  ```GSE Algebra I ``` `UNIT 1 - Relationships Between Quantities` `UNIT 2 - Linear Equations & Inequalities` `UNIT 3 - Modeling Quadratics` `UNIT 4 - Modeling & Analyzing Exponential Functions` `UNIT 5 - Comparing & Contrasting Functions` `UNIT 6 - Describing Data` `EOC Prep` ```GSE Geometry ``` `UNIT 1 - Transformations in the Coordinate Plane ` `UNIT 2 - Similarity Congruence, Proofs` `UNIT 3 - Right Triangle Trigonometry` `UNIT 4 - Circles & Volume` `UNIT 5 - Geometric & Algebraic Connections` `UNIT 6 - Applications of Probability` `EOC Prep` ```GSE Algebra II ``` `UNIT 1 - Quadratics Revisited` `UNIT 2 - Operations with Polynomials` `UNIT 3 - Polynomial Functions` `UNIT 4 - Rational & Radical Relationships` `UNIT 5 - Exponential & Logarithmic Functions` `UNIT 6 - Mathematical Modeling` `UNIT 7 - Inferences & Conclusions from Data` ```GSE PreCalc ``` UNIT 1 - Trigonometry of General Triangles UNIT 2 - Introduction to Trig Functions UNIT 3 - Trigonometric Functions `UNIT 4 - Trigonometric Identities` `UNIT 5 - Matrices` `UNIT 6 - Conics` `UNIT 7 - Vectors` `UNIT 8 - Probability` ```Other Courses ``` Calculus I ```Adv. Mathematical Decision Making ``` `UNIT 1 - Analyzing Numerical Data` `UNIT 2 - Probability` `UNIT 3 - Statistical Studies` `UNIT 4 - Recursion Models` `UNIT 5 - Trigonometry & Regression Models` `UNIT 6 - Financial Decisions` `UNIT 7 - Networks & Graphs` `UNIT 8 - Matrix Applications & Voting Methods` ```Analytical Geometry ``` `UNIT 1 - Similarity, Congruence, Proof` `UNIT 2 - Right Triangle Trigonometry` `UNIT 3 - Circles & Volumes` `UNIT 4 - Extending the Number System` `UNIT 5 - Quadratic Functions` `UNIT 6 - Modeling Geometry` `UNIT 7 - Applications of Probability` `EOC Practice Test` ```CP-Statistics ``` `All Units` ```Coordinate Algebra ``` `EOC Practice Test` ```Integrated Algebra I ``` `UNIT 1 - Function Families` `UNIT 2 - Algebra Investigations` `UNIT 3 - Geometry` `UNIT 4 - The Chance of Winning` `UNIT 5 - Algebraic Investigations` `UNIT 6 - Coordinate Geometry` `EOCT Prep` ```Integrated Geometry ``` `UNIT 1 - Quadratic Function` `UNIT 2 - Right Triangle Trigonometry` `UNIT 3 - Circles and Spheres` `UNIT 4 - Data Analysis & Probability` `UNIT 5 - Piecewise, Inverse, Exponential` `UNIT 6 - Find the Best Model` ```GPS Middle School Math ``` `6th Grade Math` `7th Grade Math` `8th Grade Math` Home >GSE Geometry >Unit 4 - Circles and Volume           Search Site:

Review

 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 EOC

Georgia
Unit 4 Frameworks All of Unit 4
Unit 4-0 :
Circles Reference Sheet (Doc, PDF) Unit 4-1 : Language of Circles (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.C.2:Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Video Lessons: (p1a, p1b, p2)

Sample Quiz: (Interactive, PDF) Unit 4-2: Inscribed Angles (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.C.2:Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

MGSE9-12.G.C.3 :Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

MGSE9-12.G.C.4 :Construct a tangent line from a point outside a given circle to the circle.

Video Lessons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF) Unit 4-3: Angles of a Circle (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.G.C.2:Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Video Lessons: (p1, p2, p3, p4, p5)

Music Video (by Russell Spicer)

Sample Quiz: (Interactive, PDF) Unit 4-4: Circle Segments (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.C.2:Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Video Lessons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF) Unit 4-5: Circumference, Perimeter, Arc Length (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.C.1:Understand that all circles are similar.

MGSE9-12.G.C.5:Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

MGSE9-12.G.GMD.1 : Give informal arguments for geometric formulas. (a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

Video Lessons: (p1, p2, p3, p4, p5, p6, p7)

Sketchpad: Deteremining The Circumferenc (gsp file)

Sample Quiz: (Interactive, PDF) Unit 4-6: Areas and Sectors (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.C.5:Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

MGSE9-12.G.GMD.1 : Give informal arguments for geometric formulas. (a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

Video Lessons: (p1, p2, p3, p4, p5)

Area & Volume Formula Sheet (Doc, PDF)

Sample Quiz: (Interactive, PDF) Unit 4-7: Surface Area (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.GMD.1 : Give informal arguments for geometric formulas. (a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

Video Lessons: (p1, p2, p3a, p3b, p4, p5)

Area & Volume Formula Sheet (Doc, PDF)

Sample Quiz: (Interactive, PDF) Unit 4-8: Volume of Prisms and Cylinders (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.GMD.1 : Give informal arguments for geometric formulas. (a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments. (b) Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

MGSE9-12.G.GMD.3:Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Video Lessons: (p1, p2, p3, p4)

Sketchpad: Volume Layers Demonstration (gsp file)

Area & Volume Formula Sheet (Doc, PDF)

Sample Quiz: (Interactive, PDF) Unit 4-9: Volume of Pyramids and Cones (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.G.GMD.1 : Give informal arguments for geometric formulas. (a) Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments. (b) Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

MGSE9-12.G.GMD.3:Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Video Lessons: (p1, p2, p3, p4)

Sketchpad: Cavalieri's Principle, Sphere Volume Proof

Area & Volume Formula Sheet (Doc, PDF)

Sample Quiz: (Interactive, PDF) TEST : Testing Item Banks for Exam View

(315 available questions for Unit 4) 