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A2.NQ Number and Quantity
- A2.NQ.A Extend and use the relationship between rational exponents and radicals.
- A2.NQ.A.1 Extend the system of powers and roots to include rational exponents.
- A2.NQ.A.2 Create and recognize equivalent expressions involving radical and exponential forms of expressions.
- A2.NQ.A.3 Add, subtract, multiply and divide radical expressions.
- A2.NQ.A.4 Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
- A2.NQ.B Use complex numbers.
- A2.NQ.B.5 Represent complex numbers.
- A2.NQ.B.6 Add, subtract, multiply and divide complex numbers.
- A2.NQ.B.7 Know and apply the Fundamental Theorem of Algebra.
A2.SSE Seeing Structure in Expressions
- A2.SSE.A Define and use logarithms.
- A2.SSE.A.1 Develop the definition of logarithms based on properties of exponents.
- A2.SSE.A.2 Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.
- A2.SSE.A.3 Use properties of logarithms to solve equations or find equivalent expressions.
- A2.SSE.A.4 Understand why logarithmic scales are used, and use them to solve problems.
A2.REI Reasoning with Equations and Inequalities
- A2.REI.A Solve equations and inequalities.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.A.2 Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.
- A2.REI.B Solve general systems of equations and inequalities.
- A2.REI.B.3 Create and solve systems of equations that may include non-linear equations and inequalities.
A2.APR Arithmetic with Polynomials and Rational Expressions
- A2.APR.A Perform operations on polynomials and rational expressions.
- A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.
- A2.APR.A.2 Understand the Remainder Theorem and use it to solve problems.
- A2.APR.A.3 Find the least common multiple of two or more polynomials.
- A2.APR.A.4 Add, subtract, multiply and divide rational expressions.
- A2.APR.A.5 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.
A2.IF Interpreting Functions
- A2.IF.A Use and interpret functions.
- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.IF.A.2 Translate between equivalent forms of functions.
A2.BF Building Functions
- A2.BF.A Create new functions from existing functions.
- A2.BF.A.1 Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).
- A2.BF.A.2 Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.
- A2.BF.A.3 Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.
- A2.FM.A Use functions to model real-world problems.
- A2.FM.A.1 Create functions and use them to solve applications of quadratic and exponential function model problems.
A2.DS Data and Statistical Analysis
- A2.DS.A Make inferences and justify conclusions.
- A2.DS.A.1 Analyze how random sampling could be used to make inferences about population parameters.
- A2.DS.A.2 Determine whether a specified model is consistent with a given data set.
- A2.DS.A.3 Describe and explain the purposes, relationship to randomization and differences among sample surveys, experiments and observational studies.
- A2.DS.A.4 Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.
- A2.DS.A.5 Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.
- A2.DS.A.6 Analyze decisions and strategies using probability concepts.
- A2.DS.A.7 Evaluate reports based on data.
- A2.DS.B Fit a data set to a normal distribution.
- A2.DS.B.8 Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.
- A2.DS.B.9 Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.