AP®︎ Calculus BC: Unit 8 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Unit 8 of AP Calculus BC – Applications of Integration.
Questions List
Unit 8 (All Topics)
Question 1 Topic 8.1Easy
The function is continuous on .
Which expression gives the average value of on ?
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 8: Applications of Integration
Apply integrals to compute areas, volumes, arc lengths, and solve net-change problems.
Topic 8.1: Finding the Average Value of a Function on an Interval
Learning Objective: CHA-4.B
Determine the average value of a function using definite integrals.
Essential Knowledge: CHA-4.B.1
The average value of a continuous function f over an interval [a, b] is (1/(b - a)) ∫_a^b f(x) dx.
Topic 8.2: Connecting Position, Velocity, and Acceleration of Functions Using Integrals
Learning Objective: CHA-4.C
Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
Essential Knowledge: CHA-4.C.1
For a particle in rectilinear motion over an interval of time, the definite integral of velocity represents the particle’s displacement over the interval of time, and the definite integral of speed represents the particle’s total distance traveled over the interval of time.
Topic 8.3: Using Accumulation Functions and Definite Integrals in Applied Contexts
Learning Objective: CHA-4.D
Interpret the meaning of a definite integral in accumulation problems.
Essential Knowledge: CHA-4.D.1
A function defined as an integral represents an accumulation of a rate of change.
Essential Knowledge: CHA-4.D.2
The definite integral of the rate of change of a quantity over an interval gives the net change of that quantity over that interval.
Learning Objective: CHA-4.E
Determine net change using definite integrals in applied contexts.
Essential Knowledge: CHA-4.E.1
The definite integral can be used to express information about accumulation and net change in many applied contexts.
Topic 8.4: Finding the Area Between Curves Expressed as Functions of x
Learning Objective: CHA-5.A
Calculate areas in the plane using the definite integral.
Essential Knowledge: CHA-5.A.1
Areas of regions in the plane can be calculated with definite integrals.
Topic 8.5: Finding the Area Between Curves Expressed as Functions of y
Learning Objective: CHA-5.A
Calculate areas in the plane using the definite integral.
Essential Knowledge: CHA-5.A.2
Areas of regions in the plane can be calculated using functions of either x or y.
Topic 8.6: Finding the Area Between Curves That Intersect at More Than Two Points
Learning Objective: CHA-5.A
Calculate areas in the plane using the definite integral.
Essential Knowledge: CHA-5.A.3
Areas of certain regions in the plane may be calculated using a sum of two or more definite integrals or by evaluating a definite integral of the absolute value of the difference of two functions.
Topic 8.7: Volumes with Cross Sections: Squares and Rectangles
Learning Objective: CHA-5.B
Calculate volumes of solids with known cross sections using definite integrals.
Essential Knowledge: CHA-5.B.1
Volumes of solids with square and rectangular cross sections can be found using definite integrals and the area formulas for these shapes.
Topic 8.8: Volumes with Cross Sections: Triangles and Semicircles
Learning Objective: CHA-5.B
Calculate volumes of solids with known cross sections using definite integrals.
Essential Knowledge: CHA-5.B.2
Volumes of solids with triangular cross sections can be found using definite integrals and the area formulas for these shapes.
Essential Knowledge: CHA-5.B.3
Volumes of solids with semicircular and other geometrically defined cross sections can be found using definite integrals and the area formulas for these shapes. Illustrative examples of other cross sections in CHA-5.B.3: The volume of a funnel whose cross sections are circles can be found using the area formula for a circle and definite integrals (see 2016 AB Exam FRQ #5(b)). The volume of a solid whose cross sectional area is defined using a function can be found using the known area function and a definite integral (see 2009 AB Exam FRQ #4(c)).
Topic 8.9: Volume With Disc Method: Revolving Around the X- or Y-Axis
Learning Objective: CHA-5.C
Calculate volumes of solids of revolution using definite integrals.
Essential Knowledge: CHA-5.C.1
Volumes of solids of revolution around the x- or y-axis may be found by using definite integrals with the disc method.
Topic 8.10: Volume with Disc Method: Revolving Around Other Axes
Learning Objective: CHA-5.C
Calculate volumes of solids of revolution using definite integrals.
Essential Knowledge: CHA-5.C.2
Volumes of solids of revolution around any horizontal or vertical line in the plane may be found by using definite integrals with the disc method.
Topic 8.11: Volume with Washer Method: Revolving Around the X- or Y-Axis
Learning Objective: CHA-5.C
Calculate volumes of solids of revolution using definite integrals.
Essential Knowledge: CHA-5.C.3
Volumes of solids of revolution around the x- or y-axis whose cross sections are ring shaped may be found using definite integrals with the washer method.
Topic 8.12: Volume with Washer Method: Revolving Around Other Axes
Learning Objective: CHA-5.C
Calculate volumes of solids of revolution using definite integrals.
Essential Knowledge: CHA-5.C.4
Volumes of solids of revolution around any horizontal or vertical line whose cross sections are ring-shaped may be found using definite integrals with the washer method.
Topic 8.13: The Arc Length of a Smooth, Planar Curve and Distance Traveled
Learning Objective: CHA-6.A
Determine the length of a curve in the plane defined by a function, using a definite integral.
Essential Knowledge: CHA-6.A.1
The length of a planar curve defined by a function can be calculated using a definite integral.
