MATH 1000 OBJECTIVES

After successful completion of MAT 1000, a student should be able to:

1. Plot points on the real number line.

2. Find the absolute value of a real number.

3. Evaluate an expression using the order of operations .

4. Evaluate an expression after replacing the variables with real values

5. Solve a linear equation.

6. Solve application problems by using a linear equation.

7. Solve geometric problems by using a linear equation.

8. Solve linear equations involving fractions and decimals.

9. Solve application problems involving principal and interest.

10. Solve application problems involving distance, rate, and time.

11. Solve application problems involving ratio and proportion.

12. Solve linear inequalities.

13. Solve a compound inequality .

14. Solve an application problem involving inequalities.

15. Solve an absolute value equation.

16. Solve an absolute value inequality.

17. Plot points on a rectangular coordinate system .

18. Use the Distance Formula to determine the distance between two points .

19. Graph a linear equation in two variables.

20. Apply the properties of exp onents to simplify an expression.

21. Evaluate expressions with scientific notation.

22. Identify the leading coefficient and the degree of a polynomial.

23. Add polynomials.

24. Subtract polynomial.

25. Multiply polynomials.

26. Use special product rules to multiply two binomials.

27. Divide a polynomial by a monomial.

28. Divide a polynomial by a polynomial of two or more terms.

29. Solve an application problem using polynomials.

30. Solve an application problem using the Pythagorean Theorem.

31. Graph nonlinear equations in two variables.

32. Factor by factoring out the greatest common factor.

33. Factor by grouping .

34. Factor trinomials with leading coefficient 1.

35. Factor trinomials with leading coefficient other than 1.

36. Factor a perfect square trinomial .

37. Factor the difference of two squares .

38. Factor the sum of two cubes.

39. Factor the difference of two cubes.

40. Solve a quadratic equation by factoring.

41. Solve a higher degree polynomial equation by factoring.

42. Graph a polynomial equation using intercepts.

43. Find the domain of a rational expression.

44. Reduce a rational expression.

45. Multiply rational expressions.

46. Divide rational expressions.

47. Find the least common denominator of two rational expressions.

48. Add or subtract rational expressions with same denominators.

49. Add or subtract rational expressions with different denominators.

50. Simplify complex fractions.

51. Solve rational equations.

52. Solve an application problem involving rational equations.

53. Given two points, find the slope of the line containing them.

54. Given the equation of a line, find the slope and y-intercept.

55. Find the equation of a line, given a point and a slope.

56. Find the equation of a line, given two points.

57. Write the equation of a line parallel or perpendicular to another line.

58. Interpret an application problem involving a linear equation in two variables.

59. Solve a system of equations using the substitution method.

60. Solve a system of equations using the addition method.

61. Identify an inconsistent system of equations.

62. Identify a dependent system of equations.

63. Solve an application problem using the solution to a system of equations.

64. Graph a system of equations and identify independent, dependent, consistent,
       and inconsistent equations.

65. Graph a linear inequality in two variables .

66. Graph a system of linear inequalities in two variables.

67. Find the principal square root of a nonnegative real number.

68. Find the nth root of a variable expression.

69. Simplify a radical expression.

70. Add and subtract radical expressions.

71. Multiply radical expressions with one term.

72. Multiply radical expressions with multiple terms.

73. Multiply conjugate radical expressions.

74. Rationalize the denominator containing one term in a radical expression.

75. Rationalize the denominator containing two terms in a radical expression.

76. Solve radical equations.

77 Solve an application problem involving a radical equation.

78. Convert radical expressions to expressions with rational exponents.

79. Find the domain and range of a relation.

80. Using the Vertical Line Test, determine whether a relation is a function.

81. Sketch the graph of a function on a rectangular coordinate system.

82. Use function notation and evaluate a function.

83. Identify transformations of the graph of a function and sketch their graphs.

84. Simplify an expression involving powers of i.

85. Add, subtract, multiply and divide complex numbers.

86. Solve a quadratic equation using the square root property.

76. Solve a quadratic equation by completing the square.

77. Solve a quadratic equation by using the quadratic formula.

78. Use the discriminant to determine the nature of the solutions to a quadratic equation.

79. Graph a quadratic function and identify the vertex and intercepts.

80. Simplify expressions involving rational exponents.

Use test intervals to solve a quadratic inequality.

Use test intervals to solve a rational inequality.

Sketch the graph of a linear inequality in two variables.

Find the equations of a parabola and sketch its graph.

Find the equation of a hyperbola and sketch its graph.

Use horizontal and vertical asymptotes and a table of values to sketch the graph of a
rational function.

Solve a linear system in three variables.

Evaluate and graph exponential functions.

Use the Horizontal Line Test to determine if a function has an inverse.

Find the inverse of a function.

Evaluate and graph a logarithmic function .