Mathematics
Crosswalk: Comparison of the 1999 Core Curriculum and 2005 Core Curriculum for High School Mathematics
September 2005
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.
The following chart lists the concepts and skills in Geometry (2005 Core) and indicates where it was included in the 1999 Core.
Number Sense and Operations Strand / Algebra / Measurement / Statistics and Probability
2005 Core Curriculum 
1999 Core Curriculum 

Performance 
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 
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

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 quadraticlinear pair by substitution method and additionsubtraction method Solve systems of linear equations, inequalities, and quadraticlinear 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

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 realworld 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

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

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

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
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

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

A2.A.30 
Determine the common difference in an arithmetic sequence 
Related to Math B – 4A 
Represent problem situations symbolically by using sequences

A2.A.31 
Determine the common ration in a geometric sequence 
Related to Math B – 4A 
Represent problem situations symbolically by using sequences

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

A2.A.33 
Specify terms of a sequence, given its recursive definition 
Related to Math B – 4A 
Represent problem situations symbolically by using sequences

A2.A.34 
Represent the sum of a series, using sigma notation 
Related to Math B – 4A 
Represent problem situations symbolically by using sequences

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

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 onetoone, 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

A2.A.47 
Determine the centerradius 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 

Not directly addressed 
A2.A.50 
Approximate the solution to polynomial equations of higher degree by inspecting the graph 

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

Not directly addressed 
A2.A.52 
Identify relations and functions, using graphs

Implied in Math B –7A 
Use function vocabulary and notation Determining if a relation is a function 
2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
A2.A.53 
Graph exponential functions of the form y = bx for positive values of b, including b= e 
Math B – 4J 
Be able to sketch the effects of changing the value of a in the function y = ax B = e not addressed 
A2.A.54 
Graph logarithmic functions, using the inverse of the related exponential function 
Math B – 7B 
Represent and analyze logarithmic and exponential functions 
A2.A.55 
Express and apply the six trigonometric functions as ratios of the sides of right triangle 
Math B – 5A 
Use trigonometry as a method to measure indirectly

A2.A.56 
Know the exact and approximate values of the sine, cosine, and tangent of 0˚, 30˚ 45˚, 60˚, 90˚ 180˚, and 270˚ angles 
Math B – 5E 
Determine the trigonometric functions in terms of the unit circle

A2.A.57 
Sketch and se the reference angle for angles in standard position 
Math B – 5C
Math B – 5E 
Derive and apply formulas relating angle measure and arc degree measure in a circle
Reference angles 
A2.A.58 
Know and apply the cofunction and reciprocal relationships between trigonometric ratios 

Not directly addressed 
A2.A.59 
Use the reciprocal and cofunction relationships to find the value of the secant, cosecant, and cotangent of 0˚, 30˚ 45˚, 60˚, 90˚ 180˚, and 270˚ angles 
Math B – 5E 
Special angles 30˚, 45˚, 60˚ 
A2.A.60 
Sketch the unit circle and represent angles in standard position 
Math B – 5E 
Define the trigonometric functions in terms of the unit circle

2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
A2.A.61 
Determine the length of an arc of a circle, given its radius and the measure of its central angle 

Not addressed 
A2.A.62 
Find the value of trigonometric functions, if given a point on the terminal side of angle θ 
Application of 5E 
Define the trigonometric functions in terms of the unit circle 
A2.A.63 
Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function 

Not addressed 
A2.A.64 
Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent 

Not directly addressed 
A2.A.65 
Sketch the graph of the inverses of the sine, cosine, and tangent functions 

Not addressed 
A2.A.66 
Determine the trigonometric functions of any angle, using technology 

Technology not addressed 
A2.A.67 
Justify the Pythagorean identities 
Math B – 7H 
Apply axiomatic structure to algebra and geometry

A2.A.68 
Solve trigonometric equations for all values of the variable from 0˚ to 360˚ 
Math B – 7Q 
Develop methods to solve trigonometric equations and verify trigonometric functions 
A2.A.69 
Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function 

Not directly addressed 
A2.A.70 
Sketch and recognize one cycle of a function of the form y = AsinBx or y = Acos Bx 

Not addressed 
A2.A.71 
Sketch and recognize the graphs of the functions y = sec(x), y = csc(x), y = tan(x), and y = cot(x) 

Not addressed 
2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
A2.A.72 
Write the trigonometric function that is represented by a given periodic graph 

Not addressed 
A2.A.73 
Solve for an unknown side of angle, using the Law of Sines or the Law of Cosines 
Math B – 5F 
Relate trigonometric relationships to general solutions of triangles

A2.A.74 
Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle 
Math B – 5F 
Relate trigonometric relationships to the area of a triangle

A2.A.75 
Determine the solution(s) from the SSA situation (ambiguous case) 
Math B 5F 
The ambiguous case 
A2.A.76 
Apply the angle sum and difference formulas for trigonometric functions 
Math B – 5C 
Derive and apply formulas relating angle measure and arc degree measure in a circle

A2.A.77 
Apply the doubleangle and halfangle formulas for trigonometric functions 
Math B – 5C 
Derive and apply formulas relating angle measure and arc degree measure in a circle

2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
A2.M.1 
Define radian measure 
Math B  4M Math B – 5E 
Radian measure Radian measure 
A2.M.2 
Convert between radian and degree measures 

Not specifically addressed 
2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
A2.S.1 
Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment) 

Not directly addressed 
A2.S.2 
Determine factors which may affect the outcome of a survey 

Not directly addressed 
A2.S.3 
Calculate measures of central tendency with group frequency distributions 
Math A – 5D
Math B – 6F 
Use statistical methods including the measures of central tendency to describe and compare data Create and interpret applications of discrete and continuous probability distributions

A2.S.4 
Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations 
Math A  5D
Math B – 6F 
Use statistical methods including the measures of central tendency to describe and compare data Create and interpret applications of discrete and continuous probability distributions

2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
A2.S.5 
Know and apply the characteristics of the normal distribution 
Math B – 5G
Math B – 7P 
Apply the normal curve and its properties to familiar contexts Use the normal curve to answer questions about data

A2.S.6 
Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate 
Math B – 6E 
Use curve fitting to fit data

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 
Math B – 6G 
Make predictions based on interpolations and extrapolations of 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 
Math B – 6E 
Use curve fitting to fit data

A2.S.9 
Differentiate between situations requiring permutations and those requiring combinations 
Math A – 6D 
Determine probabilities, using permutations and combinations 
A2.S.10 
Calculate the number of possible permutations (nPr) of n items taken r at a time 
Math A – 6D 
Determine probabilities, using permutations and combinations 
A2.S.11 
Calculate the umber of possible combinations (nCr) of n items taken r at a time 
Math A – 6D 
Determine probabilities, using permutations and combinations 
2005 Core Curriculum 
1999 Core Curriculum 

Performance Indicator 
Concept/Skill 
Key Idea 
Concept/Skill 
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) 
Math A – 6D 
Use the concept of random variable in computing probabilities

A2.S.13 
Calculate theoretical probabilities, including geometric applications 
Math A – 6A 
Theoretical versus empirical probability 
A2.S.14 
Calculate empirical probabilities 
Math 7/8 – 6C Math A – 6A 
Conduct and predict outcomes of experiments with independent events Theoretical versus empirical probability 
A2.S.15 
Know and apply the binomial probability formula to events involving he terms exactly, at least, and at most 
Math B – 6C 
Interpret probabilities in realworld situations

A2.S.16 
Use the normal distribution as an approximation for binomial probabilities 
Math B – 6F 
Create and interpret applications of discrete and continuous probability distributions
