AP®︎ Precalculus: Topic 1.2 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 1.2 of AP Precalculus – Rates of Change.

Questions List

Topic 1.2

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Question 1 Easy

Let a<ba<b, and let ff be a function defined on [a,b][a,b].

Which expression gives the average rate of change of ff from x=ax=a to x=bx=b?

Af(b)−f(a)a−b\dfrac{f(b)-f(a)}{a-b}
Bf(b)−f(a)b−a\dfrac{f(b)-f(a)}{b-a}
Cf(b)−f(a)b\dfrac{f(b)-f(a)}{b}
Db−af(b)−f(a)\dfrac{b-a}{f(b)-f(a)}

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Precalculus 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.

Topic 1.2: Rates of Change

Learning Objective: 1.2.A

Compare the rates of change at two points using average rates of change near the points.

Essential Knowledge: 1.2.A.1

The average rate of change of a function over an interval of the function’s domain is the constant rate of change that yields the same change in the output values as the function yielded on that interval of the function’s domain. It is the ratio of the change in the output values to the change in input values over that interval.

Essential Knowledge: 1.2.A.2

The rate of change of a function at a point quantifies the rate at which output values would change were the input values to change at that point. The rate of change at a point can be approximated by the average rates of change of the function over small intervals containing the point, if such values exist.

Essential Knowledge: 1.2.A.3

The rates of change at two points can be compared using average rate of change approximations over sufficiently small intervals containing each point, if such values exist.

Learning Objective: 1.2.B

Describe how two quantities vary together at different points and over different intervals of a function.

Essential Knowledge: 1.2.B.1

Rates of change quantify how two quantities vary together.

Essential Knowledge: 1.2.B.2

A positive rate of change indicates that as one quantity increases or decreases, the other quantity does the same.

Essential Knowledge: 1.2.B.3

A negative rate of change indicates that as one quantity increases, the other decreases.

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