HIBBING COMMUNITY COLLEGE COURSE OUTLINE

Transcription

1 HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam, or Equivalent CATALOG DESCRIPTION: Beginning Algebra is designed to study operations on real numbers, manipulations of basic algebraic expressions, operations with linear and absolute value expressions, solving equations and inequalities, graphs, functions, solving systems of equations and inequalities, operations on polynomials and polynomial functions including factoring, and applications. The use of graphing utilities to solve equations and graph functions will be investigated. Beginning Algebra may not be taken for credit by students who have earned credit with a grade of C or better in courses for which Beginning Algebra is a prerequisite. OUTLINE OF MAJOR CONTENT AREAS: I. Review of basic algebra A. Operations 1. The set of real numbers 2. Operations with real numbers 3. Exponential notation and order of operations B. Manipulations 1. Introduction to algebraic expressions 2. Equivalent algebraic expressions 3. Simplifying algebraic expressions 4. Properties of exponents and scientific notation II. Solving linear equations and inequalities A. Solving equations B. Formulas and applications C. Applications and problem solving D. Sets, interval notation, and inequalities E. Intersections, unions, and compound inequalities F. Absolute-value equations and inequalities G. Graphing utility use in solving equations III. Graphs, functions, and applications A. Graphs of equations B. Functions and graphs C. Finding domain and range D. Linear functions: graphs and slope E. Finding equations of lines 1

2 1. The slope-intercept equation 2. The point-slope equation F. Mathematical modeling with linear functions G. Graphing utility use in graphing functions IV. Systems of equations A. Graphing systems of equations in two variables B. Solving by substitution or elimination C. Solving applied problems: systems of two equations D. Systems of linear inequalities in two variables E. Business and economics applications F. Graphing utility use in solving systems of equations V. Polynomials and polynomial functions A. Introduction to polynomials and polynomial functions B. Multiplication of polynomials C, Factoring by removing a common factor D. Factoring by grouping E. Factoring trinomials 1. x 2 + bx +c 2. ax 2 + bx +c where a is not 1 F. Special factoring G. Factoring differences of n th powers H. Factoring using a graphing utility I. Applications of polynomial equations and functions COURSE GOALS/OBJECTIVES/OUTCOMES: Students will 1. use roster and set-builder notation to name sets, and distinguish among various kinds of real numbers. 2. graph inequalities on a number line. 3. find the absolute value of a real number. 4. add, subtract, multiply and divide real numbers. 5. find the opposite of a number. 6. rewrite expressions with whole-number exponents, and evaluate exponential expressions. 7. rewrite expressions with or without negative integers as exponents. 8. simplify expressions using the rules for order of operations. 9. translate a phrase to an algebraic expression. 10. evaluate an algebraic expression by substitution. 11. find equivalent fractional expressions by multiplying by 1, and simplify fractional expressions. 12. use the commutative and the associative laws to find equivalent expressions. 13. use the distributive laws to find equivalent expressions by multiplying and factoring. 14. simplify an expression by removing parentheses and/or collecting like terms. 15. use exponential notation in multiplication and division. 2

3 16. use exponential notation in raising a power to a power, and in raising a product or quotient to a power. 17. convert between decimal notation and scientific notation and use scientific notation with multiplication and division. 18. determine whether a given number is a solution of a given equation. 19. solve equations using the addition principle and/or the multiplication principle. 20. evaluate formulas and solve a formula for a specified variable. 21. solve applied problems by translating to equations. 22. solve basic motion problems. 23. determine whether a given number is a solution of an inequality. 24. write interval notation for the solution set or graph of an inequality. 25. solve an inequality using the addition and multiplication principles and then graph the inequality. 26. solve applied problems by translating to inequalities. 27. find the intersections and unions of sets. 28. solve and graph compound inequalities. 29. simplify expressions containing absolute-value symbols. 30. find the distance between two points on a number line. 31. solve equations and inequalities with absolute value expressions. 32. use a graphing utility to solve equations. 33. plot points associated with ordered pairs of numbers. 34. determine whether an ordered pair of numbers is a solution of an equation. 35. graph linear and nonlinear equations using tables. 36. determine whether a correspondence is a function. 37. given a function described by an equation, find function values for specified values. 38. draw the graph of a function. 39. determine whether a graph is that of a function using the vertical-line test. 40. find the domain and range of a function. 41. find the y-intercept of a line using the slope-intercept equation. 42. given two points on a line, find the slope of the line. 43. given a linear equation, derive the equivalent slope-intercept equation and determine the slope and the y-intercept. 44. graph linear equations using intercepts. 45. given a linear equation in slope-intercept form, use the slope and the y-intercept to graph the line. 46. graph linear equations of the form x = a or y = b. 47. given the equations of two lines, determine whether their graphs are parallel, perpendicular, or neither. 48. find an equation of a line when the slope and the y-intercept are given. 49. find an equation of a line using the point-slope formula. 50. find an equation of a line when two points are given. 51. given a line and a point not on the given line, find an equation of the line parallel to the given line and containing the point, and find an equation of the line perpendicular to the given line and containing the point. 52. using a set of data, draw a representative graph of a linear function and make predictions from the graph. 3

4 53. using a set of data, choose two representative points, find a linear function using the two points, and make predictions from the function. 54. use a graphing utility to graph functions. 55. solve a system of two linear equations or two functions by graphing and determine whether a system is consistent or inconsistent and whether it is dependent or independent. 56. solve systems of equations in two variables by the substitution method and by the elimination method. 57. solve applied problems, including those involving motion, using systems of two equations. 58. determine whether an ordered pair of numbers is a solution of an inequality in two variables. 59. graph linear inequalities in two variables. 60. graph systems of linear inequalities and find coordinates of any vertices. 61. find cost functions, revenue functions, profit functions and break-even points in applied problems. 62. given supply and demand functions, find the equilibrium point. 63. use a graphing utility to solve systems of equations. 64. identify the degree of each term and the degree of a polynomial; identify terms, coefficients, monomials, binomials, and trinomials; arrange polynomials in ascending or descending order; and identify the leading coefficient. 65. evaluate a polynomial function for given inputs. 66. collect like terms in a polynomial and add polynomials. 67. find the opposite of a polynomial and subtract polynomials. 68. multiply any two polynomials. 69. use the FOIL method to multiply two binomials. 70. use a rule to square a binomial. 71. use a rule to multiply a sum and a difference of the same two terms. 72. find and simplify function values for inputs which are binomial. 73. factor polynomials whose terms have a common factor. 74. factor certain polynomials with four terms by grouping. 75. factor certain trinomials which are not squares. 76. factor trinomial squares. 77. factor differences of squares. 78. factor sums and differences of cubes. 79. factor differences of n th powers. 80, use a graphing utility to factor polynomials. 81. solve quadratic and other polynomial equations by first factoring and then using the principle of zero products. MNTC GOALS AND COMPETENCIES MET: N/A 4

5 HCC COMPETENCIES MET: Communicating Clearly & Effectively Thinking Creatively & Critically STUDENT CONTRIBUTIONS: The student will attend class regularly, participate in class discussion, complete daily assignments, in class exercises, exams, and a comprehensive final examination. The student will spend a minimum of two hours completing assignments for every hour in class. These must be accomplished in such a way that they meet minimum standards set by the instructor. STUDENT ASSESSMENT SHALL TAKE PLACE USING INSTRUMENTS SELECTED/DEVELOPED BY THE COURSE INSTRUCTOR. SPECIAL INFORMATION: The student may be required to provide a calculator for this course. If a specific calculator model is required, this model will be specified by the instructor on the course syllabus. Examples of calculators which may be required include but are not limited to the following: the TI89 and the TI Voyage 200. AASC APPROVAL DATE: October 20, 2010 REVIEW DATE: October 2015 MATH0971: so