About This Chapter
NMTA Math: Rate of Change - Chapter Summary
These quick, entertaining videos can be viewed on any Internet-enabled device so you can study the rate of change and prepare for the NMTA Math assessment while you're on the go. As you work through this chapter, you'll get illustrations of the following concepts:
- Slope and graphical representations of rate of change
- The difference between average and instantaneous rates of change
- The mean value theorem and Rolle's theorem
- Derivatives and the property of being differentiable
After each video, make sure to take the follow-up quiz so you can practice using the theorems and graphing techniques presented in the lesson. If you have any questions about the rate of change, please let our instructors know.
Objectives of the NMTA Math: Rate of Change Chapter
You'll have four hours and fifteen minutes to work through the 150 multiple-choice questions on the NMTA Math certification assessment. The lesson quizzes in this chapter let you practice using the rate of change concepts you'll need to know for the exam, and they let you get comfortable with the NMTA format. You can also use them to get an idea of how quickly you'll be able to work through the test.
The NMTA Math exam evaluates New Mexico educators in five areas: calculus and trig; stats, probability and discrete math; geometry and measurement; math processes and number sense; and patterns, algebra and functions. The first four areas take up 19% of the test each, and the last takes up the final 24%.
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.
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Other chapters within the NMTA Mathematics (304): Practice & Study Guide course
- NMTA Math: Properties of Real Numbers
- NMTA Math: Fractions
- NMTA Math: Decimals & Percents
- NMTA Math: Ratios & Proportions
- NMTA Math: Units of Measure & Conversions
- NMTA Math: Logic
- NMTA Math: Reasoning
- NMTA Math: Vector Operations
- NMTA Math: Matrix Operations & Determinants
- NMTA Math: Exponents & Exponential Expressions
- NMTA Math: Algebraic Expressions
- NMTA Math: Linear Equations
- NMTA Math: Inequalities
- NMTA Math: Absolute Value
- NMTA Math: Quadratic Equations
- NMTA Math: Polynomials
- NMTA Math: Rational Expressions
- NMTA Math: Radical Expressions
- NMTA Math: Systems of Equations
- NMTA Math: Complex Numbers
- NMTA Math: Functions
- NMTA Math: Piecewise Functions
- NMTA Math: Exponential & Logarithmic Functions
- NMTA Math: Continuity of a Function
- NMTA Math: Limits
- NMTA Math: Derivative Rules
- NMTA Math: Graphing Derivatives
- NMTA Math: Applications of Derivatives
- NMTA Math: Area Under the Curve & Integrals
- NMTA Math: Integration Techniques
- NMTA Math: Applications of Integration
- NMTA Math: Foundations of Geometry
- NMTA Math: Geometric Figures
- NMTA Math: Properties of Triangles
- NMTA Math: Triangle Theorems & Proofs
- NMTA Math: Parallel Lines & Polygons
- NMTA Math: Quadrilaterals
- NMTA Math: Circles & Arc of a Circle
- NMTA Math: Conic Sections
- NMTA Math: Geometric Solids
- NMTA Math: Analytical Geometry
- NMTA Math: Trigonometric Functions
- NMTA Math: Trigonometric Graphs
- NMTA Math: Solving Trigonometric Equations
- NMTA Math: Trigonometric Identities
- NMTA Math: Sequences & Series
- NMTA Math: Graph Theory
- NMTA Math: Set Theory
- NMTA Math: Statistics Overview
- NMTA Math: Summarizing Data
- NMTA Math: Tables, Plots & Graphs
- NMTA Math: Probability
- NMTA Math: Discrete Probability Distributions
- NMTA Math: Continuous Probability Distributions
- NMTA Math: Sampling
- NMTA Math: Regression & Correlation
- NMTA Mathematics Flashcards