Test II Review Sheet for
Colorado State University, Pueblo
Math 124 — Pre-calculus Math — Spring 2015

Topics

Things we discussed, which you should be able to work with:
  1. polynomial and degree
  2. polynomial graphs: no "corners" or jumps (the Intermediate Value Theorem
  3. multiplicity of a root
  4. max number of zeros and local extrema of polynomials
  5. graphing polynomials, particularly near zeros
  6. end behavior of graphs of polynomials
  7. equivalence of zeros, factors, and $x$-intercepts for polynomials
  8. long division of polynomials
  9. the Remainder Theorem: to calculate the remainder or function value
  10. synthetic division of polynomials
  11. factoring polynomials by guessing, looking at the calculator graph, and testing possible roots
  12. complex numbers: definition, arithmetic, conjugate
  13. finding real and complex solutions of quadratic equations
  14. The Fundamental Theorem of Algebra
  15. The Complete Factorization Theorem
  16. The Zeros Theorem
  17. The Conjugate Zeros Theorem
  18. The Linear and Quadratic Factors Theorem
  19. constructing real or imaginary polynomials with specified roots
  20. factoring polynomials over the real and complex numbers
  21. rational functions: vertical, horizontal, and slant asymptotes
  22. exponential functions: basic properties, graphing, domain, range, asymptotes
  23. the natural exponential function
  24. continuously compounded interest
  25. logarithms: definition, basic properties, graphing, domain, range, asymptotes
  26. common logarithm, natural logarithm
  27. the 4 Log Laws, using them to expand and multiply expressions
  28. solving exponential and logarithmic equations
  29. applications: population growth, radioactive decay, Newton's Law of Cooling

Format of the test

There will be problems from the material corresponding to each section we've done in the textbook, of a level of difficulty and wording similar to the problems which you have done for homework and quizzes. The total points for the test will be well more than 100, you can choose which 100 points you want to do out of the available problems.

Don't forget your calculator, you will need it!