Introductory Algebra Final Exam Review Note: This review represents the topics covered by the final exam. It is in no way intended to represent the quantity of any particular type of problem on the final exam. The answers are provided at the end of this packet. Note: Problem numbers 1 – 28, 51 – 56, 64, 65, and 68 – 112 serve as a review of the concepts covered on the midterm. Terminology: Be able to recognize, identify and use these terms. absolute value equation factor multiple LCD reciprocal solution inequality interval notation x-intercept y-intercept origin quadrant ordered pair slope slope-intercept form parallel lines perpendicular lines linear system system of linear inequalities For #1–20, simplify the expression. You could use a calculator, but it’s best to have an understanding of order of operations (and fraction operations) without a calculator. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. A pipe 24 feet long is cut into three pieces. The first piece is twice as long as the second piece and the third piece is 6 feet longer than the second piece. What are the lengths of all 3 pieces? 22. One number is 4 times a second number and their sum is 120. Find the numbers. 23. A major-league pitcher throws a ball upward with an initial rate of 130 feet per second. The height h (in feet) of the ball after t seconds is given by the formula. Determine the height of the ball after 4 seconds. 24. In a physics class of 36 students, 5 more students received B’s than A’s and twice as many students received C’s as A’s. Seven people received a grade below C. How many students received A’s, B’s and C’s?
Solve the absolute value equations. Write the solution using set notation. 106. |2x – 1| + 2 = 3 107. |5x + 3| = 0 108. |2x + 5| + 7 = 3 Solve and graph the inequalities. Then write the solution using interval notation. 109. -15 < 20 110. 10 – s ≥ 4 or -1 < 2s + 3 111. -16 < -4(9 – x) ≤ 24 112. 1 ≥ -(4x + 1) ≥ 25 For #113-117, factor the following expressions. 113.12y2 + 8y 114. 9x2 +12x – 6 115. 6a4b – 36a2b2 +12ab3 116. 20a2 -5ab + 8ac – 2bc 117. 4p2 – p2r – q3r + 4q3 For #118-120, add/subtract as directed. 118. Subtract (3n4 – 2n2 – 6) from (2n2 -3n +1) 119. Add: 5x3 + 2x2 – 1 and 3 – 7x + x2 – 4 x3 120. (4x3 – 3x2) + (x2 + 2x -10) – (x3 - 15) For #121-126, multiply: 121. (x + y) (4x – 7y) 122. (t – 10) (t + 10) 123. (x – 2y2) (4 + 4x – x3) 124. (2n – 5)2 125. (4p + 7q) 2 126. (x – 12y) (x – 4y) For #127-130, divide: 127. 128. (x2 + x -12) ÷ (x + 4) 129. 130. 131. Given f(x) and g(x), find. f(x) = a2 – 3a – 28 and g(x) = a + 4 132. Given: g(x) = - 2x + 4 Find the following: g(-3) g(a) g(a +4) 133. State the domain and range of the following relation. {(4, -1), (1, -1), (0, 0), (4, 2)}
61. intersection 62. intersection 63. intersection 64. 11 dimes, 21 nickels 65. 8 ft by 6 ft 66. 3 oz Del Monte; 9 oz Rockstar 67. 300 calls 68. 60 69. < 70. $23 71. 1.6 hours 72. 6.6 hours 73. 3.7 hours 74. 200 mph 75. 4 min. 76. 77. 78. 79. 35 grams of fat 80. 81. 82. 83. , 84. Juan $11,000, Roberto $9000 85. 86. 87. 88. 89.
90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. ; ; 104. ; ; 105. ; ; 106. 107. 108. no solution 109. ; ; 110. all real numbers ; ; 111. ; ; 112. no solution ; ; 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. (a.)