# Ch 26: OAE Mathematics: Rate of Change

### About This Chapter

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

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

- OAE Mathematics: Properties of Real Numbers
- OAE Mathematics: Fractions
- OAE Mathematics: Decimals & Percents
- OAE Mathematics: Ratios & Proportions
- OAE Mathematics: Units of Measure & Conversion
- OAE Mathematics: Logic
- OAE Mathematics: Reasoning
- OAE Mathematics: Vector Operations
- OAE Mathematics: Matrix Operations & Determinants
- OAE Mathematics: Exponents & Exponential Expressions
- OAE Mathematics: Algebraic Expressions
- OAE Mathematics: Linear Equations
- OAE Mathematics: Inequalities
- OAE Mathematics: Absolute Value
- OAE Mathematics: Quadratic Equations
- OAE Mathematics: Polynomials
- OAE Mathematics: Rational Expressions
- OAE Mathematics: Radical Expressions
- OAE Mathematics: Systems of Equations
- OAE Mathematics: Complex Numbers
- OAE Mathematics: Functions
- OAE Mathematics: Piecewise Functions
- OAE Mathematics: Exponential & Logarithmic Functions
- OAE Mathematics: Continuity of a Function
- OAE Mathematics: Limits
- OAE Mathematics: Derivative Rules
- OAE Mathematics: Graphing Derivatives
- OAE Mathematics: Applications of Derivatives
- OAE Mathematics: Area Under the Curve & Integrals
- OAE Mathematics: Integration Techniques
- OAE Mathematics: Applications of Integration
- OAE Mathematics: Foundations of Geometry
- OAE Mathematics: Geometric Figures
- OAE Mathematics: Properties of Triangles
- OAE Mathematics: Triangle Theorems & Proofs
- OAE Mathematics: Parallel Lines & Polygons
- OAE Mathematics: Quadrilaterals
- OAE Mathematics: Circles & Arc of a Circle
- OAE Mathematics: Conic Sections
- OAE Mathematics: Geometric Solids
- OAE Mathematics: Analytical Geometry
- OAE Mathematics: Trigonometric Functions
- OAE Mathematics: Trigonometric Graphs
- OAE Mathematics: Solving Trigonometric Equations
- OAE Mathematics: Trigonometric Identities
- OAE Mathematics: Sequences & Series
- OAE Mathematics: Set Theory
- OAE Mathematics: Statistics Overview
- OAE Mathematics: Summarizing Data
- OAE Mathematics: Tables, Plots & Graphs
- OAE Mathematics: Probability
- OAE Mathematics: Discrete Probability Distributions
- OAE Mathematics: Continuous Probability Distributions
- OAE Mathematics: Sampling
- Ohio Assessments for Educators Mathematics Flashcards