1 Pre-AP Geometry Chapter 4 Test Review Standards/Goals: (Algebra I/II): D.1.a./A.REI.3./A.CED.1.: o I can solve a multi-step inequality in one variable. o I can solve and graph a compound inequality and write the answer in interval notation. (Algebra II): D.1.b.: A.CED.1.: I can solve an absolute value inequality. (AP Statistics): S.CP.8(+): I can use the Multiplication rule for find the probability of 2 or more events. (AP Statistics): S.MD.7.: I can calculated expected values. E.1.a.: I can determine points or lines of and apply the properties of to figures. E.1.e./G.CO.4.: I can identify and draw images of transformations and use their properties to solve problems. o I can understand the image, pre-image, scale factor, center, and similar figures as how they relate to transformations. E.1.e./G.CO.5.: I can draw a transformed figure and describe the sequence of transformations that were used to carry the given figure onto the other. E.1.e./G.CO.7.: I can understand the definition of congruence and how it relates to a transformation that is a rigid motion. G.1.e./G.CO.2.: o I can determine the effect of reflections and their compositions on the coordinate plane. o I can determine the effect of rotations and their compositions on the coordinate plane. G.1.e./G.SRT.1a: I can understand the idea of a dilation in the context of transformations. o I can identify the scale factor from a dilation. o I can understand the image, pre-image, scale factor, center, and similar figures as how they relate to transformations. G.1.e./G.SRT.1b: I can explain how a scale factor shows how much larger or smaller a figure becomes after a dilation. (Algebra II): E.2.a.: o I can identify the shape of a quadratic function & both the standard & vertex form of a quadratic function. o I can determine whether a quadratic function has a maximum or minimum value. o I can determine the domain & range of a quadratic function & graph it with & without technology. o I can determine the translations that may occur with a quadratic function and decide whether it is a reflection, stretch, compression, or a shift and in what direction and by how many units. (Algebra II): G.GPE.2.: I can derive the equation of a parabola based on a given focus or directrix. IMPORTANT VOCABULARY Transformation Rigid Motion/ Isometry Pre-Image Image Translation Reflection Line of Reflection Rotation Clockwise/ Protractor Dilation Similar figures Scale Factor Reduction Counterclockwise Enlargement Ratio Symmetry Line of line (reflectional) Rotational Order of Magnitude of Point Plane Axis Quadratics Parabola Standard form of an quadratic equation Vertex Directrix Vertex form of of an quadratic equation Focal length Axis of Maximum/Minimum Values Parent function Equidistant Focus
2 PRACTICE MULTIPLE CHOICE QUESTIONS: #1. E.1.e.: Which type of transformation moves all points the same distance in the same direction? a. Rotation b. Translation c. Reflection d. Dilation #2. E.1.a.: How many lines of does a square have? a. 0 b. 2 c. 4 d. 6 e. 8 #3. G.1.e./G.SRT.1a.: What type of dilation occurs with a scale factor of? a. Rotation b. Enlargement c. Reduction d. Reflection e. Translation #4. E.1.e./G.CO.7.: Which type of transformation moves all points the same distance in the same direction? a. Rotation b. Translation c. Reflection d. Dilation #5. E.1.a.: Which letter has rotational, but NOT reflectional? a. A b. C c. O d. Z #6. G.CO.7.: Which transformation turns every point of the pre image through a specified angle and direction about a fixed point? a. Reflection b. Rotation c. Translation d. Dilation #7. E.1.e.: Which of the following is true for an isometry? a. The preimage and image are congruent b. The preimage is larger than the image c. The preimage is smaller than the image d. The preimage is in the same position as the image.
3 #8. E.1.e.: An isometry is a transformation of an object in which the original object and its image are congruent. Which transformation is NOT always an isometry? a. Dilation b. Reflection c. Rotation d. Translation #9. E.1.a.: Which letter has rotational, but NOT reflectional? a. A b. C c. O d. Z #10. E.1.e.: Which action represents the reflection of a figure? a. Slide b. Shift c. Turn d. Flip Given A(2, -6), under which reflection is #11. A (2, 6)? #12. A (-2, -6)? What type of dilation occurs with a scale factor of #13. #14. A point Y with coordinates (-8, 6) is rotated about the origin. What would the resulting coordinates be for the following rotations? #15. 90 #16. 180 #18. 270 #19. 360 Find the coordinates of K with K(-5, 7) for a dilation centered at the origin with a scale factor of #20. 3 #21. ½
4 What is the image of A(-6, 9) under the following translations? #22. (4, -5) #23. (-10, 1) #24. (-5, -3) #25. Which of the following letters have point? A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Which type of do the following figures have? #26. #27. #28. Point 0 is the center of regular hexagon ABCDEF. Determine the following: #29. 180 rotation of F about O. #30. 120 rotation of F about 0. #31. 240 rotation of B about O #32. 300 rotation of BG about O. #33. The coordinates of point A are (-3, b). Point B is created by reflecting point A across the x-axis and then translating the image point 4 units to the right. What are the coordinates of point B?
5 #34. The coordinates of point B are (a, 5). Point C is created by reflecting point B across the x-axis and then translating the image point 7 units to the right and then 5 units up. What are the coordinates of point C? #35. The vertices of ΔABC are A(-4, -1), B(-2, -1) and C(-2, -4). Triangle A B C is created through a translation of (x, y) (x + 5, y 8), followed by a reflection across the y-axis. What are the vertices of ΔA B C? Consider the quadrilateral MNOP with coordinates: M(2, 1), N(5, 7), O(-3, -6) and P(8, -4). #36. Carry out the following transformations: Reflect each point across the x-axis. Translate each point 3 units to the right. Translate each point 7 units down. Dilate by a factor of 2 #37. Carry out the following transformations: Reflect each point across the y-axis. Translate each point 2 units up. Translate each point 5 units to the left. Dilate by a factor of 2.5.
6 Plot the points. J(5, 10) and D(-8, -4). #38. Given D(-8, -4), under what reflection is D (8, -4)? #39. Given J(5, 10), under what reflection is J (5, -10)? #40. Reflect point D first across y = 2 and then across the line x = -2. #41. Reflect point J first across x = -1 and then across y = 3. #42. Reflect point J across the line y = -x. Then, the point should be translated m units right and then n units down. What are the coordinates of the final image? #43. Reflect point D across the line y = -x. Then, the point should be translated m units left and then n units up. What are the coordinates of the final image?
7 #44. Shane is working with transformations of an arrow shape about line l and point P. a. Draw the image of the arrow after 2 successive transformations: 1 st : A reflection across l. 2 nd : Then, a rotation of 270 degrees CLOCKWISE around P. SHOW the image after EACH transformation. 1 st transformation: 2 nd transformation: b. Suppose you draw a dilation of the original arrow centered at P with a scale factor of 3. How does the area of the arrow after the dilation compare to the area of the original area? Consider the following quadratic equation to answer the questions. #45. What is the vertex of the parabola #46. What is the axis of of the parabola given above? #47. What is the y-intercept? #48. Does the parabola have a minimum or a maximum? Where is the min/max?
8 Consider the following quadratic equation to answer the questions. f(x) = #49. What is the vertex of the parabola #50. What is the axis of of the parabola given above? #51. What is the y-intercept? #52. Does the parabola have a minimum or a maximum? Where is the min/max? Solve AND graph the following: #53. 4x + 8 < 12 OR 5 8x -35 #54. #55. #56. #57. #58.
9 Graph each image of the figure using the transformation given. #59. Translate 2 units down and 3 units to the left. #60. Reflect across x-axis and translate 5 right. #61. Reflection across the x-axis. #62. Dilation by a scale factor of 3. Additional Quadratic Practice: Identify the vertex, whether it has a minimum or maximum, the axis of and the intercept for each: #63. #64. y =
10 A bag contains 10 red balls, 5 yellow balls, and 9 white balls. If Brian randomly draws a ball from the bag, puts it aside, and randomly draws another ball from the bag. #65. What is the probability that Brian will draw 2 yellow balls? #66. What is the probability that Brian will draw a red ball and then a yellow ball? FREE RESPONSE PRACTICE: A psychologist studied the number of puzzle subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution: Value of X 1 2 3 4 Probability 0.2 0.4 0.3 0.1 #67. Verify that this is a legitimate probability distribution. #68. Referring to the information above, the probability that a randomly chosen subject completes at least three puzzles in the five-minute period while listening to soothing music is: a. 0.3 b. 0.4 c. 0.6 d. 0.9 #69. Referring to the information above, P (3 or 4) has value a. 0.3 b. 0.4 c. 0.6 d. 0.9 #70. Referring to the information above, the mean (expected)number of puzzles completed successfully, μ x is a. 1 b. 2 c. 2.3 d. 2.5 Consider: y 8 = ¾ (x + 16) #71. What is the slope of a line perpendicular to the one above? Write the equation in slope intercept and in standard form.