Ch 5: Cambridge Pre-U Math Short Course: Differentiation

About This Chapter

Use this chapter to broaden your knowledge of mathematics and study up on the concept of differentiation. Questions on the topic will be found on the Cambridge Pre-U Math Short Course test.

Cambridge Pre-U Math Short Course: Differentiation - Chapter Summary

This chapter outlines concepts you need to know about differentiation to correctly answer questions on the final assessment for the Cambridge Pre-U Math Short Course. The text and video lessons focus on topics like graphical representations, the instantaneous rate of change and the properties of derivatives. Review how to write derivatives and apply the distributive type rule. By the time you complete the chapter, you should be able to:

  • Understand the rate of change, including average and instantaneous
  • Define, graph and calculate derivatives
  • Explain the concept of differentiability
  • Calculate limits to find a derivative
  • Find global maximum and minimum values with differentiation
  • Solve problems with logarithms and natural base e

Take advantage of the flexibility of online study and the unlimited access you'll have to this chapter's information. You can watch the videos as often as necessary to get a handle on differentiation. Your mobile device allows you to watch anywhere and learn visually at any point in time. If you'd prefer to study offline and learn through reading, print the quiz results. The text transcripts often include bold key terms that can further your understanding of the material when researched.

Cambridge Pre-U Math Short Course: Differentiation Chapter Objectives

The written Cambridge Pre-U Math Short Course assessment is comprised of Paper 1 and Paper 2. Named Pure Mathematics and adding up to 45% of the assessment weighting, Paper 1 will evaluate your proficiency in solving differentiation problems. In part, you'll need to recognize the difference between maximum and minimum points and apply differentiation to rates of change. You'll have one hour and 45 minutes to answer this component's 65 questions. When you begin working on Paper 2, Statistics, you'll have two hours to complete 80 questions and earn 55% of the assessment score.

10 Lessons in Chapter 5: Cambridge Pre-U Math Short Course: Differentiation
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.

Derivatives: The Formal Definition

3. 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

4. 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'

5. 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.

Using Limits to Calculate the Derivative

6. Using Limits to Calculate the Derivative

If you know the position of someone as a function of time, you can calculate the derivative -- the velocity of that person -- as a function of time as well. Use the definition of the derivative and your knowledge of limits to do just that in this lesson.

The Linear Properties of a Derivative

7. The Linear Properties of a Derivative

In this lesson, learn two key properties of derivatives: constant multiples and additions. You will 'divide and conquer' in your approach to calculating the limits used to find derivatives.

How to Determine Maximum and Minimum Values of a Graph

8. How to Determine Maximum and Minimum Values of a Graph

What is the highest point on a roller coaster? Most roller coasters have a lot of peaks, but only one is really the highest. In this lesson, learn the difference between the little bumps and the mother of all peaks on your favorite ride.

Using Differentiation to Find Maximum and Minimum Values

9. Using Differentiation to Find Maximum and Minimum Values

If you are shot out of a cannon, how do you know when you've reached your maximum height? When walking through a valley, how do you know when you are at the bottom? In this lesson, use the properties of the derivative to find the maxima and minima of a function.

Using the Derivatives of Natural Base e & Logarithms

10. Using the Derivatives of Natural Base e & Logarithms

In this lesson, we learn the derivative formulas for exponential and logarithmic functions. In addition, we learn how to apply them through several concrete examples.

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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