Ch 26: OAE Mathematics: Rate of Change

About This Chapter

This chapter uses quick, entertaining videos to demonstrate the rate of change concepts you could be tested on as you work through your OAE Mathematics certification exam. If you have any questions about the rate of change ideas and methods illustrated here, submit them to our instructors for help.

OAE Mathematics: Rate of Change - Chapter Summary

Use these appealing videos, most less than ten minutes long, to review the rate of change concepts you're expected to demonstrate mastery of on the OAE Mathematics exam. Chapter topics include:

  • Graphical representations of slope and rate of change
  • The difference between average and instantaneous rates of change
  • The mean value theorem
  • Rolle's theorem
  • Derivatives
  • The property of being differentiable

Each lesson is followed by a short quiz that evaluates your understanding of the rate of change concepts and theorems from the lesson. Let our instructors know if you need any help.

Objectives of the OAE Mathematics: Rate of Change Chapter

The lesson quizzes in this chapter require you to actively use the rate of change topics and theories illustrated by the video lessons, improving your retention of the concepts and solidifying your understanding. As an added bonus, they mimic the OAE Math test format so you can get a preview of what the exam will look like.

The computer-administered OAE Mathematics exam lasts four and a half hours. The 150 multiple-choice questions cover five content domains. Accounting for 19% of the questions apiece are geometry and measurement; trig and calculus; statistics, probability and discrete mathematics; and math processes and number sense. The remaining 24% of the questions cover algebra, patterns and functions. The trig and calculus section is where you may find questions related to rates of change.

7 Lessons in Chapter 26: OAE Mathematics: Rate of Change
Test your knowledge with a 30-question chapter practice test
Slopes and Rate of Change

1. Slopes and Rate of Change

If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.

Average and Instantaneous Rates of Change

2. Average and Instantaneous Rates of Change

When you drive to the store, you're probably not going the same speed the entire time. Speed is an example of a rate of change. In this lesson, you'll learn about the difference between instantaneous and average rate of change and how to calculate both.

What is the Mean Value Theorem?

3. What is the Mean Value Theorem?

Three people set off on a car trip. They all start at the same time and end at the same time. Learn what calculus says about how fast they traveled along the way as you study the Mean Value Theorem in this lesson.

Rolle's Theorem: A Special Case of the Mean Value Theorem

4. Rolle's Theorem: A Special Case of the Mean Value Theorem

Super C, the human cannonball, is shot into the air at 35 mph, but his average vertical velocity is zero. In this lesson, you will use Rolle's theorem to explain what this means about Super C's flight.

Derivatives: The Formal Definition

5. Derivatives: The Formal Definition

The derivative defines calculus. In this lesson, learn how the derivative is related to the instantaneous rate of change with Super C, the cannonball man.

Derivatives: Graphical Representations

6. Derivatives: Graphical Representations

Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.

What It Means To Be 'Differentiable'

7. What It Means To Be 'Differentiable'

Lots of jets can go from zero to 300 mph quickly, but super-jets can do this instantaneously. In this lesson, learn what that means for differentiability.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the Ohio Assessments for Educators - Mathematics (027): Practice & Study Guide course