PENNCREST HIGH SCHOOL SUMMER REVIEW PACKET For students in entering PRE­CALCULUS (All Levels) Name: __________________________________________________________ Assigning Teacher: q Ms. Cristaldi q Ms. Sweeney q Mrs. Price q Ms. Matlock q Other: _____________________________________ 1. This packet is to be handed in to your Pre­Calculus 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 Pre­Calculus (all levels) Radicals: Simplify each of the following. 1. 32 2. (2 x ) 8 3. 5. 11 9 6. 60 · 105
7.
3 (
- 64
4. 5- 6
)(
5 + 2
) 8. Complex Numbers: Simplify. 9. - 49
2 12. ( 3 - 4i ) 10. 6 - 12
11. -6(2 - 8i ) + 3(5 + 7i) 13. (6 - 4i )(6 + 4i ) 14. 2 1 + 6 i
5 i
49m 2 n 8 3 2 - 5
Geometry: Find the value of x. 15. 16. 9 x x 12 17. x x 8 5 5 12 18. A square has perimeter 12 cm. Find the length of the diagonal. A A 19. If DE = 24, Find: 20. If BD = 16, Find: 45 30 AE = _______ D EB = _______ 45 45 AB = _______ 60 D 30 E 45 AD = ________ DC = ________ 45 C 45 B 60 B 30 E C AC = ________ AB = _______ AD = ________ BD = ________ DC = _______ CE = _______ BC = ________ AC = _______ EB = ________ CB = _______ DE = ________
3 Radical Equations: Solve each equation. Be sure to check for extraneous solutions. 21. 4 x - x 3 = 6 23. 9u - 4 = 7u - 20 22. x + 8 - 5 = 0 24. k + 9 - k = 3 Equations of Lines: 25. State the slope and y­intercept of the linear equation: 5x – 4y = 8. 26. Find the x­intercept and y­intercept of the equation: 2x – y = 5 27. Write the equation in standard form: y = 7x – 5 Write the equation of the line in slope­intercept form with the following conditions: 28. slope = ­5 and passes through the point (­3, ­8) 29. passes through the points (4, 3) and (7, ­2) 30. x­intercept = 3 and y­intercept = 2
4 Graphing: Graph each function, inequality, and / or system. ì2 x + y = 4
32. í
î x - y = 2 31. 3 x - 4 y = 12 6 6 4 4 2 2 ­5 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 33. y < -4 x - 2 34. y + 2 = x + 1 6 6 4 4 2 2 ­5 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 36. y = § 2 x - 1 ¨ 35. y > x - 1 6 6 4 4 2 2 ­5 5 ­5 5 ­2 ­2 ­4 ­4 ­6 ­6 5 Systems of Equations: Solve each system of equations. Use any method. ì2 x + y = 4 37. í
î 3 x + 2 y = 1 ì2 x + y = 4 38. í
î 3 x - y = 14 ì2w - 5 z = 13 39. í
î 6 w + 3 z = 10 Exponents: Express each of the following in simplest form. Answers should not have any negative exponents. 0 40. 5a 3c
41. - 1 c
2ef -1 42. - 1 e
(n3 p -1 ) 2 43. (np ) - 2 45. (a 3 ) 2 46. (- b3c 4 ) 5 47. 4m(3a 2 m) Simplify. 44. 3m 2 · 2 m
6 Polynomials: Simplify. 48. 3 x3 + 9 + 7 x 2 - x3 49. 7m - 6 - (2m + 5) Multiply. 50. (3a + 1)(a – 2) 51. (s + 3)(s – 3) 52. (c – 5) 2 53. (5x + 7y)(5x – 7y) Factor completely. If the polynomial is prime, state so. 54. x 2 - 5 x + 4 55. a 2 - a - 6 56. z 2 + 4 z - 12 57. 6 - 5e - e 2 58. n 2 - 3n + 4 59. 60 - 5h - 5 h 2 60. 2k 2 + 2k - 60 61. -10b 4 - 15 b 2 62. 9c 2 + 30c + 25 63. 9n 2 - 4 64. 27 z 3 - 8 65. 2mn - 2 mt + 2 sn - 2 st
7 Polynomials Continued: Solve each equation. 66. x 2 - 4 x - 12 = 0 67. x 2 + 25 = 10 x
68. x 2 - 14 x + 19 = 0 Find the value of the discriminant, describe the nature of the roots, then solve each quadratic. Use EXACT values. 69. x 2 - 9 x + 14 = 0 70. 5 x 2 - 2 x + 4 = 0 Divide each polynomial. 71. c 3 - 3c 2 + 18c - 16 c 2 + 3c - 2 72. x 4 - 2 x 2 - x + 2 x + 2 Evaluate each function for the given value. 73. f ( x ) = x 2 - 6 x + 2 f (3) = ________ 74. g ( x ) = 6 x - 7 g ( x + h) = ________ 8 75. f ( x) = 3 x 2 - 4 5 [ f ( x + 2) ] = ________ Composition and Inverses of Functions: Suppose f ( x) = 2 x, g ( x ) = 3 x - 2, and h( x) = x 2 - 4 . Find the following: 76. f [ g (2) ] = ________ 77. f [ g ( x) ] = ________ 78. f [ h (3) ] = ________ 79. g [ f ( x) ] = ________ Find the inverse, f ­1 (x) , if possible. 80. f ( x) = 5 x + 2 81. f ( x) =
1
1 x - 2
3 Solving Polynomial Equations: 82. Use Descartes’ Rule of Signs to determine the most possible positive, negative, and imaginary roots. x 3 + 2 x 2 - 5 x + 5 = 0 P N i 83. List all the possible rational roots for the function: f ( x) = x 3 - 5 x 2 + 2 x + 12 p : q 84. Find ALL of the zeros for the function: f ( x) = x 3 + 3x 2 - 6 x - 8 9 Rational Algebraic Expressions: Simplify. 85. 5 z 3 + z 2 - z 3 z
86. m 2 - 25 m 2 + 5 m
87. 10r 5 3 s · 21s 2 5 r 3 88. a 2 - 5a + 6 3a + 12 ·
a+4
a - 2 89. 2 x x
- 5 3 90. b - a a + b + 2 a2b
ab
91. 2 - a 2 3a + 4 +
a 2 + a 3a + 3 1 2 93. 1 2 + 4
1 -
1 6 m m 2 2 2 - m m 2 5 +
95. 92. 6d - 9 6 - 13d + 6 d 2 ¸
5d + 1 15d 2 - 7 d - 2 1 z 94. z + 1 1 +
1 1 x x 2 96. 4 3 1 + + 2 x x
2 +
10 Solving Rational Equations: Solve each equation. Check your solutions. 97. 12 3 3 + = x 4 2 98. x + 10 4 =
x 2 - 2 x
99. 5 x =
- 1 x - 5 x - 5 Probability: Find each value. 100. P(9, 4) = ______ 101. P(7, 0) = ______ 103. C (6,5) · C (4, 2) = ______ 104. 102. C (10,8) = ______ P (10,3) = ______ P(5,3) 105. A company manufactures bicycles in 8 different styles. Each style comes in 7 different colors. How many different bicycles does the company make? 106. How many was can 6 children form a line to use the drinking fountain? 107. What is the probability that the numbers that result from tossing two dice have a sum of 2? 108. The probability that an event will occur is 2 . What are the ODDS that the event will occur? 7 109. There are 7 women and 4 men on a committee. If a 4­person subcommittee is selected at random, what are the odds that it will consist of 3 men and 1 woman? 110. How many different ways can the letter of the word MINIMUM be arranged?
11 Statistics: Given the following data set: 44, 31, 24, 36, 28, 42, 39, 36, 28, 36, 43, 44 111. Find the mean, median, and mode(s) 112. Draw a line plot for the data. 113. Draw a stem­and­leaf plot for the data. 114. Draw a box and whisker graph and identify the quartiles, range, and outliers. 115. Find the standard deviation for the data and draw and identify the values for + 1, + 2, and + 3 standard deviations from the mean. 116. Given the following set of data on attendance at North Stadium, make a scatter plot, find the prediction equation (best fit line), and predict the attendance when the temperature is 64 ◦ . 14 12 Temperature Attendance 10 25 30,000 41 43,000 55 52,000 60 60,000 20 25,000
8 6 4 2 I 12 5 10 15