Learning Standards
Geometry
for Grades 11-12
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Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships |
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Specify locations and describe spatial relationships using coordinate geometry and other representational systems |
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Apply transformations and use symmetry to analyze mathematical situations |
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Use visualization, spatial reasoning, and geometric modeling to solve problems |
Learning Standards
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
| 12.G.1 |
Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
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| 12.G.2 |
Derive and apply basic trigono-metric identities (e.g., sin2θ + cos2θ = 1, tan2θ + 1 = sec2θ) and the laws of sines and cosines.
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| 12.G.3 |
Use the notion of vectors to solve problems. Describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically. Use vector methods to obtain geometric results.
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| 12.G.4 |
Relate geometric and algebraic representations of lines, simple curves, and conic sections.
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| 12.G.5 |
Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems. |
Exploratory Concepts and Skills
for Grades 11-12 and Single-Subject Courses
- Investigate and compare the axiomatic structures of Euclidean and non-Euclidean geometries.
- Explore the use of conic sections in engineering, design, and other applications.
- Investigate the notion of a fractal.
- Use graphs (networks) to investigate probabilistic processes and optimization problems.
last updated: November 1, 2000
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