Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Note: some or all of the courses in the subjects marked as "Transfer" can be used towards a transfer degree: Associate of Science and Arts or Associate of Engineering Science at DACC. Transferability for specific institutions and majors varies. Consult a counselor for this information.

Areas of Study | | MATH111 syllabus




COURSE NUMBER: MATH111
COURSE TITLE:College Algebra
DIVISION:Sciences
IAI CODE(S):
SEMESTER CREDIT HOURS:5
CONTACT HOURS:75
STUDENT ENGAGEMENT HOURS:225
DELIVERY MODE:In-Person, Hybrid

COURSE DESCRIPTION:
A review of the fundamental topics of algebra, including the complex number systems, simplification and manipulation of algebraic expressions involving polynomials, rational exponents, radicals, fractions, the solution of polynomial equations and inequalities. Emphasis is placed on the study of the following functions: polynomial, rational, exponential, logarithmic and their applications. These will be explored using traditional graphing techniques, graphing calculators and other online tools.

PREREQUISITES:
Place into MATH111 with approved and documented math placement scores or by completing MATH108 with a grade of C or better.

NOTES:

STUDENT LEARNING OUTCOMES:
Students are expected to achieve strong critical thinking skills in terms of problem solving skills. Students are expected to be able to determine from any initial question of any of the following that apply:
  1. the meaning and importance of all given information
  2. the primary unknown for which a solution is desired
  3. all secondary unknowns that will be needed to determine the primary unknown
  4. all formulas and/or theorems that are applicable to a solution, and/or
  5. a proper understanding of the meaning/interpretation of the solution
Upon completion of this course, students will be able to:
  • Use, understand and write all required algebraic symbols and abbreviation.
  • Clearly relate interpretation of solutions to standard algebraic application problems.
  • Clearly show work or provide clear explanation as how to setup and generate a solution for application problems.
  • Correctly make use of graphing calculators as a supplemental tool and to check work through graphing technique.
  • Achieve strong critical thinking skills in terms of problem solving.
  • Represent subsets of the real number system using set notation, interval notation, inequalities and graphing on the real number line.
  • Demonstrate knowledge of general algebraic skills in the following areas:
    • Use understand and write all required algebraic symbols and abbreviations
    • Simplifying algebraic expressions involving polynomials, rational exponents, radicals, absolute value and fractions
    • Factoring polynomials
    • Basic operations and simplifications of numbers in the complex number system
    • Solving linear, quadratics and high order polynomial equations
    • Solving applications of linear and quadratic equations
    • Solving equations involving radicals
    • Solving linear inequalities and inequalities involving absolute value
    • Solving compound inequalities
    • Solving quadratic and rational inequalities using sign graph method and test point method
  • Use formulas associated with the cartesian coordinate system to calculate the following:
    • Distance between two points
    • Midpoint between two points
    • Slope of a line
      • Given the equation of line:
        • Equation of a line given a point on the line and the slope
        • Equation of a line given the slope and y intercept
        • Equation of a line given two points on the line
        • Equations of vertical and horizontal lines
  • Demonstrate knowledge of the general principles of functions:
    • Defining a function algebraically, graphically and by using tabulation
    • Determining the domain and range of a function
    • Using function notation
    • Identifying intervals over which a function is increasing, decreasing, and/or constant
    • Determining symmetry with respect to y axis and origin
    • Performing operations with functions
  • Graph the following in a cartesian coordinate plane. These will be explored with traditional graphing methods, by using graphing calculators or other online tools:
    • Points
    • Circles
    • Inequalities
    • Linear functions
    • Quadratic functions
    • Polynomial functions
    • Rational functions
    • Exponential functions
    • Logarithmic functions
    • Functions and their inverses
    • Systems of equations and inequalities
  • Apply concepts of variation to application problems.
    • Clearly relate interpretation of solutions to standard algebraic application problems.
    • Clearly show work or provide clear explanation as how to setup and generate a solution for application problems.
    • Students are expected to achieve strong critical thinking skills in terms of problem solving.
  • Use translations, reflection, stretching and shrinking to sketch the graph of a function.
  • Determine the complex roots of higher order polynomial equations using appropriate tools.
  • Work applications using formulas involving variable exponents and logarithms.
  • Solve linear systems of equations:
    • Using graph methods
    • Using algebraic methods
    • Using methods of matrices and determinants
    • Using graphing calculators or other online tools
  • Solve non-linear systems of equations.
  • Students are expected to correctly make use of calculators as a supplemental tool and to check work.
  • A student should obtain a 60% competency in the mentioned objectives
  • A student who is taking this course as a prerequisite for another math course should receive a 70% competency before taking the succeeding course

TOPICAL OUTLINE:
Fundamental algebraic skills:
  • Set notation, interval notation, graphical notation, and conversion from one form to another. 2%
  • Addition, subtraction, multiplication, and division of polynomials 2%
  • Addition, subtraction, multiplication, and division of expressions 1%
  • Evaluation and simplification of expressions with rational exponents 1%
  • Evaluation of radical expressions 2%
  • Factoring polynomials 2%
  • Solving equations: 12%
    • Linear equations (with and without absolute value)
    • Quadratic equations using methods of square root property, factoring, completing the square, and the quadratic formula
    • Rational equations
    • Radical equations
    • Equations with rational exponents
  • Solving application problems, including the following types: number, mixture, geometry, consecutive integer, uniform motion, investment and work problem. 7%
  • Solving inequalities: 6%
    • Linear inequalities using rules for inequalities
    • Linear inequalities with absolute value
    • Compound inequalities
    • Quadratic inequalities using sign graph method, and test point method
    • Rational inequalities using sign graph method, and test point method
  • Formulas of the cartesian coordinate plane: 2%
    • Distance between two points
    • Midpoint between two points
    • Slope of a line: by given two points on the line, and given equation of line
    • Equation of a vertical line
    • Equation of a horizontal line
    • Equation of a line given slope and a point on the line
    • Equation of a line given slope and the y intercept of the line
    • Slopes of parallel lines and perpendicular lines
  • Graphing relations in the cartesian coordinate plane: 6%
    • Points
    • Circles
    • Lines
    • Inequalities
  • General Topics on Functions: 2%
    • Definition
    • Function notation
    • Domain and range of functions
  • Quadratic functions: 5%
    • Determining vertex, and axis of symmetry
    • Determining maximum or minimum values
    • Determining domain, range, increasing and decreasing intervals
    • Sketching the graph
    • Applications
  • Other standard functions: 4%
    • Absolute value function
    • Squaring function
    • Cubing function
    • Square root function
  • Graphing concepts of functions: 4%
    • Vertical line test for functions
    • Increasing, decreasing, and constant functions
    • Symmetry
    • One-to-one functions and horizontal line test for functions
    • Inverse functions
  • Transformations: 4%
    • Vertical and horizontal shifts
    • Reflections
    • Stretching and shrinking
  • Operations with functions: 2%
    • Addition
    • Subtraction
    • Multiplication
    • Division
    • Composition
  • Polynomial functions: 11%
    • Synthetic division
    • Finding zeros using the following tools:
      • Factoring
      • Rational root theorem
      • Descartes' rule of signs
      • Upper and lower bound theorem
      • Conjugate zero theorem
      • Graphing calculators and other online tools
    • Graphing techniques
  • Rational functions: 2%
    • Vertical, horizontal and oblique asymptotes
    • Sketching rational functions using asymptotes
  • Exponential functions: 2%
    • Definition
    • Exponential functions with base e
    • Graphs of exponential functions with base greater than 1 and base between 0 and 1
  • Logarithmic functions: 3%
    • Fundamental algebraic skills:
      • Set notation, interval notation, graphical notation, and conversion from one form to another. 2%
      • Addition, subtraction, multiplication, and division of polynomials 2%
      • Addition, subtraction, multiplication, and division of expressions 1%
      • Evaluation and simplification of expressions with rational exponents 1%
      • Evaluation of radical expressions 2%
      • Factoring polynomials 2%
      • Solving equations: 12%
        • Linear equations (with and without absolute value)
        • Quadratic equations using methods of square root property, factoring, completing the square, and the quadratic formula
        • Rational equations
        • Radical equations
        • Equations with rational exponents
      • Solving application problems, including the following types: number, mixture, geometry, consecutive integer, uniform motion, investment and work problem. 7%
      • Solving inequalities: 6%
        • Linear inequalities using rules for inequalities
        • Linear inequalities with absolute value
        • Compound inequalities
        • Quadratic inequalities using sign graph method, and test point method
        • Rational inequalities using sign graph method, and test point method
      • Formulas of the cartesian coordinate plane: 2%
        • Distance between two points
        • Midpoint between two points
        • Slope of a line: given two points on the line, and given equation of line
        • Equation of a vertical line
        • Equation of a horizontal line
        • Equation of a line given slope and a point on the line
        • Equation of a line given slope and the y intercept of the line
        • Slopes of parallel lines and perpendicular lines
      • Graphing relations in the cartesian coordinate plane: 6%
        • Points
        • Circles
        • Lines
        • Inequalities
      • General Topics on Functions: 2%
        • Definition
        • Function notation
        • Domain and range of functions
      • Quadratic functions: 5%
        • Determining vertex, and axis of symmetry
        • Determining maximum or minimum values
        • Determining domain, range, increasing and decreasing intervals
        • Sketching the graph
        • Applications
      • Other standard functions: 4%
        • Absolute value function
        • Squaring function
        • Cubing function
        • Square root function
      • Graphing concepts of functions: 4%
        • Vertical line test for functions
        • Increasing, decreasing, and constant functions
        • Symmetry
        • One-to-one functions and horizontal line test for functions
        • Inverse functions
      • Transformations: 4%
        • Vertical and horizontal shifts
        • Reflections
        • Stretching and shrinking
      • Operations with functions: 2%
        • Addition
        • Subtraction
        • Multiplication
        • Division
        • Composition
      • Polynomial functions: 11%
        • Synthetic division
        • Finding zeros using the following tools:
          • Factoring
          • Rational root theorem
          • Descartes' rule of signs
          • Upper and lower bound theorem
          • Conjugate zero theorem
          • Graphing calculators and other online tools
        • Graphing techniques
      • Rational functions: 2%
        • Vertical, horizontal and oblique asymptotes
        • Sketching rational functions using asymptotes
      • Exponential functions: 2%
        • Definition
        • Exponential functions with base e
      • Graphs of exponential functions with base greater than 1 and base between 0 and 1 Logarithmic functions: 3%
        • Definition
        • Natural vs common logarithms
      • Graphs of logarithmic functions with base greater than 1 and base between 0 and 1 Equations using logarithms and exponents: 4%
        • Converting equations form logarithmic form to exponential form and vice versa
        • Applying laws of logarithms in solving exponential and logarithmic equations
        • Applications; exponential growth and decay, pH scale, Richter scale, decibel scale, periodic compounding and continuous compounding interest.
      • Systems of equations: 11%
        • Solution of linear equations using the following methods:
          • Substitution
          • Elimination (addition)
          • Matrices
        • Solution of nonlinear systems using substitution, elimination, or graph method
      • Solution of systems of inequalities by graphing 3%

TEXTBOOK / SPECIAL MATERIALS:

College Algebra, 6th Edition, by Mark Dugopolski, Published by Addison-Wesley, 2003
***Some instructors may use the 4th or 5th edition
Calculator (Graphing calculator required)

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:

Quizzes and homework.
At least five 50 minute exams.
Comprehensive final exam.
Determination of grade is according to the following scale:

A- 90%-100%
B- 80%-89%
C- 70%-79%
D- 60%-69%
F- 0%-59%

BIBLIOGRAPHY:
  • College Algebra, 10th Edition, by Margaret L. Lial, John Hornsby, and David I. Schneider, 2008
STUDENT CONDUCT CODE:
Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

DISABILITY SERVICES:
Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

REVISION:
Spring 2019

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