Skill plan for Clarksville-Montgomery County School System - Algebra 2
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1
Unit 1
Systems and Intro to Inverse Functions
A2.A.REI.D.6: 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 approximate solutions using technology.
A2.A.REI.D.6: 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 approximate solutions using technology.
A2.A.REI.C.4: Write and solve a system of linear equations in context.
Systems of equations in two variables
Systems of equations in three variables
A2.A.REI.C.4: Write and solve a system of linear equations in context.
Systems of equations in two variables
Systems of equations in three variables
A2.F.BF.B.4: Find inverse functions.
A2.F.BF.B.4: Find inverse functions.
A2.F.BF.B.4.a: Find the inverse of a function when the given function is one-to-one.
A2.F.BF.B.4.a: Find the inverse of a function when the given function is one-to-one.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1.b: Combine standard function types using arithmetic operations.
A2.F.BF.A.1.b: Combine standard function types using arithmetic operations.
2
Unit 2
Quadratics
A2.N.CN.A.2: Know and use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
A2.N.CN.A.2: Know and use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
A2.N.CN.A.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.
A2.N.CN.A.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.
A2.A.REI.B.3: Solve quadratic equations and inequalities in one variable.
A2.A.REI.B.3: Solve quadratic equations and inequalities in one variable.
A2.A.REI.B.3.a: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Equations
Inequalities
A2.A.REI.B.3.a: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Equations
Inequalities
A2.N.CN.B.3: Solve quadratic equations with real coefficients that have complex solutions.
A2.N.CN.B.3: Solve quadratic equations with real coefficients that have complex solutions.
A2.A.REI.C.5: Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
A2.A.REI.C.5: Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
A2.N.Q.A.1: Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling.
A2.N.Q.A.1: Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
3
Unit 3
Polynomials
A2.A.APR.A.2: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
A2.A.APR.A.2: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.
A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.
A2.F.IF.B.3.b: Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
A2.F.IF.B.3.b: Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
A2.F.IF.A.1: For 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.
A2.F.IF.A.1: For 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.
A2.F.IF.A.2: Calculate 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.
A2.F.IF.A.2: Calculate 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.
A2.A.APR.A.1: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
A2.A.APR.A.1: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
A2.A.APR.C.4: Rewrite rational expressions in different forms.
A2.A.APR.C.4: Rewrite rational expressions in different forms.
A2.A.SSE.A.1: Use the structure of an expression to identify ways to rewrite it.
Factor quadratics
Factor polynomials
A2.A.SSE.A.1: Use the structure of an expression to identify ways to rewrite it.
Factor quadratics
Factor polynomials
A2.F.BF.B.3: 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.
Translations
Reflections
Dilations
Mixed transformations
A2.F.BF.B.3: 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.
Translations
Reflections
Dilations
Mixed transformations
A2.A.APR.B.3: Know and use polynomial identities to describe numerical relationships.
A2.A.APR.B.3: Know and use polynomial identities to describe numerical relationships.
A2.A.REI.D.6: 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 approximate solutions using technology.
A2.A.REI.D.6: 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 approximate solutions using technology.
A2.F.IF.B.5: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
A2.F.IF.B.5: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
4
Unit 4
Rational Expressions and Equations
A2.A.APR.C.4: Rewrite rational expressions in different forms.
A2.A.APR.C.4: Rewrite rational expressions in different forms.
A2.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.

A2.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
A2.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.

A2.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
A2.A.REI.A.1: Explain 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.
A2.A.REI.A.1: Explain 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.
A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1.b: Combine standard function types using arithmetic operations.
A2.F.BF.A.1.b: Combine standard function types using arithmetic operations.
5
Unit 5
Radicals and Rational Exponents
A2.N.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
A2.N.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
A2.N.RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Radical expressions
Rational exponents
A2.N.RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Radical expressions
Rational exponents
A2.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.
A2.A.REI.A.2: Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.
A2.A.REI.A.1: Explain 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.
A2.A.REI.A.1: Explain 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.
A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.
A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.
A2.F.IF.B.3.a: Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions.
A2.F.IF.B.3.a: Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions.
6
Unit 6
Exponential and Logarithmic Functions
A2.A.SSE.B.2: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A2.A.SSE.B.2: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A2.A.SSE.B.2.a: Use the properties of exponents to rewrite expressions for exponential functions.
A2.A.SSE.B.2.a: Use the properties of exponents to rewrite expressions for exponential functions.
A2.F.IF.B.4: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
A2.F.IF.B.4: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
A2.F.IF.B.4.a: Know and use the properties of exponents to interpret expressions for exponential functions.
A2.F.IF.B.4.a: Know and use the properties of exponents to interpret expressions for exponential functions.
A2.F.LE.B.3: Interpret the parameters in a linear or exponential function in terms of a context.
A2.F.LE.B.3: Interpret the parameters in a linear or exponential function in terms of a context.
A2.A.SSE.A.1: Use the structure of an expression to identify ways to rewrite it.
A2.A.SSE.A.1: Use the structure of an expression to identify ways to rewrite it.
A2.F.LE.A.2: 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.
Exponential and logarithmic form
Exponential equations
A2.F.LE.A.2: 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.
Exponential and logarithmic form
Exponential equations
A2.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
A2.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A2.A.CED.A.2: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A2.A.REI.D.6: 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 approximate solutions using technology.
A2.A.REI.D.6: 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 approximate solutions using technology.
A2.F.IF.A.2: Calculate 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.
A2.F.IF.A.2: Calculate 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.
A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.
A2.F.IF.B.3: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.
A2.F.IF.B.3.c: Graph exponential and logarithmic functions, showing intercepts and end behavior.
A2.F.IF.B.3.c: Graph exponential and logarithmic functions, showing intercepts and end behavior.
A2.F.IF.A.1: For 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.
A2.F.IF.A.1: For 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.
A2.F.BF.B.3: 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.
A2.F.BF.B.3: 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.
A2.F.IF.B.5: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
A2.F.IF.B.5: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
7
Unit 7
Sequences and Series
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1: Write a function that describes a relationship between two quantities.
A2.F.BF.A.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
A2.F.BF.A.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
A2.F.BF.A.2: Know and write arithmetic and geometric sequences with an explicit formula and use them to model situations.
A2.F.BF.A.2: Know and write arithmetic and geometric sequences with an explicit formula and use them to model situations.
A2.F.LE.A.1: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.
A2.F.LE.A.1: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.
A2.A.SSE.B.3: Recognize a finite geometric series (when the common ratio is not 1), and know and use the sum formula to solve problems in context.
A2.A.SSE.B.3: Recognize a finite geometric series (when the common ratio is not 1), and know and use the sum formula to solve problems in context.
8
Unit 8
Trigonometry
A2.F.TF.A.1: Understand and use radian measure of an angle.
A2.F.TF.A.1: Understand and use radian measure of an angle.
A2.F.TF.A.1.a: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
A2.F.TF.A.1.a: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
A2.F.TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
A2.F.TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
A2.F.TF.A.1: Understand and use radian measure of an angle.
A2.F.TF.A.1: Understand and use radian measure of an angle.
A2.F.TF.A.1.b: Use the unit circle to find sin θ, cos θ, and tan θ when θ is a commonly recognized angle between 0 and 2π.
A2.F.TF.A.1.b: Use the unit circle to find sin θ, cos θ, and tan θ when θ is a commonly recognized angle between 0 and 2π.
A2.F.TF.B.3: Know and use trigonometric identities to to find values of trig functions.
A2.F.TF.B.3: Know and use trigonometric identities to to find values of trig functions.
A2.F.TF.B.3.a: Given a point on a circle centered at the origin, recognize and use the right triangle ratio definitions of sin θ, cos θ, and tan θ to evaluate the trigonometric functions.
A2.F.TF.B.3.a: Given a point on a circle centered at the origin, recognize and use the right triangle ratio definitions of sin θ, cos θ, and tan θ to evaluate the trigonometric functions.
A2.F.TF.B.3.b: Given the quadrant of the angle, use the identity sin² θ + cos² θ = 1 to find sin θ given cos θ, or vice versa.
A2.F.TF.B.3.b: Given the quadrant of the angle, use the identity sin² θ + cos² θ = 1 to find sin θ given cos θ, or vice versa.
9
Unit 9
Probability
A2.S.CP.A.1: 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").
A2.S.CP.A.1: 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").
A2.S.CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
A2.S.CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
A2.S.CP.A.3: Know and 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.
A2.S.CP.A.3: Know and 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.
A2.S.CP.A.4: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
A2.S.CP.A.4: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
A2.S.CP.B.5: 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.
A2.S.CP.B.5: 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.
A2.S.CP.B.6: Know and 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.
A2.S.CP.B.6: Know and 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.
10
Unit 10
Statistics
A2.S.IC.A.1: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
A2.S.IC.A.1: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
A2.S.IC.A.2: Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.
A2.S.IC.A.2: Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.
A2.S.ID.A.1: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.
A2.S.ID.A.1: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.
A2.S.ID.B.2: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
A2.S.ID.B.2: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
A2.S.ID.B.2.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
A2.S.ID.B.2.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
11
Unit 11
Skills Reinforcement for 4th-Year Math and ACT
Final Exam Review
Review skills from previous weeks. Or, use the IXL Real-Time Diagnostic to receive a personalized action plan for each student.
Final Exam Review
Review skills from previous weeks. Or, use the IXL Real-Time Diagnostic to receive a personalized action plan for each student.