Name: 9th Grade Final Test Review160 pts Class: Date: Indicate the answer choice that best completes the statement or answers the question. Use the Distributive Property to write each expression as an equivalent algebraic expression. 1. 7(y + 11) a. 7y + 77 b. 7y + 11 c. 7y + 70 d. 18y 2. 6(t 1) a. 6t + 6 b. 6t 1 c. 6t 6 d. 7t 3. 8(u 2) a. 8u 2 b. 8u 16 c. 8u + 16 d. 10u 4. (r + 9)( 4) a. r 36 b. 4r 36 c. 4r + 36 d. 5r 5. 1( h + 5) a. h + 5 b. h 5 c. 4h d. h 5 6. 2(f + 3) a. 2f 6 b. 2f + 3 c. 2f 5 d. 2f + 6 Page 1
7. 4(b 1) a. 4b + 4 b. 4b 1 c. 4b 4 d. 5b 8. 2(d 5) a. 2d + 10 b. 2d 5 c. 2d 10 d. 7d 9. 12(g + 12) a. 12g + 12 b. 12g 120 c. 12g 144 d. 24g 144 10. 18( q 5) a. 18q + 90 b. 18q 5 c. 18q + 90 d. 18q 5 Identify the terms, like terms, coefficients, and constants in each expression. 11. 6y 4 + y a. terms: 6y, 4, y; like terms: 6, 4; coefficients: 6, 1; constant: 4 b. terms: 6y, 4, y; like terms: 6y, y; coefficients: 6, 1; constant: 4 c. terms: 6y, 4, y; like terms: 6y, y; coefficients: 6; constant: 4 d. terms: 6y, 4, y; like terms: 6y, y; coefficients: 6, 1; constant: 6 12. 8u + 2u 3u a. terms: 8u, 2u, 3u; like terms: 8u, 2u; coefficients: 8, 2, 3; constants: none b. terms: 8u, 2u, 3u; like terms: 8u, 2u, 3u; coefficients: 8, 2, 3; constants: none c. terms: 8u, 2u, 3u; like terms: 8u, 2u, 3u; coefficients: 8, 2; constants: none d. terms: 8u, 2u, 3u; like terms: 8u, 2u, 3u; coefficients: 8, 2, 3; constants: 8, 2 13. 21w + 5 + 3w 1 a. terms: 21w, 5, 3w, 1; like terms: 21w, 3w; coefficients: 21, 3; constants: 5, 1 b. terms: 21w, 5, 3w, 1; like terms: 21w, 5, 3w; coefficients: 21, 3; constants: 5, 1 c. terms: 21w, 5, 3w, 1; like terms: 21w, 3w; coefficients: 21, 3; constants: 5, 1 d. terms: 21w, 5, 3w, 1; like terms: 21w, 3w; coefficients: 21, 3; constants: 5, 1 Page 2
14. f 3fg + 2g fg + 1 a. terms: f, 3fg, 2g, fg, 1; like terms: f, 3fg, 2g, fg; coefficients: 1, 3, 2, 1; constant: 1 b. terms: f, 3fg, 2g, fg, 1; like terms: 3fg, fg; coefficients: 1, 3, 2, 1; constant: 1 c. terms: f, 3fg, 2g, fg, 1; like terms: 3fg, fg; coefficients: 3, 2; constant: 1 d. terms: f, 3fg, 2g, fg, 1; like terms: 3fg, fg; coefficients: 1, 3, 2, 1; constant: 1, 1 Simplify each expression. 15. 8q + 6 + 5q 3 a. 3q + 3 b. 8q + 3 + 5q c. 3q + 3 d. 3q 3 16. 8 + 5( g + 2) 2 a. 5g b. 8 + 5g c. 12 + 5g d. 20 + 5g 17. 4(y 3) + 9 3y a. y 3 b. y + 6 c. 7y 3 d. y + 21 18. 19g 4h + 4 20(g 1) a. g 4h + 24 b. g 4h + 3 c. g 4h 16 d. g 4h + 5 19. (8 b)( 3) + 6b + 12 10b a. b + 20 b. b 12 c. 7b 12 d. b + 36 Page 3
20. 12z + 4(z 9) + 30 + z a. 7z 6 b. 7z + 21 c. 7z + 66 d. 15z 6 Find the GCF of each pair of monomials. 21. 20, 45x a. 5x b. 180x c. 5 d. 2.5 22. 15r, 25 a. 5 b. 1.67 c. 5r d. 75r 23. 11gh, 33g a. 3 b. 3h c. 11gh d. 11g 24. 16mn, 24m a. 1.5n b. 48mn c. 8 d. 8m 25. 33c, 55cd a. 1.7d b. 11cd c. 11c d. 11 Page 4
Determine whether the triangle with sides of given lengths is a right triangle. Justify your answer. 26. 7 yd, 24 yd, 25 yd a. yes; 7 + 24 = 625 = 25 b. yes; 7 + 25 = 674 = 24 c. no; 7 + 24 = 625 25 d. no; 7 + 25 = 674 24 27. 18 ft, 23 ft, 29 ft a. yes; 18 + 23 = 853 = 29 b. yes; 18 + 29 = 1,165 23 c. no; 18 + 23 = 853 29 d. no; 18 + 29 = 1,165 23 Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary. 28. a, 16 yd; b, 22 yd a. 16 + 22 = c ; 27.2 yd b. 16 + 22 = c ; 740 yd c. 16 + c = 22 ; 15.1 yd d. 16 + 22 = c; 38 yd 29. a, 65 cm; c, 95 cm a. 65 + b = 95; 30 cm b. 65 + 95 = b ; 115.1 cm c. 65 + b = 95 ; 69.3 cm d. 65 + b = 95 ; 4,800 cm 30. The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. Find the length of the other leg. a. 4 in. b. about 10.2 in. c. about 18.6 in. d. 104 in. 31. A leg of a right triangle is 30 meters long, and the hypotenuse is 35 meters long. What is the length of the other leg? a. about 18.0 m b. 30 m c. about 46.1 m d. 325 m Page 5
Evaluate each expression if a = 1, b = 8, c = 5, and d = 1.4. 32. 2b + 4 a. 12 b. 12 c. 20 d. 24 33. 17c + 3b 5 a. 114 b. 114 c. 56 d. 66 34. 4d + 5 2a a. 12.6 b. 12.6 c. 16 d. 16 35. a b + b a a. 16 b. 18 c. 14 d. 14 36. 2 2d 3 b a. 19.2 b. 19.2 c. 20.2 d. 20.2 Solve each equation. Check your solutions. 37. n 4 = 13 a. {9, 17} b. {9, 17} c. { 9, 17} d. { 9, 17} Page 6
38. x 13 = 2 a. {11, 15} b. {11, 15} c. { 11, 15} d. { 11, 15} 39. 2y 3 = 29 a. { 13, 16} b. {13, 16} c. {13, 16} d. { 13, 16} 40. 7 x + 3 = 42 a. { 9, 3} b. {9, 3} c. {9, 3} d. { 9, 3} 41. 3u 6 = 42 a. { 12, 16} b. {12, 16} c. {12, 16} d. { 12, 16} 42. 3 4x 9 = 24 a. {4.25, 0.25} b. Ø c. {4.25, 0.25} d. { 4.25, 0.25} 43. 2 7 3y 6 = 14 a. b. c. d. Ø Page 7
Solve each inequality. Then graph the solution set on a number line. 44. 8x 6 10 a. b. c. d. 45. 23 4u < 11 a. {u u 3} b. {u u 3} c. {u u < 3} d. {u u > 3} 46. 14c < 9c + 5 a. {c c 1} b. {c c > 1} c. {c c < 1} d. {c c < 1} 47. 9(2r 5) 3 < 7r 4 a. {r r > 4} b. {r r 4} c. {r r < 4} d. {r r 4} Page 8
48. 9x 11 > 6x 9 a. b. c. d. 49. 4n 5(n 3) > 3(n + 1) 4 a. {n n > 4} b. {n n < 4} c. {n n 4} d. {n n 4} Solve each inequality. Graph the solution set on a number line. 50. y + 5 < 2 a. {y 7 > y < 3} b. {y 7 > y > 3} c. {y 7 y 3} d. {y 7 < y < 3} 51. x 8 3 a. {x x 5 and x 11} b. {x x 5 or x 11} c. {x x > 5 and x < 11} d. {x x < 5 or x > 11} Page 9
52. 2z 2 3 a. b. c. d. 53. 3n 2 2 < 1 a. b. c. d. 54. 3b + 5 2 a. {x x 1} b. all real numbers c. d. Both B and C are true. Page 10
State the domain and range of each relation. Then determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both or neither. 55. a. D = {5, 10, 15}, R = {105, 110}; no b. D = {5, 10, 15}, R = {105, 110}; yes; onto c. D = {5, 10, 15}, R = {105, 110}; yes; one-to-one d. D = {5, 10, 15}, R = {105, 110}; yes; both 56. a. D = {2, 8}, R = {21, 25, 30}; yes; one-to-one b. D = {2, 8}, R = {21, 25, 30}; no c. D = {21, 25, 30}, R = {2, 8}; no d. D = {2, 8}, R = {21, 25, 30}; yes; onto 57. a. D = { 1, 0, 1}, R = { 2, 1, 1, 2}; no b. D = { 2, 1, 1, 2}, R = { 1, 0, 1}; yes; one-to-one c. D = { 2, 1, 1, 2}, R = { 1, 0, 1}; yes; onto d. D = { 2, 1, 1, 2}, R = { 1, 0, 1}; no Page 11
Graph each equation and determine the domain and range. Determine whether the relation is a function, is one-toone, onto, both, or neither. Then state whether it is discrete or continuous. 58. y = 2x 1 a. D = {all real numbers}, R = {all real numbers}; yes; both; continuous b. D = {all real numbers}, R = {all real numbers}; yes; both; continuous c. D = {all real numbers}, R = {all real numbers}; yes; both; continuous d. D = {all real numbers}, R = {all real numbers}; no; continuous Find each value if and g(x) = 2x + 3. 59. f(3) a. 3 b. 0 c. 5 d. 1 60. f( 4) a. b. c. d. 11 Page 12
61. a. 4 b. 2 c. 2 d. 4 62. f( 2) a. 1 b. c. 0 d. undefined 63. g( 6) a. 15 b. 15 c. 9 d. Find the slope of the line that passes through each pair of points. Express as a fraction in simplest form. 64. (3, 8), ( 5, 2) a. b. c. d. 65. ( 10, 3), (7, 2) a. b. c. d. Page 13
66. ( 7, 6), (3, 6) a. undefined b. c. 3 d. 0 67. (8, 2), (8, 1) a. 0 b. 16 c. d. undefined 68. ( 6, 3), ( 8, 4) a. b. c. d. Write an equation in slope-intercept form for the line described. 69. slope 2, y-intercept at 0 a. x = 2y b. 2x + y = 0 c. y = 2x d. y = x 70. parallel to y = 4x + 2, y-intercept at 4 a. y = 4x + 4 b. 4x + y = 4 c. y = 4x + 2 d. y = x + Page 14
71. perpendicular to, passes through (0, 0) a. y = 4x b. c. d. y = 4x + 2 72. perpendicular to, passes through (2, 3) a. b. c. y = 2x 1 d. y = 2x + 1 73. parallel to y = 3x + 4, x-intercept at 4 a. y = x + 12 b. y = 3x + 12 c. y = 3x + 4 d. y = 3x + 12 Write an equation in slope-intercept form for the line that satisfies each set of conditions. 74. slope 5, passes through ( 3, 8) a. y = 15x + 40 b. y = 3x 8 c. y = 5x 8 d. y = 5x 23 75. perpendicular to y = 3x 2, passes through (6, 1) a. b. c. d. Page 15
Graph each function. Identify the domain and range. 76. a. D = {x x 0}, R = {all real numbers} b. D = {x x 0}, R = {all real numbers} c. D = {x x 0 or x 0}, R = {all real numbers} d. D = {x x 0}, R = {all real numbers} Page 16
77. a. D = {all real numbers}, R = {all real numbers} b. D = {all real numbers}, R = {all real numbers} c. D = {all real numbers}, R = {all real numbers} d. D = {x x 2}, R = {all real numbers} Page 17
78. f(x) = x + 1 a. D = {all real numbers}, R = {f(x) f(x) > 0} b. D = {all real numbers}, R = {f(x) f(x 0} c. D = {all real numbers}, R = {f(x) f(x 0} d. D = {all real numbers}, R = {f(x) f(x 0} Page 18
79. g(x) = 2 x a. D = {all real numbers}, R = {g(x) g(x) 0} b. D = {all real numbers}, R = {g(x) g(x) 0} c. D = {all real numbers}, R = {g(x) g(x) 0} d. D = {g(x) g(x) 0}, R = {g(x) g(x) 0} Page 19
80. BUSINESS A wholesaler charges a store $3.00 per pound for less than 20 pounds of candy and $2.50 per pound for 20 or more pounds. Draw a graph of the function that represents this situation. a. b. c. d. Page 20