Mathematics Standards
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Arithmetic with Polynomials and Rational Expressions
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Expressions and Equations
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Interpreting Categorical and Quantitative Data
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Linear, Quadratic, and Exponential Models
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Number and Operations—Fractions
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Showing 101 - 110 of 129 Standards
Standard Identifier: A-APR.4
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Algebra II
Conceptual Category:
Algebra
Cluster:
Use polynomial identities to solve problems.
Standard:
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)2= (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
Use polynomial identities to solve problems.
Standard:
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)2= (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
Standard Identifier: A-APR.4
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Math III
Conceptual Category:
Algebra
Cluster:
Use polynomial identities to solve problems.
Standard:
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2= (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
Use polynomial identities to solve problems.
Standard:
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2= (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
Standard Identifier: A-APR.5
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Math III
Conceptual Category:
Algebra
Cluster:
Use polynomial identities to solve problems.
Standard:
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
Footnote:
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
Use polynomial identities to solve problems.
Standard:
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
Footnote:
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
Standard Identifier: A-APR.5
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Algebra II
Conceptual Category:
Algebra
Cluster:
Use polynomial identities to solve problems.
Standard:
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
Footnote:
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
Use polynomial identities to solve problems.
Standard:
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
Footnote:
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
Standard Identifier: A-APR.6
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Algebra II
Conceptual Category:
Algebra
Cluster:
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
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.
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
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.
Standard Identifier: A-APR.6
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Math III
Conceptual Category:
Algebra
Cluster:
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
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.
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
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.
Standard Identifier: A-APR.7
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Math III
Conceptual Category:
Algebra
Cluster:
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Standard Identifier: A-APR.7
Grade Range:
9–12
Domain:
Arithmetic with Polynomials and Rational Expressions
Discipline:
Algebra II
Conceptual Category:
Algebra
Cluster:
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Rewrite rational expressions. [Linear and quadratic denominators]
Standard:
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Standard Identifier: F-LE.4
Grade Range:
9–12
Domain:
Linear, Quadratic, and Exponential Models
Discipline:
Algebra II
Conceptual Category:
Functions
Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems.
Standard:
For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. * [Logarithms as solutions for exponentials]
Construct and compare linear, quadratic, and exponential models and solve problems.
Standard:
For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. * [Logarithms as solutions for exponentials]
Standard Identifier: F-LE.4
Grade Range:
9–12
Domain:
Linear, Quadratic, and Exponential Models
Discipline:
Math III
Conceptual Category:
Functions
Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems.
Standard:
For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. * [Logarithms as solutions for exponentials]
Construct and compare linear, quadratic, and exponential models and solve problems.
Standard:
For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. * [Logarithms as solutions for exponentials]
Showing 101 - 110 of 129 Standards
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