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LSU College Readiness Program COURSE PROFILE with LMSCOURSE NAME:High School Algebra II PRIMARY ONLINE CONTENT SOURCE:Algebra II in MyMathLab Elayn Martin-Gay, with contributions from Robert BlitzerCOURSE/UNIT CREDIT:1 Carnegie UnitGRADE(S):9, 10, or 11PREREQUISITE(S):Successful Completion of GeometryCHAPTERS1 – Real Numbers and Algebraic Expressions8 – Rational Exponents, Radicals, and Complex Numbers2 – Equations, Inequalities, and Problem Solving9 - Quadratic and Higher Degree Equations and Functions3 - Graphs and Functions10 - Exponential and Logarithmic Functions4 – Systems of Equations11 – Graphing Quadratic Functions, Rational Functions, and Conic Sections6 - Exponents, Polynomials, and Polynomial Functions13 - Counting Methods and Probability7 - Rational Expressions14 and 15 - Trigonometric FunctionsX – Statistics (from another book)SECTION NAMES (NUMBER OF EXERCISES), LEARNING OBJECTIVES, AND LOUISIANA MATHEMATICS STANDARDS CORRELATIONSCHAPTER 1: Real Numbers and Algebraic Expressions*1.2 Algebraic Expressions and Sets of Numbers (50)Identify and evaluate algebraic expressionsIdentify natural numbers, whole numbers, integers, and rational and irrational numbersFind the absolute value of a numberFind the opposite of a numberWrite phrases as algebraic expressions8.NS.1*1.3 Operations on Real Numbers (61)Add and subtract real numbersMultiply and divide real numbersEvaluate expressions containing exponentsFind roots of numbersUse the order of operationsEvaluate algebraic expressions8.EE.18.EE.2*1.4 Properties of Real Numbers (60)Use operation and order symbols to write mathematical sentencesIdentify identity numbers and inversesIdentify and use the commutative, associative, and distributive propertiesWrite algebraic expressionsSimplify algebraic expressionsAlgII.A.1CHAPTER 2: Equations, Inequalities, and Problem Solving*2.1 Linear Equations in One Variable (47)Solve linear equations using properties of equalitySolve linear equations that can be simplified by combining like termsSolve linear equations containing fractions or decimalsAlgI.A.11*2.2 An Introduction to Problem Solving (44) Write algebraic expressions that can be simplifiedApply the steps for problem solvingAlgI.A.1a*2.3 Formulas and Problem Solving (38)Solve a formula for a specified variableUse formulas to solve problemsAlgII.A.8AlgI.A.9*2.4 Linear Inequalities and Problem Solving (53)Graph inequalitiesSolve linear inequalities using the multiplication and addition property of inequalitySolve problems that can be modeled by linear inequalitiesAlgI.A.11*2.5 Compound Inequalities (49)Find the union and the intersection of two setsSolve compound inequalities involving “and” and “or”AlgI.A.11*2.6 Absolute Value Equations (43)Solve absolute value equationsAlgI.A.11*2.7 Absolute Value Inequalities (51)Solve absolute value inequalitiesAlgI.A.11CHAPTER 3: Graphs and Functions*3.1 Graphing Equations (46)Plot ordered pairsDetermine whether an ordered pair is a solution to an equation in two variablesGraph linear and nonlinear equationsAlgI.A.15*3.2 Introduction to Functions (56)Define relation, domain, and rangeUse the vertical line test for functionsIdentify functionsUse function notationAlgI.F.1AlgI.F.2*3.3 Graphing Linear Functions (39)Graph linear functionsGraph linear functions using interceptsGraph vertical and horizontal linesAlgI.F.7a*3.4 The Slope of a Line (50)Find the slope of a line given two points on the lineFind the slope of a line given the equation of the lineInterpret the slope-intercept form in an applicationCompare the slopes of parallel and perpendicular linesFind the slope as a ratio of vertical change to horizontal changeAlgII.F.10AlgII.F.12Geom.G.283.5 Equations of a Line (50)Use the slope intercept form to write the equation of lineGraph a line using its slope and y-interceptUse the point slope form to write the equation of lineRead a graph to find the function valueWrite equations of vertical and horizontal linesFind equations of parallel and perpendicular linesAlgI.A.7AlgI.F.1AlgII.A.8Geom.G.283.6a Graph Piece-Wise-Defined (11)Graph piecewise-defined functionsAlgII.F.3a3.6b Shift and Reflect Graphs (18)Graph functions using vertical and horizontal shiftsReflect graphsAlgII.F.83.7 Graphing Linear Inequalities (33)Graph linear inequalitiesGraph the intersection or union of two linear inequalitiesAlgI.A.173.8 Stretching and Compressing Absolute Value Functions (12)Graph the absolute value functionFind the equation of a graphed absolute value functionAlgII.F.3aCHAPTER 4: Systems of Equations4.1 Solving Systems of Equations in Two Variables (40) Determine whether an ordered pair is solution of a system of two linear equationsSolve a system by graphingSolve a system by substitutionSolve a system by eliminationSolve applicationsAlgII.A.12 4.2 Solving Systems of Equations in Three Variables (22) Determine whether an ordered triple is solution of system of three linear equationsSolve a system of three linear equations in three variablesAlgII.A.124.3 Systems Used in Problem Solving (30) Solve problems that can be modeled by a system of two linear equationsSolve problems with cost and revenue functionsSolve problems that can be modeled by a system of three linear equationsAlgII.F.6aAlgII.A.12CHAPTER 6: Exponents, Polynomials, and Polynomial Functions6.1 Use the Product Rule for Exponents (69) Use the product rule for exponentsUse the quotient rule for exponentsEvaluate expressions raised to the 0 powerEvaluate expressions raised to the negative nth powerConvert between scientific notation and standard notationAlgII.A.18.EE.18.EE.46.2 Use the Power Rule for Exponents (53) Use the power rules for exponentsUse exponent rules and definitions to simplify exponential expressionsCompute, using scientific notation8.EE.18.EE.46.3 Identify and Evaluate, Add and Subtract Polynomials (61) Identify polynomials, parts of polynomials, and degree of term and of polynomialEvaluate polynomial functionsReview combining like termsAdd polynomialsSubtract polynomials AlgI.A.1AlgI.F.2AlgII.A.1AlgI.A.46.4 Multiplying Polynomials (45)Multiply two polynomialsMultiply binomialsSquare binomialsMultiply the sum and difference of two termsMultiply three or more polynomialsEvaluate polynomial functionsAlgI.A.4AlgI.F.26.5 The GCF and Factoring by Grouping Polynomials (43)Identify the GCFFactor out the GCF of a polynomial's termsFactor polynomials by groupingAlgI.A.1AlgII.A.16.6 Factoring Trinomials (57) Factor trinomials of the form x^2+bx+cFactor trinomials of the form ax^2+bx+c by trial and check or by groupingFactor by substitutionAlgII.A.16.7 Factoring by Special Products (46) Factor a perfect square trinomialFactor the difference of two squaresFactor the sum or difference of two cubesAlgII.A.16.8 Solving Equations by Factoring and Problem Solving (52)Solve polynomial equations by factoringSolve problems that can be modeled by polynomial equationsFind the x-intercepts of a polynomial functionAlgII.A.5AlgII.A.11a 6.9 Even and Odd Power Functions and End Behavior (15)Graph even and odd power functionsDescribe the end behavior of a polynomial functionGraph even and odd power functionsAlgII.F.8AlgII.F.3bCHAPTER 7: Rational Expressions7.1 Rational Functions and Mult/Div Rational Expressions (49)Find the domains of rational expressionsSimplify rational expressionsMultiply rational expressionsDivide rational expressionsMultiply and divide rational expressionsUse rational functions in applications7.2 Adding and Subtracting Rational Expressions (46)Add and subtract rational expressions with common denominatorsIdentify the least common denominator of two or more rational expressionsAdd and subtract rational expressions with unlike denominatorsAdd and subtract rational expressions with common denominatorsMixed Practice7.3 Simplifying Complex Fractions (37)Simplify complex fractions by simplifying numerator/denominator and dividingSimplify complex fractions by multiplying by a common denominatorSimplify expressions with negative exponents7.4 Dividing Polynomials: Long & Synthetic Division, Remainder Theorem (54)Divide a polynomial by a monomialDivide by a polynomialUse synthetic division to divide a polynomial by a binomialUse the remainder theorem to evaluate polynomialsUse the factor theoremAlgII.A.4AlgII.A.77.5 Solving Equations Containing Rational Expressions (39)Solve equations containing rational expressionsAlgII.A.107.6 Rational Equations and Problem Solving (45)Solve equations that contain radical expressionsUse the Pythagorean theorem to model problemsSolve application problemsAlgII.A.10AlgII.A.8 7.7 Variation and Problem Solving (33)Solve problems involving direct variationSolve problems involving joint variationSolve problems involving inverse variationSolve problems involving combined variationAlgII.A.8AlgII.F.6CHAPTER 8: Rational Exponents, Radicals, and Complex Numbers8.1 Radicals and Radical Functions (56)Find square rootsApproximate rootsFind cube rootsFind nth rootsFind the nth root of a^n, where a is a real numberFind function values of square and cube rootsGraph square and cube root functionsAlgII.NQ.1AlgII.NQ.2AlgI.F.2AlgII.F.3aAlgII.F.88.2 Rational Exponents for Radicals (60)Understand the meaning of a^(1/n)Understand the meaning of a^(m/n)Understand the meaning of a^(-m/n)Use rules for exponents to simplify expressions that contain rational exponentsUse rational exponents to simplify radical expressionsAlgII.NQ.1AlgII.NQ.28.3 Simplifying Radical Expressions (57)Use the product rule for radicalsUse the quotient rule for radicalsSimplify radicalsUse the distance and midpoint formulasAlgII.NQ.18.G.8 8.4 Adding, Subtracting, and Multiplying Radical Expressions (43)Add or subtract radical expressionsMultiply radical expressionsAlgII.A.18.5 Rationalizing Radical Denominators and Numerators (42) Rationalize denominatorsRationalize denominators having two termsRationalize numeratorsAlgII.A.18.6 Radical Equations and Problem Solving (45)Solve equations that contain radical expressionsUse the Pythagorean theorem to model problemsSolve application problemsAlgII.A.10 8.7 Complex Numbers (58)Write square roots of negative numbers in the form biGraph complex numbers on the complex planeAdd or subtract complex numbersDivide complex numbersMultiply complex numbersRaise i to powersAlgII.NQ.4AlgII.NQ.5CHAPTER 9: Quadratic and Higher Degree Equations and Functions9.1 Solving Quadratics by Completing the Square (51)Use the square root property to solve quadratic equationsComplete and factor the perfect square trinomialSolve quadratic equations by completing the squareUse quadratic equations to solve problemsAlgII.A.11aAlgII.A.8AlgII.NQ.6 9.2 Solving Quadratics by Quadratic Formula (51)Solve quadratic equations by using the quadratic formulaDetermine number and type of solutions of quadratic equation using discriminantSolve geometric problems modeled by quadratic equationsAlgII.A.11aAlgII.NQ.6 9.3 Solving Quadratic by Quadratic Methods (42) Solve quadratic equations by squaring both sidesSolve quadratic equations by multiplying by the lowest common denominatorSolve higher degree equations in quadratic formSolve equations by converting to a quadratic with substitutionSolve various equations that are quadratic in formSolve problems that lead to quadratic equationsAlgII.A.11aAlgII.NQ.69.4 Zeros of Polynomial Functions (19)Use the rational zero theorem to find possible rational zerosFind zeros of a polynomial functionAlgII.F.3bAlgII.A.4AlgII.A.59.5 Fundamental Theorem of Algebra (18)Solve polynomial equationsFind polynomials with given zerosAlgII.A.4AlgII.A.59.6 Nonlinear Inequalities in One Variable (33) Solve polynomial inequalities of degree 2 or higherSolve inequalities that contain rational expressions with variables in denominatorSolve polynomial inequalities of degree 2 or higherSolve inequalities that contain rational expressions with variables in denominatorAlgII.A.8CHAPTER 10: Exponential and Logarithmic Functions10.1 The Algebra of Functions; Composite Functions (26) Add, subtract, multiply, and divide functionsConstruct composite functionsAlgII.F.6b10.2 Inverse Functions (34) Determine whether a function is a one-to-one functionFind the inverse of a functionUse the horizontal line test to decide whether a function is a one-to-one functionFind the equation of the inverse of a functionGraph functions and their inversesDetermine whether two functions are inverses of each otherAlgII.F.9a10.3 Exponential Functions (36) Graph exponential functionsSolve equations of the form b^x = b^ySolve problems modeled by exponential equationsAlgII.F.3cAlgII.F.8AlgII.A.8 10.4 Logarithmic Functions (49) Convert between logarithmic and exponential notationFind the value of logarithmic expressionsSolve logarithmic equations by using exponential notationSimplify using the properties of logarithmsIdentify and graph logarithmic functionsAlgII.A.8AlgII.F.3cAlgII.F.810.5 Properties of Logarithms (38) Use the product property of logarithmsUse the quotient property of logarithmsUse the power property of logarithmsUse the properties of logarithms together.AlgII.A.110.6 Common and Natural Logs and Change of Base (45) Identify and approximate natural logarithmsIdentify and approximate common logarithmsEvaluate common logarithms of powers of 10Evaluate natural logarithms of powers of eSolve logarithmic equationsUse the change of base formulaSolve applicationsAlgII.A.8 10.7 Exponential and Log Equations and Applications (40) Solve exponential equationsSolve logarithmic equationsSolve problems that can be modeled by exponential and logarithmic equationsAlgII.A.8AlgII.F.11AlgII.SP.2a CHAPTER 11: Graphing Quadratic Functions, Rational Functions, and Conic Sections11.1 Quadratic Functions and Their Graphs (38)Graph quadratic functions of the form f(x) = x^2 + kGraph quadratic functions of the form f(x) = (x - h)^2 + kGraph quadratic functions of the form f(x) = ax^2Graph quadratic functions of the form f(x) = a(x - h)^2 + kAlgII.F.8AlgI.F.7a11.2 Further Graphing of Quadratic Functions (40) Write quadratic functions in the form of a(x-h)^2+kDerive a formula for finding the vertex of a parabolaFind the minimum or maximum value of a quadratic functionAlgI.F.7a AlgI.F.8a11.3 Graphing Rational Functions by Transformations (23)Find the domains of rational functionsIdentify vertical asymptotesIdentify horizontal asymptotesUse transformations to graph rational functionsGraph f(x)=1/x and f(x)=1/x^2AlgI.F.1AlgII.F.811.4 Further Graphing of Rational Functions (22)Graph rational functionsIdentify slant asymptotesSolve applied problems involving rational functions*11.5 The Parabola and the Circle (68)Graph parabolas of the form x=a(y-k)^2+k and y=a(x-h)^2+kGraph circles of the form (x-h)^2+(y-k)^2=r^2Write the equation of a circle given its center and radiusFind the centers and radii of circles or vertices of parabolas, given the equationGeom.G.26*11.6 The Ellipse and the Hyperbola (53)Define and graph an ellipseDefine and graph a hyperbolaIdentify and graph conic sectionsCHAPTER 13: Counting Methods and Probability13.4 Fundamentals of Probability ( 26) Compute empirical probabilityCompute theoretical probabilityGeom.SP.113.8 The Normal Distribution (15) Find scores at a specified standard deviation from the meanUse the 68-95-99.7 ruleAlgII.SP.1CHAPTER 14 and 15: Trigonometric Functions and Identities14.1 Angles and Radian Measure (54) Recognize and use the vocabulary of anglesUse radian measureConvert between degrees and radiansDraw angles in standard positionFind coterminal anglesFind the length of a circular arcUse linear and angular speed to describe motion on a circular pathGeom.G.1AlgII.F.13AlgII.F.14Geom.G.2514.2 Right Triangle Trigonometry (43) Use right triangles to evaluate trigonometric functionsFind function values for 30 degrees (pi/6), 45 degrees (pi/4), and 60 degrees (pi/3)Recognize and use fundamental identitiesUse equal cofunctions of complementsEvaluate trigonometric functions with a calculatorUse right triangle trigonometry to solve applied problemsAlgII.F.16Geom.G.19Geom.G.20 Geom.G.2114.3 Trigonometric Functions of Any Angle (54) Use the definitions of trigonometric functions of any angleUse the signs of the trigonometric functionsFind reference anglesUse reference angles to evaluate trigonometric functionsAlgII.F.14 14.4 Trig Functions of Real Numbers; Periodic (25) Use a unit circle to define trigonometric functions of real numbersUse even and odd trigonometric functionsUse periodic propertiesSolve application problemsAlgII.F.14 14.5 Graphs of Sine and Cosine Functions (45) Understand the graph of y=sin(x)Graph variations of y=sin(x)Understand the graph of y=cos(x)Graph variations of y=cos(x)Use vertical shifts of sine and cosine curvesSolve application problemsSolve technology exercisesAlgII.F.1514.6 Graph of the Tangent Function (11) Understand the graph of y=tan(x)Graph variations of y=tan(x)Solve application problemsSolve technology exercisesAlgII.F.1514.8 Applications of Trigonometric Functions (11) Solve a right triangleSolve application problemsGeom.G.2115.1 Verifying Trigonometric Identities (15) Use the fundamental trigonometric identities to verify identitiesAlgII.F.16CHAPTER X: StatisticsX.1 Measures of Central Tendency (21) Identify characteristics of the design of an experimental studyFind the meanFind the medianFind the modeSolve application problems involving mean, median, and modeRead a histogramDetermine the arithmetic mean of a variable from raw dataDetermine the median and mode of a variable from raw dataUse the mean and the median to help identify the shape of a distributionAlgII.SP.3AlgI.SP.1AlgII.SP.1X.2 Data Gathering (18) Describe effects of an experimental study design on its outcomeUnderstand the process of statisticsExplain the sources of bias in samplingFind the margin of errorIdentify methods of data collectionIdentify bias or any potential problemsIdentify subject, sample and population, and type of analysisAlgII.SP.5AlgII.SP.6AlgII.SP.8X.3 Standard Deviation (18) Determine the standard deviation for a data setConvert a data item to a z-scoreUnderstand percentiles and quartilesAlgII.SP.6AlgI.SP.1X.4 Normal Distribution (22) Use and interpret margins of errorFind scores at a specified standard deviation from the meanUse the 68–95–99.7 RuleSolve applied problems involving normal distributionsUnderstand percentiles and quartilesConvert a data item to a z-scoreAlgII.SP.1AlgII.SP.6*Optional or considered to be for individual students needing reviewLouisiana Mathematics Standards for Algebra II that are not reflected in MyMathLab course exercises:Standard #Standard DescriptionCommentAlgII.NQ.3Define appropriate quantities for the purpose of descriptive modeling.Requires paper and pencil work.AlgII.A.2aUse the properties of exponents to transform expressions for exponential functions.Not included in the course.AlgII.A.3Apply the formula for the sum of a finite geometric series (when the common ratio is not 1) to solve problems.Included in the CLEP prep portion of the College Algebra course.AlgII.A.6Use polynomial identities to describe numerical relationships.Not included in the course.AlgII.A.9Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.Requires paper and pencil work.AlgII.A.13Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.Included in the CLEP prep portion of the College Algebra course.AlgII.A.14Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.Not included in the course.AlgII.F.1For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Not included in the course.AlgII.F.2Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.Not included in the course.AlgII.F.4aUse the properties of exponents to interpret expressions for exponential functions.Not included in the course.AlgII.F.5Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Not included in the course.AlgII.F.7Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two formsIncluded in the Algebra I course.AlgII.SP.4Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.Not included in the course.AlgII.SP.7Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.Not included in the course. ................
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