MCS   118, Calculus with Precalculus Review I

Spring 2008
Suggestions for Studying


Preparing for  Final Exam

The final exam will be comprehensive.  It will cover all of the material in chapters P - 6. You won't be explicitly tested on the material in chapter P; however, you need to know this material and use it in almost all of the problems on the final. Roughly two thirds of the material will be on the material we've covered since  the midterm (chain rule, plus chapters 5 and 6).  The final is on  Monday, at 1:00 pm in Olin 320.

Topics from calculus you should know:

• Finding antiderivatives
• Finding definite integrals from a graph
• Finding definite integrals using geometry
• Finding definite integrals using Fundamental Theorem
• Solve a differential equation with initial conditions
• Sketching the derivative (or second derivative) of a function or vice versa
  
• Limits  (both as x -> a number and as x-> infinity).  You should understand the epsilon-delta definition and be able to calculate limits.
  
• Definition of derivative
• Finding derivatives using rules
• Finding derivatives using graphs
• Optimization problems
• Using derivatives to find instantaneous rate of change
• Using derivatives to figure out when a graph is increasing/decreasing and concave up/down.
  

Topics from pre-calculus you should know

• Types of functions (linear, quadratic, polynomial, rational, power, etc.), what their graphs look like, what their formulas look like, etc.
• Basic algebra techniques such as factoring, solving equations, simplifying formulas, using the exponent rules, etc.
• Graphing linear functions, finding their equations, finding slope and intercepts
• Graphing polynomial functions, figuring out x-intercepts, y-intercept, long-term behavior, and whether the graph lies above or below x-axis from formula and vice versa
  
• Graphing rational functions, finding intercepts and asymptotes using the formula and vice versa