# Ch 45: CEOE Advanced Math: Rate of Change

### About This Chapter

## CEOE Advanced Math: Rate of Change - Chapter Summary

The lessons in this chapter examine key components of rate of change in mathematics as well as related mathematical principles. By the time you finish going through these lessons, you'll be ready to tackle questions involving:

- Velocity, slopes, and the rate of change
- The mean value theorem
- Rolle's theorem
- The formal definition and graphic representation of derivatives
- What it means to be 'differentiable'

You'll be able to check your understanding after every lesson with a practice quiz that you can also print as a worksheet for further study offline. These quizzes will help you familiarize yourself with the kind of questions you may encounter on the exam, and you'll be able to take them as many times as you like.

### CEOE Advanced Math: Rate of Change Chapter Objectives

The CEOE Advanced Mathematics exam is a key component of the teacher certification process in Oklahoma for those who are planning to teach advanced math classes. The exam includes 80 multiple-choice questions spread across five subareas as well as one written response assignment that will pertain to the relations, functions, and algebra subarea.

Studying with this chapter will come in handy on the trigonometry and calculus subarea, which makes up 23% of the exam's total content. You can use these lessons to make sure this section of the test does not create any holes in your performance.

### 1. Velocity and the Rate of Change

Running from your little sister or just window-shopping, your speed is just a measure of how fast you move, or how your position is changing over time. In this lesson, learn about how velocity is a rate of change.

### 2. 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.

### 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.

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### Other Chapters

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

- CEOE Advanced Math: Mathematical Reasoning & Ideas
- CEOE Advanced Math: Origins of Math
- CEOE Advanced Math: Absolute Value
- CEOE Advanced Math: Inequalities
- CEOE Advanced Math: Integers
- CEOE Advanced Math: Operations with Fractions
- CEOE Advanced Math: Operations with Decimals
- CEOE Advanced Math: Percents
- CEOE Advanced Math: Rational & Irrational Numbers
- CEOE Advanced Math: Complex Numbers
- CEOE Advanced Math: Properties of Numbers
- CEOE Advanced Math: Exponents & Exponential Expressions
- CEOE Advanced Math: Roots & Radical Expressions
- CEOE Advanced Math: Number Theory
- CEOE Advanced Math: Vectors, Matrices & Determinants
- CEOE Advanced Math: Properties of Functions
- CEOE Advanced Math: Graphing Functions
- CEOE Advanced Math: The Coordinate Graph & Graph Symmetry
- CEOE Advanced Math: Linear Equations
- CEOE Advanced Math: Systems of Linear Equations
- CEOE Advanced Math: Quadratic Functions
- CEOE Advanced Math: Polynomial Functions Basics
- CEOE Advanced Math: Higher-Degree Polynomial Functions
- CEOE Advanced Math: Piecewise, Absolute Value & Step Functions
- CEOE Advanced Math: Rational Expressions & Function Graphs
- CEOE Advanced Math: Exponential & Logarithmic Functions
- CEOE Advanced Math: Measurement
- CEOE Advanced Math: Perimeter & Area
- CEOE Advanced Math: Symmetry, Similarity & Congruence
- CEOE Advanced Math: Properties of Lines
- CEOE Advanced Math: Angles
- CEOE Advanced Math: Triangles
- CEOE Advanced Math: Triangle Theorems & Proofs
- CEOE Advanced Math: Similar Polygons
- CEOE Advanced Math: The Pythagorean Theorem
- CEOE Advanced Math: Circles
- CEOE Advanced Math: Circular Arcs & Measurement
- CEOE Advanced Math: Transformations
- CEOE Advanced Math: Analytic Geometry & Conic Sections
- CEOE Advanced Math: Trigonometric Functions
- CEOE Advanced Math: Trigonometric Graphs
- CEOE Advanced Math: Trigonometric Applications
- CEOE Advanced Math: Limits
- CEOE Advanced Math: Continuity
- CEOE Advanced Math: Derivative Calculations & Rules
- CEOE Advanced Math: Graphing & Applying Derivatives
- CEOE Advanced Math: Area Under the Curve & Integrals
- CEOE Advanced Math: Integration Techniques
- CEOE Advanced Math: Differential Equations
- CEOE Advanced Math: Data & Graphs
- CEOE Advanced Math: Samples & Populations
- CEOE Advanced Math: Probability
- CEOE Advanced Math: Sets
- CEOE Advanced Math: Statistics
- CEOE Advanced Math: Number Patterns & Sequences
- CEOE Advanced Math: Number Patterns & Series
- CEOE Advanced Math: Discrete Math
- OSAT Advanced Mathematics (CEOE) (111) Flashcards