10804140Elementary Algebra
Course Information
Description
Introductory algebra course provides a thorough coverage of beginning algebra with an emphasis on problem solving for real world applications. Topics covered include operating with real numbers and applying the order of operations to simplify numeric expressions, applying the laws of exponents to perform operation on polynomials, factoring quadratic expressions, simplifying and solving linear and quadratic equations in one variable, solving 2x2 systems of equations, graphing linear equations in two variables, simplifying rational expressions.
Total Credits
3
Course Competencies
  1. Use the properties of real numbers and variables
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    calculate the sum, difference, product and quotient of two integers individually according to the standard order of operations
    calculate the sum, difference, product and quotient of two integers in combination according to the standard order of operations
    simplify all numeric results using the Commutative, Associative and Distributive properties
    calculate the sum, difference, product and quotient of two rational numbers individually according to the standard order of operations
    calculate the sum, difference, product and quotient of two rational numbers in combination according to the standard order of operations
    apply the properties of exponents
    simplify a variable expression by combining like terms

  2. Solve first-degree equations and inequalities including those that arise from concrete applications
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    use multiplication and addition properties of equality to solve a first-degree equation
    use multiplication and addition properties of inequality to solve a first-degree inequality
    solve a problem involving ratios and proportions
    apply solution algorithms to solve word problems
    validitate an answer

  3. Use the Cartesian coordinate system
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    plot points on the Cartesian plane
    find points for a given linear equation
    determine the slope of a line
    determine the equation of a line given the slope and a point, two points, and one point and the relationship of the line to another line
    graph an inequality in two variables in the Cartesian plane
    solve a problem situation using the Cartesian plane

  4. Solve systems of two linear equations and inequalities in two variables
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    solve a system of linear equations using elimination
    solve a system of linear equations using substitution
    solve a system of linear equations by graphing on the Cartesian coordinate system
    solve a system of linear inequalities by graphing on the Cartesian coordinate system
    use a system of linear equations to represent and solve an application problem

  5. Perform operations with polynomials
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    identify type of polynomial and its degree
    rewrite polynomials in standard form
    perform the basic operations of addition and subtraction of polynomials including monomials, binomials, trinomials
    multiply two binomials using FOIL and two polynomials using a grouping method
    divide a polynomial by a binomial using long division

  6. Solve factorable quadratic equations and their applications
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    factor out the greatest common factor
    recognize the standard forms of quadratic expressions including the difference of two squares and perfect squares
    apply the appropriate factoring algorithm
    solve application problems involving factorable quadratic equations

  7. Perform basic operations on rational expressions and solve rational equations
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    simplify a rational expression by recognizing common factors in the numerator and denominator
    find the least common multiple of two or more denominators
    operate with rational expressions including addition, subtraction, multiplication and division of two or more rational expressions
    simplify a rational expression containing one or more fractions in the numerator and/or denominator
    solve rational equations by multiplying both sides by the least common denominator
    solve application problems involving rational equations including work, distance and proportion problems

  8. Solve quadratic equations and their applications by selecting an appropriate method
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    solve a quadratic equation by factoring
    apply the completing the square process to solve a quadratiac equation (optional)
    solve a quadratic equation by using the quadratic formula
    select the most appropriate method to solve a particular quadratic equation from the following methods: factoring method, square root method, quadratic formula
    apply concepts involving a quadratic equation to solve application problems

  9. Simplify radical expressions
    Assessment Strategies
    by active participation in class discussions and activities
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments and laboratory work with passing grades according to the grading scale contained in the syllabus
    Criteria
    examine what it means to take the square (or cube) root of a number
    use the Product Rule for Radicals to multiply and simplify by factoring out perfect squares (or cubes) from under a square (or cube) root symbol
    add and/or subtract two or more radical terms, simplifying as necessary
    apply the Quotient Rule to simplify a radical expression (optional)
    rationalize a denominator containing one or two terms (optional)
    solve an equation containing a square root by isolating the square root and squaring both sides of the equation (optional)