Download Analytic Geometry Stndrs - Greater Nanticoke Area School District

Greater Nanticoke Area School District
Analytic Geometry
Analytic Geometry uses coordinate systems to apply algebraic methods in the study of
geometry. Calculators and computers are used regularly.
Standard 2.4: Mathematical Reasoning and Connections
CS 2.4.11A. Use proofs to validate conjecture
38. Apply theorems, formulas, postulates, definitions and undefined terms in a logical
manner to prove or disprove conjecture.
39. Write and interpret statements in if-then form.
CS 2.4.11B. Construct valid arguments from stated facts
40. Attack or defend a problem, solution or procedure based on known facts.
CS 2.4.11C. Determine the validity of an argument
41. Determine if a solution is correct.
42. Use counter examples to test conjecture.
43. Use direct and indirect proofs to test validity.
A. Use coordinate systems to prove theorems analytically.
CS 2.4.11E. Demonstrate mathematical solutions to problems across the curriculum
44. Use algebraic formulas that apply to other disciplines.
45. Use geometric formulas that apply to other disciplines.
46. Write a valid proof using a variety of reasoning strategies.
47. Write analytic proofs of geometric theorems.
Standard 2.5. Mathematical Problem Solving and Communication
CS 2.5.11C. Present procedure s with precision in problem solving.
48. Develop a written and oral justification, which presents results clearly, systematically,
and succinctly.
CS 2.5.11D. Summarize and evaluate results to problem solutions.
49. Write and describe a summary of results to determine validity.
Math Standards: Analytic Geometry
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Standard 2.8: Algebra and Functions
CS 2.8.11A. Analyze and represent data.
98. Represent a pattern algebraically by using a rule or function.
99. Represent a pattern graphically.
A. Plotting points on a number line.
B. Plotting points on a coordinate plane.
C. Determining slope.
D. Plotting polar coordinates.
E. Plotting vectors in a rectangular coordinate plane.
CS 2.8.11D. Model routine and non-routine problem situations.
106. Use geometric patterns to model a problem.
109. Use equations and inequalities to model a problem.
A. Use parametric equations
B. Use polar equations
CS 2.8.11E. Use standard polar or parametric equations to represent graphs of comic
sections.
112. Circles
113. Ellipses
114. Parabolas
115. Hyperbolas
CS 2.8.11H. Use technology to solve systems of equations and inequalities.
122. Use graphing calculator.
A. Graph functions
B. Graph polar equations
C. Graph parametric equations
CS 2.8.11J. Demonstrate the connection between algebra and geometry in the coordinate
plane.
131. Graph algebraic equations.
A. Functions
B. Polar equations
C. Parametric equations
133. Determine if two lines are parallel, perpendicular, or neither.
Math Standards: Analytic Geometry
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CS 2.8.11K. Select, justify and apply an appropriate technique to graph a line ar function
in two variables.
134. Use slope intercept form to graph.
135. Use the x and y intercept to graph.
136. Graph by transformations.
137. Use a graphing calculator.
CS 2.8.11L. Write the equation of a line.
138. Given the graph of a line.
139. Given two points on the line.
140. Given the slope of the line and point on the line.
CS 2.8.11M. Write an equation for a line of best fit from a set of data points.
141. Draw a line of best-fit and determine the equation which best fits (linear,
exponential, quadratic.)
Standard 2.9. Geometry
CS2.9.11G. Solve problems using analytic geometry.
201. Write the equation of a line parallel or perpendicular to a given line through a given
point.
202. Use slope to determine if two lines are parallel or perpendicular.
203. Determine coordinates of the vertices of polygons in a plane.
204. Use coordinate geometry to verify conclusions regarding polygons.
205.Given quadrilaterals in a coordinate plane, solve problems and construct proofs.
206.Given triangles in a coordinate plane, solve problems and construct proofs.
CS 2.9.11H. Construct a geometric figure and its image using various transformations.
207. Investigate a variety of transformations on polygons in a coordinate plane.
A. Reflections.
B. Translations.
C. Rotations.
D. Dilations.
208. Incorporate various types of transformations to illustrate composition of reflections
such as Glide Reflection.
Math Standards: Analytic Geometry
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