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Algebra I Summer Review Problems Students, please use the packets as a review to help you identify the areas where you may need some extra practice. On one of the first three days of school next year, you will take a prerequisite skills test. This test will identify the areas that you will need to review in order to be successful in Algebra I and it comes directly from the material covered in the review packet. These topics are not covered in the Algebra I course, so any review necessary will require time outside of class. You need to purchase a TI-30XIIS to use in your math and science class. You may use it on this packet…. But need to show all work. This assignment provides a review of mathematical and algebraic skills that are required for success in Algebra I. You are expected to be fluent with these skills, showing complete algebraic work where appropriate, so this assignment has been provided for your practice toward mastery. This packet will be your first grade in Algebra I. Bring it to class the first day of school. All work needs to be on a separate sheet of paper NEAT and NUMBERED and record answers on this sheet. Looking forward to seeing you. SETS OF NUMBERS: 1. –2 is a rational number. __________(true or false) 2. 5 is a natural number and a whole number. __________ (true or false) 3. A number can be rational and irrational. __________ (true or false) 4. Give one number that is real and rational, but NOT an integer. __________ 5. Give an example of an irrational number. __________ REAL NUMBERS & THE NUMBER LINE: 6. Graph the real numbers on the number line: –3, 0.8, 7. Put the numbers in order: 3 , -0.4, 4 , -5. 3 7 . 2 ORDER OF OPERATIONS: Evaluate. 8. 3 5 4 9. 12 3 2 8 12. d e2 when d = 16 and e = 3 2 10. 9 7 5 26 13. 11. 8 2 5 12 22 9 7 1 1 y when y 8 4 2 SIMPLIFYING ALGEBRAIC EXPRESSIONS: Simplify each expression. 14. 4x + 3 + 2x + 1 15. 4x + 5(x + 3) 16. – (2x – 5) 17. ½ (10x – 4) 18. 3x 5( x 2) 8 19. 2 x 3( x 2) (2 x 5) 1 PROPERTIES OF REAL NUMBERS: Match. _____ 20. 4x + 0 = 4x a. inverse property _____ 21. 26 + (–26) = 0 b. commutative property _____ 22. 2a + (3b + 4c) = (2a + 3b) + 4c c. zero property _____ 23. –12(0) = 0 d. associative property _____ 24. 5(3x) = (3x)5 e. identity property SOLVING LINEAR EQUATIONS: Solve each equation. 25. 5x + 2 = 3x + 24 26. 3(5x – 1) = 3x + 3 27. – x + 3 = 7x + 8 28. Jeff earns $4 an hour baby-sitting. He is saving to buy a pair of in-line skates that costs $116. If Jeff already has $60 saved, how many hours must he baby-sit in order to buy the skates? 29. An awards dinner costs $225 plus $5 per person. The total bill is $735. How many people attended the dinner? 30. 11y 9 13 31. 7 x 9 10 x 12 32. 3(1 + x) =1 + 5x GRAPHING LINEAR EQUATIONS: Graph (on graph paper). 2 33. y = x + 2 3 34. x – 3y = – 3 35. y = – 3 36. y = 2x – 3 37. x = 2 38. 3x – 2y = 6 FUNCTIONS: 39. Is the following a function: (2,4),(4,2),(2,6),(6, 2) 40. Is the following a function: (1,6),(1,2),(2,6),(1, 2) 41. Is the following a linear function: y x 4 42. Is the following a linear function: 2 x 4 y 3 43. Is the following a linear function: x 4 44. Is the following a linear function: y 2 2 45. Is the following a linear function: y 3 4 x SLOPE: Find the slope of the line passing through the given pairs of points. 46. (2, –5), (–1, 3) 47. (4, 2), (–1, 2) 48. (–7, 0), (2, 5) 49. (3, –1), (3, 0) Identify the slope and the y-intercept 50. 4 x 2 y 12 51. 6 y 3x 12 52. y 12 53. x 12 EQUATIONS OF LINES: Write the equation of each line described in slope-intercept form. 54. slope 5 and y-intercept -3 55. Write the equation of the line graphed to the right. 56. Write the equation represented here. ________________ 57. Write the equation represented here _________________ 58. I need to take a taxi cab ride to the airport. The taxi charges a fee of $10 and then $.20 per mile. Write an equation of a line represented in this situation. How much would I pay for a 42 mile ride. 59. I have $500 in my savings account. I plan on spending $10 a week on food. Write an equation of a line represented in this situation and then find out how much will be in there after 7 weeks. THE PYTHAGOREAN THEOREM: Use the Pythagorean Theorem to answer each question.. 60. Given the right triangle to the right, what is the length of the hypotenuse? 10 m 16 m 61. Given a right triangle, a = 4 and c = 7. Find the length of side b. 62. Is a triangle with sides of length 10 cm, 24 cm, and 26 cm a right triangle? 63. A 12-foot ladder is leaning against the side of a house. The base of the ladder is 5 feet from the side of the house. How far up the side of the house does the ladder reach? To get to the store from his house, Ralph biked 5 km due west and then 12 km due north. On the way back he cut across a field, taking the shortest possible route home. How far did Ralph bike on the round trip? 64. store 12 km 5 km Multiply and put in simplest form. 65. 2 x(4 x 5) 66. 3x(2 x 4 y 4) 67. 4(8 x 3x 5) 2 68. 6x(2x2 – 5x +1) 69. (-x)(4x2 – 7x) 70. 2x2(x3 – x2 + 8x – 5) 71. (-5a2)(3a2 – 7a +9) 1 72. ( x ) (6x + 4x2 – 8) 2 73. 1 (6x - 18) 3 Add, subtract, combine like terms. 74. 6x – 4(7+x) 75. 3x2 – x(3 + 2x) 76. (3n2 – 5n) – ( 4n3 + 5n2+n+7) 77. 2(x2 – 4x + 5) – (x)(x – 4) C ANGLES: 78. Use the diagram to the right to label the sides, vertex, and name the angle. A B home 79. What does “congruent” mean? What would it mean for two angles to be congruent? Draw an example of two congruent angles and write a congruence statement for the two angles. 80. Supplementary angles are angles whose measures add to _______________. 81. Complementary angles are angles whose measures add to _______________. PARALLEL LINES CUT BY A TRANSVERSAL: Using the diagram below: 82. List all pairs of vertical angles: ________________________________ 83. List all pairs of corresponding angles: _____________________________ 84. List all pairs of alternate interior angles: ________________________________ 85. List all pairs of alternate exterior angles: ________________________________ 86. List all pairs of consecutive interior angles: ________________________________ TRIANGLES: Classify each triangle by the angle measures. 87. A right triangle is a triangle with one _________ angle. 88. An obtuse triangle is a triangle with one __________ angle. 89. An acute triangle is a triangle with three ___________ angles. Classify each triangle by the side lengths. 90. A scalene triangle is a triangle with 3 ________________ side lengths. 91. An isosceles triangle is a triangle with at least ____ congruent sides. 92. An equilateral triangle is a triangle with exactly ____ congruent sides. Match the correct classification with the correct description. 93. scalene triangle F. has a right angle 94. right triangle H. all sides are congruent 95. isosceles triangle I. no sides are congruent 96. acute triangle J. has two congruent angles 97. equilateral triangle K. all angles are acute 98. equiangular triangle L. all angles are congruent VOLUME Use 3.14 for π—you may use a calculator for this—round to two decimal places. 99. Find the volume of a cylinder whose height is 12 cm and radius is 3cm. 100. Find the volume of a cone whose height is 18cm. and diameter of 12cm. 101. Find the volume of a sphere whose radius is 4cm. 102. Find the height of a cylinder whose volume is 125.6 cubic centimeters and radius is 2cm. 103. Find the diameter of a cone whose volume is 84.78cubic centimeters and height is 9 cm.