in context.
Essential Knowledge: CHA-3.A.1
The derivative of a function can be interpreted as the instantaneous rate of change with respect to its independent variable.
Essential Knowledge: CHA-3.A.2
The derivative can be used to express information about rates of change in applied contexts.
Essential Knowledge: CHA-3.A.3
The unit for f'(x) is the unit for f divided by the unit for x.
Topic 4.2: Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Learning Objective: CHA-3.B
Calculate rates of change in applied contexts.
Essential Knowledge: CHA-3.B.1
The derivative can be used to solve rectilinear motion problems involving position, speed, velocity, and acceleration.
Topic 4.3: Rates of Change in Applied Contexts Other Than Motion
Learning Objective: CHA-3.C
Interpret rates of change in applied contexts.
Essential Knowledge: CHA-3.C.1
The derivative can be used to solve problems involving rates of change in applied contexts.
Topic 4.4: Introduction to Related Rates
Learning Objective: CHA-3.D
Calculate related rates in applied contexts.
Essential Knowledge: CHA-3.D.1
The chain rule is the basis for differentiating variables in a related rates problem with respect to the same independent variable.
Essential Knowledge: CHA-3.D.2
Other differentiation rules, such as the product rule and the quotient rule, may also be necessary to differentiate all variables with respect to the same independent variable.
Topic 4.5: Solving Related Rates Problems
Learning Objective: CHA-3.E
Interpret related rates in applied contexts.
Essential Knowledge: CHA-3.E.1
The derivative can be used to solve related rates problems; that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known.
Topic 4.6: Approximating Values of a Function Using Local Linearity and Linearization
Learning Objective: CHA-3.F
Approximate a value on a curve using the equation of a tangent line.
Essential Knowledge: CHA-3.F.1
The tangent line is the graph of a locally linear approximation of the function near the point of tangency.
Essential Knowledge: CHA-3.F.2
For a tangent line approximation, the function’s behavior near the point of tangency may determine whether a tangent line value is an underestimate or an overestimate of the corresponding function value.
Topic 4.7: Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms
Learning Objective: LIM-4.A
Determine limits of functions that result in indeterminate forms.
Essential Knowledge: LIM-4.A.1
When the ratio of two functions tends to 0/0 or ∞/∞ in the limit, such forms are said to be indeterminate. Exclusion: There are many other indeterminate forms, such as , for example, but these will not be assessed on either the AP Calculus AB or BC Exam. However, teachers may include these topics, if time permits.
Essential Knowledge: LIM-4.A.2
Limits of the indeterminate forms 0/0 or ∞/∞ may be evaluated using L’Hospital’s Rule.
