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, onetoone 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
4
Course Competencies

Demonstrate knowledge of the real number systemAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou identify the different sets of real numbersyou use set builder notationyou distinguish finite/infinite setsyou identify subsetsyou graph real numbers on the number lineyou add real numbersyou subtract real numbersyou multiply real numbersyou manipulate expressions using the correct order of operationsyou simplify expressions with exponents and radicalsyou demonstrate correct use of the commutative, on algebraic expressionsyou demonstrate correct use of the associative algebraic expressionsyou demonstrate correct use of the distributive laws on algebraic expressionsyou demonstrate correct use of the additive identities on algebraic expressionsyou demonstrate correct inverses on algebraic expressionsyou define and graph the absolute value of a real numberyou translate phrases into algebraic formyou translate sentences into algebraic formyou divide real numbers

Solve linear equations and linear inequalitiesAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou solve equations in one variableyou solve formulas for a specific variableyou generate equations from given informationyou solve applications using formulas and linear equationsyou solve simple and compound inequalities in one variableyou translate absolute value inequalities into their corresponding compound inequalities and then solvesyou solve translated compound inequalitiesyou solve applications using single inequalitiesyou solve applications using compound inequalities

Demonstrate graphing skills on the Cartesian coordinate planeAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou plot ordered pairsyou read coordinatesyou identify x and y interceptsyou calculate the distance, midpoint, and slope between two pointsyou identify the slope of a line on the xy planeyou use slope to determine if two lines are parallel, perpendicular, or neitheryou graph a line given its slope and a point on the line or 2 points on the line or given a slope and the yinterceptyou graph a line given 2 points on the line or given a slope and the yinterceptyou graph a line a slope and the yinterceptyou write the equation of a line in standard or pointslope form

Analyze linear equations and inequalitiesAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou graph any linear equationyou generate the equation of a line given varying conditionsyou solve applications problems involving rates of changeyou graph linear inequalitiesyou determine intersections or unions of linear inequalitiesyou solve application problems using linear inequalities

Demonstrate knowledge of functions and relationsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou distinguish between relations or functionsyou generate graphs of linear functionsyou identify domains and ranges of a relation or functionyou interpret function notation correctlyyou use function notation correctlyyou solve applications involving functions

Solve 2x2 and 3x3 systems of equations and inequalitiesAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou solve systems of two linear equations by graphing methodsyou solve systems of two linear equations by elimination methodsyou solve systems of two linear equations by substitution methodsyou solve systems of two linear equations by determinants methodsyou solve systems of two linear equations by matrix methodsyou classify systems as consistent, inconsistent, or dependentyou solve systems of three linear equations using elimination methodsyou solve systems of three linear equations using matrix methodsyou translate application problems into appropriate system of equationsyou solve application problems with systems of equationsyou solve systems of 2x2 systems of linear inequalities

Perform operations on exponents and polynomialsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou apply product, quotient, and power rules to integer exponentsyou identify the degree of a polynomialyou add polynomialsyou subtract polynomialsyou multiply polynomialsyou divide polynomialsyou illustrate the difference between factoring, the verb, and factor, the nounyou factor out the greatest common factorsyou factor trinomialsyou factor by substitutionyou factor the difference of two squaresyou factor the difference of two cubesyou factor the difference of the sum of two cubesyou identify when to use the zero factor propertyyou solve quadratic equations by factoringyou factor by groupingyou solve cubic equations by factoring

Evaluate rational expressions and solve corresponding rational equationsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou identify rational expressionsyou simplify rational expressionsyou identify the domain of a rational expressionyou add rational expressionsyou subtract rational expressionsyou multiply rational expressionsyou divide rational expressionsyou simplify complex fractionsyou solve equations with rational expressionsyou translate applications dealing with variationsyou solve applications dealing with variationsyou solve application problem involving rational expressions

Evaluate radical expressions and solve corresponding radical equationsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou convert from radical notation to exponential notationyou convert from exponential notation to radical notationyou apply the rules of integer exponents to rational exponentsyou simplify radicalsyou add radicalsyou subtract radicalsyou multiply radicalsyou divide radicalsyou solve equations which involve radicalsyou solve applications involving radicalsyou identify complex numbersyou add complex numbersyou subtract complex numbersyou multiply complex numbersyou simplify radicals that include complex numbersyou divide complex numbers

Graphing quadratic functions and solving quadratic equationsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou use the square root property to solve a quadratic equationyou use the factoring to solve a quadratic equationyou use the completing the square formula to solve a quadratic equationyou use quadratic formula to solve a quadratic equationyou distinguish which of the above four techniques should be used to most efficiently solve a quadratic equationyou solve application problems which involve quadraticsyou use the Pythagorean Theorem to solve problems involving right trianglesyou graph quadratic functionsyou identify quadratic functions and its xand yinterceptsyou identify quadratic functions and its domainyou identify quadratic functions and its rangeyou identify quadratic functions and its vertexyou identify quadratic functions and its axis of symmetryyou identify quadratic functions and its concavityyou identify quadratic functions and where the function increasesyou identify quadratic functions and where the function decreasesyou sketch the corresponding quadratic function for a given quadratic application problemyou solve quadratic inequalitiesyou solve rational inequalitiesyou use distance formula to determine the basic equation of a circleyou graph equations of a circle

Using Algebra on FunctionsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou add functionsyou subtract functionsyou multiply functionsyou divide functionsyou find the composites of functionsyou identify onetoone functionsyou find and graph inverse functionsyou sketch miscellaneous functions (square root, cubics, absolute values)

Illustrate knowledge of exponential and logarithmic functionsAssessment Strategiesby a satisfactory score on all tests, quizzes, or graded assignments incorporating this competencyCriteriayou identify exponential functionsyou graph exponential functionsyou infer graph of the logarithmic function by using the inverse of the exponentialyou graph logarithmic functionsyou rewrite exponential equations as logarithmicyou rewrite logarithmic equations as exponentialyou use properties of logarithmsyou solve exponential equationsyou solve logarithmic equationsyou solve applied problems involving exponential equationsyou solve applied problems involving logarithmic equations