2019 Porcelli Lectures by Robert Bryant | LSUMath
LSU College Readiness ProgramCOURSE PROFILE11-16-15COURSE NAME:High School Algebra I PRIMARY ONLINE CONTENT SOURCE:Algebra 1 in MyMathLabElayn Martin-Gay, with contributions from Robert BlitzerCOURSE/UNIT CREDIT:1 Carnegie UnitGRADE(S):7, 8, or 9PREREQUISITE(S):Completion of 8th grade math or placement by high schoolCHAPTERS1 - Review of Real Numbers6 - Exponents and Polynomials2 - Solving Equations and Problem Solving7 - Factoring Polynomials3 - Graphs and Functions8 - Rational Expressions4 - Solving Inequalities and Absolute Value Equations and Inequalities9 – Roots and Radicals5 - Solving Systems of Linear Equations and Inequalities10 - Quadratic EquationsSECTION NAMES (NUMBER OF EXERCISES), LEARNING OBJECTIVES, AND CCSS CORRELATIONSCHAPTER 1: Review of Real Numbers1.2 Symbols and Sets of Numbers (47)Use a number line to order numbersTranslate sentences into mathematical statementsUse integers to express values in statementsUse a graph to answer questionsIdentify types of numbersDetermine if a statement is true or falseOrder numbers involving absolute value1.3 Fractions (51)Write numbers as products of primesWrite fractions in simplest formMultiply and divide fractionsAdd and subtract fractionsWrite equivalent fractions1.4 Variable Expressions and Equations (52)Evaluate expressions with exponentsSimplify expressions using the order of operationsEvaluate algebraic expressions, given replacement values for variablesDetermine whether a number is a solution of a given equationTranslate phrases to algebraic expressionsTranslate sentences to equations or inequalities1.5 Adding Real Numbers (47)Add real numbers with the same signAdd real numbers with unlike signsSolve problems that involve addition of real numbersFind the opposite of a numberDetermine if a given number is a solution to a given equation1.6 Subtracting Real Numbers (48)Subtract real numbersAdd and subtract real numbersEvaluate algebraic expressions using real numbersSolve problems that involve subtraction of real numbersDetermine if a given number is a solution to a given equation1.7 Adding and Subtracting Matrices (13)Use matrix notationFind the value of the variables that will make the matrices equalAdd and subtract matricesSolve problems involving addition and subtraction of matrices1.8 Multiplying and Dividing Real Numbers (73)Multiply real numbersSimplify using the order of operationsIdentify the reciprocal of a real numberDivide real numbersSimplify using the order of operationsEvaluate algebraic expressions using real numbersDetermine if a given number is a solution to a given equation1.9 Properties of Real Numbers (51)Vocabulary and Readiness CheckUse the commutative and associative propertiesUse the distributive propertyName the properties illustrated by the statements1.4,5,6,8 Real Life Linear Relationships (23)Evaluate algebraic expressions, given replacement values for variablesSolve problems that involve addition of real numbersSolve problems that involve subtraction of real numbersMultiply real numbers1.10 Data: Probability and Odds (29)Compute theoretical probabilityUnderstand and use oddsDetermine effects of linear transformations of dataDetermine effects of outliersCHAPTER 2: Solving Equations and Problem Solving2.1 Simplifying Algebraic Expressions (57)Combine like termsUse the distributive property to remove parenthesesWrite word phrases as algebraic expressionsName the properties illustrated by the statementsReview and Preview2.2 Addition Property of Equality (54)Use the addition property of equality to solve linear equationsSimplify an equation and then use the addition property of equalityWrite word phrases as algebraic expressions2.3 Multiplication Property of Equality (53)Use the multiplication property of equality to solve linear equationsUse addition and multiplication properties of equality to solve linear equationsWrite word phrases as algebraic expressions2.4 Solving Multi-step Equations (40)Apply a general strategy for solving a linear equationSolve equations containing fractionsWrite word phrases as algebraic expressions2.5 Introduction to Problem Solving (33) Solve problems involving direct translationsSolve problems involving relationships among unknown quantitiesSolve problems involving consecutive integers2.6 Formulas and Problem Solving (45)Substitute values into a formula and solve for the unknown variableSolve a formula for one of its variablesUse formulas to solve problems2.7 Percent and Problem Solving (36)Solve percent equationsSolve discount and mark-up problemsSolve percent increase and percent decrease problems2.8 Mixture and Distance Problem Solving (21)Solve mixture problemsSolve uniform motion problemsCHAPTER 3: Graphs and Functions3.1 Reading Graphs and Rectangular Coordinate System (54)Read bar and line graphsDefine the rectangular coordinate system and plot ordered pairs of numbersGraph paired data to create a scatter diagram and determine correlationDetermine whether an ordered pair is a solution of an equation in two variablesFind missing coordinate of an ordered pair solution given one coordinate of the pairInterpret information given in a scatter plot3.2 Graphing Linear Equations (38)Identify linear equationsGraph an equation by finding and plotting ordered pair solutionsSolve application problems3.3 Intercepts (35)Identify intercepts of a graphGraph a linear equation by finding and plotting interceptsIdentify and graph vertical and horizontal lines3.4a Slope and Rate of Change (37)Find the slope of a line given points on the lineFind the slopes of horizontal and vertical linesFind the slope of a line given its equationCompare the slopes of parallel and perpendicular linesSlope as a rate of change3.4b Slope and Rate of Change - Review and Preview (20)Slope as a rate of change3.5a Equations of a Line (25)Use the slope-intercept form to write an equation of a lineUse the slope-intercept form to graph a linear equationUse the point-slope form to find equation of line given slope and a point on the lineUse the point-slope form to find an equation of a line given two points of the lineFind equations of vertical and horizontal lines3.5b Equations of a Line - Review and Preview (23)Use the point-slope form to solve problems3.6a Functions (28)Identify relations, domains, and rangesIdentify functionsUse the vertical line testUse function notation3.6b Function Review and Graphing Functions (30)Identify relations, domains, and rangesGraph linear functionsGraph linear functions by finding interceptsGraph vertical and horizontal linesDecide whether a situation describes a linear function3.7 Graphing Functions (25) Graph piecewise-defined functionsUse vertical and horizontal shifts to graph a functionUse function notationGraph nonlinear equationsVertical and horizontal shiftsCHAPTER 4: Solving Inequalities and Absolute Value Equations and Inequalities4.1 Linear Inequalities and Problem Solving (40)Graph inequalities on number linesSolve inequalitiesSolve inequality applications4.2 Compound Inequalities (49)Find the union of two setsFind the intersection of two setsSolve compound inequalities involving orSolve compound inequalities involving and4.3 Absolute Value Equations (42)Solve absolute value equations4.4a Absolute Value Inequalities (29)Solve absolute value inequalities of the form |x|Solve absolute value inequalities of the form |x|>a4.4b Absolute Value Inequalities (26)Solve absolute value inequalities of the form |x|Solve absolute value inequalities of the form |x|>aMixed Practice4.5a Graphing Linear Inequalities (25)Determine ordered pairs that are solutions to linear inequalities in two variablesGraph linear inequalities in two variables4.5b Graphing Linear Inequalities (12)Review and PreviewCHAPTER 5: Solving Systems of Linear Equations and Inequalities5.1 Systems of Linear Equations by Graphing (36)Determine if an ordered pair is a solution of a system of equations in two variablesSolve a system of linear equations by graphingWithout graphing, determine the number of solutions of a system5.2 Systems of Linear Equations by Substitution (29)Use the substitution method to solve a system of linear equations5.3a Systems of Linear Equations by Addition (20)Use the addition method to solve a system of linear equations5.3b Systems of Linear Equations by Addition (19)Use the substitution method to solve a system of linear equations5.4a Systems of Linear Equations and Problem Solving (15)Choose a solution that satisfies the given conditionsWrite a system of equations to describe a situationUse a system of equations to solve problems5.4b Systems of Linear Equations and Problem Solving (16)Choose a solution that satisfies the given conditionsWrite a system of equations to describe a situationUse a system of equations to solve problems5.5 Systems of Linear Inequalities (23)Solve systems of linear inequalitiesUse mathematical models involving linear inequalities5.6a Frequency Distributions (6)Organize and present data using frequency distributions5.6b Statistical Graphs (15)Answer questions involving concepts and/or definitionsMake data displays to convey information about dataConstruct a frequency distribution and/or statistical graphsUse a given statistical graph to answer questionsOrganize and present data using histograms and frequency polygons5.7a Mean, Median, Mode and Trends in Statistics (23)Calculate mean, median, and modeDetermine effects of linear transformations of dataWork with box plotsUse box plots to discuss and compare data setsDetermine the median, first and third quartiles, and interquartile range of a data setWork with measures of central tendency5.7b Review Mean, Median, Mode, and Range (15)Review mean, median, and modeDetermine the range for a data setCalculate mean, median, and mode5.7c Standard Deviation for a Data Set (11)Determine the standard deviation for a data setCHAPTER 6: Exponents and Polynomials6.1a Exponents (12)Evaluate exponential expressions6.1b Properties of Exponents (35)Use the product rule for exponentsUse the power rules for products and quotientsUse the quotient rule for exponents, and define a number raised to the 0 powerDecide which rule(s) to use to simplify an expression6.1c Negative Exponents (34)Simplify expressions containing negative exponentsUse all the rules and definitions for exponents to simplify exponential expressions6.1d The Meaning of a^(1/n) Rational Exponents (11)Understand the meaning of a^(1/n)Understand the meaning of a^(m/n)Simplify expressions containing negative exponents6.1e Rational Exponents (12)Understand the meaning of a^(m/n)Understand the meaning of a^(1/n)Solve equations of the form b^x = b^y6.2a Adding and Subtracting Polynomials (35)Vocabulary and Readiness CheckDefine polynomial, monomial, binomial, trinomial, and degreeFind the value of a polynomial given replacement values for the variablesSimplify a polynomial by combining like termsAdd and subtract polynomials6.2b Adding and Subtracting Polynomials (29)Define polynomial, monomial, binomial, trinomial, and degreeFind the value of a polynomial given replacement values for the variablesSimplify a polynomial by combining like termsAdd and subtract polynomials6.3a Multiplying Polynomials (26)Use the distributive property to multiply polynomialsMultiply polynomials vertically6.3b Multiplying Polynomials (27)Use the distributive property to multiply polynomialsMultiply polynomials vertically6.4a Special Products (24)Multiply two binomials using the FOIL methodSquare a binomial6.4b Special Products (14)Multiply the sum and difference of two terms6.4c Special Products (11)Square a binomial6.4d Special Products – Distributive Property (14)Multiply the sum and difference of two terms6.4e Special Products - Review and Extension (22)Multiply the sum and difference of two termsSquare a binomialUse the distributive property to find the product of two polynomials6.5a Scientific Notation and Review of Negative Exponents (44)Simplify expressions containing negative exponentsUse all the rules and definitions for exponents to simplify exponential expressions6.5b Computing Scientific Notation (10)Perform operations on numbers written in scientific notationCompute, using scientific notation6.6a Graphing Exponential Functions (23)Graph exponential functionsGraph transformations of exponential functions6.6b Compound Interest Formula - Review and Preview (38)Graph exponential functionsGraph transformations of exponential functionsUse the compound interest formula6.7 Exponential Growth and Decay Functions (14)Model exponential growthModel exponential decayModel exponential decay with half-life6.8a Dividing Polynomials (25)Divide a polynomial by a monomialUse long division to divide a polynomial by another polynomialUse synthetic division to divide a polynomial by a binomialUse the remainder theorem to evaluate polynomials6.8b Dividing Polynomials - Review and Extension (18)Use synthetic division to divide a polynomial by a binomialUse the remainder theorem to evaluate polynomialsDivide a polynomial by a monomialUse long division to divide a polynomial by another polynomialCHAPTER 7: Factoring Polynomials7.1a Greatest Common Factor and Factoring (27)Find the greatest common factor of a list of integersFactor out the greatest common factor from a polynomial7.1b Factoring Four-term Polynomials by Grouping (16)Factor a polynomial by groupingFactor out the greatest common factor from a polynomial7.1c Factoring - Review and Preview (16)Find the greatest common factor of a list of integersFactor out the greatest common factor from a polynomialFactor a polynomial by groupingFactor out the greatest common factor from a polynomial7.2a Factoring Trinomials of the Form x^2+bx+c (27)Factor trinomials of the form x^2+bx+cFactor out greatest common factor and factor a trinomial of the form x^2+bx+c7.2b Factoring Trinomials of the Form x^2+bx+c (21)Factor out greatest common factor and factor a trinomial of the form x^2+bx+c7.5a Factoring Binomials (22)Factor the difference of two squaresFactor the sum or difference of two cubesFactor other binomials7.5b Factoring Binomials (21)Factor other binomials7.6a Solving Quadratic Equations (22)Use the zero factor theoremSolve quadratic equations by factoring7.6b Solving Quadratic Equations (22)Solve equations with degree greater than 2 by factoringSolve quadratic equations by factoringFind the x-intercepts of the graph of a quadratic equation in two variables7.7 Solving Quadratic Equations by Problem Solving (33)Solve problems that can be modeled by quadratic equationsCHAPTER 8: Rational Express8.1a Simplifying Rational Expressions (11)Find the value of a rational expression given a replacement numberIdentify values for which a rational expression is undefinedSimplify or write rational expressions in lowest terms8.1b Simplifying Rational Expressions (22)Simplify or write rational expressions in lowest termsSimplify expressions with 4-term polynomials and sums and differences of cubes8.2a Multiplying and Dividing Rational Expressions (15)Multiply rational expressionsDivide rational expressionsMultiply or divide rational expressions8.2b Multiplying and Dividing Rational Expressions (14)Multiply or divide rational expressions8.3 Adding and Subtracting Rational Expressions – Basic (8)Add and subtract rational expressions with the same denominator8.5 Equations Containing Rational Expression (30)Solve equations containing rational expressionsSolve equations containing rational expressions for a specified variable8.6a Proportions and Problem Solving with Rational Numbers (25)Solve proportionsUse proportions to solve problemsSolve problems about numbersSolve problems about workSolve problems about distance8.6b Proportions and Problem Solving with Rational Numbers (25)Use proportions to solve problemsSolve problems about workSolve problems about distance8.7 Variation and Problem Solving (28)Solve problems involving direct variationSolve problems involving inverse variationOther types of direct and inverse variationSolve applications involving variation8.8a Operations with Complex Numbers (11)Add or subtract complex numbersMultiply complex numbers8.8b Operations with Complex Numbers (11)Divide complex numbersMultiply complex numbersCHAPTER 9: Roots and Radicals9.1a Radicals and Radical Functions (41)Evaluate square rootsEvaluate cube rootsEvaluate nth rootsApproximate square rootsSolve application problemsSimplify radicals containing variables9.1b Radicals and Radical Functions (13)Find function values of square and cube rootsGraph square and cube root functions9.2a Simplifying Radicals (27)Use the product rule to simplify square rootsUse the quotient rule and the product rule to simplify square rootsSimplify radicals containing variables9.2b Simplifying Radicals (27)Simplify radicals containing variablesSimplify higher rootsSolve application problems9.3 Adding and Subtracting Radicals (32)Add or subtract like radicalsSimplify radical expressions, and then add or subtract any like radicals9.4 Multiplying and Dividing Radicals (45)Multiply radicalsDivide radicalsRationalize denominatorsRationalize denominators using conjugatesSimplify radical expressions9.5 Solving Equations Containing Radicals (18)Solve radical equations by using the squaring property of equality once9.6 Radical Equations and Problem Solving (35)Use the Pythagorean formula to solve problemsUse the converse of the Pythagorean TheoremUse the distance formulaUse the midpoint formulaSolve problems using formulas containing radicals9.7 Radicals, Negative Numbers, and Graphing Complex Numbers (11)Write square roots of negative numbers in the form biEvaluate cube rootsGraph complex numbers on the complex plane9.8 Scatterplots (13)Determine an appropriate function for modeling dataFind a correlation coefficient and/or interpret aspects of a linear relationshipDetermine whether linear, quadratic, or exponential curve best fits scatterplot/data Define terms related to correlation and regressionIdentify factors that contribute to random component of linear regression modelCalculate the correlation coefficient of dataCHAPTER 10: Quadratic Equations10.1 Quadratics: Using the Square Root Property (27)Use the square root property to solve quadratic equationsSolve problems modeled by quadratic equations10.2 Quadratics: Completing the Square (30)Write perfect square trinomialsSolve quadratic equations of the form x^2+bx+c=0 by completing the squareSolve quadratic equations of the form ax^2+bx+c=0 by completing the square10.3a Quadratics: Using the Quadratic Formula (15)Use the quadratic formula to solve quadratic equations10.3b Quadratics: Using the Quadratic Formula (25)Use the quadratic formula to solve quadratic equationsApproximate solutions to quadratic equationsDetermine the number of solutions of a quadratic equation using the discriminantSolve quadratic equations by using the quadratic formulaDetermine number and type of solutions of quadratic equation using discriminantSolve geometric problems modeled by quadratic equations10.3c Quadratic Formula - Review and Extension (18)Solve geometric problems modeled by quadratic equations10.4a Graphing Quadratic Equations (24)Graph quadratic equations of the form y=ax^2Use the vertex formula to help graph quadratic equations of the form y=ax^2+bx+c10.4b The Parabola and Circle Graphs (15)Determine an appropriate function for modeling dataGraph quadratic equations of the form y=ax^2Use the vertex formula to help graph quadratic equations of the form y=ax^2+bx+cGraph circles of the form (x-h)^2+(y-k)^2 =r^2Write the equation of a circle, given its center and radius10.4c The Parabola and Circle Graphs (11)Find centers and radii of circles or vertices of parabolas, given the equation10.5 Linear, Quadratic, and Exponential Models (17)Determine an appropriate function for modeling dataSolve application exercises involving exponential, linear, and quadratic modelsSolve problems modeled by exponential equationsA.C The Fundamental Counting Principle (12)Use Fundamental Counting Principle to find number of possible outcomesSolve Critical Thinking ExercisesA.D Permutations (27)Use the Fundamental Counting Principle to count permutationsEvaluate factorial expressionsUse the permutations formulaFind the number of permutations of duplicate itemsSolve Critical Thinking ExercisesA.E Combinations (26)Distinguish between permutation and combination problemsUse the combinations formulaSolve problems involving combinationsSolve Critical Thinking ExercisesA.F Arithmetic and Geometric Sequences (28)Identify arithmetic sequences and their common differencesIdentify geometric sequences and their common ratiosDetermine if a sequence is arithmetic or geometric ................
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