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BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 1st 9 Weeks Domain Seeing Structure in Expressions Seeing Structure in Expressions Creating Equations Creating Equations Page 1 of 26 Content Content Standard Description Standard # and Identifier 12, 12a, Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] 12b a). Interpret parts of an expression such as terms, factors, and coefficients. [A-SSE1a] b). Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] Use the structure of an expression to identify ways to 13 rewrite it. [A-SSE2] 20 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1] 22 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3] AHSGE ACT/Quality Core Standards Description G.1.a F.1.b. G.1.c AHSGE: VII-8 item spec pg 70-71 Standards for Mathematic al Practice 1, 2, 4, 7 Quality Core Prerequisite s Skill Textbook Resources McGraw Hill – Algebra 2 1.1, 1.4 2, 7 Precalculus 1.2 D.2.b, E.1.a, E.1.d, E.2.a, , G.1.a 1, 2, 4, 5 1.3, 1.4, 1.5, 1.6 D.2.a, D.2.b, E.2.c 1, 2, 4, 5 1.4, 1.5, 1.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 1st 9 Weeks Domain Content Content Standard Description Standard # and Identifier For a function that models a relationship between two Arithmetic 18 quantities, interpret key features of graphs and tables in with terms of the quantities, and sketch graphs showing key Polynomials features given a verbal description of the relationship. and Key features include intercepts; intervals where the Rational function is increasing, decreasing, positive, or negative; Expressions relative maximums and minimums; symmetries; end behavior; and periodicity.* [F-IF4] Seeing Structure in Expressions 12, 12b Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] b). Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] Interpreting Functions 32 Creating Equations 21 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9] . Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Creating Equations 22 Interpreting Functions 29 Page 2 of 26 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3] Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5] AHSGE ACT/Quality Core Standards Description AHSGE: V-2 item spec pg 4851 G.1.a Standards for Mathematic al Practice 2, 4, 5, 6, 7, 8 Quality Core Prerequisite s Skill 1, 2, 4, 7 6, 7 Textbook Resources McGraw Hill – Algebra 2 2.1, 2.1 extend 2.2, 2.2 extend, 2.4, 2.6, 2.7, 2.7 explore Precalculus 2.2, 2.2 extend D.2.a, D.2.b, D.1.c, E.1.d, E.2.a, E.2.c 1, 2, 4, 5 2.4 D.2.a, D.2.b, E.2.c 1, 2, 4, 5 2.6, 2.7, 2.7 explore, 2.8 E.2.a, E.2.b 2, 4, 6 Precalculus 2.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 1st 9 Weeks Domain Content Content Standard Description Standard # and Identifier Interpreting 30, 30a Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using Functions technology for more complicated cases.* [F-IF7] a. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [F-IF7b] Interpreting Functions 32 Building Functions 34 Creating Equations 21 Creating Equations 22 Page 3 of 26 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9] Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3] Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3] AHSGE AHSGE: V-I, 4 item specs pg 40-42 ACT/Quality Core Standards Description F.2.d, G.2.a E.2.b Standards for Mathematic al Practice 2, 7 Quality Textbook Core Resources Prerequisite McGraw Hill s Skill – Algebra 2 Precalculus 2.6 6, 7 Precalculus 2.7, 2.7 explore 4, 5, 7 Precalculus 2.7, 2.7 explore D.2.a, D.2.b, D.1.c, E.1.d, E.2.a, E.2.c 1, 2, 4, 5 3.1 D.2.a, D.2.b, E.2.c 1, 2, 4, 5 3.1, 3.2, 3.3, 3.4 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 1st 9 Weeks Domain Reasoning with Equations and Inequalities Page 4 of 26 Content Content Standard Description Standard # and Identifier Explain why the x-coordinates of the points where the 27 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.* [A-REI11] AHSGE ACT/Quality Core Standards Description D.1.a, D.1.b Standards for Mathematic al Practice 2, 4, 5, 6 Quality Textbook Core Resources Prerequisite McGraw Hill s Skill – Algebra 2 Precalculus 3.1 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 2nd 9 Weeks Domain Content Standard # and Identifier Content Standard Description Vector and Matrix Quantitie s Vector and Matrix Quantitie s Vector and Matrix Quantitie s Vector and Matrix Quantitie s 7 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [N-VM6] 8 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. [N-VM7] I.1.a., I.1.b, I.1.f. 3.5 9 (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8] I.1.a., I.1.f. 3.5, 3.6 10 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. [N-VM9] I.1.a., I.1.b., I.1.f. 3.6 Page 5 of 26 AHSGE ACT/Qualit y Core Standards Descriptio n I.1.f. Standards for Mathematic al Practice Quality Core Prerequisites Skill Textbook Resources McGraw Hill – Algebra 2 3.5 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 2nd 9 Weeks Domain Content Standard # and Identifier Content Standard Description Vector and Matrix Quantitie s Reasonin g with Equation s and Inequaliti es Seeing Structure in Expressio ns 11 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. [N-VM10] 26 (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimensions 3x3 or greater). [A-REI9] I.1.e. 1, 2, 4, 7 3.8 Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] a). Interpret parts of an expression such as terms, factors, and coefficients. [A-SSE1a] b). Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5] G.1.a 1, 2, 4, 7 4.1, 4.6, 4.7, 4.7 extend, 4.7 explore Interpreti ng Functions Interpreti ng Functions Page 6 of 26 12, 12a, 12b 29 32 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9] AHSGE ACT/Qualit y Core Standards Descriptio n I.1.c., I.1.e., I.1.d. E.2.a, E.2.b Standards for Mathematic al Practice Quality Core Prerequisites Skill Textbook Resources McGraw Hill – Algebra 2 3.7 (example 1), 3.8 2, 4, 6 Precalculus 4.1 6, 7 Precalculus 4.1 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 2nd 9 Weeks Domain Content Standard # and Identifier Content Standard Description Creating Equation s 21 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Reasonin g with Equation s and Inequaliti es 27 Explain 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.* [A-REI11] Seeing Structure in Expressio ns Arithmeti c with Polynomi als and Rational Expressio ns 13 Use the structure of an expression to identify ways to rewrite it. [A-SSE2] 18 Prove polynomial identities and use them to describe numerical relationships. [A-APR4] Page 7 of 26 AHSGE ACT/Qualit y Core Standards Descriptio n D.2.a, D.2.b, D.1.c, E.1.d, E.2.a, E.2.c D.1.a, D.1.b Standards for Mathematic al Practice Quality Core Prerequisites Skill 2, 4, 5, 6 Precalculus 4.2, 4.2 extend F.1.b, G.1.c 2, 7 Precalculus 4.3, 4.5 1, 2, 4, 5 7, 8 Textbook Resources McGraw Hill – Algebra 2 4.2, 4.2 extend 4.3, 4.5, 4.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 2nd 9 Weeks Domain Content Standard # and Identifier Creating Equation s 20 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1] Interpreti ng Functions 31 The Complex Number System The Complex Number System The Complex Number System The Complex Number System Page 8 of 26 Content Standard Description AHSGE ACT/Qualit y Core Standards Descriptio n D.2.b, E.1.a, E.1.d, E.2.a, , G.1.a Standards for Mathematic al Practice Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8] E.3.a, E.3.b, E.3.c, E.3.d 2, 7 1 Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. [NCN1] C.1.a 2, 6 2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. [N-CN2] C.1.b 2, 7, 8 3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. [N-CN3] C.1.a 5 (+) Extend polynomial identities to the complex numbers. [NCN8] AHSG E: VII8 item spec pg 70-71 1, 2, 4, 5 Quality Core Prerequisites Skill Textbook Resources McGraw Hill – Algebra 2 4.3, 4.5, 4.6, 4.8 4.3, 4.5, 4.7, 4.7 extend, 4.7 explore 4.4 4.4 4.4 4.4, 4.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 2nd 9 Weeks Domain Content Standard # and Identifier The Complex Number System Creating Equation s Reasonin g with Equation s and Inequaliti es Building Functions 4 Solve quadratic equations with real coefficients that have complex solutions. [N-CN7] 23 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] 1, 2, 4, 5, 7 25 Recognize when the quadratic formula gives complex solutions, and write them as a+bi for real numbers a and b. [AREI4b] 2, 7, 8 34 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1] 22 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3] Creating Equation s Page 9 of 26 Content Standard Description AHSGE AHSG E: VII8 item spec pg 70-71 ACT/Qualit y Core Standards Descriptio n E.1.c. Standards for Mathematic al Practice Quality Core Prerequisites Skill 1, 7 Precalculus E.2.b. 1, 2, 4, 5 D.2.a, D.2.b, E.2.c. 1, 2, 4, 5 Textbook Resources McGraw Hill – Algebra 2 4.5, 4.6 4.6 4.6 and supplemen t for a + bi Precalculus 4.7, 4.7 extend, 4.7 explore 4.8 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Domain 3rd 9 Weeks AHSGE Content Content Standard Description Standar d # and Identifie r Understand that polynomials form a system analogous Arithme 15 to the integers; namely, they are closed under the tic with operations of addition, subtraction, and multiplication; Polynom add, subtract, and multiply polynomials. [A-APR1] ials and Rational Expressi ons Rewrite simple rational expressions in different forms; Arithme 19 write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), tic with b(x), q(x), and r(x) are polynomials with the degree of Polynom r(x) less than the degree of b(x), using inspection, long ials and division, or for the more complicated examples, a Rational computer algebra system. [A-APR6] Expressi ons Relate the domain of a function to its graph and, where Interpre 29 applicable, to the quantitative relationship it describes.* ting [F-IF5] Function s Interpre 30, 30b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using ting technology for more complicated cases.* [F-IF7] Function b. Graph polynomial functions, identifying zeros when s suitable factorizations are available, and showing end behavior. [F-IF7c] Page 10 of 26 ACT/Quality Core Standards Description Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 A.1.b 2, 7 5.1 F.1.b 2, 5, 7, 8 5.2 E.2.a., E.2.b. 2, 4, 6 Precalculus 5.3 F.2.d, G.2.a. 5, 6 Precalculus 5.3, 5.4, 5.4 extend, 5.6, 5.7, 5.7 extend BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 3rd 9 Weeks AHSGE Domain Content Content Standard Description Standar d # and Identifie r Compare properties of two functions each represented in Interpre 32 a different way (algebraically, graphically, numerically ting in tables, or by verbal descriptions). [F-IF9] Function s Seeing 12, 12b Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] Structur b). Interpret complicated expressions by viewing one e in or more of their parts as a single entity. [A-SSE1b] Expressi ons Create equations and inequalities in one variable and use Creating 20 them to solve problems. Include equations arising from Equatio linear and quadratic functions, and simple rational and ns exponential functions. [A-CED1] Reasoni ng with Equatio ns and Inequalit ies Page 11 of 26 27 Explain 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.* [A-REI11] AHSGE : VII-8 item spec pg 70-71 ACT/Quality Core Standards Description Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 6, 7 Precalculus 5.3 G.1.a 1, 2, 4, 7 5.4, 5.4 extend D.2.b, E.1.a., E.1.d., E.2.a., G.1.a 1, 2, 4, 5 5.5, 5.5 extend, 5.6, 5.7, 5.7 extend D.1.a, D.1.b. 2, 4, 5, 6 Precalculus 5.5, 5.5 extend BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Domain 3rd 9 Weeks AHSGE Content Content Standard Description Standar d # and Identifie r Know and apply the Remainder Theorem: For a Arithme 16 polynomial p(x) and a number a, the remainder on tic with division by x – a is p(a), so p(a) = 0 if and only if (x – a) Polynom is a factor of p(x). [A-APR2] ials and Rational Expressi ons (+) Know the Fundamental Theorem of Algebra; show The 6 that it is true for quadratic polynomials. [N-CN9] Complex Number System Identify zeros of polynomials when suitable Arithme 17 factorizations are available, and use the zeros to tic with construct a rough graph of the function defined by the Polynom polynomial. [A-APR3] ials and Rational Expressi ons Prove polynomial identities and use them to describe Arithme 18 numerical relationships. [A-APR4] tic with Polynom ials and Rational Expressi ons Page 12 of 26 ACT/Quality Core Standards Description F.1.a. Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 2, 3, 8 Precalculus 5.6 F.2.c., E.1.b. F.1.b., F.2.a., F.2.b., E.1.a., F.2.d. 5.7. 5.7 extend 1, 2, 4, 5, 8 7, 8 Precalculus 5.7. 5.7 extend 5.7, 5.7 extend BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Domain 3rd 9 Weeks AHSGE Content Content Standard Description Standar d # and Identifie r Compare properties of two functions each represented in Interpre 32 a different way (algebraically, graphically, numerically ting in tables, or by verbal descriptions). [F-IF9] Function s Building 33, 33a Write a function that describes a relationship between two quantities.* [F-BF1] Function a. Combine standard function types using arithmetic s operations. [F-BF1b] Relate the domain of a function to its graph and, where Interpre 29 applicable, to the quantitative relationship it describes.* ting [F-IF5] Function s Building 35, 35a Find inverse functions. [F-BF4] a.Solve an equation of the form f(x) = c for a simple Function function f that has an inverse, and write an expression s for the inverse. [F-BF4a] Create equations in two or more variables to represent Creating 21 relationships between quantities; graph equations on Equatio coordinate axes with labels and scales. [A-CED2] ns Interpre 30, 30a Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using ting technology for more complicated cases.* [F-IF7] Function a. Graph square root, cube root, and piecewise-defined s functions, including step functions and absolute value functions. [F-IF7b] Page 13 of 26 ACT/Quality Core Standards Description C.1.d. E.2.a., E.2.b. AHSGE : V-I, 4 item spec 4041 D.2.a., D.2.b., D.1.c., E.1.d., E.2.a., E.2.c F.2.d., G.2.a. Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 6, 7 Precalculus 6.1, 6.3, 6.3 extend 1, 2, 3, 4, 5, 6, 7, 8 2, 4, 6 6.1 Precalculus 6.2, 6.3, 6.3 extend 2, 4, 5, 7 6.2 1, 2, 4, 5 6.3, 6.3 extend 5, 6 Precalculus 6.3, 6.3 extend, 6.4, 6.4 extend, BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Domain 3rd 9 Weeks AHSGE Content Content Standard Description Standar d # and Identifie r Identify the effect on the graph of replacing f(x) by f(x) Building 34 + k, k f(x), f(kx), and f(x + k) for specific values of k Function (both positive and negative); find the value of k given s the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3] Use the structure of an expression to identify ways to Seeing 13 rewrite it. [A-SSE2] Structur e in Expressi ons Solve simple rational and radical equations in one Reasoni 24 variable, and give examples showing how extraneous ng with solutions may arise. [A-REI2] Equatio ns and Inequalit ies Explain why the x-coordinates of the points where the Reasoni 27 graphs of the equations y = f(x) and y = g(x) intersect are ng with the solutions of the equation f(x) = g(x); find the Equatio solutions approximately, e.g., using technology to graph ns and the functions, make tables of values, or find successive Inequalit approximations. Include cases where f(x) and/or g(x) are ies linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11] Page 14 of 26 ACT/Quality Core Standards Description Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 4, 5, 7 Precalculus 6.3, 6.3 extend, 6.4, 6.4 extend F.1.b., G.1.c. 2, 7 Precalculus 6.4, 6.4 extend, 6.5 G.1.b., G.1.c., G.1.d., G.1.e., G.1.f, G.1.g. 1, 2, 3, 7 Precalculus 6.7, 6.7 extend D.1.a., D.1.b. 2, 4, 5, 6 Precalculus 6.7, 6.7 extend E.2.b. BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Domain 3rd 9 Weeks AHSGE Content Content Standard Description Standar d # and Identifie r Relate the domain of a function to its graph and, where Interpre 29 applicable, to the quantitative relationship it describes.* ting [F-IF5] Function s Interpre 30, 30c Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using ting technology for more complicated cases.* [F-IF7] Function c.) Graph exponential and logarithmic functions, s showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [FIF7e] Write a function defined by an expression in different Interpre 31 but equivalent forms to reveal and explain different ting properties of the function. [F-IF8] Function s Compare properties of two functions each represented in Interpre 32 a different way (algebraically, graphically, numerically ting in tables, or by verbal descriptions). [F-IF9] Function s Identify the effect on the graph of replacing f(x) by f(x) Building 34 + k, k f(x), f(kx), and f(x + k) for specific values of k Function (both positive and negative); find the value of k given s the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3] Page 15 of 26 ACT/Quality Core Standards Description Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 E.2.a., E.2.b. 2, 4, 6 Precalculus 7.1, 7.3 F.2.d., G.2.a. 5, 6 Precalculus 7.1, 7.3 E.3.a., E.3.b., E.3.c, E.3.d. 2, 7 E.2.b. 7.1, 7.8, 7.8 extend 6, 7 Precalculus 7.1 4, 5, 7 Precalculus 7.1, 7.3 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Domain Seeing Structur e in Expressi ons Creating Equatio ns 3rd 9 Weeks AHSGE Content Content Standard Description Standar d # and Identifie r Use the structure of an expression to identify ways to 13 rewrite it. [A-SSE2] 20 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1] Reasoni ng with Equatio ns and Inequalit ies 27 Linear, Quadrati c, and Exponen tial Models 36 Explain 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.* [A-REI11] For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology. [F-LE4] Page 16 of 26 AHSGE : VII-8 item spec pg 70-71 ACT/Quality Core Standards Description Standards for Mathemati cal Practice Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 F.1.b., G.1.c. 2, 7 Precalculus 7.2, 7.2 extend, 7.3, 7.4, 7.7, 7.8, 7.8 extend D.2.b., E.1.a., E.1.d., E.2.a., G.1.a. 1, 2, 4, 5 D.1.a., D.1.b. 2, 4, 5, 6 G.2.b. 4, 5, 7 7.2, 7.2 extend, 7.4, 7.5, 7.6, 7.6 extend, 7.8, 7.8 extend Precalculus 7.2, 7.2 extend, 7.6, 7.6 extend 7.2, 7.2 extend, 7.8, 7.8 extend BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 3rd 9 Weeks AHSGE Domain Content Content Standard Description Standar d # and Identifie r Represent constraints by equations or inequalities, and Creating 22 by systems of equations and/or inequalities, and Function interpret solutions as viable or nonviable options in a s modeling context. [A-CED3] Building Function s 33, 33a Page 17 of 26 Write a function that describes a relationship between two quantities.* [F-BF1] a. Combine standard function types using arithmetic operations. [F-BF1b] ACT/Quality Core Standards Description Standards for Mathemati cal Practice D.2.a., D.2.b., E.2.c. 1, 2, 4, 5 7.8, 7.8 extend 1, 2, 3, 4, 5, 6, 7, 8 7.8, 7.8 extend C.1.d. Quality Core Prerequisit es Skill Textbook Resources McGraw Hill – Algebra 2 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Content Standard Description Interpre ting Function s Building Function s 29 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] 34 Interpre ting Function s Creating Equatio ns 32 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3] Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9] 20 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1] Creating Equatio ns 22 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3] Page 18 of 26 AHSGE ACT/Qualit y Core Standards Descriptio n E.2.a, E.2.b. E.2.b. AHSG E: VII8 item spec pg 70-71 Standards for Mathematical Practice Quality Core Prerequisite s Skill Textbook Resources McGraw Hill – Algebra 2 2, 4, 6 Precalculus 8.3, 8.4 4, 5, 7 Precalculus 8.3 6, 7 Precalculus 8.4 D.2.b., E.1.a., E.1.d., E.2.a., G.1.a. 1, 2, 4, 5 8.6, 8.6 extend D.2.a., D.2.b., E.2.c. 1, 2, 4, 5 8.6, 8.6 extend BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Reasoni ng with Equatio ns and Inequalit ies Reasoni ng with Equatio ns and Inequalit ies 24 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2] 27 Creating Equatio ns Seeing Structur e in Expressi ons 23 Explain 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.* [A-REI11] Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] 12, 12b Page 19 of 26 Content Standard Description Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] b). Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] AHSGE ACT/Qualit y Core Standards Descriptio n G.1.b., G.1.c., G.1.d., G.1.e., G.1.f., G.1.g. D.1.a., D.1.b. Standards for Mathematical Practice Quality Core Prerequisite s Skill Textbook Resources McGraw Hill – Algebra 2 1, 2, 3, 7 Precalculus 8.6, 8.6 extend 2, 4, 5, 6 Precalculus 8.6, 8.6 extend 1, 2, 4, 5, 7 G.1.a. 1, 2, 4, 7 9.1, 9.3 9.2, 9.3, 9.4 enrichment, 9.5 enrichment, 9.6, 9.6 enrichment, 9.6 extend BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Creating Equatio ns 21 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Interpre ting Function s 32 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9] Reasoni ng with Equatio ns and Inequalit ies 27 Conic Sections 28, 28a Creating Equatio ns 23 Explain 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.* [A-REI11] Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. a. Formulate equations of conic sections from their determining characteristics. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] Page 20 of 26 Content Standard Description AHSGE ACT/Qualit y Core Standards Descriptio n D.2.a., D.2.b., D.1.c., E.1.d., E.2.a., E.2.c. D.1.a., D.1.b. Standards for Mathematical Practice Quality Core Prerequisite s Skill 1, 2, 4, 5 Textbook Resources McGraw Hill – Algebra 2 9.3 6, 7 Precalculus 9.6, 9.6 enrichment, 9.6 extend 2, 4, 5, 6 Precalculus 9.7 Precalculus 9.2, 9.3, 9.4, 9.5, 9.6 E.3.a., E.3.b., E.3.c., E.3.d 1, 2, 4, 5, 7 10.2 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Seeing Structur e in Expressi ons Seeing Structur e in Expressi ons Conditio nal Probabil ity and the Rules of Probabil ity Conditio nal Probabil ity and the Rules of Probabil ity 14 12, 12b Page 21 of 26 Content Standard Description AHSGE ACT/Qualit y Core Standards Descriptio n Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* [A-SSE4] Standards for Mathematical Practice Quality Core Prerequisite s Skill Textbook Resources McGraw Hill – Algebra 2 3, 4, 7, 8 10.3 10.7 Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] b). Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] G.1.a. 1, 2, 4, 7 39 Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). [S-CP1] H.1.a., H.1.b., H.1.c., H.1.e. 1, 2, 4, 6, 7 0.4, 0.5, 0.6 40 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. [S-CP3] H.1.f. 1, 2, 4, 6, 7 0.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Conditio nal Probabil ity and the Rules of Probabil ity 41 Conditio nal Probabil ity and the Rules of Probabil ity 42 Page 22 of 26 Content Standard Description Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. [S-CP4] AHSGE ACT/Qualit y Core Standards Descriptio n H.1.d., H.1.f. Standards for Mathematical Practice 1, 2, 3, 4, 5, 6, 7, 8 Quality Core Prerequisite s Skill Textbook Resources McGraw Hill – Algebra 2 0.6 Example: Collect data from a random sample of students in your school on their favorite subject among mathematics, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S-CP5] Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. H.1.d., H.1.f. 1, 4, 6, 8 0.4, 0.5, 0.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Content Standard Description Conditio nal Probabil ity and the Rules of Probabil ity Conditio nal Probabil ity and the Rules of Probabil ity Conditio nal Probabil ity and the Rules of Probabil ity 43 Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. [S-CP6] 44 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. [S-CP7] 45 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8] Page 23 of 26 AHSGE ACT/Qualit y Core Standards Descriptio n H.1.f. Standards for Mathematical Practice Quality Core Prerequisite s Skill Textbook Resources McGraw Hill – Algebra 2 1, 4, 5, 7 0.5 H.1.d. 1, 4, 5, 6, 7 0.5 H.1.d. 1, 4, 5, 6, 7 0.6 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II 4th 9 Weeks Domain Content Standard # and Identifier Conditio nal Probabil ity and the Rules of Probabil ity Using Probabil ity to Make Decision s Using Probabil ity to Make Decision s 46 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] 38 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] 37 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] Page 24 of 26 Content Standard Description AHSGE ACT/Qualit y Core Standards Descriptio n H.1.b H.1.a, H.1.b, H.1.c, H.1.d, H.1.e, H.1.f. H.1.a, H.1.b, H.1.c, H.1.d, H.1.e, H.1.f. Standards for Mathematical Practice Quality Core Prerequisite s Skill 1, 4, 5, 6, 7 Textbook Resources McGraw Hill – Algebra 2 0.4 1, 4, 5, 6, 7 Precalculus 11.3, 11.4, 11.6 1, 4, 5, 6, 7 Precalculus 11.4 BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II Essential Vocabulary st 1 9 Weeks Chapter 1: algebraic expressions, order of operations, formula, real numbers, rational numbers, irrational numbers, integers, whole numbers, natural numbers, open sentence, equation, solution, absolute value, empty set, constraint, extraneous solution, set-builder notation, compound inequality, intersection, union Chapter 2: one-to-one function, onto function, discrete relation, continuous relation, vertical line test, independent variable, dependent variable, function notation, linear relation, nonlinear relation, linear equation, standard form, y-intercept, x-intercept, root, slope, slopeintercept form, point-slope form, parallel, perpendicular, piecewisedefined function, piecewise-linear function, step function, greatest integer function, absolute value function, family of graphs, parent graph, parent function constant function, identity function, quadratic function, translation, reflection, line of reflection, dilation, linear inequality, boundary Chapter 3: system of equations, Page 25 of 26 nd 2 9 Weeks Chapter 3: scalar, scalar multiplication, determinant, secondorder determinant, third-order determinant, diagonal rule, identity matrix, square matrix, inverse matrix, matrix equation, variable matrix, constant matrix Chapter 4: quadratic function, quadratic term, linear term, constant term, parabola, axis of symmetry, vertex, maximum value, minimum value, quadratic equation, standard form, root, zero, factored form, FOIL method, imaginary unit, pure imaginary number, complex number, complex conjugates, completing the square, Quadratic Formula, discriminant, vertex form, quadratic inequality 3rd 9 Weeks Chapter 5: simplify, degree of a polynomial, synthetic division, polynomial in one variable, leading coefficient, polynomial function, power function, quartic function, quintic function, end behavior, Location Principle, relative maximum, relative minimum, extrema, turning points, prime polynomials, quadratic form, synthetic substitution, depressed polynomial Chapter 6: composition of functions, inverse relation, inverse function, square root function, radical function, square root inequality, nth root, radical sign, index, radicand, principal root, rationalizing the denominator, like radical expressions, conjugate, radical equation, extraneous solution, radical inequality Chapter 7: exponential function, exponential growth, asymptote, growth factor, exponential decay, decay factor, exponential equation, compound interest, exponential inequality, logarithm, logarithmic function, logarithmic equation, logarithmic inequality, common 4th 9 Weeks Chapter 8: reciprocal function, hyperbola, rational function, vertical asymptote, horizontal asymptote, oblique asymptote, point discontinuity, rational equation, weighted average, rational inequality Chapter 9: parabola, focus, directrix, latus rectum, standard form, general form, circle, center, radius, ellipse, focus, major axis, minor axis, center, vertices, co-vertices, constant sum, hyperbola, transverse axis, conjugate axis, foci, vertices, co-vertices, constant difference Chapter 10: arithmetic means, series, arithmetic series, partial sum, sigma notation, geometric means, geometric series, mathematical induction, induction hypothesis Prerequisites Chapter: outcome, probability experiment, sample space, tree diagram, permutation, factorial, combination, probability, probability model, uniform or simple probability model, theoretical probability, experimental probability, simple event, compound event, mutually exclusive event, odds, independent events, dependent events, conditional probability, two- BCSS Mathematics Pacing Guide 2013 - 2014 Algebra II break-even point, consistent, inconsistent, independent, dependent, substitution method, elimination method, system of inequalities, linear programming, feasible region, bounded, unbounded, optimize, ordered triple Page 26 of 26 logarithm, Change of Base Formula, natural base – e, natural base exponential function, natural logarithm way frequency table Chapter 11: random variable, discrete random variable, continuous random variable, probability distribution, theoretical probability distribution, experimental probability distribution, Law of Large Numbers, expected value, binomial experiment, binomial, distribution, inferential statistics, statistical inference, confidence interval, maximum error of estimate, hypothesis test, null hypothesis, alternative hypothesis, critical region, left-tailed test, two-tailed test, right-tailed test