Mathematics Standards
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Showing 31 - 40 of 43 Standards
Standard Identifier: G-C.3
Grade Range:
8–12
Domain:
Circles
Discipline:
Geometry
Conceptual Category:
Geometry
Cluster:
Understand and apply theorems about circles.
Standard:
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Understand and apply theorems about circles.
Standard:
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Standard Identifier: G-C.4
Grade Range:
8–12
Domain:
Circles
Discipline:
Geometry
Conceptual Category:
Geometry
Cluster:
Understand and apply theorems about circles.
Standard:
(+) Construct a tangent line from a point outside a given circle to the circle.
Understand and apply theorems about circles.
Standard:
(+) Construct a tangent line from a point outside a given circle to the circle.
Standard Identifier: G-C.4
Grade Range:
8–12
Domain:
Circles
Discipline:
Math II
Conceptual Category:
Geometry
Cluster:
Understand and apply theorems about circles.
Standard:
(+) Construct a tangent line from a point outside a given circle to the circle.
Understand and apply theorems about circles.
Standard:
(+) Construct a tangent line from a point outside a given circle to the circle.
Standard Identifier: G-C.5
Grade Range:
8–12
Domain:
Circles
Discipline:
Math II
Conceptual Category:
Geometry
Cluster:
Find arc lengths and areas of sectors of circles. [Radian introduced only as unit of measure]
Standard:
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. CA
Find arc lengths and areas of sectors of circles. [Radian introduced only as unit of measure]
Standard:
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. CA
Standard Identifier: G-C.5
Grade Range:
8–12
Domain:
Circles
Discipline:
Geometry
Conceptual Category:
Geometry
Cluster:
Find arc lengths and areas of sectors of circles. [Radian introduced only as unit of measure]
Standard:
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. CA
Find arc lengths and areas of sectors of circles. [Radian introduced only as unit of measure]
Standard:
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians. CA
Standard Identifier: N-RN.1
Grade Range:
8–12
Domain:
The Real Number System
Discipline:
Math II
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:
8–12
Domain:
The Real Number System
Discipline:
Math II
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:
8–12
Domain:
The Real Number System
Discipline:
Math II
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.11
Grade Range:
9–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Algebra II
Conceptual Category:
Algebra
Cluster:
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]
Standard:
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. *
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]
Standard:
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. *
Standard Identifier: A-REI.11
Grade Range:
9–12
Domain:
Reasoning with Equations and Inequalities
Discipline:
Math III
Conceptual Category:
Algebra
Cluster:
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]
Standard:
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. *
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]
Standard:
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. *
Showing 31 - 40 of 43 Standards
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