West Virginia

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Skills available for West Virginia Algebra 2 standards

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College- and Career-Readiness Standards: Algebra II College- and Career-Readiness Standards: Algebra II
College- and Career-Readiness Standards: Mathematics I College- and Career-Readiness Standards: Mathematics I
College- and Career-Readiness Standards: Mathematics II College- and Career-Readiness Standards: Mathematics II
College- and Career-Readiness Standards: Mathematics III LA College- and Career-Readiness Standards: Mathematics III LA
College- and Career-Readiness Standards: Mathematics III STEM College- and Career-Readiness Standards: Mathematics III STEM
College- and Career-Readiness Standards: Mathematics III Technical Readiness College- and Career-Readiness Standards: Mathematics III Technical Readiness
College- and Career-Readiness Standards: Mathematics IV Technical Readiness College- and Career-Readiness Standards: Mathematics IV Technical Readiness
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics III West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics III
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics IV West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics IV
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics STEM Readiness West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics STEM Readiness
West Virginia Next Generation Content Standards and Objectives (Common Core): Transition Mathematics for Seniors West Virginia Next Generation Content Standards and Objectives (Common Core): Transition Mathematics for Seniors

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10-11.M.3HS.IC Inferences and Conclusions from Data

10-11. Summarize, represent, and interpret data on a single count or measurement variable
- 10-11.M.3HS.IC.1 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
10-11. Understand and evaluate random processes underlying statistical experiments
- 10-11.M.3HS.IC.2 understand that statistics allows inferences to be made about population parameters based on a random sample from that population.
- 10-11.M.3HS.IC.3 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
10-11. Make inferences and justify conclusions from sample surveys, experiments, and observational studies
- 10-11.M.3HS.IC.4 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
  - Experiment design (A2-FF.12)
  - Experiment design (PC-Z.15)
- 10-11.M.3HS.IC.5 Use 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.
- 10-11.M.3HS.IC.6 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
  - Analyze the results of an experiment using simulations (A2-FF.13)
  - Analyze the results of an experiment using simulations (PC-Z.16)
- 10-11.M.3HS.IC.7 Evaluate reports based on data.
10-11. Use probability to evaluate outcomes of decisions
- 10-11.M.3HS.IC.8 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
- 10-11.M.3HS.IC.9 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
  - Choose the better bet (A2-EE.9)
  - Choose the better bet (PC-Y.9)

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10-11.M.3HS.IC Inferences and Conclusions from Data

10-11. Summarize, represent, and interpret data on a single count or measurement variable

10-11. Understand and evaluate random processes underlying statistical experiments

10-11.M.3HS.IC.2 understand that statistics allows inferences to be made about population parameters based on a random sample from that population.

10-11.M.3HS.IC.3 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

10-11. Make inferences and justify conclusions from sample surveys, experiments, and observational studies

10-11.M.3HS.IC.4 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

10-11.M.3HS.IC.5 Use 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.

10-11.M.3HS.IC.6 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

10-11.M.3HS.IC.7 Evaluate reports based on data.

10-11. Use probability to evaluate outcomes of decisions

10-11.M.3HS.IC.8 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

10-11.M.3HS.IC.9 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

10-11.M.3HS.PR Polynomials, Radical Relationships

10-11. Use complex numbers in polynomial identities and equations.

10-11.M.3HS.PR.1 Extend polynomial identities to the complex numbers.

10-11.M.3HS.PR.2 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

10-11. Interpret the structure of expressions

10-11.M.3HS.PR.3 Interpret expressions that represent a quantity in terms of its context.

10-11.M.3HS.PR.3.a Interpret parts of an expression, such as terms, factors, and coefficients.

10-11.M.3HS.PR.3.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

10-11.M.3HS.PR.4 Use the structure of an expression to identify ways to rewrite it.

10-11. Write expressions in equivalent forms to solve problems

10-11.M.3HS.PR.5 derive the formula for the sum of a geometric series (when the common ratio is not 1), and use the formula to solve problems.

10-11. Perform arithmetic operations on polynomials

10-11.M.3HS.PR.6 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

10-11. Understand the relationship between zeros and factors of polynomials

10-11.M.3HS.PR.7 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).

10-11.M.3HS.PR.8 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.

10-11. Use polynomial identities to solve problems

10-11.M.3HS.PR.9 Prove polynomial identities and use them to describe numerical relationships.

10-11.M.3HS.PR.10 Know and apply the Binomial Theorem for the expansion of (x + y) to the n power 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.

10-11. Rewrite rational expressions

10-11.M.3HS.PR.12 Understand 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.

10-11. Understand solving equations as a process of reasoning and explain the reasoning

10-11.M.3HS.PR.13 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

10-11. Represent and solve equations and inequalities graphically

10-11. Analyze functions using different representations

10-11.M.3HS.PR.15 graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.

10-11.M.3HS.TF Trigonometry of General Triangles and Trigonometric Functions

10-11. Apply trigonometry to general triangles

10-11.M.3HS.TF.1 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

10-11.M.3HS.TF.2 Prove the Laws of Sines and Cosines and use them to solve problems.

10-11.M.3HS.TF.3 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).

10-11. Extend the domain of trigonometric functions using the unit circle

10-11.M.3HS.TF.4 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

10-11.M.3HS.TF.5 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.

10-11. Model periodic phenomena with trigonometric functions

10-11.M.3HS.TF.6 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

10-11.M.3HS.MM Mathematical Modeling

10-11. Create equations that describe numbers or relationships

10-11.M.3HS.MM.1 Create equations and inequalities in one variable and use them to solve problems.

10-11.M.3HS.MM.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

10-11.M.3HS.MM.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

10-11.M.3HS.MM.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

10-11. Interpret functions that arise in applications in terms of the context

10-11.M.3HS.MM.5 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.

10-11.M.3HS.MM.6 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

10-11.M.3HS.MM.7 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.

10-11. Analyze functions using different representations

10-11.M.3HS.MM.8 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

10-11.M.3HS.MM.8.a Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

10-11.M.3HS.MM.8.b Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

10-11.M.3HS.MM.9 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

10-11.M.3HS.MM.10 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

10-11. Build a function that models a relationship between two quantities

10-11.M.3HS.MM.11 write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations.

10-11. Build new functions from existing functions

10-11.M.3HS.MM.13 find inverse functions. 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.

10-11. Construct and compare linear, quadratic, and exponential models and solve problems

10-11.M.3HS.MM.14 For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

10-11. Visualize relationships between two-dimensional and three-dimensional objects

10-11.M.3HS.MM.15 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

10-11. Apply geometric concepts in modeling situations

10-11.M.3HS.MM.16 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

10-11.M.3HS.MM.17 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

10-11.M.3HS.MM.18 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).