lg1p Sem2 Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Simplify y 5 y 3. y 2 y 8 y 15 2y 8 2. Simplify (6x 3 )(x 2 ). 6x 5 6x 6 7x 5 7x 6 3. Simplify (b 4 ) 3. b 7 3b 4 b 12 3b 7 4. Simplify. ssume the denominator is not equal to zero. a 11 a 28 a 3 1 5. rectangle has a length of 25x 3 and a width of 5x 2. Find the area in square units. 25x 6 25x 5 125x 6 125x 5 6. Simplify. ssume the denominator is not equal to zero. 7. Simplify. ssume the denominator is not equal to zero. m 7 n 5 m 3 n 8. Find the degree of the polynomial b 5 + 2b 3 + 7. 3 8 5 7 9. Which of the following polynomials shows the terms of x 2 + 5x 3 4 2x arranged so that the powers of x are in descending order? 5x 3 2x + x 2 4 4 2x + x 2 + 5x 3 5x 3 4 2x + x 2 5x 3 + x 2 2x 4 10. Find (2a 5) (3a + 1). 5a + 6 a 4 a 6 a 4 11. Find 3m 2 (2m 2 m). 5m 4 3m 3 6m 4 3m 2 5m 4 3m 6m 4 3m 3
12.Kiki and Jasmine are both saving money for the same amount of time to buy cars. The equations below represent the amount of money Kiki K and Jasmine J saves in m months. Which equation represents the total amount of money T both girls save? K = 2,500 + 125m J = 1,750 + 180m T = 4,250 + 305m T = 2,680 + 305m 13. Simplify 3(x 2 + 2x) x(x 1). 4x 2 + x 2x 2 + 7x 2x 2 + 3x 2x 2 + 5x 14. Solve 3(2n 6) = 4(n 3). 3 T = 1,875 + 260m T = 3,250 + 205m 4x 2 + 25 20. Each side y of a square is increased by 5 units. Which expression represents the number of square units in the area of the new square? y 2 + 25 2y + 10 y 2 + 10y + 10 y 2 + 10y + 25 6 15. square can be changed into a rectangle by increasing the length of the square by 5 units and increasing the width by 3 units. Which expression represents the area of the rectangle in square units? x 2 + 8x + 15 x 2 + 15 2x + 8 2x + 15 16. Find (2n 3)(n + 4). 3n + 1 2n 2 + 5n 12 2n 2 12 2n 2 + 11n + 1 17. Find (x + 3)(2x 2 4x + 8). 2x 3 + 10x 2 + 20x + 24 12x 2 + 20x + 24 4x 2 4x + 24 2x 3 + 2x 2 4x + 24 18. Find (3y 1) 2. 6y 2 6y + 1 9y 2 6y + 1 9y 2 3y + 1 9y 2 6y 1 21. Factor the monomial 20a 2 b 2 completely. 2 2 5 a a b 2 10 a a b b 1 2 2 5 a a b b 4 5 a a b b 22. Factor 12x 3 y completely. 2 3 x y 2 2 3 x x x y 4 3 x 3 y 12 x x x y 23. Find the GF of 24a and 32b. 2 6ab 4ab 8 24. Which binomial is a factor of 2n 2 32n? 2n 8 n + 16 n 16 n + 4 25. Factor xy + 3x 2x 2 completely. x(y + 3 2x) (2x 3y)(y + x) x(y + 3) + 2x y(x + 3x 2x 2 ) 19. Find (2x 5)(2x + 5). 4x 4x 2 25 4x 2 20x 25
26.Solve b(b + 17) 0. { 17, 0} {0, 17} {17} Factor each trinomial. 27. m 2 + 13m + 42 (m + 1)(m + 13) (m + 6)(m + 7) (m + 10)(m + 3) (m 6)(m 7) 28. The area of a rectangle is (y 2 8y + 15) square inches. Which expression represents a possible length for the rectangle? (y + 5) (y 2) (y 15) (y 3) 29. 3m 2 + 14m 5 (3m + 1)(m 5) (3m 1)(m + 5) (3m + 5)(m 1) (3m 5)(m + 1) 30. Which binomial is a factor of 4x 2 13x + 3? 2x 3 2x 1 4x 3 4x 1 31. Solve 2x 2 5x 3 = 0. (2m 5)(2m 5) prime 33. x 2 + 16 (x + 4)(x + 4) (x + 4)(x 4) (x 4)(x 4) prime 34. Solve 64y 2 = 25 by factoring. 35. Which trinomial is a perfect square trinomial? 3x 2 6x + 9 x 2 + 10x + 25 x 2 + 8x 16 x 2 + 12x 36 36. The area of a circle is given by ( k 2 12 k + 36 ) square inches. What is the radius of the circle? k + 3 k + 4 k 6 k 12 37. Solve x 2 16x + 64 = 0. {8} { 8, 8} {4} { 4} 38. Solve 2x 2 + 12x 18. { 3} {3} { 3, 3} { 9} Factor each polynomial, if possible. If the polynomial cannot be factored, choose prime. 32. 4m 2 25 (2m + 5)(2m + 5) (2m + 5)(2m 5)
39.-Find two different integers such that the square of the integer is 12 less than seven times the integer. 3 and 4 3 and 4 4 and 3 3 and 4 40. GEOMETRY The length of a rectangle is 5 centimeters more than the width. The area of the rectangle is 36 square centimeters. What is the length? 1, 3 1, 1 3, 1 1, 3 45. One root of the quadratic equation whose related function is graphed lies between which consecutive integers? 4 cm 9 cm 14 cm 26 cm 41. Which equation corresponds to the graph shown? y = x 2 + 1 y = x 2 1 y = x 2 1 y = x 2 42. What is the equation of the axis of symmetry of the graph of y = x 2 + 6x 7? x = 6 x = 3 x = 3 x = 6 43. Find the coordinates of the vertex of the graph of y = 4 x 2. Identify the vertex as a maximum or a minimum. (2, 0); maximum (0, 4); minimum (0, 4); maximum (2, 0); minimum 1 and 2 2 and 3 0 and 1 0 and 1 46. Solve k 2 + 4k + 4 = 25 by taking the square root of each side. 5, 5 5 3, 7 7, 3 47. Which value of c makes y 2 + 8y + c a perfect square? 4 16 64 8 48. Which equation is equivalent to x 2 + 2x 3 = 0? (x + 1) 2 = 2 (x 1) 2 = 4 (x 1) 2 = 2 (x + 1) 2 = 4 44. What are the roots of the quadratic equation whose related function is graphed below?
49.Solve the equation 2x 2 + 3x 5 = 0 by using the Quadratic Formula. 5, 1 1, 5 50. State the value of the discriminant for y = x 2 8x + 10. 4.9 24 104 10.2 51. etermine the number of real roots of n 2 5n 6 = 0. 1 real root 2 real roots infinitely many real roots no real roots 52. Which function is quadratic? y = x(3x + 2) x 5y = 9 y = 5 x 2 y = x 3 + 2x 2 53. Which equation corresponds to the graph shown? 1 0 1 55. TOURNMENTS chess tournament starts with 16 people competing. The exponential function describes how many people are remaining in the tournament after x rounds. How many people are left in the tournament after 2 rounds? 4 2 8 1 56. Which set of data displays exponential behavior? y = 2 x + 2 y = 2 x 2 54. What is the y-intercept on the graph shown? 57. Which equation represents exponential decay? y = 0.5(1.2) x y = 10(1.1) x y = 100(0.9) x y = 0.1x 2 Simplify each expression.
58. 59. 60. 61. 62. 4 12 63. Solve. 4 7 8 64. Solve. 2, 4 4 2 2, 4 65. Find the length of the hypotenuse of a right triangle if a = 3 and b = 4. 5 25 7 66. etermine which side measures form a right triangle. 4, 5, 6 3, 4, 5 5, 11, 12 4, 8, 12 67. Find the distance between the points at (1, 3) and (9, 9). 8 10 6 14 68. What is the length of a diagonal of a rectangle with a length of 8 meters and a width of 6 meters? 10 m 14 m 48 m 100 m 69. etermine which side measures form a right triangle. 10, 24, 28 13, 17, 21 5, 12, 13 70. If y varies inversely as x and y = 18 when x = 2, find y when x = 4. 144 36 9 71. State the excluded value(s) of. 2 2, 2 2, 4 4
72. Simplify. 90m 3 n 3 6mn 73. Find. 77. Find (x 2 5x 14) (x + 2). x 7 5x 7 x + 7 x 2 6x 12 78. Express 3600 minutes in days. 150 days 60 days 79. Find. 74. Find. 75. Find. 80. Find. 81. Find. 76. Find (a 2 + 4a 5) (5a). a 2 + 3a
82. Find. 83. Write as a rational expression. 1 2 87. Find. 300 km/hr 12 km/hr 300 m/hr 12 m/hr 88. basketball team uses red or white jerseys and red or white shorts. Which tree diagram shows the possible uniforms the team can wear? 15a 84. Simplify. 85. Solve. 1 89. store sells shirts with 3 designs and 4 colors. How many different shirts are possible if there is only 1 design and 1 color per shirt? 7 12 4 24 5 86. Which value is an extraneous solution of 0 4?
The table shows the attendance of 300 ninth graders over the past month. Number of Number of bsences Students 0 50 1 120 2 75 3 or more 55 90. Find the probability that a randomly-chosen ninth grader will be absent 2 days next month. 91. Find the probability that a randomly-chosen ninth grader will be absent fewer than 2 days next month.