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# Mathematics Curriculum Framework - November 2000

## Learning Standards

 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Specify locations and describe spatial relationships using coordinate geometry and other representational systems Apply transformations and use symmetry to analyze mathematical situations 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. 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. 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. 12.G.4 Relate geometric and algebraic representations of lines, simple curves, and conic sections. 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.

Geometry