Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name ________________________________________ Honors Trig/PreCalc Summer Assignment 1. Completion of this summer assignment is a requirement of the course. You are responsible for handing in the completed packet to your Honors Trig/Pre-Calculus teacher the first day of school. If you do NOT have this completed by the first day of school, you will receive a zero for the assignment. 2. The problems are designed as a review and to ensure the student’s readiness for Honors Trig/PreCalculus. If you do not know how to do some of these problems, utilize your resources and/or ASK someone. 3. Allow several hours to complete this packet. Do not procrastinate. 4. You MUST SHOW ALL WORK under each problem and the work must be neat, organized and completed in pencil to receive any credit. Circle all answers on your work. 5. It is important that you know how to do ALL of these problems. 6. You will have a test on these concepts the 1st week of school. Be prepared. 7. I will be checking my email throughout the summer. So if you have a question, email me at [email protected] Determine which numbers in the set are (a) natural numbers, (b) integers, (c) rational numbers, and (d) irrational numbers. 3 1 1. 22, , 31, , 7,0.1234 4 Determine the domain and the range of the function. Write answers in interval notation. 5. f (x) 36 x2 3 7. Graph y 9 4 2. 16, 57, ,0,8.32, 17 5 Evaluate the following. 3. If f (x) x 2 10 , find f (5) and f (t ) 1 x 1 if x 2 g( x ) 3 find g(10), and g(2) 4. 20 if x 2 1 2 x 2 7 2 6. h(x) x 1 x 2 7x 10 if x 0 3x 2 2 x 1 if x 0 8. Graph f (x) 10. f (x) 1 x In problems #9 & 10, a) find f 1 (x) b) graph f ( x ) and f 1 (x) on the same graph 1 3 9. f (x) x 2 11. if f (x) 2 3x and g(x) x find a) ( f g)(5) b) (g f )(x) 12. Describe the transformation(s) that have been done to f (x) x to get g(x) 4 x 2 13. Describe the transformation(s) that have been done to f (x) x to get g(x) x 7 6 14. Find the vertex and intercepts of the graph of y x2 4 x 3 15. The path of a ball is given by y 1 2 x 3x 5 , 20 25. 4 x 2/7 3x 1 7 1 26. 38 3 4 3 where y is the height in feet and x is the horizontal distance in feet. a) Find the maximum height of the ball. Simplify each expression with positive exponents only. 9 u4v 2 812 u5v b) What is the horizontal distance at the maximum height? 27. 16. Divide by synthetic division (3x 4 x 1) (x 1) Is there a remainder? If so, what is it? 29. 2 x 4 y x 4 y 28. 2 4 3 m3n5 121 mn4 30. x 3 y 2 1 For problems # 31 & 32, write the number in scientific notation. Simplify each expression without a calculator. Rationalize all radicals. Write all answers in simplified radical form. 17. 2 12 3 48 5 27 18. 31. Number of cars in the United States: 143,781,202 28x 5 7x 32. Number of yards in 1centimeter: 0.010936133 yards 19. 2 2 x 4 xy 3 3 20. 4 50 5 90 Rewrite the expression by rationalizing the denominator or numerator. Simplify your answer. 33. 21. 7 4(3) 10 23. 27 2 3 22. 321 3(8 15) 24. 50x8b7 5 3 7 34. 7 5 2 For problems # 35-38, perform the operations. Write the result in standard form. 35. 4 x2 6 x 3 6 x 37. (2x 9)(7 x 6) 49. 2 x 3 2(x 4) 50. 3 4 x2 5 2 x 2 2 x 3x 2 36. 9y 4 y 2 5y 10 38. (4 x 5)3 Simplify the complex fraction. For problems # 39-46, factor completely. 39. 2x2 14 x 16 40. 8 x 3 343 41. 12x2 67x 50 42. 4x4 21x2 27 43. x 3 4 x2 3x 12 44. y 4 16 45. 2x2 13x 7 46. 4ax 14ay 10bx 35by For problems 47-50, write the rational expression in simplest form. State any domain restrictions. 47. 1 4 y2 x2 51. x 2y 3 y x 6 1 52. x 2 x 15 x 3 1 1 x5 2 For problems # 53-56, solve the equation (if possible) and check your solution. Put all answers in reduced fraction form. 53. 3x 2(x 5) 10 54. 4(x 3) 3 2(4 3x) 4 55. .5(x 3) 2(x 1) 5 56. 4 x 2(7 x) 5 4x 6 x 2 3x 1 x 1 2 48. 2 2 (x 1) x 2 x 3 x x 1 For problems # 57-65, use any method to solve the equation (if possible). 57. 2 x 3(4 x) 5 58. 5 2 13 2 t 1 t 2 t t 2 59. 4y 2 8y 2 0 60. 61. 3 x 2x 1 0 62. 2x 1 5 6 63. x2 6 x 3 0 65. x 5 x 1 71. x 5 4 2 x 5 3x 2 72. 73. 4 x 30 2x 74. 75. x 2 3 36 0 76. 64 x 3 125 0 77. 2x 3 7 78. 2 4 x 6 18 5 x 5 9 7 64. 20 4 x 3x2 0 y 5 1 3 y2 y 2 y 2 y 1 2 66. Solve by completing the square: x2 6 x 247 0 For problems #67-79, find all solutions of the equations. Check for extraneous solutions. 67. 4 x 3 6x2 0 68. 3x2 6 x 9 79. 69. x 4 5x2 6 0 70. x 3 3x2 4 x 12 0 1 5 6 x 4 x 2 x2 2x 8 5 2 80. Simplify. Use positive exponents only. 8(4 x 3)1 10(5x 1)(4 x 3)1 88. 3 4 x 3 19 For problems # 81 – 91, solve each linear, compound, or absolute value inequality. Use interval notation to express the solutions sets. 90. 3(x 1) 2 20 81. 2 3(x 4) 13 82. 1 3 x x 5 91. 12 2x 6 3 83. 4(x 1) 2 3x 6 84. 3x 1 x 1 10 5 10 2 3 89. 3 x 5 1 85. 4x 3 2x 1 2 6 12 86. 1 2x x 7 3x 1 87. 3 3 x 5 8 x 7 53(x 6) 2(3x 5) 2(4 x 3) For problems # 92 & 93, find the midpoint of the line segment joining the points and the distance between the two points. 92. (3,5),(7, 4) 93. (11,3),(1,9) 94. A total of 200 feet of fencing are available to enclose a rectangular area with 4 subdivisions, as show below. Find the maximum possible area that can be enclosed. 99. A car radiator contains 20 liters of 40% antifreeze solution. How many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze? 95. For what value of k will the graph of kx 7y 10 0 be perpendicular to the graph of 100. Suppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use? 8 x 14 y 3 0 96. For what value of k is the graph of kx 7y 10 0 parallel to the graph of 8 x 14 y 3 0 97. Find a 4th degree polynomial in standard form that has -1, -1, and 3i as zeros. 98. A biologist introduces 1000 ladybugs into a crop field. The population P of the ladybugs is approximated by the model P 1000(1 4t) where 6t t is the time in days. Find the time required for the population to increase to at least 2000 ladybugs.