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COURSE NUMBER: MATH101
COURSE TITLE:Basic Algebra
DIVISION:Sciences
IAI CODE(S):
SEMESTER CREDIT HOURS:4.0
DELIVERY MODE: Multiple sections taught face to face or online


COURSE DESCRIPTION:
An introductory study of real numbers, polynomials, rational expressions, first and second degree equations, first degree inequalities, integer exponents, radicals and systems of linear equations.  Course offered for S/U grade only.


PREREQUISITES:
Place into MATH101 with approved and documented math placement test scores or by completing DEVM099 with a grade of C or S (or better) or by completing DEVM100 with a grade of C (or better).


NOTES:

COURSE OBJECTIVES / GOALS:
Illustrate the similarities between arithmetic and algebra.  A student should be able to:
  • Learn and apply algebraic processes to problems, and be able to write math in exact symbolic forms.  Students must have the ability to do basic arithmetic by hand. Therefore, calculator usage and other technology is not allowed. In the circumstance that a student has a disability exception, with approved accommodation, the student may use a calculator on quizzes and tests taken in the Assessment Center.
  • Identify the similarities of factoring prime numbers and polynomials.
  • Compare graphical representations of numbers in the basic operations of addition and subtraction to the same operations with variables.
  • Identify and relate the basic multiplication and division patterns of arithmetic and algebra.
  • Implement formulas with real numbers.
  • Compare the reductions of arithmetic and algebraic fractions.
  • Illustrate basic real number properties of algebra by using both variables and real numbers.
  • Identify general notation in algebra and use that notation in solving verbal problems.
  • State numerical examples of the definitions of absolute value, subtraction and division.
  • Use the basic order of operations in simplifying both arithmetic and algebraic expressions.
A student should be able to graph the following:
  • Points on a real number line.
  • Points in the coordinate plane.
  • Linear equations.
  • Systems of linear equations.(optional)
  • Linear inequalities.(optional)
    • Each student should be able to simplify the following:
    • Simple arithmetic calculations involving adding, subtracting, multiplying, dividing and exponents.
    • Basic algebraic simplifications using addition, subtraction, multiplication, division, exponents, and radicals.
    • Simple fractional expressions using addition, subtraction, multiplication and division.
    • Complex fractions.
    • Long division (quotients of polynomials).
    The student should be able to factor a polynomial using the following methods:
    • Greatest common factor.
    • Trinomial (trial factors or grouping).
    The student should be able to solve the following types of equations:
    • Linear equations.
    • First degree literal equations.
    • Fractional equations.
    • Systems of linear equations. (optional)
    • Quadratic equations using factoring and the quadratic formula.
    A student should be able to solve the following types of verbal problems using only linear or quadratic equations:
    • Consecutive integer, consecutive even integer, and consecutive odd integer problems.
    • Geometric figure problems.
    • Coin problems.
    • Mixture problems.
    • Distance problems.
    • Work problems using a linear system of equations in two variables. (Optional)
    • Ratio and proportion problems.



    TOPICAL OUTLINE:
    Fundamental operations with natural numbers, integers, and variables representations for them:
    • Graphical representations of numbers and variables.
    • Order of operations in simplifying arithmetic and algebraic expressions.
    • Sums of natural numbers, integers and polynomials.
    • Differences of natural numbers, integers and polynomials.
    • Products of natural numbers, integers and polynomials.
    • Quotients of natural numbers, integers and polynomials.
    First degree equations and inequalities:
    • Writing equations from English.
    • Solving equations using addition, subtraction, multiplication, and division properties.
    • Solving literal equations.
    • Verbal first degree equations.
    • Solving inequalities using addition, subtraction, multiplication, and division properties.
    Simplifying exponential expressions.
    • Product rule.
    • Quotient rule.
    • Power rule.
    Factoring:
    • Factoring monomials from polynomials using distributive property.
    • Factoring trinomials using trial and error or the "ac" method
    • Recognizing and factoring perfect square trinomials.
    • Factoring the difference of two squares.
    • Solving equations using factoring.
    Fraction simplifications and equations:
    • Graphical representatives of fractions.
    • Reducing fractions to lowest terms.
    • Quotients of polynomials by long division.
    • Sums and differences of fractions with like denominators.
    • Sums and differences of fractions with unlike denominators.
    • Products of fractions.
    • Quotients of fractions.
    • Complex fraction simplifications. (optional)
    • Solving fractional equations.
    • Word problems with fractions.
    • Ratio and proportion word problems.
    First degree equations in two variables:
    • Graphing ordered pairs and first degree equations in two variables.
    • Direct variation.
    Solving systems of linear equations:
    • Graphical solutions.(Optional)
    • Algebraic solutions.(Optional)
    • Solving word problems using two variables.(Optional)
    Radical simplifications:
    • Monomial.
    • Addition and subtraction.
    • Quotients of radicals (including simplifying)
    • Multiplication of radicals.
    Quadratic equation solutions:
    • Factoring.
    • Completing the square (optional).
    • Quadratic formula.



    TEXTBOOK / SPECIAL MATERIALS:
    • Beginning Algebra with Applications, 7th Edition, Aufmann, Barker and Lockwood, 2008, Houghton Mifflin.
    • Textbook Used for Pilot Project: Elementary Algebra, 1st Edition, John Redden, 2010, Flatworld.



    EVALUATION:
    • Tests - 60%
    • Final - 15%
    • Midterm - 10%
    • General Assessment - 15%
    • Determination of grade is according to the following:
      • S = 70% - 100%
      • U = Below 70%



    BIBLIOGRAPHY:

    REVISION:
    Fall 2012

    RECORD UPDATED:
    2013-02-11 11:28:00