Ch 28: Calculus: NBPTS Math - Adolescence & Young Adult

About This Chapter

This Calculus chapter was constructed to heighten your understanding of the related material you'll encounter within the NBPTS Math (Adolescence & Young Adult) exam. Engaging video lessons making for an entertaining learning process.

NBPTS Math - Adolescence & Young Adult: Calculus - Chapter Summary

Get ready to answer the NBPTS Math (Adolescence & Young Adult) exam's calculus questions. This chapter includes easy-to-follow lessons that give thorough attention to the various aspects and applications of calculus. The lessons define relevant mathematical terms while showing you how they're put into practice. By the time you finish with this chapter, you'll have tightened your grasp of:

  • Defining calculus
  • Derivatives
  • Defining limits through graphs
  • Understanding limit notation
  • Function continuity
  • Vertical and horizontal asymptotes
  • Differential calculus
  • Differentiation and optimization
  • Integrals and calculating volumes using them
  • Dynamic motion and integration
  • Integration and root finding

The dashboard feature will provide you with the ability to monitor your progress through the chapter and keep up with your recent study activities. While there, you can also explore links to self-assessment quizzes and related courses.

14 Lessons in Chapter 28: Calculus: NBPTS Math - Adolescence & Young Adult
Test your knowledge with a 30-question chapter practice test
What is Calculus? - Definition & History

1. What is Calculus? - Definition & History

In this lesson, you're going to learn about some of the history of calculus: who discovered it, and the three major stages with which it developed through time.

Derivatives: The Formal Definition

2. 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

3. 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.

Using a Graph to Define Limits

4. Using a Graph to Define Limits

My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.

Understanding Limits: Using Notation

5. Understanding Limits: Using Notation

Join me on a road trip as we define the mathematical notation of limits. As time goes by and I traverse hills and highways, the limit of my speed changes. Learn how to write these limits in this lesson.

Continuity in a Function

6. Continuity in a Function

Travel to space and explore the difference between continuous and discontinuous functions in this lesson. Learn how determining continuity is as easy as tracing a line.

Horizontal and Vertical Asymptotes

7. Horizontal and Vertical Asymptotes

No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.

Differential Calculus: Definition & Applications

8. Differential Calculus: Definition & Applications

This lesson is an introduction to differential calculus, the branch of mathematics that is concerned with rates of change. If you ever wanted to know how things change over time, then this is the place to start!

Optimization and Differentiation

9. Optimization and Differentiation

In this lesson, you can learn what optimization means from a mathematical standpoint. Using the techniques taught in this lesson, you can use the five steps to optimization to figure out practical things, like how much sleep you need to get before an exam.

Definite Integrals: Definition

10. Definite Integrals: Definition

Explore how driving backwards takes you where you've already been as we define definite integrals. This lesson will also teach you the relationship between definite integrals and Riemann sums. Then, discover how an integral changes when it is above and below the x-axis.

Integration and Dynamic Motion

11. Integration and Dynamic Motion

This lesson uses driving to demonstrate how graphing can help you use calculus to figure out how fast you were going at a given time. Using this lesson, you can learn how to integrate your velocity to find your position.

How to Calculate Volumes Using Single Integrals

12. How to Calculate Volumes Using Single Integrals

Ever wonder where the equation for the volume of a cone comes from? Or the equation for the volume of a sphere? In this lesson, learn how to use a slicing technique to find the volume of a region by solving a single integral.

How to Find Simple Areas With Root Finding and Integration

13. How to Find Simple Areas With Root Finding and Integration

Combine your calculus tools in this lesson! Find the area enclosed by multiple arbitrary functions by first finding the root of an equation and then integrating over the resulting range.

How to Find Area Between Functions With Integration

14. How to Find Area Between Functions With Integration

Sometimes you aren't looking for the area under the curve; after all, not every region is between a curve and axis! In this lesson, learn how to find areas between curves as well as areas with complicated boundaries.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the National Board Certification Exam - Mathematics/Adolescence & Young Adulthood: Practice & Study Guide course