2019 Porcelli Lectures by Robert Bryant | LSUMath



LSU College Readiness Program COURSE PROFILE11-9-15COURSE NAME:High School Advanced Math – Precalculus paired with LSU Math 1021 College Algebra (including CLEP Prep) and LSU Math 1022 TrigonometryPRIMARY ONLINE CONTENT SOURCEAlgebra and Trigonometry, 2e, MyMathLabKirk TrigstedCOURSE/UNIT CREDIT:1 Carnegie UnitGRADE(S):10, 11, or 12PREREQUISITE(S):Successful Completion of Algebra IICHAPTERS FOR MATH 1021 COLLEGE ALGEBRA1 - Equations, Inequalities, and Applications4 - Polynomial and Rational Functions2 - The Rectangular Coordinate System, Lines, and Circles5 - Exponential and Logarithmic Functions and Equations3 - Functions12 - Systems of EquationsSECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVES FOR MATH 1021 COLLEGE ALGEBRACHAPTER 1: Equations, Inequalities, and Applications 1.1 Linear Equations (42)Find the least common denominator of an expressionRecognize linear equationsSolve linear equations with integer coefficientsSolve linear equations involving fractionsSolve linear equations involving decimalsSolve equations that lead to linear equations 1.4 Quadratic Equations (39)Simplify radical expressionsFactor trinomialsSolve quadratic equations by factoringSolve quadratic equations using the square root propertySolve quadratic equations using the quadratic formulaUse the discriminant to determine the type of solutions of a quadratic equation1.6 Other Types of Equations (34)Simplify expressionsSolve higher-order polynomial equationsSolve equations that are quadratic in formSolve equations involving single radicals1.7 Linear Inequalities (19)Solve linear inequalitiesSolve three-part inequalities1.8 Absolute Value Equations and Inequalities (29)Solve an absolute value equationSolve an absolute value “less than” inequalitySolve an absolute value “greater than” inequalityCHAPTER 2: The Rectangular Coordinate System, Lines, and Circles2.1 The Rectangular Coordinate System (25)Find the average of two numbersSimplify radicalsPlot ordered pairsFind the midpoint of a line segment using the midpoint formulaFind the distance between two points using the distance formula2.2 Circles (32)Complete the square to form perfect square trinomialsWrite the standard form of an equation of a circleSketch the graph of a circle given its equation in general formFind the center and radius of a circle given its equation in general form2.3 Lines (56)Solve a linear equation for the variable yDetermine the slope of a line through two given pointsSketch a line given a point and the slopeFind the equation of a line using the point-slope formFind the equation of a line using the slope-intercept formWrite the equation of a line in standard formFind the slope and the y-intercept of a line in standard formSketch lines by plotting interceptsSketch a line given its equation in standard formFind the equation of a horizontal line and a vertical line2.4 Parallel and Perpendicular Lines (38)Determine whether two lines are parallel, perpendicular, or neitherFind the equations of parallel and perpendicular linesCHAPTER 3: Functions3.1 Relations and Functions (62)Simplify algebraic expressionsUnderstand the definitions of relations and functionsDetermine whether equations represent functionsUse function notation and evaluate functionsUse the vertical line testDetermine the domain of a function given the equation3.2 Properties of a Function’s Graph (48)Evaluate f(-x) given a function f(x)Determine the intercepts of a functionDetermine the domain and range of a function from its graphDetermine whether a function is increasing, decreasing, or constantDetermine relative maximum and relative minimum values of a functionDetermine whether a function if even, odd, or neitherDetermine information about a function from a graph3.3 Graphs of Basic Functions; Piecewise Functions (28)Sketch the graphs of the basic functionsAnalyze piecewise-defined functions3.4 Transformations of Functions (53)Use vertical shifts to graph functionsUse horizontal shifts to graph functionsUse vertical stretches and compressions to graph functionsUse combinations of transformations to graph functions3.5 Composite Functions (25)Simplify fractional expressionsForm and evaluate composite functionsDetermine the domain of composite functions3.6 One-to-One Functions; Inverse Functions (43)Understand the definition of a one-to-one functionDetermine whether a function is one-to-one using the horizontal line testUnderstand and verify inverse functionsSketch the graphs of inverse functionsFind the inverse of a one-to-one functionCHAPTER 4: Polynomial and Rational Functions4.1 Quadratic Functions (35)Determine whether the graph of a quadratic function opens up or downDetermine properties of quadratic function in standard form and graphDetermine properties of quadratic function using the vertex formula and graph Determine the equation of a quadratic function given its graph4.2 Applications of Quadratic Functions (10)Find the maximum value for projectile motion functionsFind the maximum value for functions in economics4.3 Graphs of Polynomial Functions (46)Identify polynomial functions, degree, constant and leading coefficientsSketch the graphs of power functionsDetermine the end behavior of polynomial functionsDetermine the intercepts of a polynomial functionDetermine the real zeros of polynomial functions and their multiplicitiesSketch the graph of a polynomial functionDetermine a possible equation of a polynomial function given its graph4.6 Rational Functions and Their Graphs (35)Find the domain and intercepts of rational functionsIdentify vertical asymptotesIdentify horizontal asymptotesUse transformations to sketch the graphs of rational functionsSketch rational functionsCHAPTER 5: Exponential and Logarithmic Functions and Equations5.1 Exponential Functions (53)Rewrite expressions in exponential formEvaluate exponential expressionsSketch the graphs of exponential functionsDetermine possible equations of exponential functions given their graphsSketch the graphs of exponential functions using transformationsSolve exponential equations by relating the bases5.2 Logarithmic Functions (62)Change equations between exponential form and logarithmic formEvaluate logarithmic expressionsUse properties of logarithms to evaluate expressionsUse common and natural logarithmsSketch the graphs of logarithmic functionsFind the domain of logarithmic functions5.3 Properties of Logarithms (41)Expand and evaluate logarithmic expressionsCondense and evaluate logarithmic expressionsSolve logarithmic equations using the logarithm property of equalityUse the change of base formula5.4 Exponential and Logarithmic Equations (42)Evaluate exponential and logarithmic expressions using a calculatorSolve exponential equationsSolve logarithmic equations5.5 Applications of Exponential and Logarithmic Functions (27)Solve applications involving exponential functionsSolve compound interest applicationsSolve exponential growth and decay applicationsCHAPTER 12: Systems of Equations12.1 Systems of Linear Equations in Two Variables (23)Verify solutions to a system of linear equations in two variablesSolve a system of linear equations using the substitution methodSolve a system of linear equations using the elimination methodSolve systems of linear equations in two variables using either methodSolve applied problems using a system of linear equationCHAPTERS FOR MATH 1022 TRIGONOMETRY6 - An Introduction to Trigonometric Functions9 - Applications of Trigonometry7 - The Graphs of Trigonometric Functions10 - Polar Equations, Complex Numbers, and Vectors8 - Trigonometric Identities, Formulas, and EquationsSECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVES FOR MATH 1022 TRIGONOMETRYCHAPTER 6: An Introduction to Trigonometric Functions6.1 An Introduction to Angles: Degree and Radian Measure (50)Understand degree measureUnderstand radian measureConvert between degree measure and radian measureFind coterminal angles using degree measureFind coterminal angles using radian measure6.2 Applications of Radian Measure (19)Determine the area of a sector of a circleDetermine the arc length of a sector of a circle6.3 Triangles (20)Classify trianglesUse the Pythagorean TheoremUnderstand similar trianglesUnderstand the special right triangles6.4 Right Triangle Trigonometry (52)Understand the right triangle definitions of the trigonometric functionsUse the special right trianglesUnderstand the fundamental trigonometric identitiesUnderstand cofunctionsEvaluate trigonometric functions using a calculator6.5 Trigonometric Functions of General Angles (84)Understand the four families of special anglesUnderstand the definitions of the trigonometric functions of general anglesFind the values of the trigonometric functions of quadrantal anglesUnderstand the signs of the trigonometric functionsDetermine reference anglesEvaluate trigonometric functions of angles belonging to π/3, π/4, and π/6 families6.6 The Unit Circle (10)Understand the definition of the unit circleUnderstand the unit circle definitions of the trigonometric functionsCHAPTER 7: The Graphs of Trigonometric Functions7.1 Graphs of Sine and Cosine Functions (31)Perform operations on fractions containing πUnderstand graph of the sine function and its propertiesUnderstand graph of the cosine function and its propertiesDetermine properties and sketch graphs of form y=Asinx and y=AcosxDetermine properties and sketch graphs of form y=sinBx and y=cosBxDetermine properties and sketch graphs of form y=AsinBx and y=AcosBxDetermine eq. of a function of the form y=AsinBx and y=AcosBx given graph7.2a Graphs of Sine and Cosine: Phase Shift (22)Solve inequalities, factor expressions, perform operations on fractions containing πDetermine properties and sketch graphs of form y=sin(x-C) and y=cos(x-C)Determine properties and sketch graphs of form y=Asin(Bx-C) and y=Acos(Bx-C)7.2b Graphs of Sine and Cosine: Vertical Shift (14)Determine properties, sketch graphs of y=Asin(Bx-C)+D and y=Acos(Bx-C)+D7.3 Graphs of Secant, Cosecant, Tangent, and Cotangent (46)Solve inequalities involving radian measureUnderstand the graph of the tangent function and its propertiesSketch graphs of the form y=Atan(Bx-C)+DUnderstand the graph of the cotangent function and its propertiesSketch graphs of the form y=Acot(Bx-C)+DUnderstand the graph of the cosecant and secant functions and their propertiesSketch graphs of the form y=Asec(Bx-C)+D and y=Acsc(Bx-C)+D7.4 Inverse Trigonometric Functions Part I (34)Understand and find the exact and approximate values of inverse sine functionUnderstand and find the exact and approximate values of inverse cosine functionUnderstand and find the exact and approximate values of inverse tangent function7.5 Inverse Trigonometric Functions Part II (54)Evaluate composite functions of the form f(f^(-1)(x)) and f^(-1)(f(x))Evaluate composite functions of the form f(g^(-1)(x)) and f^(-1)(g(x))CHAPTER 8: Trigonometric Identities, Formulas, and Equations8.1 Trigonometric Identities (36)Review and use the fundamental identitiesVerify trigonometric identities8.2 The Sum and Difference Formulas (47)Review simplifying radical expressionsUse the sum and difference formulas for the cosine functionUse the sum and difference formulas for the sine functionUse the sum and difference formulas for the tangent functionUse the sum and difference formulas to verify identitiesUse sum and difference formulas to evaluate inverse trigonometric functions8.3 The Double-Angle and Half-Angle Formulas (45) Review simplifying radical expressionsUse the double-angle formulasUse the half-angle formulasUse the double-angle and half-angle formulas to verify identitiesUse the double-angle and half-angle formulas to evaluate inverse trigonometric functions8.5 Trigonometric Equations (47) Solve quadratic equationsSolve trigonometric equations that are linear in formSolve trigonometric equations that are quadratic in formSolve trigonometric equations using identitiesSolve other types of trigonometric equationsSolve trigonometric equations using a calculatorCHAPTER 9: Applications of Trigonometry9.1 Right Triangle Applications (18)Solve right trianglesSolve applied problems using right triangles9.2 The Law of Sines (30) Determine if the Law of Sines can be used to solve an oblique triangleUse the Law of Sines to solve the SAA case or the ASA caseUse the Law of Sines to solve the SSA (ambiguous) case9.3 The Law of Cosines (27) Use a calculator to approximate trig and inverse trigonometric expressionsDetermine whether Law of Sines or Cosines should be used to solve an oblique triangleUse the Law of Cosines to solve the SAS caseUse the Law of Cosines to solve the SSS caseUse the Law of Cosines to solve applied problems involving oblique triangles9.4 Area of Triangles (17) Determine the area of oblique trianglesUse Heron’s Formula to determine the area of an SSS triangleSolve applied problems involving the area of trianglesCHAPTER 10: Polar Equations, Complex Numbers, and Vectors10.1 Polar Coordinates and Equations (62)Plot points using polar coordinatesDetermine different representations of a point (r, θ)Convert from polar to rectangular coordinatesConvert from rectangular to polar coordinatesConvert equations from rectangular to polar formConvert equations from polar to rectangular form10.2 Graphing Polar Equations (65) Simplify expressions for given value of kSketch equations of the form rcosθ = a, rsinθ = a, arcosθ + brsinθ = c, and θ = αSketch equations of the form r = a, r = asinθ, and r = acosθSketch equations of the form r = a + bsinθ and r = a + bcosθSketch equations of the form r = asin(nθ) and r = acos(nθ)Sketch equations of the form r^2 = a^2sin(2θ) and r^2 = a^2cos(2θ)Identify types of graphs of polar equations10.4 Vectors (31) Determine magnitudes of vectors that are represented geometricallyPerform operations on vectors that are represented geometricallyDetermine components and magnitudes of vectorsWrite vectors in terms of i and jPerform operations on vectors written in ai+bj form and find magnitudesFind unit vectorsDetermine direction angles of vectorsWrite vectors in the form v=ai+bj given magnitudes and direction anglesSolve applied problems involving velocity using vectorsCOLLEGE ALGEBRA CLEP PREPARATIONSECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVESCLEP 1: Factoring and Expanding Polynomials (38)Multiply polynomialsFactor out a greatest common factorFactor by groupingFactor trinomials with a leading coefficient equal to oneFactor using special factoring formulasCLEP 2: Operations with Algebraic Expressions (13)Use the order of operations to simplify numeric and algebraic expressionsCLEP 3: Operations with Exponents (52)Simplify exponential expressions involving integer exponentsSimplify radical expressionsSimplify exponential expressions involving rational exponentsCLEP 4: Quadratic Inequalities (16)Solve polynomial inequalitiesCLEP 5: Systems of Non-linear Equations (16)Determine the number of solutions to a system of nonlinear equationsSolve systems of nonlinear equations using substitution, elimination, or graphingSolve applied problems using systems of nonlinear equationsCLEP 6: Inequalities in Two Variables (18)Determine whether ordered pairs are solutions to inequalities in two variablesGraph linear inequalities in two variablesCLEP 7: Systems of Inequalities in Two Variables (21)Determine if ordered pairs are solutions to systems of inequalities in two variablesGraph systems of linear inequalities in two variablesCLEP 8: Algebra of Functions (25)Evaluate a combined functionFind combined functions and their domainsCLEP 9: Real Numbers (12)Understand and classify real numbersUnderstand absolute value and use it to find distanceCLEP 10: Complex Numbers (37)Simplify powers of iAdd and subtract complex numbersMultiply complex numbersFind the quotient of complex numbersSimplify radicals with negative radicandsSolve quadratic equations using the quadratic formulaCLEP 11: Sequences and Series (42)Write the terms of a sequenceWrite the terms of a recursive sequenceWrite a formula for the general terms of a sequenceCompute partial sums of a seriesDetermine the sums of a finite series written in summation notationWrite a series using summation notationSolve applications involving sequences and seriesCLEP 12: Arithmetic Sequences and Series (35)Determine if a sequence is arithmeticFind the general term of an arithmetic sequenceFind a specific term of an arithmetic sequenceCompute the nth partial sum of an arithmetic seriesSolve applications of arithmetic sequences and seriesCLEP 13: Geometric Sequences and Series (38)Write the terms of a geometric sequenceDetermine whether a sequence is geometric and find its common ratioFind the general term of a geometric sequenceFind a specific term of a geometric sequenceCompute the nth partial sum of a geometric seriesDetermine if an infinite geometric series converges or diverges and find its sumSolve applications of geometric sequences and seriesCLEP 14: Binomial Theorem (25)Expand binomials raised to a power using Pascal's triangleEvaluate binomial coefficientsExpand binomials raised to a power using the Binomial TheoremFind a particular term of a binomial expansionFind a particular coefficient of a binomial expansionCLEP 15: Determinants of 2 by 2 Matrices (14)Determine the size of matrices and their typesEvaluate second-order determinantsEvaluate determinants of 2x2 matricesSolve equations involving determinantsWrite systems of linear equations given determinants and solve equations ................
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