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MAT-099 Objectives

MAT-099 Intermediate Algebra

Course Description

This course is a continuation of MAT-097, Foundations of Algebra. Topics in this course include polynomial arithmetic, introduction to functions, factoring, roots and radicals, rational expressions, absolute value inequalities, quadratic equations and the quadratic formula, and solving applied problems. This course does not satisfy degree requirements. PREREQUISITE: Grade of C or better in MAT-097, Foundations of Algebra or placement. Course may require an additional lab hour. Credit hours: 3.0.

Learning Outcomes

  1. Rewrite expressions by understanding and applying the concepts of combining like terms, the distributive property, and factoring
  2. Write equivalent forms of equations and inequalities and solve them with fluency
  3. Apply knowledge of a variety of types of equations, including linear, quadratic, rational, and radical equations, to solve real world problems

Instructional Objectives

POLYNOMIALS

  1. Define and identify: monomial, binomial, polynomial
  2. State the degree of a term, the degree of a polynomial, and write a polynomial in descending powers of a variable
  3. Find the sum and difference of two polynomials
  4. Multiply a polynomial by a monomial or a binomial
  5. Divide a polynomial by a monomial
  6. Use long division to divide a polynomial by a binomial

    FUNCTIONS

  7. Understand the concepts of relation and function
  8. Decide whether an equation defines a function
  9. Use function notation
  10. Apply the function concept in applications and graphing

    FACTORING
  11. Define and identify: factor, common factor, greatest common factor
  12. Factor out the greatest common factor from a polynomial
  13. Factor by grouping
  14. Factor the difference of two squares as a sum and difference of binomials
  15. Factor the sum and difference of cubes
  16. Factor a perfect square trinomial as the square of a binomial
  17. Factor a trinomial into two binomial factors
  18. Factor binomials and trinomials completely

    INEQUALITIES

  19. Solve linear inequalities, including compound linear inequalities
  20. Graph the solution set of a linear inequality
  21. Use interval notation to describe the solution set of a linear inequality
  22. Solve equations and inequalities involving absolute value
  23. Solve linear inequalities in two variables and graph their solution sets

    RATIONAL EXPRESSIONS

  24. Define a rational expression
  25. Find the values of the variable for which a rational expression is undefined
  26. Write rational expressions in lowest terms
  27. Multiply and divide rational expressions
  28. Add and subtract rational expressions
  29. Simplify a complex fraction involving rational expressions
  30. Solve equations involving rational expressions
  31. Solve applied problems using equations involving rational expressions

    RADICALS

  32. Find roots of real numbers
  33. Decide whether a given root is rational, irrational, or not a real number
  34. Use the Pythagorean Theorem
  35. Simplify radical expressions
  36. Convert between radical expressions and expressions using rational exponents
  37. Add and subtract radical expressions
  38. Multiply and divide radical expressions
  39. Rationalize the denominator of a radical expression
  40. Find values for which a radical expression is undefined
  41. Solve equations involving radical expressions

    QUADRATIC EQUATIONS

  42. Solve quadratic equations by factoring
  43. Solve quadratic equations by the square root property
  44. Solve quadratic equations by completing the square
  45. Solve quadratic equations using the quadratic formula
  46. Graph quadratic equations
  47. Solve applied problems using quadratic equations