Test 1, Chapters 10 and 11

The material in this course can, for the most part, be divided into three categories. The first category represents background information. This category includes ideas and concepts that are used, primarily, to develop the main fundamental concepts. For example, we spent time looking at limits and continuity primarily to develop the concept of a derivative. While limits and continuity are important topics, in this course we basically used them as a means to an end.

The second category represents fundamental concepts and techniques. Clearly, the focus in chapters 10 and 11 is the derivative of a function. Consequently, I expect you to understand the difference between average rate of change (the slope of the secant) and instantaneous rate of change (the slope of the tangent which is the derivative). I expect you to know how to apply the basic differentiation rules (the constant function rule, the constant multiple rule, the addition/subtraction rule, and the power rule). I expect you to know how to apply the more advanced differentiation rules (the product rule, the quotient rule, and the chain rule). I expect you to know how to find the derivative of exponential functions, logarithmic functions, and implicit functions.

While fundamental concepts and technique are clearly vital, these things alone are virtually useless. What is really important is the ability to use these concepts and techniques as problem-solving tools. This requires a higher level of knowledge in that you must not only know the concepts and techniques but you must also know when to use them. Consequently, the third category of material in this course represents applications. The applications we have covered in chapters 10 and 11 include marginal analysis, exponential growth (including continuously compounded interest), related rates, relative rates, and elasticity of demand.

This first test will not include questions directly related to background information nor will it include any questions related to spreadsheets. Approximately 40% of the points will come from questions directly related to concepts and techniques. The remaining 60% will come from questions that require you to apply the basic concepts and techniques to solve problems.

Rather than supplying a sample test, I'm going to refer you to the review exercises in the book. The answers to all of the review exercises are in the back of the book so you can check your work (after you have worked the exercise, not before or during). These review questions are representative of what will be on the test. The test questions will be similar in nature but different. I suggest that you work through the following review exercises:

Chapter 10: 1, 21-31, 38-45, 48, 49, 52, 53, 85-90, 93-95

Chapter 11: 1-9, 11-31, 34-44

The mathematics department provides the 7-11 Lab in HR 314 for any students who want help. A mathematics major is available to help you every Monday through Thursday from 7:00 to 11:00 p.m. You may have to explain some of the business terms (such as "marginal cost") but they should be able to help you with the concepts and techniques.