MCS   119, Calculus with Precalculus Review IB

Spring 2007
Suggestions for Studying for the Final



Studying for The Final

The final is comprehensive and covers all of the material in both MCS118 and MCS119.  It is similar in scope to a MCS121 final. The problems will include:

• Differentiate a variety of functions, including polynomials, trig functions, exponentials and logarithms - sample problems
  
• Find derivatives and antiderivatives graphically
• Find the maximum/minimum of a function on an interval
• Find a derivative from the definition
• Use implicit differentiation -sample problems
  
• Solve a related rates problem - a tutorial on related rates (check out the other links on that page)
• Solve an exponential growth/decay problem - sample problems
  
• Find an equation of a tangent line
• Find antiderivatives and indefinite integrals
  
• Calculate limits using various techniques, including l'Hopital's rule
• Find the value of definite integrals using Riemann sums, using area formulas, and using antiderivatives

You will also need to be able to use a variety of precalculus skills or techniques.  In particular, you should be able to

• Find the equation of a line given the slope and a point on that line
• Graph several types of functions (linear, quadratic, exponential, logarithmic, and trig functions)
• Solve an equation
• Know your unit circle
• Be able to find areas of triangles, rectangles, and circles
• Be able to find the volume of a sphere, a cone, and a cylinder
  
• Use similar triangles and the Pythagorean theorem
  
• Be able to use your calculator
  

You may bring  one 8.5x11" paper with notes, formulas, sample problems, or whatever to help you on the final.

Finally, I strongly suggest that you start reviewing early and often (but in small amounts) for the final.  The best way to do this is to work problems.  Here are some sample exams that I found on the web.