Secondary Mathematics II

Strand: GEOMETRY - Expressing Geometric Properties With Equations (G.GPE)

Translate between the geometric description and the equation for a conic section (Standard G.GPE.1). Use coordinates to prove simple geometric theorems algebraically. Include simple proofs involving circles (Standard G.GPE.4). Use coordinates to prove simple geometric theorems algebraically (Standard G.GPE.6).

Standard G.GPE.1

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.

• Coordinates of Points on a Circle
The purpose of this task it to use geometry and algebra in order to understand the behavior of the trigonometric function f(x)=sinx+cosx. The task has been stated in an open ended fashion as there are natural solutions using geometry, or using the trigonometric identity sin2x=2sinxcosx, or algebraically solving a system of equations.
• Explaining the equation for a circle
Starting with explicit cases, this task derives the formula for an arbitrary circle in the plane.
• GEOMETRY - Expressing Geometric Properties With Equations (G.GPE) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Expressing Geometric Properties with Equations (G.GPE).
• Module 8: Circles & Other Conics - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 8, Circles and Other Conics, takes an algebraic approach to solving problems with circles, parabolas, and in the Honors course, ellipses and hyperbolas. The module includes several hands- on explorations to develop the equations for circles, parabolas, and ellipses.
• Module 8: Circles & Other Conics - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 8, Circles and Other Conics, takes an algebraic approach to solving problems with circles, parabolas, and in the Honors course, ellipses and hyperbolas. The module includes several hands- on explorations to develop the equations for circles, parabolas, and ellipses.
• Slopes and Circles
The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever AXB is a right angle.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen.

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