Math | Graded Assignment | Unit Test, Part 2 | Conic Sections Name: Date: Graded Assignment Unit Test, Part 2: Conic Sections Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 22 points (Score for Question 1: ___ of 10 points) 1. The equation of an ellipse is given by  x  3 2 64   y  5 2 100  1. (a) Identify the coordinates of the center of the ellipse. (b) Find the length of the major and minor axes. (c) Graph the ellipse. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 2 Math | Graded Assignment | Unit Test, Part 2 | Conic Sections (Score for Question 2: ___ of 12 points) y 2  x  6  2. The equation of a hyperbola is given by 25 144 2  1. (a) Identify the coordinates of the center of the hyperbola. (b) Find the length of the transverse and conjugate axes. (c) Find the slopes of the asymptotes. (d) Graph the hyperbola. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 2 of 2 Math | Graded Assignment | Semester Test, Part 2 Name: Date: Graded Assignment Semester Test, Part 2 Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 38 points (Score for Question 1: ___ of 10 points) 1. Consider the function f  x   x 4  3x 3  7x 2  15x  18 . (a) Find the possible rational roots of f  x   0 . (b) Use synthetic division to divide f ( x) by x  3 . Show all your work. Use your answer to explain whether or not x  3 is a factor of f ( x) . (c) Factor f ( x) completely. Show all your work. (d) Sketch the graph of f ( x) by plotting the x-intercepts, finding and plotting additional points on the graph, and using what you know about the graph’s end behavior. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 4 Math | Graded Assignment | Semester Test, Part 2 (Score for Question 2: ___ of 10 points) 2. The population of frogs in a park is decreasing exponentially at a rate of 2% each year. In the year 2006, the population was estimated to be 4800. (a) Use the exponential decay formula to write an equation to model the situation. (b) Use your equation from Part a to predict the frog population in the year 2018. (c) Sketch the graph of the equation you wrote in Part a. Find its asymptote, domain, and range. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 2 of 4 Math | Graded Assignment | Semester Test, Part 2 (Score for Question 3: ___ of 8 points) 3. An office manager recorded the number of reams of paper that were used for a printer each month for six months: 15, 10, 25, 19, 10, 17. (a) Identify the five-number summary of the data set. (b) Draw the box-and-whisker plot. (c) Compute the standard deviation. Show all your work. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 3 of 4 Math | Graded Assignment | Semester Test, Part 2 (Score for Question 4: ___ of 10 points) 4. A home furnishings store has two locations, one in the north and one in the south. The matrices below show the costs of their most popular sheet set, in dollars, and the current inventory of the sets in two colors at both locations. Northern Location Twin Queen King C  cost 24 39 49 Southern Location White Beige Twin  6 N  Queen  8 King  7 11 4  3  White Twin  14 S  Queen  1 King  5 Beige 13  6  8  (a) Find CN and CS. (b) Tell which location has the greater dollar value of beige sheets in their inventory, and find the difference in these dollar values. (c) Find CN + CS. Describe what each element in the matrix represents. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 4 of 4
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