Mathematics Standards
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Showing 101 - 110 of 123 Standards
Standard Identifier: 8.G.5
Grade:
8
Domain:
Geometry
Cluster:
Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard:
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Understand congruence and similarity using physical models, transparencies, or geometry software.
Standard:
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Standard Identifier: 8.G.6
Grade:
8
Domain:
Geometry
Cluster:
Understand and apply the Pythagorean Theorem.
Standard:
Explain a proof of the Pythagorean Theorem and its converse.
Understand and apply the Pythagorean Theorem.
Standard:
Explain a proof of the Pythagorean Theorem and its converse.
Standard Identifier: 8.G.7
Grade:
8
Domain:
Geometry
Cluster:
Understand and apply the Pythagorean Theorem.
Standard:
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Understand and apply the Pythagorean Theorem.
Standard:
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Standard Identifier: 8.G.8
Grade:
8
Domain:
Geometry
Cluster:
Understand and apply the Pythagorean Theorem.
Standard:
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Understand and apply the Pythagorean Theorem.
Standard:
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Standard Identifier: 8.G.9
Grade:
8
Domain:
Geometry
Cluster:
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Standard:
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Standard:
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
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-BF.1.a
Grade Range:
8–12
Domain:
Building Functions
Discipline:
Math II
Conceptual Category:
Functions
Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]
Standard:
Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *
Build a function that models a relationship between two quantities. [Quadratic and exponential]
Standard:
Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *
Standard Identifier: F-BF.1.b
Grade Range:
8–12
Domain:
Building Functions
Discipline:
Math II
Conceptual Category:
Functions
Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]
Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *
Build a function that models a relationship between two quantities. [Quadratic and exponential]
Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *
Showing 101 - 110 of 123 Standards
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