Skill plan for the New York Regents Examinations - Algebra 2
IXL provides skill alignments with recommended IXL skills for every student. Find the IXL skills that are right for you below!
Conceptual Category
Print skill plan
Number and Quantity
The Real Number System
Extend the properties of exponents to rational exponents (major cluster)
Extend the properties of exponents to rational exponents (major cluster)
N-RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
N-RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
N-RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Operations with radical expressions
Simplify radical expressions
Operations with rational exponents
Simplify expressions with rational exponents
N-RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Operations with radical expressions
Simplify radical expressions
Operations with rational exponents
Simplify expressions with rational exponents
Quantities
Reason quantitatively and use units to solve problems (supporting cluster)
Reason quantitatively and use units to solve problems (supporting cluster)
N-Q.A.2: Define appropriate quantities for the purpose of descriptive modeling.
N-Q.A.2: Define appropriate quantities for the purpose of descriptive modeling.
The Complex Number System
Perform arithmetic operations with complex numbers (additional cluster)
Perform arithmetic operations with complex numbers (additional cluster)
N-CN.A.1: Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.
N-CN.A.1: Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.
N-CN.A.2: Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N-CN.A.2: Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Use complex numbers in polynomial identities and equations (additional cluster)
Use complex numbers in polynomial identities and equations (additional cluster)
N-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
N-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
Algebra
Seeing Structure in Expressions
Interpret the structure of expressions (major cluster)
Interpret the structure of expressions (major cluster)
A-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Polynomial expressions
Radical expressions
Rational exponents
A-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Polynomial expressions
Radical expressions
Rational exponents
Write expressions in equivalent forms to solve problems (major cluster)
Write expressions in equivalent forms to solve problems (major cluster)
A-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
A-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
A-SSE.B.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A-SSE.B.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A-SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
A-SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
A-SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
A-SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Arithmetic and Polynomials with Rational Expressions
Understand the relationship between zeros and factors of polynomials (major cluster)
Understand the relationship between zeros and factors of polynomials (major cluster)
A-APR.B.2: 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).
A-APR.B.2: 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).
A-APR.B.3: 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.
Quadratic equations
Polynomials
A-APR.B.3: 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.
Quadratic equations
Polynomials
Use polynomial identities to solve problems (additional cluster)
Use polynomial identities to solve problems (additional cluster)
A-APR.C.4: Prove polynomial identities and use them to describe numerical relationships.
A-APR.C.4: Prove polynomial identities and use them to describe numerical relationships.
Rewrite rational expressions (supporting cluster)
Rewrite rational expressions (supporting cluster)
A-APR.D.6: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
A-APR.D.6: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Creating Equations
Create equations that describe numbers or relationships (supporting cluster)
Create equations that describe numbers or relationships (supporting cluster)
A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning (major cluster)
Understand solving equations as a process of reasoning and explain the reasoning (major cluster)
A-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A-REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
A-REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable (supporting cluster)
Solve equations and inequalities in one variable (supporting cluster)
A-REI.B.4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
A-REI.B.4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
A-REI.B.4b: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
A-REI.B.4b: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Solve systems of equations (additional cluster)
Solve systems of equations (additional cluster)
A-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Understand solutions
Solve by graphing
Solve using substitution
Solve using elimination
Solve using any method
A-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Understand solutions
Solve by graphing
Solve using substitution
Solve using elimination
Solve using any method
A-REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
A-REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Represent and solve equations and inequalities graphically (major cluster)
Represent and solve equations and inequalities graphically (major cluster)
A-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
A-REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section (additional cluster)
Translate between the geometric description and the equation for a conic section (additional cluster)
G-GPE.A.2: Derive the equation of a parabola given a focus and directrix.
G-GPE.A.2: Derive the equation of a parabola given a focus and directrix.
Functions
Interpreting Functions
Understand the concept of a function and use function notation (supporting cluster)
Understand the concept of a function and use function notation (supporting cluster)
F-IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Arithmetic sequences
Geometric sequences
Explicit formulas
Recursive formulas
Mixed sequences
F-IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Arithmetic sequences
Geometric sequences
Explicit formulas
Recursive formulas
Mixed sequences
Interpret functions that arise in application in terms of the context (major cluster)
Interpret functions that arise in application in terms of the context (major cluster)
F-IF.B.4: 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.
Linear functions
Quadratic functions
Polynomial functions
Rational functions
Variation
Exponential functions
F-IF.B.4: 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.
Linear functions
Quadratic functions
Polynomial functions
Rational functions
Variation
Exponential functions
F-IF.B.6: 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.
F-IF.B.6: 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.
Analyze functions using different representations (supporting cluster)
Analyze functions using different representations (supporting cluster)
F-IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F-IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Exponential functions
Sine functions
Cosine functions
Sine and cosine functions
F-IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Exponential functions
Sine functions
Cosine functions
Sine and cosine functions
F-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
F-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
F-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
F-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Building Functions
Build a function that models a relationship between two quantities (major cluster)
Build a function that models a relationship between two quantities (major cluster)
F-BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-BF.A.1b: Combine standard function types using arithmetic operations.
Polynomials
Rational expressions
Functions
F-BF.A.1b: Combine standard function types using arithmetic operations.
Polynomials
Rational expressions
Functions
F-BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
F-BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Build new functions from existing functions (additional cluster)
Build new functions from existing functions (additional cluster)
F-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Translations
Reflections
Dilations
Mixed transformations
F-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Translations
Reflections
Dilations
Mixed transformations
F-BF.B.4a: 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.
Find inverse functions
Exponential equations
Logarithmic equations
F-BF.B.4a: 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.
Find inverse functions
Exponential equations
Logarithmic equations
Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems (supporting cluster)
Construct and compare linear, quadratic, and exponential models and solve problems (supporting cluster)
F-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F-LE.A.4: 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.
Exponential and logarithmic form
Solve exponential equations
F-LE.A.4: 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.
Exponential and logarithmic form
Solve exponential equations
Interpret expressions for functions in terms of the situation they model (additional cluster)
Interpret expressions for functions in terms of the situation they model (additional cluster)
F-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
F-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle (additional cluster)
Extend the domain of trigonometric functions using the unit circle (additional cluster)
F-TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
F-TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
F-TF.A.2: 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.
F-TF.A.2: 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.
Model periodic phenomena with trigonometric functions (additional cluster)
Model periodic phenomena with trigonometric functions (additional cluster)
F-TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Sine functions
Cosine functions
F-TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Sine functions
Cosine functions
Prove and apply trigonometric identities (additional cluster)
Prove and apply trigonometric identities (additional cluster)
F-TF.C.8: Prove the Pythagorean identity sin2(theta) + cos2(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.
F-TF.C.8: Prove the Pythagorean identity sin2(theta) + cos2(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.
Statistics and Probability
Interpreting Categorical and Quantitative Data
Summarize, represent and interpret data on a single count or measurement variable (additional cluster)
Summarize, represent and interpret data on a single count or measurement variable (additional cluster)
S-ID.A.4: 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.
S-ID.A.4: 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.
Summarize, represent and interpret data on two categorical and quantitative variables (supporting cluster)
Summarize, represent and interpret data on two categorical and quantitative variables (supporting cluster)
S-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
S-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical experiments (supporting cluster)
Understand and evaluate random processes underlying statistical experiments (supporting cluster)
S-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
S-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
S-IC.A.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
S-IC.A.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
Make inferences and justify conclusions from sample surveys, experiments, and observational studies (major cluster)
Make inferences and justify conclusions from sample surveys, experiments, and observational studies (major cluster)
S-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
S-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
S-IC.B.4: 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.
S-IC.B.4: 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.
S-IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
S-IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
S-IC.B.6: Evaluate reports based on data.
S-IC.B.6: Evaluate reports based on data.
Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data (additional cluster)
Understand independence and conditional probability and use them to interpret data (additional cluster)
S-CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or", "and", and "not").
S-CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or", "and", and "not").
S-CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S-CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S-CP.A.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S-CP.A.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S-CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
S-CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
S-CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
S-CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Use the rules of probability to compute probabilities of compound events in a uniform probability model (additional cluster)
Use the rules of probability to compute probabilities of compound events in a uniform probability model (additional cluster)
S-CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S-CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S-CP.B.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
S-CP.B.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
This document includes IXL skill alignments to the New York Regents Examinations. IXL provides skill alignments as a service to teachers, students, and parents. The skill alignments are not affiliated with, sponsored by, or endorsed by New York State Education Department. IXL and IXL Learning are registered trademarks of IXL Learning, Inc. All other trademarks and registered trademarks and copyrights are the property of their respective owners.