Mathematics Standards
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Showing 21 - 30 of 42 Standards
Standard Identifier: G-GPE.5
Grade Range:
7–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Math I
Conceptual Category:
Geometry
Cluster:
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]
Standard:
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]
Standard:
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Standard Identifier: G-GPE.7
Grade Range:
7–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Math I
Conceptual Category:
Geometry
Cluster:
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]
Standard:
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]
Standard:
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *
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: G-GPE.1
Grade Range:
8–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Math II
Conceptual Category:
Geometry
Cluster:
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Standard Identifier: G-GPE.1
Grade Range:
8–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Geometry
Conceptual Category:
Geometry
Cluster:
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Standard Identifier: G-GPE.2
Grade Range:
8–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Geometry
Conceptual Category:
Geometry
Cluster:
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a parabola given a focus and directrix.
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a parabola given a focus and directrix.
Standard Identifier: G-GPE.2
Grade Range:
8–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Math II
Conceptual Category:
Geometry
Cluster:
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a parabola given a focus and directrix.
Translate between the geometric description and the equation for a conic section.
Standard:
Derive the equation of a parabola given a focus and directrix.
Standard Identifier: G-GPE.4
Grade Range:
8–12
Domain:
Expressing Geometric Properties with Equations
Discipline:
Math II
Conceptual Category:
Geometry
Cluster:
Use coordinates to prove simple geometric theorems algebraically.
Standard:
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). [Include simple circle theorems.]
Use coordinates to prove simple geometric theorems algebraically.
Standard:
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). [Include simple circle theorems.]
Showing 21 - 30 of 42 Standards
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