2014 2015 Bishop Kelley High School Summer Math Program ... · Math Teachers will be available in C-1 the following dates/times if you need help. Date Time Wednesday, July 30th 8-9:30am

Bishop Kelley High School Math Department

2014 – 2015

Bishop Kelley High School

Summer Math Program

Course: Honors Calculus

NAME:

DIRECTIONS: Show all work in the packet or on loose-leaf paper, which you will turn in with the

packet.

Put final answer on the answer sheet.

This material will be collected, graded, and points awarded at the discretion of each

teacher on the first day of the math class.

A test on this material will be administered during the first week of the class.

An additional resource for help with this packet is http://www.khanacademy.org. It

provides videos of about 10 minutes in length on hundreds of different math topics.

Math Teachers will be available in C-1 the following dates/times if you need help.

Date Time

Wednesday, July 30th 8-9:30am

Monday, August 4th 8-9:30am

Tuesday, August 5th 8-9:30am

http://www.khanacademy.org/

Honors Calculus Summer Packet


Simplify the following:

1. 1 1

x y 2.

2

1 1

x x 3.

x hh

h

4.

11

1x

x

5.

x

x y

x

6.

52

2

2

xx

x

7. 3

3

x

x y 8.

1 1

x h x

x

9.

3 2

5 7

2

3

x y

y x

10. 2

2

4 5

2 1

x x

x x

11.

4

4

x

x

12.

1 3

3 5x x

13.

2

1 1

51 1

25

x

x

14. 2ln 5 ln 1 ln 1x x 15. 32log 53

Solve for 'y

16. ' 1 'xy y y 17. 23 ' 2 ' 5 ' 2y y yy y x 18. 2 23 ' 2 2 'x yy xy yy

Factor each expression

19. 3 24 16 64x x x 20. 2 12x x 21. 26 2x x

22. 3 24 19 5x x x 23. 3 9x x 24. 4 213 30x x

25. 22x x xe xe x e 26. 35 40x 27. 3 27x

28. 3 2

2 3 1 3 2 3x x x x 29. 4 2 3

3 2 3 3 3 2x x x x



Solve the following equations for x analytically (use algebra techniques).

30. 2 5 24 0x x 31. 2 9 5x 32. 3 2 0x x x

33. 23 5 2 0x x 34. 21 11 30 0x x x 35. 2 4 0x x

36. 1 41x 37. 1

y z

x x

38. 3 1 4 1x

39. 5log 2x 40. 2 1

9x 41. 3

1log

81x

42. 2 3x x 43. 8log 1/ 3x 44. 8

5 0x

x

45. 1 3x 46. 43 81x 47. 2 1 0x x

48. 3x x 49. 2

3 9 25x 50. 23 6 24x x

51. 2

2 10

( 2)( 3)

x

x x

52. 3 22 5 6 0x x x 53.

2 1

2 2 1 5

x

x x

54. 3xy z z wx x 55. 2

41 0

3

x

x

56. 2 2 3

2 1 5 2 1 5 0x x x x

Show that each equation is true by simplifying the following:

57. 1 x y

x yx y

58.

1x h x

h x h x

59. x y

x yx y

60.

4 2 1

4 2

x

x x



Write an equation of a line based on the given information:

61. Find the equation of the line that has a slope of 5 and passes through the point 3, 4 .

62. Find the equation of the line that passes through the points 4,1 and 3, 2 .

63. Find the equation of the line that passes through the point 2,1 and is parallel to the line

4 2 1x y .

64. Find the equation of the line with slope of zero and passes through the point 5,1 .

65. Find the equation of the line through (3, -5) and perpendicular to the line 3 4 7x y .

66. Find the equation of the line that has undefined slope and passes through the point 4, 5 .

67. Find the equation of the line that has an x-intercept of 5 and a y-intercept of 3.

68. Find the equation of the vertical line that passes through the point 3,2 .

69. Find the equation of the horizontal line that passes through the point 1, 7 .

Find the x & y intercepts (be sure to write them as point(s)):

70. Find the x and y intercepts of the line that passes through the point 3, 2 and is

perpendicular to the line 3 2x y .

71. Find the x and y intercepts of 2 2

14 9

x y .

72. Find the x and y intercepts of 2 2

14 16

y x

73. Find the x and y intercepts of 2 2 9x y .



Sketch the following graphs. Use the included graph paper. Do not use the calculator. Do

use transformations where appropriate. Plot important points.

74. 3 1y x 75. 2

3 1y x 76. 2 1 3y x

77. 4x 78. y x 79. 1

yx

80. 2

1y

x 81.

32y x 82. log( )y x

83. xy e 84. 2 2 25x y 85. 2

1 1

1

x for xy

x for x

Find the domain and range of each function. Use the graphing calculator for help in

finding the range. Write the answers in INTERVAL NOTATION.

86. 1y x 87. 1

yx

88. 2

1

1y

x

89. 2

1

1y

x x

90. 4y x 91. 1 2y x

92. 2xy 93. 2 3 4y x x 94. 2 2 5y x x

95. 3 2y x for x 96. 2 2y x for x

Find the inverse of each function and solve for y. Use proper notation: 1( )f x

97. ( ) 3 5f x x 98. ( ) 1f x x 99. 3( ) 4f x x

100. ( )2

xf x

x

101. ( ) 3xf x 102. 2( ) 2 5f x x



Find the compositions of the function if:

3( ) 1f x x 2( ) 2g x x ( ) 3j x x

103. (2)f 104. ( ( ))f j x 105. ( (2))f g

106. ( ( ))g g x 107. ( ( ))g f g f x 108. ( ( ))j g x

109. 2( )j x 110. ( )f x h 111. ( ) ( )j x h j x

h

112. ( ) ( )g x h g x

h

Find the difference quotient, ( ) ( )f x h f x

h

for the following functions:

113. 2( ) 2 3f x x x 114. 2( ) 8 1f x x 115. 1

( )f xx

Solve the simultaneous equations analytically. Check graphically.

116. 2 3 8

2 5

x y

x y

117.

2 2 9

7 19

y x x

x y

Find the intersection of the curves graphically. (Use your graphing Calculator)

118. Find the point of intersection between the lines 1y x and 3 5y x .

119. Find the points of intersection between the line 7y x and the curve 2 2 5y x x .

Also, sketch the area between the graphs on the included graph paper.



Solve by using similar triangles.

120. A six-foot man is standing 10 feet away from a 20-foot lamppost. What is the length of

his shadow?

121. Water is dripping out of conical figure that has a diameter of 8 inches and a height of

12 inches. When the depth of the water is 8 inches, what is the radius of the water?

Describe the symmetry of the following functions. Are the functions symmetric with the x-

axis, y-axis, origin, or not at all?

122. 2 3y x 123. 3 1y x 124. y x

125. 3y x x 126. sin( )y x 127. 1

yx

Find the equations for the horizontal and vertical asymptotes of each function. Use the

graphing calculator to look at the graphs for #131, #132 and #133.

128. 1

1y

x

129.

2 9

xy

x

130.

3

3 1

xy

x

131. 2 1

xy

x

132.

2 5 7

1

x xy

x

133.

2

2

5 70

1

xy

x



Exponent Rules: True/False

134. 0 1x 135. 2

2

1x

x

136. x y x y

137. 5 3 15x x x 138. 55 5x y xy 139.

53 8x x

140. 5

5 w

w

xx

x

141. 5

5t tx x 142. 9 3

4 2

143. 124 2x x 144. 1/ 21

xx

145. 2x x

146. 2 1 1x x 147. 43 34x x 148.

1 12 2

2

x y x y

149. 2

3

3 2

1x

x

150. 2ln( ) 2xe x

151. 3ln( ) 3e

152. 2ln(2) ln(5) 4

5e 153.

22ln( ) ln( )x x

Use the graphing calculator for this next section.

154. Find the roots of 3 22 4 3y x x x .

155. Find the local maximum and local minimum of the function: 3 22 4 3y x x x .

156. Find the point(s) of intersection for the graphs of 3 3y x x and 2 4y x .

157. Find the maximum value for the graph of 4( ) 4f x x x .

158. On what intervals for x is ( )f x increasing for 4( ) 4f x x x .



Evaluate the following expressions without a calculator. For the inverses, use the

appropriate inverse rules and give answers in radians.

159. sin6

160. 1 3cos

2

161. 5

tan3

162. cos(0 ) 163. 3

cos4

164. 5

csc6

165. sec( ) 166. cot2

167. 1 1sin

2

168. tan2

169. 2 5sin

6

170. 2

cot3

171. sin2

172. 1cot 1 173. 3

sec4

174. 1tan 1 175. csc( ) 176. 2 11sec

6

Solve the following trig equations for the given domain.

177. ( ) cos( )sin x x 0,2on 178. 1

sin(2 )2

x 0,2on

179. 3

sin(3 )2

x 0,on 180. 1

cos(4 )2

x

0,on

181. tan(2 ) 0x 3

,2 2

on

182. sec( ) 2x 0,on

183. cot( ) 0x 0,on 184. 2sin( )cos( ) 0x x 0,2on

185. 2sin ( ) sin( ) 0x x 0,2on



Summer Packet Name: ______

1.

2. 3. 4. 5.

6.

7. 8. 9. 10.

11.

12. 13. 14. 15.

16.

17. 18. 19. 20.

21.

22. 23. 24. 25.

26.

27. 28. 29. 30.

31.

32. 33. 34. 35.

36.

37. 38. 39. 40.

41.

42. 43. 44. 45.

46.

47. 48. 49. 50.

51.

52. 53. 54. 55.

56.

57. 58. 59. 60.

61.

62. 63. 64. 65.

66.

67. 68. 69. 70.

71.

72. 73. 74. See Graph Below 75. See Graphs Below



74. 75. 76.

77. 78. 79.

80. 81. 82.

83. 84. 85.



86.

87. 88. 89. 90.

91.

92. 93. 94. 95.

96.

97. 98. 99. 100.

101.

102. 103. 104. 105.

106.

107. 108. 109. 110.

111.

112. 113. 114. 115.

116.

117. 118. 119.See Graph Below 120.

119.

121.

122. 123. 124. 125.

126.

127. 128. 129. 130.

131.

132. 133. 134. 135.

136.

137. 138. 139. 140.

141.

142. 143. 144. 145.



146.

147. 148. 149. 150.

151.

152. 153. 154. 155.

156.

157. 158. 159. 160.

161.

162. 163. 164. 165.

166.

167. 168. 169. 170.

171.

172. 173. 174. 175.

176.

177. 178. 179. 180.

181.

182. 183. 184. 185.

Documents

2014 2015 Bishop Kelley High School Summer Math Program ... · Math Teachers will be available in C-1 the following dates/times if you need help. Date Time Wednesday, July 30th 8-9:30am