Mathematics Standards
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Showing 41 - 50 of 78 Standards
Standard Identifier: N-RN.1
Grade Range:
7–12
Domain:
The Real Number System
Discipline:
Algebra I
Conceptual Category:
Number and Quantity
Cluster:
Extend the properties of exponents to rational exponents.
Standard:
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. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5(^1/3)^3 to hold, so (5^1/3)^3 must equal 5.
Extend the properties of exponents to rational exponents.
Standard:
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. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5(^1/3)^3 to hold, so (5^1/3)^3 must equal 5.
Standard Identifier: N-RN.2
Grade Range:
7–12
Domain:
The Real Number System
Discipline:
Algebra I
Conceptual Category:
Number and Quantity
Cluster:
Extend the properties of exponents to rational exponents.
Standard:
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Extend the properties of exponents to rational exponents.
Standard:
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Standard Identifier: N-RN.3
Grade Range:
7–12
Domain:
The Real Number System
Discipline:
Algebra I
Conceptual Category:
Number and Quantity
Cluster:
Use properties of rational and irrational numbers.
Standard:
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Use properties of rational and irrational numbers.
Standard:
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Standard Identifier: A-REI.4.a
Grade Range:
8–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Math II
Conceptual Category:
Algebra
Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]
Standard:
Solve quadratic equations in one variable. 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.
Solve equations and inequalities in one variable. [Quadratics with real coefficients]
Standard:
Solve quadratic equations in one variable. 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.
Standard Identifier: A-REI.4.b
Grade Range:
8–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Math II
Conceptual Category:
Algebra
Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]
Standard:
Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x^2 = 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 equations and inequalities in one variable. [Quadratics with real coefficients]
Standard:
Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x^2 = 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.
Standard Identifier: A-REI.7
Grade Range:
8–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Math II
Conceptual Category:
Algebra
Cluster:
Solve systems of equations. [Linear-quadratic systems]
Standard:
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.
Solve systems of equations. [Linear-quadratic systems]
Standard:
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.
Standard Identifier: F-IF.4
Grade Range:
8–12
Domain:
Interpreting Functions
Discipline:
Math II
Conceptual Category:
Functions
Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]
Standard:
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *
Interpret functions that arise in applications in terms of the context. [Quadratic]
Standard:
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *
Standard Identifier: F-IF.5
Grade Range:
8–12
Domain:
Interpreting Functions
Discipline:
Math II
Conceptual Category:
Functions
Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]
Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *
Interpret functions that arise in applications in terms of the context. [Quadratic]
Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *
Standard Identifier: F-IF.6
Grade Range:
8–12
Domain:
Interpreting Functions
Discipline:
Math II
Conceptual Category:
Functions
Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]
Standard:
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. *
Interpret functions that arise in applications in terms of the context. [Quadratic]
Standard:
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. *
Standard Identifier: F-IF.7.a
Grade Range:
8–12
Domain:
Interpreting Functions
Discipline:
Math II
Conceptual Category:
Functions
Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]
Standard:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. * Graph linear and quadratic functions and show intercepts, maxima, and minima. *
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]
Standard:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. * Graph linear and quadratic functions and show intercepts, maxima, and minima. *
Showing 41 - 50 of 78 Standards
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