Pre-Calculus H Summer Project Name______

Show all work on separate paper. For multi-step problems, work vertically. Write your name in pen at the top of each page. Use graph paper for all graphs. If you have any questions during the summer, email the teacher at [email protected]. Allow at least 48 hours for a response. The completed problem set is due at the beginning of the first day of class. Your first test will be on concepts and problems from the summer project.

Simplify. Assume no denominator equals zero.

63 134 5 4 1. 16. 81x2 – 12x + 52  6 134 9

2. (–4k6p10 q2) ÷ (2kp7 q4) 17. 6a4 + 3a3 – 45a2

2 4 3 18. 2ab4 – 2a 3. (2w k ) 5 2 4 2 (wk ) (w k ) 19. 2x3 – 6x2y + 9x – 27y

4. –1 2 –3 –1 2 –2 (3 m n ) (6m n) 20. 125 a 3 -27

5. 2 (7x – 3)(2x – 4) 21. 216 z 3 125a 3

 a b  3a 2b  22. 12a 6.      25 – x  4 3  4 3  p 2  7 p 18 7. 3 23. (5a – 3) 2 p 13p  22 8. (6a3 – 7a2 – 7a + 6) ÷ (3a – 2) 3 2 24. 2n  9n  7n 9. (2p4–7p3–13p2+29–12) ÷ (p2–5p+3) n 4  3n3  4n 2

10. (c3k – 2)2 6b 12 (2  b)2 25.  b  2 7b 2  28 Factor. y 4 10y 2  9 y 2  2y  3 11. 162pr5s2 + 36p3r6s – 90p2r3s 26.  y 2  y  6 y 2  3y  2 12. r2 – 20r + 64 2 1 13. 2  r + 16r – 45 27. a b 1 3 14. 2  10y + 11y + 3 a b

k 2 121m2 15.  b 169 100 28. b  4 b 1 b  4 Solve. 10 2 32. 4x y 289 29. 8(5c – 4)= –2(8 + 6c)

33. 6(3  2w) 180 30. 4+w= 5 34.  72c 5d 5 31. (a + 1)(2a–1) – (a – 1)(2a + 1) = –18 35. 48 16x 2

36. 4x 8 y Simplify #32-48. a b

37. 5 27a 3b6  5  9b9 a 2 Rewrite using exponents.

49. 3c 7 38. 48 2 50. x 4 y 7

39. 175 51. k 5m 2m 10 c d

1 2 Rewrite without any exponents. 40.  5 3 52. 1 18 2 50y 3 41. 53. 1 2y 8 16 3

7 42. 54. 2 108  27  3 125 m 2

1 43. 3 1 55. 80  2 24  125 m k 2 5

3 1 2 56. 44. 5 6  7 5  5 6  7 5  x y y y w y

45. 3 1 1  2 6  3 1 1  2 6  Simplify #57-65.

  57. 5 16 2 46. 5  10 5   58. 2 64 3

47. 9 2  11 2 59.  343 3    8  48. 3 2

5 5  6 60.  16 4 9 69. 61.  3 t  6 7 32 5

70. 3  c  5  4c 1 62.  25  2    9  71.  m  3  m  4

4 2 72. 2      0  25  p 63.  9  3 e  e      18 73. 0  t 2  2 49 3 6 64.  64a b  3     9  74. 8  2(x 1)2  125y 

75. 2 2  1 4  55  23  (7  r) 65. 3  3 3   c c  2c    76. 2 p 2  9 p  0

Solve. 77. 2k 2  6  5k  5

12 2 78. 4 2 66.  2 z  a  5a  4  0 5 5 79. r 4  7r 2 12  0 67. 2c  3  7 80. w3  2w2  49w  98  0 68. 25  7 m  5  4 Find the slope between (4, 6) and (–2, 8).

81. A line contains the points (a,b) and (a + b, c + b). What is the slope of the line?

82. Find the x- and y-intercepts of the line 6y – 3x + 5 = 0. 83. What is the slope of all lines parallel to 4y – 2x + 1 = 0? 84. What is the slope of all lines perpendicular to 4y + 9x = 0?

Write the equation of the line. 85. Slope = 3, contains (–4, 5) 86. Contains (4, 6) and (–2, 3) 87. Slope = 0, passes through (–4, –5) 88. Undefined slope, contains (–11, 4) 5 90. Passes through (–8 , –10) and is perpendicular to y = x  3 2 91. Passes through (–4 , –8) and is parallel to y + 5x – 3 = 0 92. Write the equation of the line that passes through (–2 , 4 ) and ( 5 , 4 ). Graph the line. 93. Write the equation of the line that passes through (–2 , 0 ) and ( 0 , 4 ). Graph the line.  7   9  94. Write the equation of the line that passes through  3,  and  3,  . Graph the line.  2   2  95. Write an equation for a circle with r = 5, centered at the origin. Graph the circle. 96. Write an equation for an ellipse passing through ( 0 , 2 ) and ( 4 , 0 ) with center at the origin. Graph the ellipse. 1 1 97. Write the equation of the line that passes through ( 0 , 5 ) and (–3 , 0). Graph the line. 2 2 2 3 98. Find the equation of the circle with center (–6, 2) and radius . 3 99. Alberto invested $15000, part at 6.5% annual interest and rest at 9%. If his total annual income from both investments was $1200, how much was invested at each rate? 100. A pharmacist combined some 10% saline solution with some 15% saline solution to produce 100 ml of a 12% solution. How much of the 10% solution did the pharmacist use? 101. Joan bought roses and carnations for a wedding. Roses cost $25 per dozen and carnations cost $12 per dozen. Joan spent $396 on 20 dozen flowers. How many dozen roses did she buy? 102. Sally and Sue are painting a room. By themselves, Sally can paint the room in 3 hours and Sue can paint the room in 2 hours. How long will it take them to paint the room, working together?

103. In a 30º-60º-90º ABC with hypotenuse AC  6 , find the lengths of the other two sides. 104. In a 30º-60º-90º ABC with right angle B and shortest leg AB  5 , find the lengths of the other two sides. 105. In a 45º-45º-90º ABC with right angle B , and leg AB  8 , find the length of the hypotenuse. 106. In a 45º-45º-90º ABC with hypotenuse AC  7 , find the lengths of the legs.

Solve. x  4  2y 107.  Write as a single logarithm. 3x  2y  0 128. 2 log m + 7 log n 5x  8y  2 129. 7 log w – 3 log v + 9 log u 108.  3x  2y  8 Solve for x. 3x  2y  5 130. 53x = 625 109.  1-3x 2x-1  5x  7y  1 131. 9 = 27 132. 5n =75 Divide. 133. log4(5x – 1) = 3 2 2 110. 3x 13x  5 x  4 134. log3(x – 9) – log3(x + 3) = 1 3 2 111. 10c  c  7c  2 5c  2 Graph each function. x Given f (x) = 2x + 5, g(x) = x2 – 10 135. f (x) = 4 x and h(x) = 3x – 8, find:  1  136. f (x) =   112. f (h(6))  3 113. g(h(–3)) 137. y = 2x and x = 2y 114. h(g(f (9))) 138. Graph: y + 7 = 0 115. g(f (9)) 139. Graph: –5y + 2x – 15 = 0 Given f (x) =x2, graph: 140. Graph: 5(y + 3x) = 10x – 3y 116. f (x) + 2 3 117. f (x) – 5 141. Graph: h(x) = 118. f (x – 3) x  6 5x  2 142. Graph: h(x) = Given f (x) = |x – 2|, graph: x 119. f (x) + 2 143. Graph: y = x2 + 4x – 12 120. f (x + 5) 144. Graph: (x + 2)2 + (y – 2)2 = 4 121. f (x – 3) 145. Graph: 2x2 + 2y2 +12x – 16y = –18

Name each conic section and (x  3) 2 (y  3) 2 146. Graph:   1 write in standard form. 9 64 2 2 122. 16x + 16y – 27 = 0 x 2 y 2 2 2 147. Graph:   1 123. x + 5y + 6x + 10y – 2 = 0 9 36 124. –2x2 + 3y2 –4x + 12y – 8 = 0 (x  2)2 (y  3)2 148. Graph:   1 Write as the sum or difference of 25 4 logarithms with no exponents. r 9 125. log s 4 100r 4 s 7 126. log t 5 b 2c 127. log 5 d 4