AP Calculus AB Average Value, Area and Volume Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Average Value, Area and Volume – Maths PDF

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This ap calculus area volume quiz for AP Calculus AB covers average value, area and volume (Common Core AP CALC AB 8.1, AP CALC AB 8.2, AP CALC AB 8.3, AP CALC AB 8.4, AP CALC AB 8.5, AP CALC AB 8.6, AP CALC AB 8.7, AP CALC AB 8.8, AP CALC AB 8.9, AP CALC AB 8.10, AP CALC AB 8.11, AP CALC AB 8.12), with a free PDF to print.

Test yourself on average value, motion with integrals, area between curves, volumes with cross sections and discs and washers with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 8.1, AP CALC AB 8.2, AP CALC AB 8.3, AP CALC AB 8.4, AP CALC AB 8.5, AP CALC AB 8.6, AP CALC AB 8.7, AP CALC AB 8.8, AP CALC AB 8.9, AP CALC AB 8.10, AP CALC AB 8.11, AP CALC AB 8.12

Ap calculus area volume quiz: 10 questions

Question 1

What is the average value of \(f\) on \([a,b]\)?

Question 2

A car’s position is 10 miles at \(t=1\) hour and 50 miles at \(t=5\) hours. What is its average velocity on this interval?

Question 3

The region between y = 4 and y = x².

What is the area between \(y=4\) and \(y=x^{2}\)?

Question 4

A particle has velocity \(v(t)=t-2\) on \([0,4]\). What is the displacement?

Question 5

A particle has velocity \(v(t)=t-2\) on \([0,4]\). What is the total distance?

Question 6

Revolving y = √x on [0, 9].

What is the volume when \(y=\sqrt{x}\) on \([0,9]\) is revolved about the \(x\)-axis?

Question 7

Which formula gives the volume of the washer solid between outer radius \(R(x)\) and inner radius \(r(x)\)?

Question 8

Cross sections of a solid are squares of side \(x\) on \([0,3]\). What is the volume?

Question 9

The average value of 2x on [0, 3].

The rectangle has the same area as the region under \(y=2x\) on \([0,3]\). What is its height?

Question 10

When the curves \(y=f(x)\) and \(y=g(x)\) cross on \([a,b]\), how should you find the area between them?

Remember

Average value = (1/(b – a)) times the integral of f over [a, b].
Displacement is the integral of v; total distance is the integral of |v|.
Area between curves = integral of (upper – lower); split the interval at every crossing.
Volume by cross sections = integral of A(x); disc method = pi times the integral of (radius squared); washers subtract the inner radius squared.

How to use this ap calculus area volume quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

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