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Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Indicate the answer choice that best completes the statement or answers the question. Simplify the given expression. 2. (5x2 – 10x – 20) + (9x2 – 4) 1. Graph the given relation or equation and find the domain and range. Then 2 – 24 determine whether a. 14x b. 14x2 – 10x – 24 the relation or equation is a function. c. 14x2 – 10x + 24 d. 14x2 – 10x – 16 (3.1, 5.1), (–1.9, 5.1), (–4.9, 3.1), (–4.9, –2.9) a. b. 3. (–3x2 – 7x + 17) – (20x2 + 25x – 9) a. –23x2 – 32x + 8 b. –23x2 – 32x + 26 c. –23x2 – 18x + 26 d. –23x2 – 27x + 8 4. –5xy(4xy3 – 8xy + 6y2) a. –20x2y4 – 8x2y2 + 6x2y3 c. –20x2y4 + 40x2y2 – 30xy3 b. –20x2y4 + 40xy + 30y2 d. –20x2y4 – 8xy + 6y2 Simplify the expression using synthetic division. 5. (9x3 – 151x2 + 566x – 600) ÷ (x – 12) Domain: {–4.9, –1.9, 3.1} Range: {–2.9, 3.1, 5.1} The equation is a function. c. a. quotient 9x2 – 259x – 2542 and remainder 29,904 d. b. quotient 117x2 + 1253x – 15,602 and remainder 186,624 c. quotient 9x2 – 43x + 50 and remainder 0 d. quotient 108x2 + 1145x + 14,306 and remainder 171,072 Factor the polynomial completely. 6. 26xy – 39y – 40x + 60 a. 13y(2x – 3) – b. 13y(2x – 3) – 40x + 60 20(2x – 3) c. (13y – 20)(2x – d. (26xy – 39y) – 3) (40x – 60) Domain: {–4.9, 5.1, 3.1} Range: {–2.9, 3.1, –1.9} The equation is not a function. Powered by Cognero 7. 7x2 – 19x + 10 a. 7x(x – 2) – 5(x – 2) b. 7x2 – 13x – 6x + 10 c. (7x – 5)(x – 2) d. 7x2 – 14x – 5x + 10 Page 1 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review 8. 64x3 + 125y3 a. (4x – 5y)(16x2 – b. (4x + 5y)(16x2 – 20xy + 25y2) 20xy + 25y2) c. (4x – 5y)(16x2 + d. (4x + 5y)(16x2 + 20xy + 25y2) 11. Graph the quadratic function a. b. 25y2) 9. x4 – 34x2 + 225 = 0 a. 3, –3, 5, –5 c. 5, –5 b. 3, –3, 7, –7 d. 2, –2, 9, –9 10. Graph the quadratic function a. b. c. c. Powered by Cognero d. d. Page 2 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review 12. Consider the quadratic function f(x) = –2x2 + 4x – 4. Find the y-intercept and the equation of the axis of symmetry. a. The y-intercept is 4. The equation of the axis of symmetry is x = –1. b. The y-intercept is 1. The equation of the axis of symmetry is x = –4. Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. 14. a. b. c. The y-intercept is –4. The equation of the axis of symmetry is x = 1. d. The y-intercept is –1. The equation of the axis of symmetry is x = 4. Factor the polynomial completely. 13. 4a 4b 2 – 6a 3b 2 a. 2(2a 4b 2 – 3a 3b 2) b. 2a 3b 2(2a – 3) c. a 3b 2(4a – 6) d. 2a 2b 2(2a 2 – 3) One solution is between –1 and –2, while the other solution is between 0 and 1. c. d. One solution is between 0 and –1, while the other solution is between 1 and 2. Powered by Cognero Page 3 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. 15. f(x) = –x2 + 10x + 2 a. The function has a minimum value. The minimum value of the function is –73. b. The function has a maximum value. The maximum value of the function is –73. c. The function has a maximum value. The maximum value of the function is 27. d. The function has a minimum value. The minimum value of the function is 27. 18. Write an equation for the parabola whose vertex is at (4, 6) and which passes through (5, 24). a. y = 18(x – 4)2 + 6 b. y = (x + 4)2 – 6 c. y = 18(x + 4)2 – 6 d. y = –18(x – 4)2 + 6 19. Graph the quadratic function . a. b. c. d. Write the following quadratic function in vertex form. Then, identify the axis of symmetry. 16. y = x2 + 10x – 3 a. The vertex form of the function is y = (x + 5)2 – 28. The equation of the axis of symmetry is x = –5. b. The vertex form of the function is y = (x – 5)2 – 28. The equation of the axis of symmetry is x = –5. c. The vertex form of the function is y = (x + 5)2 – 28. The equation of the axis of symmetry is x = –28. d. The vertex form of the function is y = (x + 5)2 + 28. The equation of the axis of symmetry is x = –28. 17. Write an equation for the parabola whose vertex is at (2, 8) and which passes through (4, 4). a. y = (x + 2)2 – 8 b. y = 1(x – 2)2 + 8 c. y = –1(x – 2)2 + 8 d. y = –1(x + 2)2 – 8 Powered by Cognero Page 4 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Graph the quadratic inequality. 21. 20. a. b. c. d. Powered by Cognero a. b. c. d. Page 5 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review 22. Graph the given function. State the domain and range. a. b. 23. Graph the given function. State the domain and range. a. The domain is x ≤ and the range is y 4. c. b. The domain is x ≤ and the range is y ≤ 1. d. c. The domain is x 4. d. and the range is y The domain is x ≤ y and the range is 1. 24. Determine whether each pair of functions are inverse functions. 1) f(x) = , g(x) = 2) f(x) = x – 12, g(x) = x + 12 a. Both 1 and 2 are inverse functions. b. Only 2 is an inverse function. c. Neither 1 nor 2 is an inverse function. d. Only 1 is an inverse function. Powered by Cognero Page 6 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Find the inverse of the given function. 25. f(x) = a. f –1(x) = b. f –1(x) = c. f –1(x) = d. f –1(x) = Write the given expression in radical form. 26. a. b. c. d. 27. a. b. c. d. 28. Find the value of the discriminant. Then describe the number and type of roots for the equation. 29. –x2 – 20x + 5 = 0 a. The discriminant is 400. Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. b. The discriminant is –420. Because the discriminant is less than 0, the two roots are complex. c. The discriminant is 420. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational. d. The discriminant is –380. Because the discriminant is less than 0, the two roots are complex. Find the exact solution of the following quadratic equation by using the Quadratic Formula. 30. –x2 + 5x + 7 = 0 a. b. a. {(5 c. d. c. {(–5 )/–2} )/–2} b. {(–5 )/–2} d. {(–5 )/–2} Solve the equation by completing the square. 31. 2x2 + x = 0 a. {–1, 0} c. {0} b. {0, 0.5} d. {–0.5, 0} Solve the equation by factoring. 32. x2 + 2x – 35 = 0 a. {–5, 7} b. {–7, 5} c. {5, 7} d. {–5, –7} Factor the polynomial completely. 33. 5x4y – 10x2y2 Powered by Cognero a. 5x2y(x2 – 2y) b. 5x2(x2y – 2y2) c. x2y(5x2 – 10y) d. 5(x4y – 2x2y2) Page 7 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Simplify the given expression. Assume that no variable equals 0. 34. 35. Graph the given inequality. y ≤ –3 – | x | a. b. 8x 16y8 16x 11y12 a. b. x 20 2y16 c. x 20 16y16 d. x5 16y4 Powered by Cognero x 20y–16 16 c. d. Page 8 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review 36. Graph the given inequality. y ≤ 6 – | x | a. c. 37. Graph the given inequality. b. a. b. d. c. d. Use substitution to solve each system of equations. 38. x + y = –12 –5x – 6y = 64 a. (–4, –8) b. (–3, –5) c. (–8, –4) d. (–5, –3) Powered by Cognero Page 9 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Use the elimination method to solve each system of equations. 39. 2x – 2y = –26 2x + 6y = 70 a. (12, –1) b. (–1, 12) c. (5, 6) d. (6, 5) 45. Find and . g(x) = 8x h(x) = –4x3 + 8x2 – 11x + 8 a. = –32x4 + 64x3 – 88x2 + 64x = –2048x4 + 512x3 – 88x2 + 8x b. = –32x3 + 64x2 – 88x + 64 = –2048x3 + 512x2 – 88x + 64 Simplify. 40. (3 + 5i)(8 – 6i) c. = 32x3 + 64x2 – 88x + 64 = –2048x3 + 512x2 – 88x + 8 + 22i – 30i2 a. 24 c. 33 + 40i b. 24 + 22i + 30 d. 54 + 22i 41. (–2 + 8i)(–10 – 9i) a. 92 – 62i c. 20 – 62i – 72i2 d. = –32x3 + 64x2 – 88x + 64 = –2048x3 + 512x2 – 88x + 8 b. 74 + 80i d. 20 – 62i + 72 42. a. + c. + a. – i i b. – i d. – i b. – i d. – i 43. c. + i i 44. Find and g(x) = 6x h(x) = –3x – 6 a. =– . 18x – 36 18x2 – 36x =– = –18x2 18x – 6 – 6x = –18x c. =– b. + 36 =– d. 18x – 36 = –18x +6 Powered by Cognero =– 18x – 36 Page 10 Name: Class: Date: CA2 Review/Semester 1 Final Exam Review Answer Key 27. c 1. d 28. a 2. b 29. c 3. b 30. d 4. c 31. d 5. c 32. b 6. c 33. a 7. c 34. b 8. b 35. b 9. a 36. b 10. d 37. b 11. b 38. c 12. c 39. b 13. b 40. d 14. a 41. a 15. c 42. b 16. a 43. b 17. c 44. b 18. a 45. d 19. b 20. d 21. c 22. b 23. a 24. b 25. b 26. c Powered by Cognero Page 11