20804201Intermediate Algebra
Course Information
Description
This course covers algebraic concepts with applications, an introduction to functions, and complex numbers. Students create and use equations involving one and two variables to solve problems. Topics include graphing and finding algebraic solutions for linear equations and inequalities, quadratic, exponential, polynomial, radical, and rational equations, as well as solving systems of equations. 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.
Total Credits
4
Course Competencies
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Solve linear equationsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaSolve equations in one variableSolve formulas for a specific variableGenerate equations from given informationSolve applications using formulas and linear equations
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Solve linear inequalitiesAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaSolve simple linear inequalitiesSolve compound linear inequalitiesSolve translated compound inequalitiesSolve applications using single inequalitiesSolve applications using compound inequalitiesSolve absolute value equationsSolve absolute value inequalities
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Demonstrate graphing skills on the Cartesian coordinate planeAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaIdentify x- and y- interceptsFind the distance between two pointsFind the midpoint of two pointsCalculate the slope between two pointsIdentify the slope of a line on the x-y planeUse slope to determine if two lines are parallel, perpendicular, or neitherGraph a line from given informationWrite the equation of a line in standard or point-slope form
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Analyze linear equations and inequalities in two variablesAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaGenerate the equation of a line given varying conditionsSolve application problems involving rates of changeGraph linear inequalitiesSolve application problems using linear inequalities
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Solve systems of equationsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaSolve systems of two linear equations by graphing methodsSolve systems of two linear equations by elimination methodsSolve systems of two linear equations by substitution methodsClassify systems as consistent, inconsistent, or dependentSolve systems of three linear equations using elimination methodsTranslate application problems into appropriate system of equationsSolve application problems with systems of equationsGraph the feasible region for 2x2 systems of linear inequalities
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Solve polynomial equationsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaFactor using the greatest common factorFactor binomialsFactor by groupingFactor trinomialsPerform arithmetic operations with polynomialsFactor the difference of two squaresFactor the sum or difference of two cubesUse the zero product property of real numbers to solve polynomial equationsEvaluate a polynomial function for a specified value
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Use rational equations to solve applied problemsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaSimplify rational expressionsFind the domain of rational functionsPerform arithmetic operations with rational expressionsSimplify complex fractionsUse a rational equation to solve an applied problemInterpret the solution of a rational equation in contextIdentify extraneous solutionsSolve rational equations
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Solve radical equationsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaConvert between radical and exponential notationApply rules of exponents with positive and negative rational exponentsPerform arithmetic operations with radical expressionsEvaluate a radical function for a specified valueFind the domain of a radical functionSolve equations containing radical expressions or rational exponents
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Operate within the complex number systemAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaSimplify radicals that include complex numbersPerform arithmetic operations with complex numbersSolve equations with complex solutionsDetermine a complex conjugate
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Use quadratic equations to solve applied problemsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaApply the square root principleApply the quadratic formulaGraph a quadratic function written in standard form or vertex formPerform transformations on a quadratic functionIdentify the domain and range of a quadratic functionInterpret the solution of a quadratic equation in contextUse the Pythagorean Theorem to solve an applied problemUse a quadratic equation to solve an applied problem
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Apply properties of functionsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaDistinguish the differences between relations and functionsFind the domain and range of a relationUse function notationSolve applications involving functionsPerform arithmetic operations with functionsIdentify the domain of a function algebraicallyWrite a composite functionEvaluate a composite function for a specified valueDetermine the inverse of a function algebraically
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Use exponential equations to solve applied problemsAssessment StrategiesOral, Written, Graphic and/or Skill AssessmentCriteriaIdentify an exponential function or relationGraph an exponential functionEvaluate an exponential function for specified valuesCreate an exponential function to model a given scenarioInterpret the solution of an exponential equation in contextApply the definition of a logarithm to transform exponential equationsUse properties of logarithms