Algebra II
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Algebra II
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A.APR.3Arithmetic With Polynomials And Rational ExpressionsUnderstand The Relationship Between Zeros And Factors Of PolynomialsIdentify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
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A.APR.4Arithmetic With Polynomials And Rational ExpressionsUse Polynomial Identities To Solve ProblemsProve polynomial identities and use them to describe numerical relationships.
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A.REI.11Reasoning With Equations And InequalitiesRepresent And Solve Equations And Inequalities GraphicallyExplain 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.★
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A.REI.12Reasoning With Equations And InequalitiesRepresent And Solve Equations And Inequalities GraphicallyGraph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
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A.REI.2Reasoning With Equations And InequalitiesUnderstand Solving Equations As A Process Of Reasoning And Explain The ReasoningSolve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
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A.REI.4.aReasoning With Equations And InequalitiesSolve Equations And Inequalities In One VariableUse the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
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A.REI.5Reasoning With Equations And InequalitiesSolve Systems Of EquationsProve that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
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A.REI.6Reasoning With Equations And InequalitiesSolve Systems Of EquationsSolve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables.
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A.REI.7Reasoning With Equations And InequalitiesSolve Systems Of EquationsSolve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
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A.SSE.3.bSeeing Structure In ExpressionsWrite Expressions In Equivalent Forms To Solve ProblemsComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
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A.SSE.3.cSeeing Structure In ExpressionsWrite Expressions In Equivalent Forms To Solve ProblemsUse the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
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A.SSE.4Seeing Structure In ExpressionsWrite Expressions In Equivalent Forms To Solve ProblemsDerive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
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F.BF.1Building FunctionsBuild A Function That Models A Relationship Between Two QuantitiesWrite a function that describes a relationship between two quantities.
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F.BF.1.aBuilding FunctionsBuild A Function That Models A Relationship Between Two QuantitiesDetermine an explicit expression, a recursive process, or steps for calculation from a context.
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F.BF.1.bBuilding FunctionsBuild A Function That Models A Relationship Between Two QuantitiesCombine standard function types using arithmetic operations.
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F.BF.2Building FunctionsBuild A Function That Models A Relationship Between Two QuantitiesWrite arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★
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F.BF.3Building FunctionsBuild New Functions From Existing FunctionsIdentify 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.
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F.BF.4Building FunctionsBuild New Functions From Existing FunctionsFind inverse functions.
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F.BF.4.aBuilding FunctionsBuild New Functions From Existing FunctionsSolve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
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F.IF.3Interpreting FunctionsUnderstand The Concept Of A Function And Use Function NotationRecognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
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F.IF.4Interpreting FunctionsInterpret Functions That Arise In Applications In Terms Of The ContextFor a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★
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F.IF.6Interpreting FunctionsInterpret Functions That Arise In Applications In Terms Of The ContextCalculate 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.★
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F.IF.7.bInterpreting FunctionsAnalyze Functions Using Different RepresentationsGraph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
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F.IF.7.cInterpreting FunctionsAnalyze Functions Using Different RepresentationsGraph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
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F.IF.7.eInterpreting FunctionsAnalyze Functions Using Different RepresentationsGraph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
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F.IF.8Interpreting FunctionsAnalyze Functions Using Different RepresentationsWrite a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
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F.IF.8.aInterpreting FunctionsAnalyze Functions Using Different RepresentationsUse the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
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F.IF.8.bInterpreting FunctionsAnalyze Functions Using Different RepresentationsUse the properties of exponents to interpret expressions for exponential functions.
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F.IF.9Interpreting FunctionsAnalyze Functions Using Different RepresentationsCompare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
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F.LE.1Linear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsDistinguish between situations that can be modeled with linear functions and with exponential functions.
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F.LE.1.aLinear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsProve that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
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F.LE.1.bLinear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsRecognize situations in which one quantity changes at a constant rate per unit interval relative to another.
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F.LE.1.cLinear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsRecognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
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F.LE.2Linear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsConstruct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
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F.LE.3Linear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsObserve using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
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F.LE.4Linear, Quadratic, And Exponential Models★Construct And Compare Linear, Quadratic, And Exponential Models And Solve ProblemsFor exponential models, express as a logarithm the solution to abct =dwherea,c,anddarenumbersandthebasebis2,10,ore; evaluate the logarithm using technology.
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F.LE.5Linear, Quadratic, And Exponential Models★Interpret Expressions For Functions In Terms Of The Situation They ModelInterpret the parameters in a linear or exponential function in terms of a context.
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F.TF.1Trigonometric FunctionsExtend The Domain Of Trigonometric Functions Using The Unit CircleUnderstand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
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F.TF.2Trigonometric FunctionsExtend The Domain Of Trigonometric Functions Using The Unit CircleExplain 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.
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F.TF.5Trigonometric FunctionsModel Periodic Phenomena With Trigonometric FunctionsChoose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★
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F.TF.8Trigonometric FunctionsProve And Apply Trigonometric IdentitiesProve the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to calculate trigonometric ratios.
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G.GPE.2Expressing Geometric Properties With EquationsTranslate Between The Geometric Description And The Equation For A Conic SectionDerive the equation of a parabola given a focus and directrix.
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N.CN.1The Complex Number SystemPerform Arithmetic Operations With Complex Numbers.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.
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N.CN.2The Complex Number SystemPerform Arithmetic Operations With Complex Numbers.Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
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N.CN.7The Complex Number SystemUse Complex Numbers In Polynomial Identities And Equations.Solve quadratic equations with real coefficients that have complex solutions.
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N.Q .1QuantitiesReason Quantitatively And Use Units To Solve Problems.Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
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N.RN.1The Real Number SystemExtend The Properties Of Exponents To Rational Exponents.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.
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N.RN.2The Real Number SystemExtend The Properties Of Exponents To Rational Exponents.Rewrite expressions involving radicals and rational exponents using the properties of exponents.
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N.RN.3The Real Number SystemUse Properties Of Rational And Irrational Numbers.Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
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N.VM.4.aVector And Matrix QuantitiesPerform Operations On Vectors.Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
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N.VM.4.bVector And Matrix QuantitiesPerform Operations On Vectors.Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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N.VM.4.cVector And Matrix QuantitiesPerform Operations On Vectors.Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
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N.VM.5.aVector And Matrix QuantitiesPerform Operations On Vectors.Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g. as c(vx, vy) = (cvx, cvy).
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N.VM.5.bVector And Matrix QuantitiesPerform Operations On Vectors.Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
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S.CP.1Conditional Probability And The Rules Of ProbabilityUnderstand Independence And Conditional Probability And Use Them To Interpret DataDescribe 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”).
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S.CP.3Conditional Probability And The Rules Of ProbabilityUnderstand Independence And Conditional Probability And Use Them To Interpret DataUnderstand 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.
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S.CP.4Conditional Probability And The Rules Of ProbabilityUnderstand Independence And Conditional Probability And Use Them To Interpret DataConstruct 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.
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S.CP.6Conditional Probability And The Rules Of ProbabilityUse The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability ModelFind 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.
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S.CP.7Conditional Probability And The Rules Of ProbabilityUse The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability ModelApply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
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S.IC.2Making Inferences And Justifying ConclusionsUnderstand And Evaluate Random Processes Underlying Statistical ExperimentsDecide if a specified model is consistent with results from a given data-generating process, e.g. using simulation.
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S.IC.3Making Inferences And Justifying ConclusionsMake Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational StudiesRecognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
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S.IC.4Making Inferences And Justifying ConclusionsMake Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational StudiesUse data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
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S.IC.5Making Inferences And Justifying ConclusionsMake Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational StudiesUse data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
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S.IC.6Making Inferences And Justifying ConclusionsMake Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational StudiesEvaluate reports based on data.
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S.ID.5Interpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On Two Categorical And Quantitative VariablesSummarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
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S.ID.6.aInterpreting Categorical And Quantitative DataSummarize, Represent, And Interpret Data On Two Categorical And Quantitative VariablesFit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
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S.MD.5.bUsing Probability To Make DecisionsUse Probability To Evaluate Outcomes Of DecisionsEvaluate and compare strategies on the basis of expected values.
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Complete Standards
Investigations and Functions
Transformation of Parent Graphs
Sheet12
Equivalent Forms
Solving and Intersections
Inverses and Logarithms
3-D Graphs and Logarithms
Trigonometric Functions
Polynomials
Randomization and Normal Distributions
Series
Simulating Sampling Variability
Analytic Trigonometry
 
 
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