Idaho

N Number and quantity

• N.CN The Complex Number System

  • N.CN.C Use complex numbers in polynomial identities and equations.

    • N.CN.C.8 (+) Extend polynomial identities to the complex numbers.

      • Solve polynomial equations (A2-L.8)
      • Complex conjugate theorem (PC-D.7)
      • Conjugate root theorems (PC-D.8)

    • N.CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

      • Fundamental Theorem of Algebra (A2-L.17)

A Algebra

• A.SSE Seeing Structure in Expressions

  • A.SSE.A Interpret the structure of linear, quadratic, exponential, polynomial, and rational expressions.

    • A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

      • A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

        • Interpret parts of quadratic expressions: word problems (A2-K.)
        • Polynomial vocabulary (A2-L.1)

      • A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

        • Interpret parts of quadratic expressions: word problems (A2-K.)

    • A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

      • Factor out a monomial (A2-J.1)
      • Factor using a quadratic pattern (A2-J.4)
      • Pascal's triangle and the Binomial Theorem (A2-L.19)
      • Binomial Theorem I (A2-L.20)
      • Binomial Theorem II (A2-L.21)
      • Simplify radical expressions with variables I (A2-M.4)
      • Simplify radical expressions with variables II (A2-M.5)
      • Simplify radical expressions using conjugates (A2-M.11)
      • Simplify rational expressions (A2-O.4)

  • A.SSE.B Write expressions in equivalent forms to solve problems.

    • A.SSE.B.4 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.

      • Find the sum of a finite geometric series (A2-CC.16)

• A.APR Arithmetic with Polynomials and Rational Expressions

  • A.APR.A Perform arithmetic operations on polynomials.

    • A.APR.A.1 Demonstrate understanding that polynomials form a system analogous to the integers; namely, they are closed under certain operations.

      • A.APR.A.1.a Perform operations on polynomial expressions (addition, subtraction, multiplication, division) and compare the system of polynomials to the system of integers when performing operations.

        • Add and subtract polynomials (A2-L.2)
        • Multiply polynomials (A2-L.3)
        • Divide polynomials using long division (A2-L.4)
        • Divide polynomials using synthetic division (A2-L.5)

      • A.APR.A.1.b Factor and/or expand polynomial expressions, identify and combine like terms, and apply the distributive property.

        • Factor out a monomial (A2-J.1)
        • Factor quadratics using algebra tiles (A2-J.2)
        • Factor quadratics (A2-J.3)
        • Factor using a quadratic pattern (A2-J.4)
        • Factor by grouping (A2-J.5)
        • Factor sums and differences of cubes (A2-J.6)
        • Factor polynomials (A2-J.7)

  • A.APR.B Understand the relationship between zeros and factors of polynomials.

    • A.APR.B.2 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).

      • Write a quadratic function from its zeros (A2-K.16)
      • Evaluate polynomials using synthetic division (A2-L.7)
      • Find the roots of factored polynomials (A2-L.9)
      • Write a polynomial from its roots (A2-L.10)

    • A.APR.B.3 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.

      • Solve a quadratic equation using the zero product property (A2-K.7)
      • Match quadratic functions and graphs (A2-K.14)
      • Find the roots of factored polynomials (A2-L.9)
      • Match polynomials and graphs (A2-L.15)

  • A.APR.C Use polynomial identities to solve problems.

    • A.APR.C.4 Prove polynomial identities and use them to describe numerical relationships.

      • Factor sums and differences of cubes (A2-J.6)
      • Add and subtract polynomials (A2-L.2)
      • Multiply polynomials (A2-L.3)
      • Solve equations with sums and differences of cubes (PC-D.14)

    • A.APR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal's Triangle.

      • Pascal's triangle (A2-L.18)
      • Pascal's triangle and the Binomial Theorem (A2-L.19)
      • Binomial Theorem I (A2-L.20)
      • Binomial Theorem II (A2-L.21)

  • A.APR.D Rewrite rational expressions.

    • A.APR.D.6 Rewrite simple rational expressions in different forms using inspection, long division, or, for the more complicated examples, a computer algebra system.

      • Divide polynomials by monomials (A1-HH.4)
      • Divide polynomials using long division (A2-L.4)
      • Simplify rational expressions (A2-O.4)

    • A.APR.D.7 (+) Demonstrate understanding that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

      • Multiply and divide rational expressions (A2-O.5)
      • Add and subtract rational expressions (A2-O.6)

• A.CED Creating Equations

  • A.CED.A Create equations that describe numbers or relationships.

    • A.CED.A.1 Create one-variable equations and inequalities to solve problems, including linear, quadratic, rational, and exponential functions.

      • Write exponential functions: word problems (A2-T.)
      • Solve quadratic equations: word problems (PC-C.)

    • A.CED.A.2 Interpret the relationship between two or more quantities.

      • A.CED.A.2.a Define variables to represent the quantities and write equations to show the relationship.

        • Write the equation of a linear function (A2-D.10)
        • Write equations of parabolas in vertex form using properties (A2-U.6)
        • Write equations of sine functions using properties (A2-AA.3)
        • Write equations of cosine functions using properties (A2-AA.8)

      • A.CED.A.2.b Use graphs to show a visual representation of the relationship while adhering to appropriate labels and scales.

        • Graph a quadratic function (A2-K.5)
        • Graph sine functions (A2-AA.4)
        • Graph cosine functions (A2-AA.9)
        • Graph sine and cosine functions (A2-AA.14)

    • A.CED.A.3 Represent constraints using equations or inequalities and interpret solutions as viable or non-viable options in a modeling context.

      • Write a linear inequality: word problems (A2-C.3)

    • A.CED.A.4 Represent constraints using systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.

      • Solve a system of equations by graphing: word problems (A2-E.3)
      • Solve a system of equations using substitution: word problems (A2-E.7)
      • Solve a system of equations using elimination: word problems (A2-E.9)
      • Solve a system of equations using any method: word problems (A2-E.11)

    • A.CED.A.5 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

      • Solve multi-variable equations (A2-B.6)

• A.REI Reasoning with Equations and Inequalities

  • A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.

    • A.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

      • Solve radical equations (A2-M.14)
      • Solve rational equations (A2-O.7)

  • A.REI.D Represent and solve equations and inequalities graphically.

    • A.REI.D.11 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. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

      • Find solutions using a table (A2-D.6)
      • Approximate solutions using a table (A2-D.7)
      • Solve a system of equations by graphing (A2-E.2)
      • Solve a system of equations by graphing: word problems (A2-E.3)
      • Find the number of solutions to a system of equations (A2-E.4)

F Functions

• F.IF Interpreting Functions

  • F.IF.B Interpret functions that arise in applications in terms of the context. Include linear, quadratic, exponential, rational, polynomial, square root and cube root, trigonometric, and logarithmic functions.

    • F.IF.B.4 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maxima and minima; symmetries; end behavior; and periodicity.

      • Identify graphs: word problems (A2-D.)
      • Find the slope of a linear function (A2-D.8)
      • Graph a linear function (A2-D.9)
      • Characteristics of quadratic functions: graphs (A2-K.1)
      • Characteristics of quadratic functions: equations (A2-K.2)
      • Graph a quadratic function (A2-K.5)
      • Match quadratic functions and graphs (A2-K.14)
      • Match polynomials and graphs (A2-L.15)
      • Rational functions: asymptotes and excluded values (A2-O.1)
      • Find the constant of variation (A2-R.5)
      • Match exponential functions and graphs (A2-T.4)

    • F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

      • Domain and range of polynomials (A2-L.16)
      • Domain and range of radical functions (A2-M.12)

    • F.IF.B.6 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.

      • Average rate of change (A2-D.12)

  • F.IF.C Analyze functions using different representations.

    • F.IF.C.7 Graph functions expressed symbolically and show key features of the graphs, by hand in simple cases and using technology for more complicated cases.

      • F.IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

        • Graph an absolute value function (A2-D.13)
        • Graph piecewise-defined functions (A2-D.17)

      • F.IF.C.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

        • Graph quadratic functions in standard form (A1-CC.14)
        • Graph a quadratic function (A2-K.5)
        • Match polynomials and graphs (A2-L.15)

      • F.IF.C.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

        • Graph exponential functions (A2-T.3)
        • Match exponential functions and graphs (A2-T.4)
        • Graph logarithmic functions (A2-T.)
        • Find properties of sine functions (A2-AA.1)
        • Graph sine functions (A2-AA.4)
        • Graph translations of sine functions (A2-AA.5)
        • Find properties of cosine functions (A2-AA.6)
        • Graph cosine functions (A2-AA.9)
        • Graph translations of cosine functions (A2-AA.10)
        • Graph sine and cosine functions (A2-AA.14)
        • Graph translations of sine and cosine functions (A2-AA.15)

    • F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

      • F.IF.C.8.a Use the process of factoring and/or completing the square in quadratic and polynomial functions, where appropriate, to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

        • Characteristics of quadratic functions: graphs (A2-K.1)
        • Solve a quadratic equation by factoring (A2-K.8)
        • Solve a quadratic equation by completing the square (A2-K.10)

      • F.IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as identifying appreciation and depreciation rate for the value of a house or car sometime after its initial purchase.

        • Evaluate exponential functions (A2-T.2)
        • Match exponential functions and graphs (A2-T.4)
        • Solve exponential equations by rewriting the base (A2-T.5)

    • F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

    • F.IF.C.10 Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial, rational, logarithmic, exponential, or trigonometric.

      • Identify linear and exponential functions (A2-T.11)

• F.BF Building Functions

  • F.BF.A Build a function that models a relationship between two quantities.

    • F.BF.A.1 Write a function that describes a relationship between two quantities. Functions could include linear, exponential, quadratic, simple rational, radical, logarithmic, and trigonometric.

      • F.BF.A.1.b Combine standard function types using arithmetic operations.

        • Add and subtract polynomials (A2-L.2)
        • Multiply polynomials (A2-L.3)
        • Multiply and divide rational expressions (A2-O.5)
        • Add and subtract rational expressions (A2-O.6)
        • Add, subtract, multiply, and divide functions (PC-A.10)

  • F.BF.B Build new functions from existing functions.

    • F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f (kx), and f (x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include, linear, quadratic, exponential, absolute value, simple rational and radical, logarithmic, and trigonometric functions. Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

      • Function transformation rules (A2-Q.1)
      • Translations of functions (A2-Q.2)
      • Reflections of functions (A2-Q.3)
      • Dilations of functions (A2-Q.4)
      • Transformations of functions (A2-Q.5)
      • Describe function transformations (A2-Q.6)

    • F.BF.B.4 Find inverse functions algebraically and graphically.

      • F.BF.B.4.a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. Include linear and simple polynomial, rational, and exponential functions.

        • Find inverse functions and relations (A2-P.11)
        • Solve exponential equations using common logarithms (A2-T.6)
        • Solve exponential equations using natural logarithms (A2-T.7)
        • Solve logarithmic equations I (A2-T.8)
        • Solve logarithmic equations II (A2-T.9)

• F.LE Linear, Quadratic, and Exponential Models

  • F.LE.A Construct and compare linear, quadratic, and exponential models and solve problems.

    • F.LE.A.4 For exponential models, express as a logarithm the solution to ab^ct = d where a, c and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

      • Convert between exponential and logarithmic form: rational bases (A2-S.1)
      • Convert between natural exponential and logarithmic form (A2-S.2)
      • Convert between exponential and logarithmic form: all bases (A2-S.3)
      • Evaluate logarithms (A2-S.4)
      • Solve exponential equations using common logarithms (A2-T.6)
      • Solve exponential equations using natural logarithms (A2-T.7)

• F.TF Trigonometric Functions

  • F.TF.A Extend the domain of trigonometric functions using the unit circle.

    • F.TF.A.1 Demonstrate radian measure as the ratio of the arc length subtended by a central angle to the length of the radius of the unit circle.

      • F.TF.A.1.a Use radian measure to solve problems.

        • Convert between radians and degrees (A2-Y.1)
        • Radians and arc length (A2-Y.2)
        • Sin, cos, and tan of special angles (A2-Z.7)
        • Inverses of sin, cos, and tan: radians (A2-Z.12)

    • 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.

      • Coterminal angles (A2-Y.5)
      • Reference angles (A2-Y.6)
      • Find trigonometric ratios using the unit circle (A2-Z.6)

  • F.TF.B Model periodic phenomena with trigonometric functions.

    • F.TF.B.5 Model periodic phenomena using trigonometric functions with specified amplitude, frequency, and midline.

      • Find properties of sine functions (A2-AA.1)
      • Write equations of sine functions from graphs (A2-AA.2)
      • Write equations of sine functions using properties (A2-AA.3)
      • Find properties of cosine functions (A2-AA.6)
      • Write equations of cosine functions from graphs (A2-AA.7)
      • Write equations of cosine functions using properties (A2-AA.8)

G Geometry

• G.SRT Similarity, Right Triangles, and Trigonometry

  • G.SRT.D Apply trigonometry to general triangles.

    • G.SRT.D.9 (+) Derive the formula A = ½ absin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

      • Area of a triangle: sine formula (A2-Z.22)

    • G.SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.

      • Law of Sines (A2-Z.19)
      • Law of Cosines (A2-Z.20)
      • Area of a triangle: Law of Sines (A2-Z.23)

    • G.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems; resultant forces).

      • Solve a triangle (A2-Z.21)

• G.GMD Geometric Measurement and Dimension

  • G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects.

    • G.GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

      • Cross sections of three-dimensional figures (G-H.4)
      • Solids of revolution (G-H.5)

• G.MG Modeling with Geometry

  • G.MG.A Apply geometric concepts in modeling situations.

    • G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects.

      • Pythagorean theorem (G-Q.1)

    • G.MG.A.2 Apply concepts of density based on area and volume in modeling situations.

      • Calculate density, mass, and volume (G-W.9)

    • G.MG.A.3 Apply geometric methods to solve design problems.

    • G.MG.A.4 Use dimensional analysis for unit conversions to confirm that expressions and equations make sense.

      • Convert rates and measurements: customary units (G-W.1)
      • Convert rates and measurements: metric units (G-W.2)

S Statistics and probability

• S.ID Interpreting Categorical and Quantitative Data

  • S.ID.A Summarize, represent, and interpret data on a single count or measurement variable. Use calculators, spreadsheets, and other technology as appropriate.

    • S.ID.A.4 Interpret differences in shape, center, and spread in the context of the variables accounting for possible effects of extreme data points (outliers) for measurement variables.

      • Find probabilities using the normal distribution I (A2-EE.11)
      • Find z-values (A2-EE.13)
      • Distributions of sample means (A2-EE.15)

• S.IC Making Inferences and Justifying Conclusions

  • S.IC.A Understand and evaluate random processes underlying statistical experiments. Use calculators, spreadsheets, and other technology as appropriate.

    • S.IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

      • Identify biased samples (A2-FF.1)

    • S.IC.A.2 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation or validation with given data).

  • S.IC.B Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

    • S.IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

      • Experiment design (A2-FF.12)

    • S.IC.B.4 Use data from a sample survey to estimate a population mean or proportion and a margin of error.

      • Find confidence intervals for population means (A2-FF.9)
      • Find confidence intervals for population proportions (A2-FF.10)

    • S.IC.B.5 Use data from a randomized and controlled experiment to compare two treatments; use margins of error to decide if differences between treatments are significant.

      • Analyze the results of an experiment using simulations (A2-FF.13)

    • S.IC.B.6 Evaluate reports of statistical information based on data.

      • Interpret confidence intervals for population means (A2-FF.11)
      • Analyze the results of an experiment using simulations (A2-FF.13)

• S.MD Using Probability to Make Decisions

  • S.MD.B Use probability to evaluate outcomes of decisions.

    • S.MD.B.6 Use probabilities to make objective decisions.

    • S.MD.B.7 Analyze decisions and strategies using probability concepts.

      • Choose the better bet (A2-EE.9)