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12/30/2015 Semester A Exam Semester A Exam Luigi Gjurashaj is taking this assessment. 1. Suppose you went to a carnival. The price to get in was $8, and you paid $0.50 to get on each ride. If you went to the carnival and rode 9 rides, how much did you spend? (1 point) $4.50 $17.50 $12.50 $13 2. Name the property of real numbers illustrated by the equation. –3(x + 4) = –3x – 12 (1 point) Distributive Property Associative Property of Addition Associative Property of Multiplication Commutative Property of Addition 3. Solve the compound inequality. (1 point) 3x + 12 ≥ –9 and 9x – 3 ≤ 33 x ≥ –7 and x ≤ –4 x ≥ 7 and x ≤ 4 x ≥ 1 and x ≤ 4 x ≥ –7 and x ≤ 4 https://www.connexus.com/content/render.aspx?disableAssess... 1/27 12/30/2015 Semester A Exam 4. Solve the absolute value equation. (1 point) │4x + 3│= 3 x = 0 or x = x = 0 or x = x = 1 or x = x = 1 or x = 5. Given no other restrictions, what are the domain and range of the following function? f(x) = x2 – 2x + 1 (1 point) D = all real numbers R = all real numbers D = all real numbers R = {y | y ≥ –1} D = all real numbers R = {y | y ≥ 0} D = {x | x ≥ 0} R = {y | y ≤ 1} 6. Write the equation in slope­intercept form. What are the slope and y­ intercept? –12x + 11y = –8 https://www.connexus.com/content/render.aspx?disableAssess... 2/27 12/30/2015 Semester A Exam (1 point) y=– x+ slope: ; y­intercept: y=– x– slope: y= ; y­intercept: x– slope: y= ; y­intercept: – x+ slope: ; y­intercept: 7. What is an equation of the line, in point­slope form, that passes through the given point and has the given slope? point: (11, 3); slope: (1 point) y–3= (x + 11) y–3= (x – 11) y–3=– (x – 11) y – 11 = (x – 3) https://www.connexus.com/content/render.aspx?disableAssess... 3/27 12/30/2015 Semester A Exam 8. Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the given function? y = │8x – 2│ – 7 (1 point) (– , –7); x = – ; translated to the right unit and up 7 units ( , 7); x = ; translated to the right unit and up 7 units (– , 7); x = – ; translated to the left unit and up 7 units ( unit and down 7 , –7); x = ; translated to the right units 9. Which graph best represents the following inequality? (1 point) y ≥ 3x – 5? https://www.connexus.com/content/render.aspx?disableAssess... 4/27 12/30/2015 Semester A Exam https://www.connexus.com/content/render.aspx?disableAssess... 5/27 12/30/2015 Semester A Exam 10. Which graph best represents the feasibility region for the system above? (1 point) https://www.connexus.com/content/render.aspx?disableAssess... 6/27 12/30/2015 Semester A Exam 11. https://www.connexus.com/content/render.aspx?disableAssess... 7/27 12/30/2015 11. Semester A Exam Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the corner of her cage. Zoe ran on the wheel at least twice as long as she scratched at the corners of her cage, and she spent more than hour running on her wheel. Which system of inequalities represents the time Zoe kept Julie awake last night if x is the number of hours Zoe spent running on her wheel and y is the number of hours spent scratching her cage? (1 point) 12. Which matrix represents the system of equations below? (1 point) https://www.connexus.com/content/render.aspx?disableAssess... 8/27 12/30/2015 Semester A Exam 13. Which graph represents y = 3(x –3)2 + 3? (1 point) https://www.connexus.com/content/render.aspx?disableAssess... 9/27 12/30/2015 Semester A Exam https://www.connexus.com/content/render.aspx?disableAssess... 10/27 12/30/2015 Semester A Exam 14. Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. The equation y = 12 + 105x – 16x2 can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the ground, its height is 0 feet.) (1 point) The pumpkin's maximum height is 184.27 feet and it hits the ground after 3.28 seconds. The pumpkin's maximum height is 3.28 feet and it hits the ground after 6.67 seconds. The pumpkin's maximum height is 184.27 feet and it hits the ground after 6.67 seconds. The pumpkin's maximum height is 3.28 feet and it hits the ground after 184.27 seconds. 15. What is the equation, in standard form, of a parabola that models the values in the table? x –2 0 4 f(x) 4 –6 70 (1 point) y = 3x² + 4x – 6 y = 4x² + 3x – 6 https://www.connexus.com/content/render.aspx?disableAssess... 11/27 12/30/2015 Semester A Exam y = 6x² + 3x – 4 y = –4x² – 3x + 6 16. Use the quadratic formula to solve the equation. (1 point) –x2 + 7x = 5 17. Simplify the expression. (1 point) (–6i)(–4i) –24 24i –24i 24 18. What is the solution set to the following system? (1 point) (0, –3), (3, 0) (0, 3), (–3, 0) (0, 3), (3, 0) https://www.connexus.com/content/render.aspx?disableAssess... 12/27 12/30/2015 Semester A Exam (0, –3), (­3, 0) 19. Classify 4x5 + 2x4 – 5x3 + 12 by number of terms. (1 point) binomial trinomial polynomial of 5 terms polynomial of 4 terms 20. What are the zeroes of the function? (1 point) y = (x – 2)(x – 3)(x + 3) –2, 3, –3 2, 3, –3 2, –3, –3 –2, 3, 3 21. Which of the functions graphed below could be defined by a cubic equation? (1 point) https://www.connexus.com/content/render.aspx?disableAssess... 13/27 12/30/2015 Semester A Exam 22. Find the rational roots of x4 + 5x3 + 7x2 – 3x – 10 = 0. (1 point) –2, 1 2, 1 –2, –1 https://www.connexus.com/content/render.aspx?disableAssess... 14/27 12/30/2015 Semester A Exam 2, –1 23. Find all the zeroes of the equation. (1 point) 3x2 – 4 = –x4 1, 2i –1, –2i 1, –1, 2i, –2i, 0 1, –1, 2i, –2i 24. Use the binomial theorem to expand the binomial. (1 point) (s + 3v)5 s5 + 45s4v + 270s3v2 + 810s2v3 + 1215sv4 + 729v5 s5 + 15s4v + 90s3v2 + 270s2v3 + 405sv4 + 243v5 s5 + 15s4v + 90s3 + 270s2 + 405s + 243 s5 – 5s4v + 10s3v2 – 10s2v3 + 5sv4 – v5 25. https://www.connexus.com/content/render.aspx?disableAssess... 15/27 12/30/2015 x y 1 15 2 19 3 16 4 10 5 5 6 1 7 4 Semester A Exam Which equation best represents the regression line for the data given in the table above? (1 point) y = –3x + 22 y = –3x – 22 y = 3x + 22 y = 3x – 22 26. An initial population of 293 quail increases at an annual rate of 6%. Write an exponential function to model the quail population. What will the approximate population be after 4 years? (1 point) https://www.connexus.com/content/render.aspx?disableAssess... 16/27 12/30/2015 Semester A Exam f(x) = (293 • 1.06)x; 930 f(x) = 293(0.06)x; 379 f(x) = 293(1.06)x; 370 f(x) = 293(6)x; 190 27. The half­life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth. (1 point) ; 0.318 kg ; 0.847 kg ; 442.302 kg ; 0 kg 28. Evaluate the logarithm. (1 point) log41024 5 –5 4 6 https://www.connexus.com/content/render.aspx?disableAssess... 17/27 12/30/2015 Semester A Exam 29. Simplify the following expression completely. Show your work. –3(–y – 1) + 5y (1 point) 8y + 3 8y – 3 2y + 3 2y – 3 30. Estimate the value of the logarithm to the nearest tenth. (1 point) log7 55 0.5 2.1 –2.6 6.0 31. Solve ln 3 + ln (4x) = 4. Round your answer to the nearest hundredth. (1 point) 0.01 0.91 4.55 12.90 32. Solve the equation or formula for the indicated variable. (2 points) S = 6r³t, for t https://www.connexus.com/content/render.aspx?disableAssess... 18/27 12/30/2015 Semester A Exam https://www.connexus.com/content/render.aspx?disableAssess... 19/27 12/30/2015 Select attachment 33. Semester A Exam or drag and drop a file into this area - 20 MB limit The function f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and What is the function rule for g(x)? https://www.connexus.com/content/render.aspx?disableAssess... 20/27 12/30/2015 Semester A Exam https://www.connexus.com/content/render.aspx?disableAssess... 21/27 12/30/2015 Select attachment 34. Semester A Exam or drag and drop a file into this area - 20 MB limit Solve the system by substitution. (2 points) https://www.connexus.com/content/render.aspx?disableAssess... 22/27 12/30/2015 Semester A Exam https://www.connexus.com/content/render.aspx?disableAssess... 23/27 12/30/2015 Select attachment 35. Semester A Exam or drag and drop a file into this area - 20 MB limit Suppose x varies directly with y. a. Use the fact that x = 39 when y = –117 to find the constant of variation and equation of variation. b. Find the value of x when y = –132. (2 points) 36. A factory can produce two products, x and y, with a profit approximated by 900. The production of y must exceed the production of x by at least 100 units. M production levels are limited by the formula x + 2y ≤ 1400. a. Identify the vertices of the feasible region. b. What production levels yield the maximum profit, and what is the maximu (2 points) https://www.connexus.com/content/render.aspx?disableAssess... 24/27 12/30/2015 37. Semester A Exam Explain how to solve the following system of equations. What is the solution to t 2x + 2y + z = –5 3x + 4y + 2z = 0 x + 3y + 2z = 1 (2 points) 38. Factor the expression. (2 points) 3x2 + 14x + 8 39. What are the solutions of the quadratic equation? (2 points) 4x2 – 9x – 9 = 0 https://www.connexus.com/content/render.aspx?disableAssess... 25/27 12/30/2015 40. 41. Semester A Exam What is the result when 2x3 – 9x2 + 11x – 6 is divided by x – 3? (2 points) Explain the steps you would use to solve the equation. Find the solution. 82x = 4096 https://www.connexus.com/content/render.aspx?disableAssess... 26/27 12/30/2015 Semester A Exam © 2015 Connections Education LLC. https://www.connexus.com/content/render.aspx?disableAssess... 27/27
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