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Algebra 2 and Trigonometry is the capstone course of the three units of credit required for a Regents diploma. This course is a continuation and extension of the two courses that preceded it. While developing the algebraic techniques that will be required of those students that continue their study of mathematics, this course is also intended to continue developing alternative solution strategies and algorithms. For example, technology can provide to many students the means to address a problem situation to which they might not otherwise have access. Within this course, the number system will be extended to include imaginary and complex numbers. The families of functions to be studied will include polynomial, absolute value, radical, trigonometric, exponential, and logarithmic functions. Problem situations involving direct and indirect variation will be solved. Problems resulting in systems of equations will be solved graphically and algebraically. Algebraic techniques will be developed to facilitate rewriting mathematical expressions into multiple equivalent forms. Data analysis will be extended to include measures of dispersion and the analysis of regression that model functions studied throughout this course. Associated correlation coefficients will be determined, using technology tools and interpreted as a measure of strength of the relationship. Arithmetic and geometric sequences will be expressed in multiple forms, and arithmetic and geometric series will be evaluated. Binomial experiments will provide the basis for the study of probability theory and the normal probability distribution will be analyzed and used as an approximation for these binomial experiments. Right triangle trigonometry will be expanded to include the investigation of circular functions. Problem situations requiring the use of trigonometric equations and identities will also be investigated.

CROSSWALK

Comparison of 1999 Core Curriculum and 2005 Core Curriculum for High School Mathematics
September 2005

The following chart lists the concepts and skills in Algebra (2005 Core) and indicates where it was included in the 1999 Core.

ALGEBRA 2 and Trigonometry

Number Sense and Operations Strand
2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.N.1	Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers)	Math B – 3D	Evaluate expressions with fractional exponents
A2.N.2	Perform arithmetic operations with expressions containing irrational numbers in radical form	Math A – 3A	Operate with radicals: simplification, multiplication and division, and addition and subtraction
A2.N.3	Perform arithmetic operations with polynomial expressions containing rational coefficients	Math A – 3A	Addition and subtraction of polynomials: combining like terms Multiplication of polynomials Division of polynomials by monomials
A2.N.4	Perform arithmetic operations on irrational expressions	Math A – 3A	Operations with radicals
A2.N.5	Rationalize a denominator containing a radical expression	Math B – 2A	Rationalize denominators

2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.N.6	Write square root of negative numbers in terms of i	Math B – 3D	Simplify square toots with negative radicands
A2.N.7	Simplify powers of i	Math B – 3D	Cyclic nature of the powers of i
A2.N.8	Determine the conjugate of a complex number		Implied by not directly stated
A2.N.9	Perform arithmetic operations on complex numbers	Math B – 3D	Basic arithmetic operations with complex numbers
A2.N.10	Know and apply sigma notation	Math B- 6F	Use of ∑-notation

ALGEBRA 2 and Trigonometry

Algebra Strand
2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.A.1	Solve absolute value equations and inequalities involving linear expressions in one variable	Math B- 7K	Solve equations using absolute values Absolute value inequalities
A2.A.2	Use the discriminate to determine the nature of the roots of a quadratic equation	Math B – 7I	Determine from the discriminant of a quadratic equation whether the roots are imaginary, rational, or irrational
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.	Math A – 7A Math A – 7E	Algebraic solution of systems of linear equations, inequalities, and quadratic-linear pair by substitution method and addition-subtraction method Solve systems of linear equations, inequalities, and quadratic-linear pair
A2.A.4	Solve quadratic inequalities in one and two variables, algebraically and graphically	Math B – 7K	Solve equations, using fractions, absolute values, and radicals · Linear inequalities · Quadratic inequalities
A2.A.5	Use direct and inverse variation to solve for unknown values		Not addressed
A2.A.6	Solve an application which results in an exponential function	Math B – 7E	Apply exponential functions in the solution of problems Solve real-world problems by using linear, exponential, and quadratic functions
A2.A.7	Factor polynomial expressions completely		Not specifically addressed

2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.A.8	Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents	Math B – 4B	Manipulate symbolic representations to explore concepts at an abstract level Use positive, negative, and zero exponents and be familiar with the laws used in working with expressions containing exponents
A2.A.9	Rewrite algebraic expressions that contain negative exponents using only positive exponents	Math B – 4B	Manipulate symbolic representations to explore concepts at an abstract level Use positive, negative, and zero exponents and be familiar with the laws used in working with expressions containing exponents
A2.A.10	Rewrite algebraic expressions with fractional exponents as radical expressions		Not specifically addressed
A2.A.11	Rewrite algebraic expressions in radical form as expressions with fractional exponents		Not specifically addressed
A2.A.12	Evaluate exponential expressions, including those with base e		Not addressed
A2.A.13	Simplify radical expressions	Math A – 3A	Simplification of fractions
A2.A.14	Perform addition, subtraction, multiplication, and division of radical expressions	Math A – 3A	Operations with radicals: multiplication and division and addition and subtraction
A2.A.15	Rationalize denominators involving algebraic radical expressions	Math B – 2A	Rationalize denominators

2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.A.16	Perform arithmetic operations with rational expressions and rename to lowest terms	Math B – 3A	Operations with fractions with polynomial denominators Add and subtract rational fractions with monomial and binomial denominators
A2.A.17	Simplify complex fractional expressions	Math A – 3A	Simplification of fractions – complex fractions not specifically named
A2.A.18	Evaluate logarithmic expressions in any base	Math B – 4B	Manipulate symbolic representations to explore concepts at an abstract level · Rewrite the equality log_ba = c as a = b^c · Rewrite expressions involving exponents and logarithms
A2.A.19	Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms	Math B – 4B Math B – 7A	Manipulate symbolic representations to explore concepts at an abstract level · Rewrite the equality log_ba = c as a = b^c · Rewrite expressions involving exponents and logarithms Express exponential functions as logs
A2.A.20	Determine the sum and product of the roots of a quadratic equation by examining its coefficients		Not addressed
A2.A.21	Determine the quadratic equation, given the sum and product of its roots		Not addressed
A2.A.22	Solve radical equations	Math B – 7K	Solve equations using radicals Equations with radicals
A2.A.23	Solve rational equations and inequalities	Math B – 7K	Solve fractional equations – no mention of inequalities

2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.A.24	Know and apply the technique of completing the square		Not addressed
A2.A.25	Solve quadratic equations, using the quadratic formula		Not addressed
A2.A.26	Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula		Not addressed
A2.A.27	Solve exponential equations with and without common bases		Not addressed
A2.A.28	Solve a logarithmic equation by rewriting as and exponential equation		Not addressed
A2.A.29	Identify an arithmetic or geometric sequence and find the formula for its nth term	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence
A2.A.30	Determine the common difference in an arithmetic sequence	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence
A2.A.31	Determine the common ration in a geometric sequence	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence

2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.A.32	Determine a specified term of an arithmetic or geometric sequence	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence
A2.A.33	Specify terms of a sequence, given its recursive definition	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence
A2.A.34	Represent the sum of a series, using sigma notation	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence
A2.A.35	Determine the sum of the first n terms of an arithmetic or geometric series	Related to Math B – 4A	Represent problem situations symbolically by using sequences Use symbolic form to represent an explicit rule for a sequence
A2.A.36	Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion	Math B – 6F	Binomial Theorem
A2.A.37	Define a relation and function	Math B – 7A	Definition of a relation
A2.A.38	Determine when a relation is a function	Math B – 7A	Determining if a relation is a function
A2.A.39	Determine the domain and rage of a function from its equation		Not directly addressed
A2.A.40	Write functions in functional notation		Not directly addressed
A2.A.41	Use functional notation to evaluate functions for given values in the domain	Math B – 7A	Notation for absolute value, composite functions

2005 Core Curriculum		1999 Core Curriculum
Performance Indicator	Concept/Skill	Key Idea	Concept/Skill
A2.A.42	Find the composition of functions	Math B – 3B Math B – 3E Math B – 7J	3Develop an understanding of and use the composition of functions and transformations Evaluate and form the composition of functions Determine the value of compound functions
A2.A.43	Determine if a function is one-to-one, onto, or both		Not addressed
A2.A.44	Define the inverse of a function	Math B – 7A	Definition of inverse function
A2.A.45	Determine the inverse of a function and use composition to justify the result		Not directly addressed
A2.A.46	Perform transformations with functions and relations: f(x +a) , f(x) +a, f(-x), -f(x), af(x)	Math B – 7F	Apply and interpret transformations to functions Use ideas of transformations to investigate the relationships between functions
A2.A.47	Determine the center-radius form for the equation of a circle in standard form	Math B – 4L	Use algebraic relationships to analyze the conic sections
A2.A.48	Write the equation of a circle, given its center and a point on the circle	Math B- 4L	Use algebraic relationships to analyze the conic sections – not using a point on the circle
A2.A.49	Write the equation of a circle from its graph