The first midterm is on Friday, September 26, during the regular class period.
The following is a chapter by chapter guide intended to help you organize the material we have covered as you study for your exam. It is only intended to serve as a guidline, and may not explicitly mention everything that you need to study.
Please start by taking a look at class notes and the material that we discussed in class. Then review all relevant textbook sections and homework problems for the chapters given below, and make sure you can solve all of them. I have also compiled a list of additional practice problems.
1.1: Understand what a function is, and how it is represented algebraically, graphically and numerically using tables. You should know what the domain and range of a function is and be able to find them for a given function. You should also be very comfortable with linear functions, and how to determine the slope and the equation for such a function.
1.2: Know how to identify an exponential function from a graph or a table of values. Also, given information about an exponential function, you should know how to express it in both the form P0at and the form P0ekt, and how to go between these two forms.
1.3: You should know the graphical effect of multiplying a function by a constant, of replacing a variable by itself minus a constant, and of composing two functions. You should know what it means for a function to be odd or even, both algebraically and graphically. You should also understand what the inverse of a function is and know strategies to determine the inverse of a given function.
1.4: Understand logarithms as the inverse of exponential functions, how they are represented graphically (including determining the domain and range), and know how they are used to solve problems involving exponential functions.
1.5: You should know how to work with angles in radians, including going back and forth between angles in degrees and radians. You should know the definitions and graphs of sin(x), cos(x) and tan(x). You should be able to determine the period and amplitude of functions involving these trig functions. You should also be able to determine the inverses of these functions, including finding the appropriate domain and range, and represent the inverses graphically.
1.6: Know when it is appropriate to use a polynomial function to model something and how to determine their degree and graph them. You should also know what it means to be a root of a polynomial and how to determine the roots algebraically and graphically. Know the definition of a rational function, and what we mean by the asymptotes (both horizontal and vertical) of such a function.
1.7 & 1.8: Understand the concept of a limit, including right and left hand limits, and limits involving infinity. (However, you do not need to know the formal definition in the blue box at the end of page 59.) You should know what it means for a limit to exist or not, and when it does exist, you should be able to determine these limits graphically and algebraically. Make sure you know all the properties of limits given on page 60 and how to use them to determine limits algebraically. Also, understand how limits involving infinity relate to asymptotes of the graph. Finally, you should understand what we mean by continuity, both conceptually in terms of a graph and formally in terms of limits, and you should know how continuity is used to get the Intermediate Value Theorem.
2.1 & 2.2: Know the difference between an average rate of change and an instantaneous rate of change, both algebraically and graphically. You should also understand the derivative of a function at a point as the instantaneous rate of change at that point and be able to compute it exactly, or estimate it from a graph or table of values.
2.3 & 2.4: Understand what we mean by the derivative function of a given function, and be able to describe its behaviour using a graph or a table of numerical values. You should also know the limit definition of the derivative function and use it to get a formula for the derivative, especially in the case of power functions. Finally, you should be able to recognize situations in which it is appropriate to use the derivative to model a slope or rate of change, carry out these computations, and determine the units for the derivative in those cases.
Maintained by ynaqvi and last modified 09/19/12