LA_EastBatonRouge CCSS Geometry Practice Test

Transcription

1 East aton Rouge ssessment SS Math High School I: Teacher Edition L_EastatonRouge SS Geometry Practice Test irections: Read the question. Fill in the bubble next to the corresponding question number on your answer sheet. Sample Question Sample nswer Sheet Sample Item Not vailable

2 1. Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. ll content is the private property of the copyright holders. Page 1

3 2. In this figure, a sequence of rigid motions maps triangle JKL onto triangle XYZ. Which statement explains why the two triangles must be congruent? rigid motion maps angles to congruent angles. rigid motion maps line segments to congruent line segments. rigid motion maps angles to angles with proportional measures. rigid motion maps line segments to line segments with proportional lengths. Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. ll content is the private property of the copyright holders. Page 2

4 3. Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..9 Prove theorems about lines and angles. ll content is the private property of the copyright holders. Page 3

5 4. Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..10 Prove theorems about triangles. ll content is the private property of the copyright holders. Page 4

6 5. Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..10 Prove theorems about triangles. ll content is the private property of the copyright holders. Page 5

7 6. Point P is located on circle O as shown in this figure. Point Q is also located on circle O. Which statement must be true? PQ = OQ PO OQ PO + OQ = PQ PO + OQ PQ Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. ll content is the private property of the copyright holders. Page 6

8 7. Look at this regular polygon. When the regular polygon is rotated counterclockwise about its center point,, which angle of rotation carries the regular polygon onto itself? Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. ll content is the private property of the copyright holders. Page 7

9 8. Trapezoids and '''' are shown on this coordinate plane. Which sequence of transformations can be used to map trapezoid onto trapezoid ''''? reflection across the x axis and translation one unit right and one unit down reflection across the x axis and translation one unit left and one unit up rotation of 180 around the origin and translation one unit right and one unit down rotation of 90 around the origin and translation one unit left and one unit up Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. ll content is the private property of the copyright holders. Page 8

10 9. This circle has a center at point X. Points, E, and F are on the circle. What is? Grade: High School >> ircles >> ircles >> M.9 12.HSG..2 Identify and describe relationships among inscribed angles, radii, and chords. ll content is the private property of the copyright holders. Page 9

11 10. Rectangle JKLM is shown on a coordinate plane. What is the area, in square units, of the rectangle? Grade: High School >> Expressing Geometric Properties with Equations >> Expressing Geometric Properties with Equations >> M.9 12.HSG GPE..7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. ll content is the private property of the copyright holders. Page 10

12 11. Look at this figure. What is the approximate volume of the shaded portion of the cone, in cubic meters? Grade: High School >> Geometric Measurement and imension >> Geometric Measurement and imension >> M.9 12.HSG GM..3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ll content is the private property of the copyright holders. Page 11

13 12. Grade: High School >> Geometric Measurement and imension >> Geometric Measurement and imension >> M.9 12.HSG GM..3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ll content is the private property of the copyright holders. Page 12

14 13. Triangle OPQ is revolved 360 degrees about the y axis to generate a three dimensional figure. Which best describes the shape of the figure? a rectangular solid from which a pyramid is removed a rectangular solid from which a cone is removed a cylinder from which a pyramid is removed a cylinder from which a cone is removed Grade: High School >> Geometric Measurement and imension >> Geometric Measurement and imension >> M.9 12.HSG GM..4 Identify the shapes of two dimensional cross sections of three dimensional objects, and identify three dimensional objects generated by rotations of two dimensional objects. ll content is the private property of the copyright holders. Page 13

15 14. large crowd of people has gathered in a roughly circular area at an outdoor rally. helicopter hovers 400 feet above the center of the crowd. The distance from the helicopter to the edge of the crowd is 500 feet. One method of estimating the number of people in a crowd is to use a population density of 1 person for every 4.5 square feet. ased on the information, which is the best estimate of the number of people at the rally? 7,000 63, ,000 1,300,000 Grade: High School >> Modeling with Geometry >> Modeling with Geometry >> M.9 12.HSG MG..2 pply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, TUs per cubic foot). ll content is the private property of the copyright holders. Page 14

16 15. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..1.a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. ll content is the private property of the copyright holders. Page 15

17 16. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. ll content is the private property of the copyright holders. Page 16

18 17. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. ll content is the private property of the copyright holders. Page 17

19 18. Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. ll content is the private property of the copyright holders. Page 18

20 19. Grade: High School >> Geometric Measurement and imension >> Geometric Measurement and imension >> M.9 12.HSG GM..4 Identify the shapes of two dimensional cross sections of three dimensional objects, and identify three dimensional objects generated by rotations of two dimensional objects. ll content is the private property of the copyright holders. Page 19

21 20. Grade: High School >> ircles >> ircles >> M.9 12.HSG..2 Identify and describe relationships among inscribed angles, radii, and chords. ll content is the private property of the copyright holders. Page 20

22 21. Grade: High School >> ircles >> ircles >> M.9 12.HSG..5 erive 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. ll content is the private property of the copyright holders. Page 21

23 22. Quadrilateral JKLM is inscribed in a circle. Which statements demonstrate that angles J and L are supplementary? Grade: High School >> ircles >> ircles >> M.9 12.HSG..3 onstruct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. ll content is the private property of the copyright holders. Page 22

24 23. Grade: High School >> Expressing Geometric Properties with Equations >> Expressing Geometric Properties with Equations >> M.9 12.HSG GPE..1 erive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 24. Grade: High School >> Expressing Geometric Properties with Equations >> Expressing Geometric Properties with Equations >> M.9 12.HSG GPE..5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). ll content is the private property of the copyright holders. Page 23

25 25. Grade: High School >> Expressing Geometric Properties with Equations >> Expressing Geometric Properties with Equations >> M.9 12.HSG GPE..4 Use coordinates to prove simple geometric theorems algebraically. ll content is the private property of the copyright holders. Page 24

26 26. ll content is the private property of the copyright holders. Page 25

27 Grade: High School >> Expressing Geometric Properties with Equations >> Expressing Geometric Properties with Equations >> M.9 12.HSG GPE..1 erive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. ll content is the private property of the copyright holders. Page 26

28 27. Grade: High School >> Expressing Geometric Properties with Equations >> Expressing Geometric Properties with Equations >> M.9 12.HSG GPE..6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 28. Grade: High School >> Modeling with Geometry >> Modeling with Geometry >> M.9 12.HSG MG..2 pply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, TUs per cubic foot). ll content is the private property of the copyright holders. Page 27

29 29. Grade: High School >> Modeling with Geometry >> Modeling with Geometry >> M.9 12.HSG MG..2 pply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, TUs per cubic foot). ll content is the private property of the copyright holders. Page 28

30 30. ll content is the private property of the copyright holders. Page 29

31 Grade: High School >> ongruence >> ongruence >> M.9 12.HSG O..11 Prove theorems about parallelograms. 31. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..7 Explain and use the relationship between the sine and cosine of complementary angles. ll content is the private property of the copyright holders. Page 30

32 32. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..7 Explain and use the relationship between the sine and cosine of complementary angles. ll content is the private property of the copyright holders. Page 31

33 Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ll content is the private property of the copyright holders. Page 32

34 34. Jordan is building a fence around his backyard. This diagram shows the dimensions of the yard. How many total feet of fencing material will Jordan need to completely enclose his yard? Round your answer to the nearest foot Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ll content is the private property of the copyright holders. Page 33

35 35. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ll content is the private property of the copyright holders. Page 34

36 36. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. ll content is the private property of the copyright holders. Page 35

37 37. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. ll content is the private property of the copyright holders. Page 36

38 38. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. ll content is the private property of the copyright holders. Page 37

39 39. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M. SRT..6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. ll content is the private property of the copyright holders. Page 38

40 40. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. ll content is the private property of the copyright holders. Page 39

41 41. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry ll content is the private property of the copyright holders. Page 40

42 >> M.9 12.HSG SRT..2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. 42. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. ll content is the private property of the copyright holders. Page 41

43 43. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..3 Use the properties of similarity transformations to establish the criterion for two triangles to be similar. ll content is the private property of the copyright holders. Page 42

44 44. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. ll content is the private property of the copyright holders. Page 43

45 For Questions 45 47: ll content is the private property of the copyright holders. Page 44

46 45. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..4 Prove theorems about triangles. 46. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..4 Prove theorems about triangles. ll content is the private property of the copyright holders. Page 45

47 47. Grade: High School >> Similarity, Right Triangles, and Trigonometry >> Similarity, Right Triangles, and Trigonometry >> M.9 12.HSG SRT..4 Prove theorems about triangles. ll content is the private property of the copyright holders. Page 46

48 The following question is not about a passage. 48. Part : Part : Grade: High School >> Modeling with Geometry >> Modeling with Geometry >> M.9 12.HSG MG..3 pply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ll content is the private property of the copyright holders. Page 47