College Algebra

OBJECTIVES

1. Define the set of real numbers and its subsets.
2. Write inequalities in interval notation and vice versa.
3. Define and evaluate the absolute value of a real number.
4. State and apply the properties of absolute value.
5. State and apply the field axioms of the real number system.
6. State and apply the properties of equality.
7. Solve problems using laws for rational exponents.
8. Convert numbers from scientific notation to decimal fractions and vice versa.
9. Solve problems using the laws of radicals.
10. Define and identify a polynomial.

11. Perform the four fundamental operations with polynomials.
12. Factor expressions completely.
13. Simplify rational expressions.
14. Perform the four fundamental operations with rational expressions.
15. State and apply the distance formula.
16. State and apply the midpoint formula.
17. Write the equation of a circle in standard form.
18. Graph a circle given the standard form of its equation.
19. Graph an equation in two variables by plotting points.
20. Use a graphing calculator to graph an equation in two variables.

21. With a graphing calculator be able to
  a . set the range values.
  b. zoom.
  c. trace.
  d. square the viewing rectangle.
22. Compute the slope of a given line.
23. Write equations for lines meeting various conditions.
24. Graph linear equations in two variables.
25. Define a function.
26. Define and determine the domain and range of a function.
27. Determine whether or not a relation is a function.
28. Approximate the relative minimums and relative maximums of a function.
29. Define even and odd function and determine whether a function is even or odd or neither.
30. Determine the intervals where a graph is increasing, decreasing, or constant.

31. Draw graphs of simple selected functions:
  a . linear
  b. quadratic
  c. cubic
  d. square root
  e. constant
  f . absolute value
  g. step
  h . piecewise continuous
32. Graph functions using transformations of known simple functions.
33. Find equations for functions when it is determined that its graph is a transformation of a simple function.
34. Define, evaluate, and find the domain for the sum, difference, product, quotient, and composition of functions.
35. Define, determine, and graph the inverse function, if it exists, of a given function.
36. Solve absolute value and nonlinear equations and inequalities.
37. Graph a quadratic function and determine the graph’s intercepts and vertex.
38. Determine the quadratic function given various conditions for its graph.
39. Determine end behavior of a polynomial function’s graph from its equation.
40. Find the rational zeros of a polynomial.

41. Perform the operations of long and synthetic division for polynomials.
42. State the remainder and factor theorems.
43. Solve problems involving the use of the factor theorem and the remainder theorem.
44. Define a zero of a polynomial.
45. Define imaginary numbers.
46. Define complex numbers.
47. Perform the four fundamental operations with imaginary and complex numbers.
48. Find complex zeros under certain conditions of a polynomial.
49. Define and find vertical, horizontal, and oblique asymptotes, if they exist, for graphs of
rational functions.
50. State and use guidelines for graphing rational functions.

51. Define exponential functions.
52. Graph exponential functions.
53. Apply exponential functions to solve interest problems.
54. Define logarithmic functions.
55. Graph logarithmic functions.
56. State and use the properties of logarithms to rewrite, expand, or condense logarithmic expressions.
57. Solve exponential and logarithmic equations.
58. Write linear and nonlinear models using scatter plots.
59. Work applied problems involving direct and inverse variation.
60. Solve systems of equations graphically and algebraically.

61. Define a matrix.
62. Solve linear systems of equations using Gauss-Jordan elimination.
63. Perform basic operations (addition, scaler multiplication, multiplication) on matrices.
64. Define and find, if it exists, the inverse of a square matrix.
65. Solve linear systems of equations using matrix inverses.
66. Solve systems of inequalities in two variables by use of graphs.
67. Find the determinant of a 1 x 1, 2 x 2, and 3 x 3 matrix without a calculator.
68. Find a determinant of a square matrix with a graphing calculator.
69. Use determinants to solve applied problems.
70. Define a sequence.

71. Define and use factorials.
72. Define and use summation notation.
73. Write and use formulas for the nth terms of a sequence.
74. Evaluate recursion formulas.
75. Define arithmetic sequences and series.
76. Define geometric sequences and series.
77. Solve problems pertaining to arithmetic or geometric sequences and series.
78. State the principle of mathematical induction.
79. Prove appropriate statements by use of mathematical induction.
80. State the Binomial Theorem.

81. Expand a binomial raised to a positive integer power by using the Binomial Theorem.
82. Find any term in the expansion of a binomial without writing all the terms.
83. Determine equation of “Best Fit” with graphing calculator.