A2.PS.1  Use a variety of problem solving strategies to understand new mathematical content

A2.PS.2  Recognize and understand equivalent representations of a problem situation or a mathematical concept

A2.PS.3  Observe and explain patterns to formulate generalizations and conjectures

A2.PS.4  Use multiple representations to represent  and explain problem situations (e.g., verbally, numerically, algebraically, graphically)

A2.PS.5  Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic)

A2.PS.6  Use a variety of strategies to extend solution methods to other problems

A2.PS.7  Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving

A2.PS.8  Determine information required to solve the problem, choose methods for obtaining the information, and define parameters for acceptable solutions

A2.PS.9  Interpret solutions within the given constraints of a problem

A2.PS.10 Evaluate the relative efficiency of different representations and solution methods of a problem

A2.RP.1  Support mathematical ideas using a variety of strategies

A2.RP.2  Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion

A2.RP.3  Evaluate conjectures and recognize when an estimate or approximation is more appropriate than an exact answer

A2.RP.4 Recognize when an approximation is more appropriate than an exact answer

A2.RP.5 Develop, verify, and explain an argument, using appropriate mathematical ideas and language

A2.RP.6  Construct logical arguments that verify claims or  counterexamples that refute claims

A2.RP.7  Present correct mathematical arguments in a variety of forms

A2.RP.8  Evaluate written arguments for validity

A2.RP.9  Support an argument by using a systematic approach to test more than one case

A2.RP.10 Devise ways to verify results, using counterexamples and informal indirect proof

A2.RP.11 Extend specific results to more general cases

A2.RP.12 Apply inductive reasoning in making and supporting mathematical conjectures

A2.CM.1  Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem

A2.CM.2  Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas,  functions, equations, charts, graphs, and diagrams

A2.CM.3   Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols  and other representations when sharing an idea in verbal and written form

A2.CM.4  Explain relationships among different representations of a problem

A2.CM.5  Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid

A2.CM.6  Support or reject arguments or questions raised by others about the correctness of mathematical work

A2.CM.7  Read and listen for logical understanding of mathematical thinking shared by other students

A2.CM.8  Reflect on strategies of others in relation to one’s own strategy

A2.CM.9  Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

A2.CM.10 Use correct mathematical language in developing mathematical questions that elicit, extend, or challenge other students’ conjectures

A2.CM.11 Represent word problems using standard mathematical  notation

A2.CM.12 Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale

A2.CM.13 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing  

A2.CN.1  Understand and make connections among multiple  representations of the same mathematical idea

A2.CN.2  Understand the corresponding procedures for similar problems or mathematical concepts

A2.CN.3  Model situations mathematically, using representations to draw conclusions and formulate new situations

A2.CN.4  Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics

A2.CN.5  Understand how quantitative models connect to various physical models and representations

A2.CN.6  Recognize and apply mathematics to

situations in the outside world

A2.CN.7  Recognize and apply mathematical ideas to problem situations that develop outside of mathematics

A2.CN.8  Develop an appreciation for the historical development of mathematics

A2.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts

A2.R.2  Recognize, compare, and use an array of representational forms

A2.R.3 Use representation as a tool for exploring and understanding mathematical ideas

A2.R.4  Select appropriate representations to solve problem situations

A2.R.5  Investigate relationships among different representations and their impact on a given problem

A2.R.6  Use mathematics to show and understand physical phenomena (e.g., investigate sound waves using the sine and cosine functions)

A2.R.7 Use mathematics to show and understand social phenomena (e.g., interpret the results of an opinion poll)

A2.R.8  Use mathematics to show and understand mathematical phenomena (e.g., use random number generator to simulate a coin  toss)

Algebra 2 and Trigonometry - Performance Indicators

Content Strands

Does the program/series support the development of the process/content in the performance indicator?

Are additional resources needed?

At what grade level is the indicator addressed?

Is the concept newly introduced this year?

A2.N.1  Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers)

A2.N.2  Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form

A2.N.3  Perform arithmetic operations with polynomial expressions containing rational coefficients

A2.N.4  Perform arithmetic operations on irrational expressions

A2.N.5  Rationalize a denominator containing a radical expression

A2.N.6  Write square roots of negative numbers in terms of i

A2.N.7  Simplify powers  of i

A2.N.8  Determine the conjugate of a complex number

A2.N.9  Perform arithmetic operations on complex numbers and write the answer in the form  Note: This includes simplifying expressions with complex denominators.

A2.N.10  Know and apply sigma notation

A2.A.1  Solve absolute value equations and inequalities involving linear expressions in one variable

A2.A.2  Use the discriminate to determine the nature of the roots of a quadratic equation

A2.A.3  Solve systems of equations involving one linear equation and one quadratic equation algebraically  Note: This includes rational equations that result in linear equations with extraneous roots.

A2.A.4   Solve quadratic inequalities in one and two variables, algebraically and graphically

A2.A.5  Use direct and inverse variation to solve for unknown values

A2.A.6  Solve an application which results in an exponential function

A2.A.7  Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic  trinomials

A2.A.8  Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents

A2.A.9  Rewrite algebraic expressions that contain negative exponents using only positive exponents

A2.A.10  Rewrite algebraic expressions with fractional exponents as radical expressions

A2.A.11  Rewrite algebraic expressions in radical form as expressions with fractional exponents

A2.A.12  Evaluate exponential expressions, including those with base e

A2.A.13  Simplify radical expressions

A2.A.14  Perform addition, subtraction, multiplication and division of radical expressions

A2.A.15 Rationalize denominators involving algebraic radical expressions

A2.A.16 Perform arithmetic operations with rational expressions and rename to lowest terms

A2.A.17 Simplify complex fractional expressions

A2.A.18 Evaluate logarithmic expressions in any base

A2.A.19 Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms

A2.A.20 Determine the sum and product of the roots of a quadratic equation by examining its coefficients

A2.A.21 Determine the quadratic equation, given the sum and product of its roots

A2.A.22 Solve radical equations

A2.A.23 Solve rational equations and inequalities

A2.A.24 Know and apply the technique of completing the square

A2.A.25 Solve quadratic equations, using the quadratic formula

A2.A.26 Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula

A2.A.27 Solve exponential equations with and without  common bases

A2.A.28 Solve a logarithmic equation by rewriting as an exponential equation

A2.A.29 Identify an arithmetic or geometric sequence and find the formula for its nth term

A2.A.30 Determine the common difference in an arithmetic sequence

A2.A.31 Determine the common ratio in a geometric sequence

A2.A.32 Determine a specified term of an arithmetic or geometric sequence

A2.A.33 Specify terms of a sequence, given its recursive definition

A2.A.34 Represent the sum of a series, using sigma notation

A2.A.35 Determine the sum of the first n terms of an arithmetic or geometric series

A2.A.36 Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion

A2.A.37 Define a relation and function

A2.A.38 Determine when a relation is a function

A2.A.39 Determine the domain and range of a function from its equation

A2.A.40 Write functions in functional notation

A2.A.41 Use functional notation to evaluate functions for given values in the domain

A2.A.42 Find the composition of functions

A2.A.43 Determine if a function is one-to-one, onto, or both

A2.A.44 Define the inverse  of a function

A2.A.45 Determine the inverse of a function and use composition to justify the result

A2.A.46 Perform transformations with functions and relations:

, , ,

,

A2.A.47 Determine the center-radius form for the equation of a circle in standard form

A2.A.48 Write the equation of a circle, given its center and a point on the circle

A2.A.49 Write the equation  of a circle from its graph

A2.A.50 Approximate the solution to polynomial equations of higher degree by inspecting the graph

A2.A.51 Determine the domain and range of a function from its graph

A2.A.52 Identify relations and functions, using graphs

A2.A.53 Graph exponential functions of the form  for positive values of b, including

A2.A.54 Graph logarithmic functions, using the inverse of the related exponential function

A2.A.55 Express and apply the six trigonometric functions as ratios of the sides of a right triangle

A2.A.56 Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles

A2.A.57 Sketch and use the reference angle for angles in standard position

A2.A.58 Know and apply the co-function and reciprocal relationships between trigonometric ratios

A2.A.59 Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles

A2.A.60 Sketch the unit circle and represent angles in standard position

A2.A.61 Determine the length of an arc of a circle, given its radius and the measure of its central angle

A2.A.62 Find the value of

trigonometric functions, if given a point on the terminal side of angle

A2.A.63 Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function  

A2.A.64 Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent

A2.A.65 Sketch the graph of the inverses of the sine, cosine, and tangent functions

A2.A.66 Determine the trigonometric functions of any angle, using technology

A2.A.67 Justify the Pythagorean identities

A2.A.68 Solve trigonometric equations for all values of the variable from 0º to 360º

A2.A.69 Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function

A2.A.70 Sketch and recognize one cycle of a function of the form  or

A2.A.71 Sketch and recognize the graphs of the functions ,

, , and

A2.A.72 Write the trigonometric function that is represented by a given periodic graph

A2.A.73 Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines

A2.A.74 Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle

A2.A.75 Determine the solution(s) from the SSA situation (ambiguous case)

A2.A.76 Apply the angle sum and difference formulas for trigonometric functions

A2.A.77 Apply the double-angle and half-angle formulas for trigonometric functions

A2.M.1 Define radian measure

A2.M.2  Convert between radian and degree measures

A2.S.1  Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment)

A2.S.2  Determine factors which may affect the outcome of a survey

A2.S.3  Calculate measures of central tendency with group frequency distributions

A2.S.4  Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations

A2.S.5  Know and apply the characteristics of the normal distribution

A2.S.6  Determine from a scatter plot whether a linear, logarithmic,   exponential, or power regression model is most appropriate

A2.S.7  Determine the function for the regression model, using appropriate technology, and use the regression function to interpolate and extrapolate from the data

A2.S.8  Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship   

A2.S.9  Differentiate between situations requiring permutations and those requiring combinations

A2.S.10 Calculate the number of possible permutations of n items taken r at a time

A2.S.11 Calculate the number of possible combinations of n items taken r at a time

A2.S.12 Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event)

A2.S.13 Calculate theoretical probabilities, including geometric applications

A2.S.14 Calculate empirical probabilities

A2.S.15 Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most

A2.S.16 Use the normal distribution as an approximation for binomial probabilities