MCS 118: Calculus with Pre-calculus Review I (Fall 2013)

Suggestions for Studying for Exam 2

The final exam will cover all of the material we covered this semester, with an emphasis on the material we've done since the last exam. A good way to study for this quiz is to try doing some of the review problems at the end of each chapter.

You may use your calculator as long as it is a TI83/84 Plus or TI83/84 Plus Silver Edition, or has similar capabilities. You may not use a TI/89 on the exam. If you have a calculator other than a TI83/84 Plus or TI83/84 Plus Silver Edition, please talk with me.

You may prepare a single page of notes (one side of the paper only) to bring with you to the final. Additionally, you may bring your note cards from the previous two exams.

You will be tested on three main topics:

  • Limits
    • Calculate limits using tables, graphs, and algebra
    • Be able to identify when and explain why a limit doesn't exist
  • Derivatives
    • Find the derivative of a function by using the limit definition
    • Find the derivative of a function by using the rules for differentiating
    • Find the derivative of an inverse function
    • Graph the derivatives of a function given the graph of the function (and vice versa)
    • Determine information about the graph of a function (concavity, increasing/decreasing) given information about the first and second derivatives
    • Determine the units of and interpret first and second derivatives as velocity, acceleration, a rate of change, or the rate that a rate of change is changing.
    • Find the line tangent to a curve at a given point
    • Find the tangent line approximation to a function and estimate the error
  • Functions
    • Determine if a graph is the graph of a linear function, a polynomial function, or an exponential function
    • Determine if a table of values gives the values of a linear function, an exponential function, or something else
    • Having determined what kind of function the graph or table defines, find the formula for it
    • Graph polynomials, power functions, linear functions, and exponential functions, given the formula
    • Use your knowledge about functions to solve word problems that involve linear functions, quadratic functions, and exponential functions
    • Given a function, determine whether or not it has an inverse function and explain your answer
    • Given a function that has an inverse, find the values of its inverse graphically, algebraically, and numerically
    • Given a function that has an inverse, graph is inverse

You should be able to:

  • Factor polynomials
  • Use exponent rules to simplify expressions
  • Solve linear and quadratic equations
  • Simplify complex fractions
  • Understand functions
  • Use your calculator to graph functions and to find values of functions

Students who have taken MCS118/119 in the past suggest that the best ways to study are:

  • Study frequently, in small doses.
  • Do the homework every night.
  • Go to class, pay attention, and ask questions.
  • Read the text sections to be covered before and after class.
  • Use office hours and tutors.