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MAFS.912.G-C.2.5

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Congruence, Similarity, Right Triangles & Trig - 46%

MAFS.912.G-


Circles, Geometric Measurement & Geometric Properties with Equations - 38%

MAFS.912.G-


Modeling with Geometry - 16%

MAFS.912.G-


In Your Text

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What You Need To Know...

MAFS.912.G-C.2.5 - Arc lengths, radian measure, area of a sector, proportionality of components of a circle.

1. The benchmark will be assessed using Graphic Response, Hot Text Response, Movable Text Response, Multiple Choice Response, Multi-select Response, Open Response, Selectable Text Response and Simulation Response.

2. Items may require students derive or use the formula for the area of a sector.

3. Items may require students to apply similarity to solve problems that involve the length of the arc intercepted by an angle and the radius of a circle.

4. Items may require students to use similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure as the constant of proportionality.

 

Example One

Example Two

Allison created an embroidery design of a stylized star emblem.  The perimeter of the design is made by alternating semicircle and quarter-circle arcs.  Each arc is formed from a circle with a 2½-inch diameter.  There are 4 semicircle and 4 quarter-circle arcs, as shown in the diagram below.

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To the nearest whole inch, what is the perimeter of Allison's design?

  1. 15 inches
  2. 20 inches
  3. 24 inches
  4. 31 inches

CLICK HERE FOR SOLUTION

Additional Examples

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Arc Length
Radian Measure
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Sector Area
Intercepted Angles & Radii

Reference Sheet



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Select sample problems taken from FLDVIPN teacher materials

Violet Esopakis - Palm Beach Co.
Stephanie Fitzwater - Seminole Co.
Angela Kerins - Orange Co.
Lisa Lasseter - St. Johns Co.
Jeremy Lowery - Escambia Co.
Jodi Van Wagoner - Brevard Co.

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Jeremy Lowery - Escambia Co.

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