Course | Madison College Outline of Instruction

20804201Intermediate Algebra

Course Information

Description

Studies the construction and resulting properties of the real number system. Students simplify and factor algebraic expressions using fundamental laws and order of operations, solve first and second degree equations and inequalities in one variable, solve exponential and logarithmic equations, graph first degree and second degree equations and inequalities in two variables, solve 2x2 and 3x3 systems of equations, simplify and solve equations involving rational expressions and simplify and solve equations involving fractional exponents and radicals. Students are introduced to linear, quadratic, square root, absolute value, exponential and logarithmic functions. The basic definitions of functions, relations, one-to-one functions and inverses are discussed along with the algebra and composition of functions. Functions are studied in greater detail in College Algebra. Meets five hours per week. Successful completion of this course allows students to continue on with either College Algebra or Quantitative Reasoning.

Total Credits

Course Competencies

Demonstrate knowledge of the real number system

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you identify the different sets of real numbers

you use set builder notation

you distinguish finite/infinite sets

you identify subsets

you graph real numbers on the number line

you add real numbers

you subtract real numbers

you multiply real numbers

you manipulate expressions using the correct order of operations

you simplify expressions with exponents and radicals

you demonstrate correct use of the commutative, on algebraic expressions

you demonstrate correct use of the associative algebraic expressions

you demonstrate correct use of the distributive laws on algebraic expressions

you demonstrate correct use of the additive identities on algebraic expressions

you demonstrate correct inverses on algebraic expressions

you define and graph the absolute value of a real number

you translate phrases into algebraic form

you translate sentences into algebraic form

you divide real numbers
Solve linear equations and linear inequalities

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you solve equations in one variable

you solve formulas for a specific variable

you generate equations from given information

you solve applications using formulas and linear equations

you solve simple and compound inequalities in one variable

you translate absolute value inequalities into their corresponding compound inequalities and then solves

you solve translated compound inequalities

you solve applications using single inequalities

you solve applications using compound inequalities
Demonstrate graphing skills on the Cartesian coordinate plane

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you plot ordered pairs

you read coordinates

you identify x- and y- intercepts

you calculate the distance, midpoint, and slope between two points

you identify the slope of a line on the x-y plane

you use slope to determine if two lines are parallel, perpendicular, or neither

you graph a line given its slope and a point on the line or 2 points on the line or given a slope and the y-intercept

you graph a line given 2 points on the line or given a slope and the y-intercept

you graph a line a slope and the y-intercept

you write the equation of a line in standard or point-slope form
Analyze linear equations and inequalities

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you graph any linear equation

you generate the equation of a line given varying conditions

you solve applications problems involving rates of change

you graph linear inequalities

you determine intersections or unions of linear inequalities

you solve application problems using linear inequalities
Demonstrate knowledge of functions and relations

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you distinguish between relations or functions

you generate graphs of linear functions

you identify domains and ranges of a relation or function

you interpret function notation correctly

you use function notation correctly

you solve applications involving functions
Solve 2x2 and 3x3 systems of equations and inequalities

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you solve systems of two linear equations by graphing methods

you solve systems of two linear equations by elimination methods

you solve systems of two linear equations by substitution methods

you solve systems of two linear equations by determinants methods

you solve systems of two linear equations by matrix methods

you classify systems as consistent, inconsistent, or dependent

you solve systems of three linear equations using elimination methods

you solve systems of three linear equations using matrix methods

you translate application problems into appropriate system of equations

you solve application problems with systems of equations

you solve systems of 2x2 systems of linear inequalities
Perform operations on exponents and polynomials

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you apply product, quotient, and power rules to integer exponents

you identify the degree of a polynomial

you add polynomials

you subtract polynomials

you multiply polynomials

you divide polynomials

you illustrate the difference between factoring, the verb, and factor, the noun

you factor out the greatest common factors

you factor trinomials

you factor by substitution

you factor the difference of two squares

you factor the difference of two cubes

you factor the difference of the sum of two cubes

you identify when to use the zero factor property

you solve quadratic equations by factoring

you factor by grouping

you solve cubic equations by factoring
Evaluate rational expressions and solve corresponding rational equations

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you identify rational expressions

you simplify rational expressions

you identify the domain of a rational expression

you add rational expressions

you subtract rational expressions

you multiply rational expressions

you divide rational expressions

you simplify complex fractions

you solve equations with rational expressions

you translate applications dealing with variations

you solve applications dealing with variations

you solve application problem involving rational expressions
Evaluate radical expressions and solve corresponding radical equations

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you convert from radical notation to exponential notation

you convert from exponential notation to radical notation

you apply the rules of integer exponents to rational exponents

you simplify radicals

you add radicals

you subtract radicals

you multiply radicals

you divide radicals

you solve equations which involve radicals

you solve applications involving radicals

you identify complex numbers

you add complex numbers

you subtract complex numbers

you multiply complex numbers

you simplify radicals that include complex numbers

you divide complex numbers
Graphing quadratic functions and solving quadratic equations

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you use the square root property to solve a quadratic equation

you use the factoring to solve a quadratic equation

you use the completing the square formula to solve a quadratic equation

you use quadratic formula to solve a quadratic equation

you distinguish which of the above four techniques should be used to most efficiently solve a quadratic equation

you solve application problems which involve quadratics

you use the Pythagorean Theorem to solve problems involving right triangles

you graph quadratic functions

you identify quadratic functions and its x-and y-intercepts

you identify quadratic functions and its domain

you identify quadratic functions and its range

you identify quadratic functions and its vertex

you identify quadratic functions and its axis of symmetry

you identify quadratic functions and its concavity

you identify quadratic functions and where the function increases

you identify quadratic functions and where the function decreases

you sketch the corresponding quadratic function for a given quadratic application problem

you solve quadratic inequalities

you solve rational inequalities

you use distance formula to determine the basic equation of a circle

you graph equations of a circle
Using Algebra on Functions

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you add functions

you subtract functions

you multiply functions

you divide functions

you find the composites of functions

you identify one-to-one functions

you find and graph inverse functions

you sketch miscellaneous functions (square root, cubics, absolute values)
Illustrate knowledge of exponential and logarithmic functions

Assessment Strategies

by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency

Criteria

you identify exponential functions

you graph exponential functions

you infer graph of the logarithmic function by using the inverse of the exponential

you graph logarithmic functions

you rewrite exponential equations as logarithmic

you rewrite logarithmic equations as exponential

you use properties of logarithms

you solve exponential equations

you solve logarithmic equations

you solve applied problems involving exponential equations

you solve applied problems involving logarithmic equations