Curriculum Geometry B/ Algebra II
EOCT MATERIALS
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eoctanalgeoexam_r1-2014.pdf | |
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DESCRIPTIONS |
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In this unit, students review the definitions of three types of transformations that preserve distance and angle: rotations, reflections, and translations. They investigate how these transformations are applied in the coordinate plane as functions, mapping pre-image points (inputs) to image points (outputs). Using their knowledge of basic geometric figures and special polygons, they apply these transformations to obtain images of given figures. They also specify transformations that can be applied to obtain a given image from a given pre-image, including cases in which the image and pre-image are the same figure.
This unit introduces the concepts of similarity and congruence. The definition of similarity is explored through dilation transformations. The concept of scale factor with respect to dilations allows figures to be enlarged or reduced. Rigid motions lead to the definition of congruence. Once congruence is established, various congruence criteria (e.g., ASA, SSS, SAS) can be explored. Once similarity is established, various similarity criteria (e.g., AA) can be explored. These criteria, along with other postulates and definitions, provide a framework to be able to prove various geometric proofs. In this unit, various geometric figures are constructed. These topics allow students a deeper understanding of formal reasoning, which will be beneficial throughout the remainder of Analytic Geometry. Students are asked to prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and, conversely, rectangles are parallelograms with congruent diagonals. The method for proving is not specified, so it could be done by using knowledge of congruency and establishing a formalized proof, it could be proven by constructions, or it could be proved algebraically by using the coordinate plane.
This unit investigates the properties of right triangles. The trigonometric ratios sine, cosine, and tangent along with the Pythagorean theorem are used to solve right triangles in applied problems. The relationship between the sine and cosine of complementary angles is identified.
This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors, chords, tangents, and secants. Volume formulas are derived and used to calculate the volumes of cylinders, pyramids, cones, and spheres.
This unit investigates coordinate geometry. Students look at equations for circles and use given information to derive equations for representations of these figures on a coordinate plane. Students also use coordinates to prove simple geometric theorems using the properties of distance, slope, and midpoints. Students will verify whether a figure is a special quadrilateral by showing that sides of figures are parallel or perpendicular.
This unit investigates the concept of probability. Students look at sample spaces and identify unions, intersections, and complements. They identify ways to tell whether events are independent. The concept of conditional probability is related to independence, and students use the concepts to solve real-world problems, including those that are presented in two-way frequency tables. Students find probabilities of compound events using the rules of probability.