Standardized Test Prep

SAT/ACT

80. What is the simplified form of the expression 3 18 x y 2 fraction 3 , over square root of 18 x , y squared end root end fraction  if x and y are positive?
    1. 2 x 2 x y fraction square root of 2 x end root , over 2 x y end fraction
    2. 2 y 2 x y fraction square root of 2 y end root , over 2 x y end fraction
    3. 54 x y 2 2 x y fraction square root of 54 x , y squared end root , over 2 x y end fraction
    4. 27 x y 2 2 x y fraction square root of 27 x , y squared end root , over 2 x y end fraction
81. What are the solutions, in simplest form, of the quadratic equation 3 x 2 + 6 x − 5 = 0 ? 3 x squared , plus 6 x minus 5 equals 0 question mark
    6. − 6 ± 96 6 fraction negative 6 plus minus square root of 96 , over 6 end fraction
    7. − 6 ± i 24 6 fraction negative 6 plus minus i square root of 24 , over 6 end fraction
    8. − 3 ± 2 6 3 fraction negative 3 plus minus 2 square root of 6 , over 3 end fraction
    9. − 3 ± i 6 3 fraction negative 3 plus minus i square root of 6 , over 3 end fraction
82. Which inequality is shown by the graph below?

    

    1. y ≥ 2 3 | x − 1 | − 2 y greater than or equal to , 2 thirds absolute value of , x minus 1 , end absolute value , . minus 2
    2. y ≥ 2 3 | x − 2 | − 1 y greater than or equal to , 2 thirds absolute value of , x minus 2 , end absolute value , . minus 1
    3. y ≥ 3 2 | x − 1 | − 2 y greater than or equal to , 3 halves absolute value of , x minus 1 , end absolute value , . minus 2
    4. y ≥ | 2 3 x − 1 | − 2 y greater than or equal to absolute value of . 2 thirds , x minus 1 , end absolute value , . minus 2

83. A triangle has the dimensions shown below.

    

    What is the height of a triangle with equal area but a base of 36?

    6. h 3 h over 3
    7. 2 h 3 fraction 2 h , over 3 end fraction
    8. 2h
    9. 3h

    Short Response

84. Find the axis of symmetry of the graph of the function y = − 2 x 2 − 5 x + 4 . y equals negative 2 , x squared , minus 5 x plus 4 .  Show your work.

Mixed Review

See Lesson 6-1.

Simplify each radical expression. Use absolute value symbols when needed.

85. 121 a 90 square root of 121 , eh to the ninetieth end root
86. 81 c 48 d 64 square root of 81 , c to the forty eighth . d to the sixty fourth end root
87. 64 a 81 3 cube root of 64 , eh to the eighty first end root ,
88. 32 y 25 5 the fifth , root of 32 , y to the twenty fifth end root ,

See Lesson 5-4.

Divide using synthetic division.

89. ( y 3 − 64 ) ÷ ( y + 4 ) open , y cubed , minus 64 close divides open y plus 4 close
90. ( 6 a 3 + a 2 − a + 4 ) ÷ ( a + 1 ) open 6 , eh cubed , plus , eh squared , minus eh plus 4 close divides open eh plus 1 close

See Lesson 4-6.

Complete each square.

91. x 2 + 10 x + □ x squared , plus 10 x plus white square
92. x 2 − 10 x + □ x squared , minus 10 x plus white square
93. x 2 + 11 x + □ x squared , plus 11 x plus white square
94. x 2 − 11 x + □ x squared , minus 11 x plus white square

Get Ready! To prepare for Lesson 6-3, do Exercises 95-98.

See Lesson 4-8.

Write each quotient as a complex number in the form a ± b i . eh plus minus b i .

95. 2 3 − i fraction 2 , over 3 minus i end fraction
96. 5 2 + 3 i fraction 5 , over 2 plus 3 i end fraction
97. 4 4 + i fraction 4 , over 4 plus i end fraction
98. − 1 7 − 5 i fraction negative 1 , over 7 minus 5 i end fraction

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