NAME PRE-CALCULUS SUMMER PACKET IINTRODUCTION 12-3 This packet is due on the first day of school in September. You are responsible to do and show work for any 50 problems that you decide to do. You must show work on these 50 problems to receive credit. If you choose a problem that only requires a calculator, you must write down the key strokes that you used. This assignment will count as a quiz grade so this is a great opportunity to start your senior year with an A in math. There will be a separate file on the CHS math department website that will contain some notes, hints, and worked out solutions that will help you complete this packet successfully. There are roughly 10 weeks in the summer before your senior year begins and we suggest that you try to do 5 problems a week so you will not feel overwhelmed if you wait until summer is almost over. This packet will help you review what you have already learned and give you a head start to having a great year in this course. HAVE A GREAT SUMMER AND WE LOOK FORWARD TO HAVING YOU AS A STUDENT WHEN SCHOOL STARTS IN SEPTEMBER!!!!
1. The width, w, of a rectangular rug is 4 less than its length,. Which expression represents the area of the rug? C) D) 2. If a machine that prints designs on T-shirts prints 500 shirts in 3 hours, how many hours will it take to print designs on 1,800 shirts? A) 6 B) 9.8 C) 10.8 D) 12 3. The larger of two consecutive integers is represented by x + 4. Which expression represents the smaller integer? A) x + 2 B) x + 3 C) x + 5 D) x + 6 4. If x represents a given number, the expression "5 less than twice the given number" is written as C) D) 5. The sum of Scott's age and Greg's age is 33 years. If Greg's age is represented by g, Scott's age is represented by A) 33 g B) g 33 C) g + 33 D) 33g 6. Find the value of 3x 2 y when x = 2 and y = -1 7. If x = 4 and y = -1, find the value of 3x 2 y. 15. Find the quotient. A) ( 1.8 + 2) 0.4 B) 16 0.4 C) 5 0.2 D) 6 2 16. What is the product of 2x 2 y 3 and 5x 3 y? 17. What is the value of xy 2 if x = 3 and y = 7? 18. Find the product of 6a 7, 7a 8, and 8a 9. 19. Find the product of xy 2 and 12xy 7. 20. If -18x 4 y is divided by -2xy, what is the quotient? 21. What is the product of x 3 y and xy 2? 22. The distance from the planet Pluto to the sun is approxiamately 3,700,000,000 miles. A scientist will write the distance as 3.7 x 10 n. What is the value of n? 23. If 0.000043 is expressed as 4.3 10 n, what is the value of n? 24. 0.00074 meter is the width of an unusually thin blade of grass. When expressed in the form 7.4 10 n, what is the value of n? 8. A football team assigns jersey numbers to its players by using the formula of 7y - 3x where x and y are randomly chosen. What number will a player get if x = -2 and y = 4? 9. Find the value of a 2 - b if a = 3 and b = -5. 10. Find the numerical value of 4xy 2 when x = and y = -3 11. Given the formula t = rv 2, find t if r = 3 and v = 2. 12. The expression 3x 2 + y represents the number of babies born on an exotic tropical island each month. How many babies were born in June if x =1 and y = 3. 13. Write an irrational number and explain why it is irrational. 14. Seth is thinking of a number between 20 and 30. The number is prime and not more than 2 away from a perfect square. What is the number? 25. Subtract 2x 2 5x + 8 from 6x 2 + 3x 2 and express the answer as a trinomial. 26. What is the sum of x 2 3x + 7 and 3x 2 + 5x 9? A) 4x 2 8x + 2 B) 4x 2 + 2x + 16 C) 4x 2 2x 2 D) 4x 2 + 2x 2 27. The sum of 8x 2 x + 4 and x 5 is A) 8x 2 + 9 B) 8x 2 1 C) 8x 2 2x + 9 D) 8x 2 2x 1 28. The expression 2x 2 x 2 is A) x 0 B) 2 C) x 2 D) 2x 4 29. When 3a 2 7a + 6 is subtracted from 4a 2 3a + 4, the result is A) a 2 + 4a 2 B) a 2 10a 2 C) a 2 4a + 2 D) 7a 2 10a + 10
30. The expression (x 2 5x 2) ( 6x 2 7x 3) is A) 7x 2 12x 5 B) 7x 2 2x + 1 C) 7x 2 + 2x + 1 D) 7x 2 + 2x 5 31. The width of a rectangle is represented by 2x and the length is represented by x 2 - x + 3. Which expression represents the area of the rectangle? A) 2x 3 - x + 3 B) x 2 + x + 3 C) 2x 2 + 2x + 6 D) 2x 3-2x 2 + 6x 32. Express (x 7)(x + 3) as a trinomial. 33. Express (2x 4)(x + 7) as a trinomial. 34. Find the product of 4x 2 2 and itself. 35. Find the product of 3 + 6a and 5 7a. 36. Find the product of 7x 6 and 11x + 9. 37. Express the product (x + 5)(x - 3) as a trinomial. 38. What is 6x 3 + 4x 2 + 2x divided by 2x? A) 3x 2 + 2x B) 3x 2 + 2x + 1 C) 4x 2 + 2x D) 4x 2 + 2x + 1 39. The expression (50x 3 60x 2 + 10x) 10x is equivalent to A) 5x 2 6x +1 B) 5x 3 6x 2 + x C) 5x 2 60x 2 + 10x D) 5x 2 6x 40. When 3x 2 6x is divided by 3x, the result is A) 2x B) 2x C) x + 2 D) x 2 41. Expressed in factored form, the binominal 4a 2 9b 2 is A) (2a 3b)(2a 3b) B) (2a + 3b)(2a 3b) C) (4a 3b)(a + 3b) D) (2a 9b)(2a + b) 42. Written in factored form, the binomial 4x 2 9 is A) (2x 3)(2x 3) B) (2x 3)(2x + 3) C) (4x 9)(x + 1) D) (4x + 1)(x 9) 43. One of the factors of 4x 2 9 is A) (x + 3) B) (2x + 3) C) (4x 3) D) (x 3) 44. Which expression is a factor of x 2 81? A) (x 81) B) (x 18) C) (x + 9) D) (x + 18) 45. Which is a factor of x 2 + 5x 24? A) (x + 4) B) (x 4) C) (x + 3) D) (x 3) 46. What are the factors of x 2 + 3x 4? A) (x + 1) and (x 4) B) (x 1) and (x + 4) C) (x + 3) and (x 4) D) (x + 2) and (x + 2) 47. Which expression is a factor of x 2 + 2x 15? A) (x + 5) B) (x + 3) C) (x 5) D) (x 15) 48. Which expression is a factor of x 2 + 11x + 10? A) (x + 5) B) (x + 10) C) (x 5) D) (x 10) 49. Which expression is a factor of x 2 7x + 10? A) (x + 5) B) (x + 10) C) (x + 2) D) (x 2) 50. Which expression is a factor of 3x 2 + 2x 8? A) (3x 4) B) (x 2) C) (3x + 4) D) (3x + 2) 51. When Albert flips open his mathematics textbook, he notices that the product of the page numbers of the two facing pages that he sees is 156. Which equation could be used to find the page numbers that Albert is looking at? A) x + (x + 1) = 156 B) (x + 1) + (x + 2) = 156 C) (x + 1)(x + 3) = 156 D) x(x + 1) = 156 52. Factor completely: 2x 2-50 A) 2(x - 5) 2 B) 2(x - 50) 2 C) 2(x + 5)(x - 5) D) (2x + 5)(2x - 5) 53. Which expression is the complete factorization of 32 18y 2? A) 2(16 9y 2 ) B) 2(4 3y) 2 C) 2(3y + 4)(3y 4) D) 2(4 3y)(4 + 3y) 54. Which expression is a factored form of 2x 2-2x - 12? A) 2(x + 2)(x - 3) B) 2(x + 6)(x - 1) C) 2(x + 3)(x - 2) D) 2(x + 1)(x - 6)
55. The greatest common factor of 4a 2 b and 6ab 3 is A) 2ab B) 2ab 2 C) 12ab D) 24a 3 b 4 56. What is the least common denominator of,, and? A) 9x B) 12x C) 14x D) 14x 2 57. Which number is irrational?.0 C) D) 58. If x <, x could be A) 0 B) 2 C) D) 4 59. The expression is A) 3 B) 2 C) 8 D) 4 60. If the area of a square garden is 48 square feet, what is the length, in feet, of one side of the garden? A) 12 B) 4 C) 16 D) 4 61. The expression can be simplified to A) 5 B) 5 C) 2 D) 25 62. The expression is A) 2 B) 10 C) 100 D) 2 63. The expression is equal to A) 2 B) 3 C) 5 D) 5 64. The expression is A) 50 B) 5 C) 10 D) 10 65. The sum of and is 9 C) 3 D) 4 66. What is the sum of and? 7 C) 9 D) 29 67. What is the sum +? 20 C) 9 D) 68. What is the sum of 5 and 3? A) 9 B) 11 C) 60 D) 8 69. The expression + is A) 9 B) C) 6 D) 18 70. The sum of and is 9 C) 3 D) 6 71. What is the value of m in the equation 2m (m + 1) = 0? A) 1 B) 1 C) 1 3 D) 0 72. What is the value of x in the equation 13x 2(x + 4) = 8x + 1? A) 1 B) 2 C) 3 D) 4 73. What is the value of x in the equation 5(2x 7) = 15x 10? A) 1 B) 0.6 C) 5 D) 9 74. Kevin and Hunter have $273 in total. If Kevin has $27 more than Hunter has, how much money does Kevin have? A) $27 B) $123 C) $150 D) $177 75. What is the solution of the equation 3y 5y + 10 = 36? A) 13 B) 2 C) 4.5 D) 13 76. What is the value of n in the equation 0.6(n + 10) = 3.6? A) 0.4 B) 5 C) 4 D) 4 77. A girl can ski down a hill five times as fast as she can climb up the same hill. If she can climb up the hill and ski down in a total of 9 minutes, how many minutes does it take her to climb up the hill? A) 1.8 B) 4.5 C) 7.2 D) 7.5 78. What is the value of x in the equation 2(x 3) + 1 = 19? A) 6 B) 9 C) 10.5 D) 12
79. If 3(x + 2) 2(x + 1) = 8, the value of x is A) 1 B) C) 5 D) 4 80. What is the value of x in the equation 6(x 2) = 36 10x? A) 6 B) 1.5 C) 3 D) 6 81. If 12x = 4(x + 3) then x equals A) 5 B) C) D) 1.5 82. Solve for s: 7s + 4(3 - s) = 18 A) 1 B) 2 C) -2 D) 3 83. What is the value of p in the equation 8p + 2 = 4p 10? A) 1 B) 1 C) 3 D) 3 84. What is the value of n in the equation 3n 8 = 32 n? A) 10 B) 6 C) 6 D) 10 85. If c = 2m + d, then m is equal to C) D) d 2c 86. If the temperature in Buffalo is 23 Fahrenheit, what is the temperature in degrees Celsius? [Use the formula C = (F 32).] A) 5 B) 5 C) 45 D) 45 87. What are the factors of x 2 5x + 6? A) (x + 2) and (x + 3) B) (x 2) and (x 3) C) (x + 6) and (x 1) D) (x 6) and (x + 1)