About This Chapter
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.
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. 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.
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the Cambridge Pre-U Mathematics - Short Course: Practice & Study Guide course
- Cambridge Pre-U Math Short Course: Quadratic Equations
- Cambridge Pre-U Math Short Course: Coordinate Geometry
- Cambridge Pre-U Math Short Course: Sequences & Series
- Cambridge Pre-U Math Short Course: Exponentials & Logarithms
- Cambridge Pre-U Math Short Course: Integration
- Cambridge Pre-U Math Short Course: Data Summarization
- Cambridge Pre-U Math Short Course: Correlation & Regression
- Cambridge Pre-U Math Short Course: Binomial Distribution
- Cambridge Pre-U Math Short Course: Normal Distribution
- Cambridge Pre-U Math Short Course: Sampling
- Cambridge Pre-U Math Short Course: Statistical Estimation
- Cambridge Pre-U Math Short Course: Hypothesis Testing
- Cambridge Pre-U Math Short Course: Chi-Square Test
- Cambridge Pre-U Math Short Course: Non-Parametric Tests
- Cambridge Pre-U Mathematics - Short Course Flashcards