PENNCREST HIGH SCHOOL SUMMER REVIEW PACKET For students in entering ALGEBRA 2 (Levels 1 and 2) Name: __________________________________________________________ Assigning Teacher: q Mr. Beatty q Mr. Ikeler q Mr. Graham q Mrs. Miller q Ms. Cristaldi q Mrs. Price q Mr. Ritter q Other: _____________________________________ 1. This packet is to be handed in to your Algebra 2 teacher on the first day of the school year. All work must be shown in the packet OR on separate paper attached to the packet. Completion of this packet is worth one­half of a major test grade and will be counted in your first marking period grade.
2. 3. 1 Summer Review Packet for Students Entering Algebra 2 ( levels I and II) Operations with Integers: Evaluate each expression. 1. 8 + 2 – 7 __________ 2. 23 – 8 – 2 ___________ 3. 4 ∙ 2 – 5 _________ 4. 9 ÷ 3 + 7 ___________ 5. 2 + 7 ÷ 2 – 7 ________ 6. 5 + 4 – 9 ÷ 3 _____ 7. 48 ÷ 4 ÷ 3 _________ 8. 7 ∙ (3 + 4) ___________ 9. (4 + 8) ÷ (3 – 1)___ Solve equations in one variable: Solve each and check. SHOW all work!! 10. 4x + 9x = 39 11. 2n + 7n – 4n = 15 12. 8y – 2y + 4 = 22 13. 2n – 7n = 25 14. ­3x – 7x + 4 = 34 15. ­ 4 = 2y – 6y 16. 3(x – 4) = 15 17. 4(5 – x) = 4 18. 2y + 4(y + 5) = ­16
2 19. 3y = 2y + 14 20. 7x = 2x – 20 21. r + 7 = 3r 22. ­3y = 4y + 35 23. 4n + 3 = 2n – 5 24. ­3y – 9 = 2y + 3 25. 8x + 5 = ­3x – 17 26. 6 – 9n = 4 – n 27. 5y – 7 = ­5y + 8 28. –6 + 2x = 9 – 3x 29. 9 – 2n = 14 – 2n 30. n + 4n = 2n – 15 31. –3(2x – 3) = 20 – 4x 32.
1 ( 6 x - 9 ) = 7 - 2 x
3 Exponents. Simplify each expression. 33. x( x ) = __________ 34. n5 × n 7 = __________ 35.
( - x )( - x ) = _____ 36.
y 3 ( y 4 )( - y 5 ) = _______ 37. x 4 × x 9 = __________ 38.
- y ( y 2 )( y 5 ) = ____
3 2
5 39.
( 3 x ) ( 7 x 2 ) = _________ 42.
( x ) = __________ 45.
40.
( -4 y )( - 7 y ) = _________ 41.
43.
( n ) = ____________ ( x y ) = _________ 46.
48. n 5 = ___________ n 2 51. 54. 4 3
2 8 y ( 5 y 2 )( - 2 y 3 ) = __ 3 44.
( - x ) = _________ ( 2x ) = ____________ 47.
( 4x y ) = _______ 49. x 3 = ______________ x 3 50. x 2 y 5
= __________ xy 2 x 4 y 6 = __________ xy 52. 25 x 3 y 2 = __________ 5 xy 53. 18 m8 n 5 = ________ - 3 m 6 n3 -4 x 2 y 5
= __________ - 2 xy 3 55. 81 x 4 y 5 z 7 = ___________ 9 x 2 yz 2 56. -20 x 9 y 4 z 3 = _____ - 5 x 7 y 2 z
2 2 4 9 3 3
2 3 Multiplying Binomials: Find each product. (Hint: use FOIL.) 57. (x + 2)(x + 5) = ______________ 58. (y + 4)(y – 3) = _________________ 59. (n – 5)(n – 3) = ______________ 60. (x + 3)(2x + 4) = _______________ 61. (4y – 2)(3y – 7) = ______________ 62. (5n + 3)(2n + 3) = ______________ 63. (8x – 4)(2x + 5) = ______________ 64. (9y + 7)(3y – 4) = ______________ 65. (x – 4) 2 = _________________ 66. (y + 8) 2 = _________________ 67. (x – 1) 2 = _________________ 68. (y +2) 2 = _________________ 69. (2n – 2) 2 = _________________ 70. (5y + 4) 2 = _________________
4 Factoring: Factor each completely. 71. x 2 + 4 x + 4 = _______________ 72. 25m 2 - 30m + 9 = _______________ 73. x 2 - 12 x + 36 = _______________ 74. 16 y 2 + 8 y + 1 = _______________ 75. 9 x 2 + 42 x + 49 = _______________ 76. 81n 2 - 90n + 25 = _______________ 77. x 2 - 5 x + 6 = _______________ 78. x 2 + 3x - 4 = _______________ 79. y 2 + 4 y - 21 = _______________ 80. n 2 + 3n - 18 = _______________ 81. x 2 - 6 x - 7 = _______________ 82. y 2 - 5 y - 36 = _______________ 83. m 2 + 12m + 32 = _______________ 84. x 2 - x - 30 = _______________ 85. x 2 - 3x - 4 = _______________ 86. n 2 - 3n - 18 = _______________ 87. 2 x 2 + 15 x + 7 = _______________ 88. 3 y 2 - 13 y - 10 = _______________ 89. 7 x 2 - 11x + 4 = _______________ 90. 4m 2 + 3m - 27 = _______________ 91. 2 y 2 - 17 y + 21 = _______________ 92. 4 x 2 + 8 x + 3 = _______________ 93. 10 x 2 + 21x - 10 = _______________ 94. 14 y 2 - 33 y - 5 = _______________ 95. 6n 2 - 25n + 14 = _______________ 96. 4 x 2 + 18 x - 10 = _______________ 97. 4n 2 + 18n - 10 = _______________ 98. 4 y 2 - 4 = ___________________
5 Radicals: Simplify each radical expression. Make sure there are no radicals left in the denominators. If so, rationalize the denominator. 99. 12 × 3 = __________ 100. 5 × 5 = _________ 101. 6 × 8 = ________ 102. 14 × 7 = ___________ 103. 7 × 5 = _________ 104. 5 × 10 = _______ 105. 6 10 106. 3 5 107. 3 2 3 108. 4 2
12 109. 5 8 110. 5 3x 111. 3 2 - 4 2 + 2 2
112. 7 + 8 7 - 3 7
113. 114. 12 - 4 3
115. 117. 2 5 + 3 20
118. 20 + 45 - 5
120.
5 10 + 3
121.
7 8 + 12
(
) 3 6 + 24
(
6 116. ) 3 3 + 4 3 - 9 3
32 - 5 2
119. 2 12 - 27 + 48
122.
(9 - 7 )(9 + 7 ) Slopes, Equations of Lines, and Graphing: Find the slope of each line from its graph. 123. Slope = _________ 124. Slope = __________ 125. Slope = _________ 2 2 2 ­2 ­1 0 1 2 ­2 ­2 ­1 0 1 ­1 0 1 2 3 ­2 ­2 Find the slope of the line containing the given points. (Recall: slope = m = y2 - y 1 ) x2 - x1 126. A(2, 3); B(4, 1) _____________ 127. E(­1, ­5); F(4, 3) _________________ 128. H(­3, 4); I(7, ­2) _____________ 129. L(­2, 3); M(­5, 3) ________________ Graph each linear equation. 130. y = -3 x + 4 131. y = 4 + x
6 6 4 4 2 2 ­5 ­5 5 5 ­2 ­2 ­4 ­4 ­6 ­6 132. x = ­4 133. y = 3
6 6 4 4 2 2 ­5 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 7 1 134. y = - x - 2 2 135. 2 x + y = - 3 6 6 4 4 2 2 ­5 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 Graph each linear inequality. 6 136. x > ­2 4 4 2 2 ­5 138. y < 3 6 137. y > 2x – 3 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 139. 3x – y < ­3
6 6 4 4 2 2 ­5 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 8 Write the equation of the line in slope­intercept form (y = mx +b). Then find the slope and the y­ intercept. 140. 2x + y = 7 _________________ 141. y – 4x = ­3 _____________________ Slope: ___________ Slope: ________________ y­intercept: __________ y­intercept: ______________ 142. 3y + 9 = 0 ____________ 143. 4y – 2 = 3x ______________ Slope: ___________ Slope: ________________ y­intercept: __________ y­intercept: ______________ Systems of Linear Equations: Solve each system of equations. List your answer as a point (x, y). 144. ì x + y = 6 í
î x - y = 4 145. ì y = -3 x + 7 í
î y = 3 x + 5 146. ì x - 5 y = -14 í
î 3 x + y = 6 147. ì5 x - 2 y = 11 í
î3 x + 5 y = 19 9