Next Generation Learning Standards: Algebra II
Skills available for New York Algebra 2 standards
Domain
Print skill plan
AII-N
Number and Quantity
AII-N.RN The Real Number System
Extend the properties of exponents to rational exponents.
Extend the properties of exponents to rational exponents.
AII-N.RN.1: Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
AII-N.RN.1: Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
AII-N.RN.2: Convert between radical expressions and expressions with rational exponents using the properties of exponents.
Radicals
Rational exponents
AII-N.RN.2: Convert between radical expressions and expressions with rational exponents using the properties of exponents.
Radicals
Rational exponents
AII-N.CN The Complex Number System
Perform arithmetic operations with complex numbers.
Perform arithmetic operations with complex numbers.
AII-N.CN.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.
AII-N.CN.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.
AII-N.CN.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
AII-N.CN.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
AII-A
Algebra
AII-A.SSE Seeing Structure in Expressions
Interpret the structure of expressions.
Interpret the structure of expressions.
AII-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it.
Polynomial expressions
Binomial Theorem
Radical expressions
Rational exponents
Rational expressions
AII-A.SSE.2: Recognize and use the structure of an expression to identify ways to rewrite it.
Polynomial expressions
Binomial Theorem
Radical expressions
Rational exponents
Rational expressions
Write expressions in equivalent forms to reveal their characteristics.
Write expressions in equivalent forms to reveal their characteristics.
AII-A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
AII-A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
AII-A.SSE.3a: Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
AII-A.SSE.3a: Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
AII-A.SSE.3c: Use the properties of exponents to rewrite exponential expressions.
AII-A.SSE.3c: Use the properties of exponents to rewrite exponential expressions.
AII-A.APR Arithmetic with Polynomials and Rational Expressions
Understand the relationship between zeros and factors of polynomials.
Understand the relationship between zeros and factors of polynomials.
AII-A.APR.2: 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).
AII-A.APR.2: 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).
AII-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.
Quadratics
Polynomials
AII-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.
Quadratics
Polynomials
Rewrite rational expressions.
Rewrite rational expressions.
AII-A.APR.6: Rewrite 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).
AII-A.APR.6: Rewrite 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).
AII-A.CED Creating Equations
Create equations that describe numbers or relationships.
Create equations that describe numbers or relationships.
AII-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.
AII-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.
AII-A.REI Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
Understand solving equations as a process of reasoning and explain the reasoning.
AII-A.REI.1b: Explain each step when solving rational or radical equations 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.
AII-A.REI.1b: Explain each step when solving rational or radical equations 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.
AII-A.REI.2: Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
AII-A.REI.2: Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
Solve equations and inequalities in one variable.
Solve equations and inequalities in one variable.
AII-A.REI.4: Solve quadratic equations in one variable.
AII-A.REI.4: Solve quadratic equations in one variable.
AII-A.REI.4b: Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in a + bi form.
AII-A.REI.4b: Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in a + bi form.
Solve systems of equations.
Solve systems of equations.
AII-A.REI.7b: Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
AII-A.REI.7b: Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Represent and solve equations and inequalities graphically.
Represent and solve equations and inequalities graphically.
AII-A.REI.11: Given the equations y = f(x) and y = g(x):
AII-A.REI.11: Given the equations y = f(x) and y = g(x):
AII-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
AII-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
AII-A.REI.11.ii: find the solutions approximately using technology to graph the functions or make tables of values;
AII-A.REI.11.ii: find the solutions approximately using technology to graph the functions or make tables of values;
AII-A.REI.11.iii: find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and
AII-A.REI.11.iii: find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and
AII-A.REI.11.iv: interpret the solution in context.
AII-A.REI.11.iv: interpret the solution in context.
AII-F
Functions
AII-F.IF Interpreting Functions
Understand the concept of a function and use function notation.
Understand the concept of a function and use function notation.
AII-F.IF.3: Recognize that a sequence is a function whose domain is a subset of the integers.
Find terms
Classify
Write a formula
Convert a formula
Sequence review
AII-F.IF.3: Recognize that a sequence is a function whose domain is a subset of the integers.
Find terms
Classify
Write a formula
Convert a formula
Sequence review
Interpret functions that arise in applications in terms of the context.
Interpret functions that arise in applications in terms of the context.
AII-F.IF.4: For a function that models a relationship between two quantities:
AII-F.IF.4: For a function that models a relationship between two quantities:
AII-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and
Variation
Linear functions
Quadratic functions
Exponential functions
Polynomial functions
Rational functions
Mixed functions
Word problems
AII-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and
Variation
Linear functions
Quadratic functions
Exponential functions
Polynomial functions
Rational functions
Mixed functions
Word problems
AII-F.IF.4.ii: sketch graphs showing key features given a verbal description of the relationship.
AII-F.IF.4.ii: sketch graphs showing key features given a verbal description of the relationship.
AII-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.
AII-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.
Analyze functions using different representations.
Analyze functions using different representations.
AII-F.IF.7: Graph functions and show key features of the graph by hand and using technology when appropriate.
AII-F.IF.7: Graph functions and show key features of the graph by hand and using technology when appropriate.
AII-F.IF.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
AII-F.IF.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
AII-F.IF.7e: Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
Exponential functions
Logarithmic functions
Sine functions
Cosine functions
Trigonometric functions
AII-F.IF.7e: Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
Exponential functions
Logarithmic functions
Sine functions
Cosine functions
Trigonometric functions
Analyze functions using different representations.
Analyze functions using different representations.
AII-F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.
AII-F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.
AII-F.IF.8b: Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
AII-F.IF.8b: Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
AII-F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
AII-F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
AII-F.BF Building Functions
Build a function that models a relationship between two quantities.
Build a function that models a relationship between two quantities.
AII-F.BF.1: Write a function that describes a relationship between two quantities.
AII-F.BF.1: Write a function that describes a relationship between two quantities.
AII-F.BF.1a: Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
AII-F.BF.1a: Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
AII-F.BF.1b: Combine standard function types using arithmetic operations.
Polynomials
Rational expressions
Functions
AII-F.BF.1b: Combine standard function types using arithmetic operations.
Polynomials
Rational expressions
Functions
AII-F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Write a formula
Convert a formula
AII-F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Write a formula
Convert a formula
Build new functions from existing functions.
Build new functions from existing functions.
AII-F.BF.3b: Using f(x) + k, k f(x), f(kx), and f(x + k):
AII-F.BF.3b: Using f(x) + k, k f(x), f(kx), and f(x + k):
AII-F.BF.3b.i: identify the effect on the graph when 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);
AII-F.BF.3b.i: identify the effect on the graph when 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);
AII-F.BF.3b.ii: find the value of k given the graphs;
AII-F.BF.3b.ii: find the value of k given the graphs;
AII-F.BF.3b.iii: write a new function using the value of k; and
Translations
Reflections
Dilations
Mixed transformations
AII-F.BF.3b.iii: write a new function using the value of k; and
Translations
Reflections
Dilations
Mixed transformations
AII-F.BF.3b.iv: use technology to experiment with cases and explore the effects on the graph.
AII-F.BF.3b.iv: use technology to experiment with cases and explore the effects on the graph.
AII-F.BF.4a: Find the inverse of a one-to-one function both algebraically and graphically.
AII-F.BF.4a: Find the inverse of a one-to-one function both algebraically and graphically.
AII-F.BF.5a: Understand inverse relationships between exponents and logarithms algebraically and graphically.
Exponential equations
Logarithmic equations
Convert between exponential and logarithmic form
AII-F.BF.5a: Understand inverse relationships between exponents and logarithms algebraically and graphically.
Exponential equations
Logarithmic equations
Convert between exponential and logarithmic form
AII-F.BF.6: Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
AII-F.BF.6: Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
AII-F.BF.7: Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.
AII-F.BF.7: Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.
AII-F.LE Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems.
Construct and compare linear, quadratic, and exponential models and solve problems.
AII-F.LE.2: Construct a linear or exponential function symbolically given:
AII-F.LE.2: Construct a linear or exponential function symbolically given:
AII-F.LE.2.i: a graph;
Linear functions
Exponential functions
AII-F.LE.2.i: a graph;
Linear functions
Exponential functions
AII-F.LE.2.ii: a description of the relationship; and
Linear functions
Arithmetic and geometric sequences
AII-F.LE.2.ii: a description of the relationship; and
Linear functions
Arithmetic and geometric sequences
AII-F.LE.2.iii: two input-output pairs (include reading these from a table).
AII-F.LE.2.iii: two input-output pairs (include reading these from a table).
AII-F.LE.4: Use logarithms to solve exponential equations, such as ab to the ct power = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.
Exponential and logarithmic form
Solve exponential equations
AII-F.LE.4: Use logarithms to solve exponential equations, such as ab to the ct power = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.
Exponential and logarithmic form
Solve exponential equations
Interpret expressions for functions in terms of the situation they model.
Interpret expressions for functions in terms of the situation they model.
AII-F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.
Linear function
Exponential functions
AII-F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.
Linear function
Exponential functions
AII-F.TF Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle.
Extend the domain of trigonometric functions using the unit circle.
AII-F.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
AII-F.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
AII-F.TF.2: Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
AII-F.TF.2: Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
AII-F.TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
AII-F.TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Model periodic phenomena with trigonometric functions.
Model periodic phenomena with trigonometric functions.
AII-F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
Sine functions
Cosine functions
AII-F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
Sine functions
Cosine functions
Prove and apply trigonometric identities.
Prove and apply trigonometric identities.
AII-F.TF.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.
AII-F.TF.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.
AII-S
Statistics and Probability
AII-S.ID Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable.
Summarize, represent, and interpret data on a single count or measurement variable.
AII-S.ID.4a: Recognize whether or not a normal curve is appropriate for a given data set.
AII-S.ID.4a: Recognize whether or not a normal curve is appropriate for a given data set.
AII-S.ID.4b: If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.
AII-S.ID.4b: If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.
Summarize, represent, and interpret data on two categorical and quantitative variables.
Summarize, represent, and interpret data on two categorical and quantitative variables.
AII-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variables' values are related.
AII-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variables' values are related.
AII-S.ID.6a: Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
Correlation coefficients
Regression line
AII-S.ID.6a: Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
Correlation coefficients
Regression line
AII-S.IC Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical experiments.
Understand and evaluate random processes underlying statistical experiments.
AII-S.IC.2: Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.
AII-S.IC.2: Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
AII-S.IC.3: Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.
AII-S.IC.3: Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.
AII-S.IC.4: Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.
AII-S.IC.4: Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.
AII-S.IC.6a: Use the tools of statistics to draw conclusions from numerical summaries.
AII-S.IC.6a: Use the tools of statistics to draw conclusions from numerical summaries.
AII-S.IC.6b: Use the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.
AII-S.IC.6b: Use the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.
AII-S.CP Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data.
Understand independence and conditional probability and use them to interpret data.
AII-S.CP.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," "not").
AII-S.CP.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," "not").
AII-S.CP.4: 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 calculate conditional probabilities.
AII-S.CP.4: 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 calculate conditional probabilities.
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
AII-S.CP.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.
AII-S.CP.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.