Mathematics Algebra II Unit 11: Conic Sections
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1 Mathematics Algebra II Unit 11: Conic Sections
2 1 What conic section is formed when a plane is passed through a cone parallel to its base? 5 raph the following: (x 3) 2 (y + 2) 2 = 36 2 Complete the square to find the coordinates of the center of the following conic section. Show your work. x 2 + y 2 +x + 6y + 5 = 0 3 What happens to the graph of : (x 3) 2 + 5(y 2) 2 = 20 6 Identify the conic section: y 2 + y = x 2 + 6x 8 if the 3 is changed to a 5? The x intercepts of a parabola are at ( 5, 0) and (9, 0). What is the equation of the axis of symmetry? x = 2 x = 2 7 Complete the square to find the coordinates of the vertex for: x 2 10x + 31 = 0 Show your work. x = x = Page 2 O ON
3 8 Identify the line(s) of symmetry for the rectangular hyperbola shown in the graph: y = x, y = x x = 0, y = 0 y = 0 y = x 9 Identify the conic section modeled by the equation: 11 ow many lines of symmetry does a circle have? A B C D circle hyperbola ellipse parabola 10 If the foci of an ellipse were in the same location as the center, the ellipse would be short and wide the ellipse would be tall and skinny the ellipse would become a single point the ellipse would be a circle Page 3 O ON
4 12 A double napped cone is sliced so that the cross section forms a hyperbola. Which figure illustrates the conic section described? igure A igure B igure C none of the above 13 An architect firm is designing a water pond that is to surround a newly erected statue enhancing the landscape of a local senior citizens' assisted living center. If the proposed plan shows the equation of 1 What conic section is formed when the plane intersects the cone as shown? the pond as 9x 2 + y 2 = 36, what conic section describes the shape of the pond? A circle B parabola C ellipse D hyperbola circle ellipse parabola hyperbola Page O ON
5 15 Which of the following is the correct graph of the equation shown? 16 Write the equation of the graph below after a translation of units to the right and 3 units up. A B C D Page 5 STOP
6 Test Key Mathematics Algebra II Unit 11: Conic Sections ## Item # Correct Answer Primary SE Secondary SE Obj/Cat 1 MA D Circle A2.5(A) [S] None 2 MA D (-2,-3) A2.5(E) [S] None 3 MA D graph is shifted 2 units to the right A2.5(B) [S] None AL222807CS A2.5(C) [S] None 5 MA200230RX 0 to 3 A2.5(B) [S] None 6 MA D hyperbola A2.5(D) [S] None 7 MA D (5,2) A2.5(E) [S] None 8 AL222806CS A2.5(C) [S] None 9 AL222808CS B A2.5(D) [S] None 10 AL22280CS A2.5(B) [S] None 11 MA D infinitely many through the center of the circle A2.5(C) [S] None 12 AL222802CS A2.5(A) [S] None 13 AL222809CS C A2.5(D) [S] None 1 MA200215RX A2.5(A) [S] None 15 AL222803CS C A2.5(B) [S] None 16 AL222805CS A2.5(B) [S] None
7 Scoring Rubrics 5 3 The response shows full understanding of the essential mathematics applicable to the task and a sound approach toward solution that includes logical reasoning and appropriate conclusions. Computation and procedures used are generally accurate, but the response may contain minor computational or procedural flaws that do not detract from evidence of full understanding. 2 The response shows a satisfactory understanding of the essential mathematics applicable to the task, but reasoning may not be completely clear, and there may be minor flaws in computation and/or use of procedures as a result of carelessness or non-essential misunderstandings. The flaws do not detract from evidence of satisfactory understanding. A score of 2 may also be earned if the response is partially correct but some aspect of the task is omitted. 1 The response indicates limited understanding of the essential mathematics applicable to the task. While an effort is made to address the task, omissions and/or errors related to insufficient mathematical knowledge or incorrect application of skills or procedures bring into question that student's ability to deal successfully with tasks of this type. 0 The response indicates no understanding of the essential mathematics applicable to the task, or there is no response.
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