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# MA.912.G.6.5Archived Standard

Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Idea: Level 3: Strategic Thinking & Complex Reasoning
Standard: Circles - Define and understand ideas related to circles (radius, tangent, chord, etc.). Perform constructions, and prove theorems related to circles. Find measures of arcs and angles related to them, as well as measures of circumference and area. Relate geometry to algebra by finding the equation of a circle in the coordinate plane.
Date Adopted or Revised: 09/07
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes

### Remarks/Examples

Example: Which will give you more: three 6-inch pizzas or two 8-inch pizzas? Explain your answer.

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark may be assessed using: MC , FR item(s)
• Also Assesses:

MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

MA.912.G.6.4 Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

• Clarification :
Students will solve problems related to circles.
• Content Limits :

All angle measurements will be in degrees.

Items may require statements and/or justifications to complete formal and informal proofs.

• Stimulus Attributes :

Items may be set in either real-world or mathematical contexts.

Graphics should be used in most of these items, as appropriate.

### SAMPLE TEST ITEMS (2)

• Test Item #: Sample Item 1
• Question:

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 2 1/2 -inch diameter. There are 4 semicircle and 4 quarter-circle arcs, as shown in the diagram below.

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

• Difficulty: N/A
• Type: MC: Multiple Choice

• Test Item #: Sample Item 2
• Question:

Kayla inscribed kite ABCD in a circle, as shown below.

If the measure of arc ADC is 255° in Kayla’s design, what is the measure, in degrees, of ∠ADC ?

• Difficulty: N/A
• Type: FR: Fill-in Response