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Algebra II Midterm REVIEW Name________________ 12-13 1. Find the value of 3 + 4 [10 – (4+ 2)] a. 28 b. -19 2. Find the graph of y a. c. 19 2 x4 3 b. c. 3. Simplify: 1/2(12x – 6) + 1/4(24x + 8) a. 5 b. 12x-1 c. 12x+1 4. Simplify: (3x + 2)² a. 9x² - 4 c. 9x² - 12x + 4 d. -28 d. 1/2)(x+2) b. 9x² - 6x + 4 d. 9x² + 12x + 4 5. If x²+ 6x + c is a perfect square trinomial, what is the value of c? a. 3 b. 9 c. 36 d. 12 e. 4 6. Simplify: 8 a. 8 b. | 8| 2 c. 8i Solve each equation: 7. 2(6 3x) 12 4(x 2) a. 4 b. -4 c. 1/4 d. -64i d. -1/4 d. 8. 16= 2|3x – 4| a. 4, -4/3 b. 4/3, 4 c. 4, -4 d. 1 9. Find the graph of 2x – y < 3 a. b. 10. |2x – 4|≤ 10 a. x≤ 7 b. -3≤ x ≤ 7 11. Find the graph of f (x) a. c. c. -7≤ x ≤ 3 d. All real numbers 1 x 3 b. 12. Determine how many real and imaginary solutions the equation 2x² + 3x - 8 = 0 has? a. 2 real, no imaginary b. 1 real , no imaginary c. 1 real, 1 imaginary d. no real, 2 imaginary 13. Solve: | x – 4| ≤ -8 a. All real numbers c. no solution d. b. x = -4, -12 d. x = -4, 12 c. d. 14. Give the domain of h = { (-3, 4), (1, 5), (4, 5)} tell if h is a function. a. { 4, 5}; h is a function b. { -3, 1, 4}; h is not a function c. { -3, 1, 4}; h is a function d. { 4, 5}; h is not a function 15. If g(x) 2x 3 3x 2 x 4 find g(-3). a. 74 b. -74 c. -53 d. -53 e. 12 16. What type of polynomial function is f (x) 5x 4 3x 3 2x 1 ? a. constant b. linear c. quadratic d. cubic e. quartic 17.Find the slope and y-intercept of 4x+ 6y = 12? 2 2 2 a. , (0,-2) b. , (0,-2) c. , (0,2) 3 3 3 2 d. , (0,2) 3 18.Find the graph of f (x) x(x 4)2 a. b. c. What is the x intercept of the line whose equation is 6x + 4y = 3? a. -2 b. 1/2 c. 2 d. 19. 20. a. Find the graph of f (x) x 3 2 b. d.-1/2 c. d. 21. What is the slope intercept form of the equation of a line that passes through (6, 1) and is perpendicular to the line whose equation is y = 3x - 2? 1 1 a. y x 3 b. y x 2 3 3 1 c. y = - 3x 3 d. y x 2 3 22. For which equation is the graph a vertical line? a. x = 2 b. y = 4 c. x = y d. y = |x| 23. For which pair of equations are the lines parallel? a. 4x + 2y = 8 and 8x + 16y = 4 b. x + 3y = 4 and x = 3y + 8 c. y = 1/4x + 2 and y = 4x + 1 d. y = 2x and y = -1/2 x 24. a. Find the graph of y 3x 2 7x 4 b. 25. Subtract 3x 3 4x 2 8x 1 from 4x 3 7x 2 2x 3 a. x 3 3x 2 10x 4 b. x 3 3x 2 10x 4 c. d. c. x 3 3x 2 10x 4 d. x 3 3x 2 10x 4 26. What is the vertex of the graph of y = 3(x – 2)² - 8 ? a. ( 2,8) b. (3,-8) c. (-2, -8) 27. What is the correct factorization of 6x² - 5x – 4 ? a. (3x - 4)(2x +1) b. ( 3x –1)(2x+ 4) d. ( 2x + 4)(3x – 1) e. ) (2x – 2)( 3x + 2) 28. What are the zeros of y = x² + 10x + 16 ? a. -2, -8 b. -2, 8 c. 2, -8 29. d. (2, -8) c. (6x + 4)( x – 1) d. 4, 8 e. 2, 8 You want to eliminate x by the addition method in the system: 3x – 4y = 5 -2x + 5y = 8 If you multiply each side of the top equation by 2, by which number would you multiply each side of the bottom equation? a. 2 b. -2 c. 3 d. -3 31. What does d equal in the solution of the system : 2c + d = 5 c-d=1 a. 1 b. -1 c. 2 ` 32. For which system are there infinitely many solutions? a. 2x + 6y = 7 b. x – 2y = 8 4x + 12y = 14 5x = -10y + 40 d. -2 c. 2x – y = 8 2x + y = -8 d. 3x - y = 4 y = 3x – 4 33. Simplify: ( 2 + i ) – ( 5 – 2i) a. -3 – 3i b. -3 + 3i 35. Simplify : a. 5i 3 c. 3 – 3i d. 3 + 3i 75 b. 3i 5 c. 25i 3 d. 5i 5 36. What are all the solutions of 5(x – 2)² - 4 = 21 ? a. 4 b. 7 c. 2 5 d. -2, -4 37. Simplify : 2 8 50 a. 9 2 b. 2 c. d. 2 2 38. Factor : 9x² - 1 = 0 a. ( 3x – 1)² c. ( 3x + 1) ( 3x + 1) e. 2 5 b. ( 3x – 1)( 3x + 1) d. ( 3x – 1)( 3x - 1) 39. Factor: 3x² + 18x + 27 = 0 a. 3( x+3)² b. 3(x – 3)² c. ( 3x – 9)² d. (3x + 3)² 40. What does (x+3)(x-4)(x-1) equal? a. x 3 2x 2 11x 12 b. x 3 2x 2 11x 12 41. Find the product of ( -8 + 4i)(2 – i). a. -12 + 16i b. -12 – 16i d. 20 e. -20– 16i 42. 2 is a. rational b. irrational 43. If a. 1 1 = i, b. -1 c. -20 c. real d. imaginary then i² = ______. c. 1 44. Find the graph of y (x 2)2 1 c. x 3 2x 2 11x 12 d. 1 d. x 3 2x 2 5x 12 a. b. 45. What are the solutions of x² = 25 ? a. 5 b. -1, -25 c. 5, -5 46. The graph of y = x is a a. circle b. line c. parabola c. d. 0, 25 d. rectangle 47. Which polynomial has the factorization: ( 3x + 2) ( 9x² - 6x + 4) a. 27x³ - 8 b. 9x³ - 4 c. 9x³ + 8 d. 27x³ + 8 e. 27x³ + 4 48. What is the quotient of ( 6x³ - 8x² - 2x – 3) ÷ ( x – 2) ? a. 6x³ + 4x² + 6x + 9 b. 6x² + 4x + 6 + 9 c. 6x² + 4x + 6 + __ 9__________ d. 6x² + 4x + 6 + __9__ 6x³ - 8x² - 2x – 3 x–2 e. 6x² - 4x + 6 - __15__ X- 2 49. What are all the rational zeros of f(x) = x³ +2x² - 5x - 6 a. -2, -1, -3 b. 2, 3, 1 c. 2, -3, -1 d. -2, 1 ,3 e. -2, -3, 1 50. How many zeros does the function f(x) = -2x4 + 3x + 4 have ? a. 0 b. 1 c. 2 d. 3 e.4 51. Which function is graphed? d. a. F(x) = (x+2)(x – 3)(x – 1) c. f(x) = -x(x+2)(x-3) 52. b. f(x) = x(x-1)(x + 3) d. f(x) = x(x+1)(x+3) Find the graph of y (x 2)(x 4) a. b. c. d. 53. Write the polynomial function with the solutions 4, -5i. a. f(x) = (x - 4)(x + 5i)(x – 5i) b. f(x) = (x + 4)(x – 5i)(x + 5i) c. f(x) = (x - 4)(x + 5i) d. f(x) = (x + 4)(x + 5i) 54. Solve: x 4 5x 2 36 0 a. 3,2i b. 3,i c. 3,i,2i d. 3i,2 55. 1 Describe the translation of the parent function f ( x) x 2 to obtain the graph of f (x) (x 3)2 2 . 2 a. b. c. d. 56. Vertical shift -2, Horizontal shift -3, shrink 2, reflect over x-axis Vertical shift -2, Horizontal shift -3, stretch 2, reflect over x-axis Vertical shift -3, Horizontal shift 3, stretch 2, reflect over y-axis Vertical shift 3, Horizontal shift -3, shrink 2, reflect over x-axis Find the graph of y (x 2)(x 1)(x 3) . a. b. c.. d. On the back of your answer card show your work for each of the following questions and circle your answers. 57. Solve x 2 5x 2 0 . 58. Write y 4x 2 16x 3 in vertex form.