# INTERMEDIATE ALGEBRA

**COURSE
DESCRIPTION:**

This course is designed to survey the basic topics in
algebra which

will enable the student to enter a course in college algebra.

**EXPECTED LEARNER
OUTCOMES:**

Upon completion of this course, the student will be able
to:

1. Add, subtract, multiply and divide signed numbers .

2. Solve equations and inequalities.

3. Add, subtract, multiply and divide polynomial expressions.

4. Factor polynomial expressions.

5. Simplify and solve rational expressions.

6. Simplify and solve radical expressions.

7. Solve quadratic equations and inequalities.

8. Graph linear equations and inequalities.

**LEARNING TASKS
& ACTIVITIES:**

Unit I | Real Number, Chapter 1:1-43 |

Unit II | First Degree Equations and Inequalities ins One Unknown , Chapter 2:46-93 |

Unit III | Linear Functions, Chapter 3:125-205 |

Unit IV | Systems of Equations, Chapter 4:207-276 |

Unit V | Factoring and Products, Chapter 5:278-359 |

Unit VI | Fractions, Chapter 6:361-429 |

Unit VII | Rational Exponents and Radicals , Chapter 7:432- 499 |

Unit VIII | Quadratic Functions and Inequalities, Chapters 8:499-578 |

Unit IX | Exponential and Logarithmic Functions, Chapter 9:581-647 |

**ASSESSMENT OF
OUTCOMES:**

Grades of A (90-100), B (80-89), C (70-79), D (60-69), and

F (0-59) are given in this course. An incomplete is given if

previously agreed upon by the instructor with a specific time

designated for the completion of the incomplete work. Please note

the college’s policy on incompletes as stated in the college catalog.

Tests MUST be taken on the scheduled day and during the
regular

class period. ONLY if arrangements are made with the instructor

PRIOR to the original test date will a student be allowed to take

the test early. Due to abuse in the previous policy, no student will

be allowed to makeup a test. Current policy allows each student

one drop test to accommodate unforeseen circumstances and the

subsequent failure to be tested on the scheduled test date.

A student’s final course grade will be based upon homework
and

exams. Partial credit is given on exams so show all work. In the

event that there would be extra credit given on a test, partial credit

is not given in the extra credit problems.

**Homework is due the day after it has been assigned.
LATE
HOMEWORK WILL NOT BE COLLECTED.**

**LATE TESTS ARE NOT GIVEN. IF YOU MISS A TEST IT COUNTS
AS
YOUR DROPPED TEST AT THE END OF THE SEMESTER. IF YOU ARE
GOING TO BE ABSENT DURING TEST DAY DUE TO A COLLEGE
EVENT YOU MUST TAKE THE TEST EARLY.**

**ATTENDANCE
POLICY:**

Students are expected to attend all classes. However,
attendance

will** not** be taken.

**STUDENT
CONDUCT:**

1. Behavior that interferes with the learning process will
not be

tolerated.

2. Dishonest work will result in an F for the course.

**NOTICE:**

Out of respect for your classmates, when you enter the
classroom

please turn off your cell phone. Remember that your time in the

class should be spent listening; not taking calls. Thank you.

**COMPETENCIES:**

**ADD, SUBTRACT, MULTIPLY AND DIVIDE SIGNED NUMBERS**

1. Apply the rules of addition, subtraction,
multiplication and division to fractions.

2. Apply the rules of addition, subtraction, multiplication and division to
decimals.

3. Identify natural numbers, whole numbers, integers, rational, and irrational.

4. Apply the rules of addition, subtraction, multiplication and division to
signed numbers.

5. Use the order of operation with real numbers.

6. Identify the use of the commutative, associative, identity, inverse, and
distributive

properties.

**SOLVE EQUATIONS AND INEQUALITIES**

7. Identify and solve linear equations using properties of
equality .

8. Translate sentences of a word problem into a equation, and then solve the
problem.

9. Solve a given formula or literal equation for a specified variable.

10. Solve problems involving geometric figures, percentages, uniform motion, and
liquid

mixtures.

11. Solve and graph inequalities on a number line.

12. Solve compound inequalities involving and and or statements.

13. Solve equations involving absolute value.

**ADD, SUBTRACT, MULTIPLY AND DIVIDE POLYNOMIAL
EXPRESSIONS**

14. Apply the rules of exponents for any situation.

15. Use zero and negative numbers in exponents.

16. Express numbers in scientific notation.

17. Identify terms and coefficients .

18. Learn the vocabulary for polynomials.

19. Calculate the sum or difference of polynomials.

20. Multiply any polynomial situation.

**FACTOR POLYNOMIAL EXPRESSIONS**

21. Factor out the greatest common factor.

22. Factor by grouping.

23. Factor any trinomial regardless of the lead coefficient.

24. Factor trinomials by substitution .

25. Identify and factor perfect square trinomials .

26. Factor the difference of two squares.

27. Factor the sum or difference of two cubes.

28. Apply a general strategy to factor polynomials systematically.

29. Solve certain quadratic equations by factoring.

30. Solve applied problems that lead to quadratic equations.

**SIMPLIFY AND SOLVE RATIONAL EXPRESSIONS**

31. Find the values of a variable for which a rational
expression is undefined.

32. Express rational expressions in lowest terms.

33. Multiply and divide rational expressions.

34. Rewrite rational expressions with the least common denominator.

35. Add and subtract rational expressions regardless of the denominators.

36. Simplify complex fractions.

37. Divide a polynomial by a monomial or by a polynomial with at least two
terms.

38. Divide a polynomial by a polynomial of the form x-b using synthetic
division.

39. Evaluate a polynomial using the remainder theorem.

40. Solve equations involving rational expressions.

41. Solve word problems about distance, work, and variation using rational
expressions.

**SIMPLIFY AND SOLVE RADICAL EXPRESSIONS**

42. Find square roots and principal square roots.

43. Find principal nth roots.

44. Use exponent properties to simplify expressions with rational exponents.

45. Simplify radical expressions and quotients.

46. Multiply radicals and divide radicals, and simplify where possible.

47. Add and subtract radical expressions.

48. Rationalize denominators.

49. Simplify radical expressions with sums, products, and quotients.

50. Use a conjugate to rationalize a denominator.

51. Solve equations with radicals.

52. Identify extraneous solutions.

**SOLVE QUADRATIC EQUATIONS AND INEQUALITIES**

53. Express square roots to negative numbers in terms of i.

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

55. Solve quadratic equations using the square root property.

56. Solve quadratic equations by completing the square.

57. Solve quadratic equations by using the quadratic formula.

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

59. Calculate the sum and product of roots to determine the validity of
solutions.

60. Solve fractional equations and radical equations that lead to quadratic
equations.

61. Solve quadratic inequalities.

**GRAPH LINEAR EQUATIONS AND INEQUALITIES**

62. Write a solution as an ordered pair.

63. Complete ordered pairs for a given equation.

64. Plot ordered pairs.

65. Find the midpoint and distance between two points.

66. Find x and y intercepts for a line.

67. Graph linear equations.

68. Find and interpret the slope of a line.

69. Use slope to determine the planar relationship of two lines.

70. Write the equation of a line regardless of supplied information.

71. Solve problems involving the equations of parallel and perpendicular lines.

72. Graph linear inequalities.

73. Solve problems involving direct and inverse variation.

**This syllabus is subject to revision with prior
notification to the student by the
instructor.**

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