ࡱ> QS Ppywus#` 3.bjbjmm 4-&t:t:t:t:X;l1 ;^ VEVEVEVE+ + + 0 0 0 0 0 0 0 $"2 h4 1 . ( + . . 1 VEVE&1 0 0 0 . VEVE0 0 . 0 0 0 b60 VE; _gt:. T0 0 <1 0l1 0 D5 M0 "D5 0 D5 0 `+ U, 0 , lG- + + + 1 1 o0 + + + l1 . . . . 599 AP CALCULUS SUMMER HOMEWORK 2013 Dear Parents of Calculus Students, My name is David Murnane and I am the AP Calculus teacher for next year. I have been teaching for 24 years, 15 years at Pittsburg High School and 8 years here at Freedom High School. I have taught AP Calculus for 8 years at Pittsburg High School and I have now been blessed to teach AP Calculus for seven years here at Freedom High School. I cover all topics in the AP Calculus AB topic outline as they appear in the AP Calculus Course Description. The major textbook is CalculusGraphical, Numerical, Algebraic by Finney et. al. Of course my main objective for my students is to do well on the AP exam but I also want my students to become better problem solvers using math and be able to explain solutions to each other. I also want them to become adapt at using a graphing calculator as a tool and not as a crutch and to also be aware of the drawbacks and shortcomings of a graphing calculator. My goal for my students is to learn to appreciate the power of calculus and to give them the tools necessary to be successful in future math classes. My students know that they will work harder than they ever have before but I am here to help them and we will work together to succeed in calculus. Each student is required to have a graphing calculator (TI-83 plus or higher recommended) and is expected to bring it to class everyday. I use a TI-83 plus. We use calculators on a regular basis to analyze and investigate problems both graphically and numerically. Students are allowed to use calculators on some tests and quizzes but not all. In order to get through all the material by May, I am going to assign homework over the summer. This is not optional work. This is the first major assignment for the class. Students who do not do this assignment often do not recover and end up dropping the class. Your son/daughter will need to get a Calculus book from school. If you have any questions on the homework, you can also email me at  HYPERLINK "mailto:murnaned@luhsd.net" murnaned@luhsd.net to ask questions and I will reply with helpful hints. We will have the first test on the review material from chapter 1 on the 3rd class day that we come back. This test will count towards their 1st quarter grade. The summer homework is in two parts. Part I (all exercises are in the Calculus book) p. 7 #6-36 multiples of 3 p. 17 #3-45 multiples of 3 and #49 but not #36 p. 24 #3-33 multiples of 3 p. 39 #3-36 multiples of 3, 37, 38 p. 48 #1-32 all These are all review problems from Precalculus and so their notes from last year should be helpful. This represents about 4-6 hours worth of work. Part II is attached and is all about becoming more familiar with your graphing calculator and how functions are affected by different mathematical operations. This part represents about another 4-6 hours worth of work. If this is spaced out over the summer (or you could even start now) it is only 1.5 to 2 hours per week. If your son/daughter is not able to get to this assignment during the summer then they should definitely ask themselves if they should be taking AP Calculus. Good Luck next year, David A. Murnane For problems 1-17 graph the parent function of each set using your calculator. Draw a quick sketch on your paper of each additional equation in the family (Use a different color for each equation on a graph). Check your sketch with the graphing calculator. 1) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   2) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   3) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   4) Parent Function:  EMBED Equation.DSMT4  (set mode to RADIANS) a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   5) Parent Function:  EMBED Equation.DSMT4  (set mode to RADIANS) a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   6) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   7) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   8) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   9) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   10) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   11) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   12) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   13) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   14) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   15) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   16) Parent Function:  EMBED Equation.DSMT4  a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   17) Parent Function:  EMBED Equation.DSMT4  or  EMBED Equation.DSMT4  Note:  EMBED Equation.DSMT4  or  EMBED Equation.DSMT4  is the Integer Part of x. It is found in the MATH menu, NUM submenu, #5 a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4   18) Resize your viewing window to  EMBED Equation.DSMT4 . Graph all of the following functions in the same window. List the functions from the highest graph to the lowest graph. How do they compare for values of  EMBED Equation.DSMT4 ? a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4  e)  EMBED Equation.DSMT4  f)  EMBED Equation.DSMT4  g)  EMBED Equation.DSMT4  h)  EMBED Equation.DSMT4   19) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 20) Given:  EMBED Equation.DSMT4  from  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 Note: All trig functions are done in radian mode. 21) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 22) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 23) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 24) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 25) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 26) Given:  EMBED Equation.DSMT4  Find all roots to the nearest 0.001 Solve the following inequalities without a calculator. Then check your answers with the calculator. 27)  EMBED Equation.DSMT4  28)  EMBED Equation.DSMT4  29)  EMBED Equation.DSMT4  For each of the following problems 30-33 a) Sketch the graph of  EMBED Equation.DSMT4  b) Sketch the graph of  EMBED Equation.DSMT4  c) Sketch the graph of  EMBED Equation.DSMT4  d) Sketch the graph of  EMBED Equation.DSMT4  e) Sketch the graph of  EMBED Equation.DSMT4  30)  EMBED Equation.DSMT4  31)  EMBED Equation.DSMT4    32)  EMBED Equation.DSMT4  33)  EMBED Equation.DSMT4  34) Let  EMBED Equation.DSMT4  Let  EMBED Equation.DSMT4  a) Sketch the graph of  EMBED Equation.DSMT4  b) Sketch the graph of  EMBED Equation.DSMT4  c) Sketch the graph of  EMBED Equation.DSMT4  35) Given:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Find the point of intersection. 36) Given:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Find the points of any intersection. 37) How many times does the graph of  EMBED Equation.DSMT4  intersect the graph of  EMBED Equation.DSMT4 ? 38) Given:  EMBED Equation.DSMT4  a) Determine the x- and y-coordinates of the lowest point on the graph. b) Size the x-window from [-10,10]. 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!4 @ 4 A 4 B 4 C 0 4 D 4 E 4 F 4 G 4 H 4 I P @4 J F64 K '4 L 4 M 4 N 4 O 6&4 P 4 Q 4 R 4 S 4 T 4 U V F4 V @04 W !4 X 4 Y 4 Z 4 [ 0 4 \ 4 ] 4 ^ 4 _ 4 ` 4 a P @4 b @04 c !4 d 4 e 4 f 4 g 0 4 h 4 i 4 j 4 k 4 l 4 m P @4 n @04 o !4 p 4 q 4 r 4 s 0 4 t 4 u 4 v 4 w 4 x 4 y P @4 z @04 { !4 | 4 } 4 ~ 4  0 4  4  4  4  4  4  P @4  @0w4  !w4  w4  w4  w4  0 w4  w4  w4  w4  w4  w4  P @w,t [ # #"  xw4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" r hw4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" b Xw4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" R Hw4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" B 8w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" 2 (w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4    4   4   4   4   {4  {k4  k[,t [ # #" " w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4   4 ! 4 " {4 # {k4 $ k[,t [ %# #"   w4 & {4 ' ;+4 ( 4 ) {k4 * k[4 + [K4 , K;4 - + 4 .   4 /   4 0   4 1   4 2   4 3  4 4 4 5 4 6 4 7 {4 8 {k4 9 k[Jbb P  w : #"  4 ; @ 0 4 < !  4 =   4 >   4 ?   4 @ 0  4 A   4 B   4 C   4 D   4 E   4 F P @ 4 G @W0G4 H !WG4 I WG4 J WG4 K WG4 L 0W G4 M WG4 N WG4 O WG4 P WG4 Q WG4 R P W@G4 S @ 0 4 T !  4 U   4 V   4 W   4 X 0  4 Y   4 Z   4 [   4 \   4 ]   4 ^ P @ 4 _ @ 0 4 ` !  4 a   4 b   4 c   4 d 0  4 e   4 f   4 g   4 h   4 i   4 j P @ 4 k @ 0w 4 l ! w 4 m  w 4 n  w 4 o  w 4 p 0 w 4 q  w 4 r  w 4 s  w 4 t  w 4 u  w 4 v P @w 4 w @w 0g4 x !w g4 y w g4 z w g4 { w g4 | 0w g4 } w g4 ~ w g4  w g4  w g4  w g4  P w @g4  @g0W4  !gW4  gW4  gW4  gW4  0g W4  gW4  gW4  gW4  gW4  gW4  P g@W4  @G074  !G74  G74  G74  G74  0G 74  G74  G74  G74  G74  G74  P G@74  @70'4  !7'4  7'4  7'4  7'4  07 '4  7'4  7'4  7'4  7'4  7'4  P 7@'4  @'04  !'4  '4  '4  '4  0' 4  '4  '4  '4  '4  '4  P '@4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  F64  '4  4  4  4  6&4  4  4  4  4  4  V F4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  F64  '4  4  4  4  6&4  4  4  4  4  4  V F4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4   4   4   4   0 4   4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @0w4   !w4 ! w4 " w4 # w4 $ 0 w4 % w4 & w4 ' w4 ( w4 ) w4 * P @w,t [ +# #"  xw4 , {4 - ;+4 . 4 / {k4 0 k[4 1 [K4 2 K;4 3 + 4 4   4 5   4 6   4 7   4 8   4 9  4 : 4 ; 4 < 4 = {4 > {k4 ? k[,t [ @# #" r hw4 A {4 B ;+4 C 4 D {k4 E k[4 F [K4 G K;4 H + 4 I   4 J   4 K   4 L   4 M   4 N  4 O 4 P 4 Q 4 R {4 S {k4 T k[,t [ U# #" b Xw4 V {4 W ;+4 X 4 Y {k4 Z k[4 [ [K4 \ K;4 ] + 4 ^   4 _   4 `   4 a   4 b   4 c  4 d 4 e 4 f 4 g {4 h {k4 i k[,t [ j# #" R Hw4 k {4 l ;+4 m 4 n {k4 o k[4 p [K4 q K;4 r + 4 s   4 t   4 u   4 v   4 w   4 x  4 y 4 z 4 { 4 | {4 } {k4 ~ k[,t [ # #" B 8w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" 2 (w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #" " w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [ # #"   w4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[Jbb P  w  #"  4  @ 0 4  !  4    4    4    4  0  4    4    4    4    4    4  P @ 4  @W0G4  !WG4  WG4  WG4  WG4  0W G4  WG4  WG4  WG4  WG4  WG4  P W@G4  @ 0 4  !  4    4    4    4  0  4    4    4    4    4    4  P @ 4  @ 0 4  !  4    4    4    4  0  4    4    4    4    4    4  P @ 4  @ 0w 4  ! w 4   w 4   w 4   w 4   0 w 4    w 4    w 4    w 4    w 4   w 4  P @w 4  @w 0g4  !w g4  w g4  w g4  w g4  0w g4  w g4  w g4  w g4  w g4  w g4  P w @g4  @g0W4  !gW4  gW4  gW4   gW4 ! 0g W4 " gW4 # gW4 $ gW4 % gW4 & gW4 ' P g@W4 ( @G074 ) !G74 * G74 + G74 , G74 - 0G 74 . 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 w 4 @  w 4 A P @w 4 B @w 0g4 C !w g4 D w g4 E w g4 F w g4 G 0w g4 H w g4 I w g4 J w g4 K w g4 L w g4 M P w @g4 N @g0W4 O !gW4 P gW4 Q gW4 R gW4 S 0g W4 T gW4 U gW4 V gW4 W gW4 X gW4 Y P g@W4 Z @G074 [ !G74 \ G74 ] G74 ^ G74 _ 0G 74 ` G74 a G74 b G74 c G74 d G74 e P G@74 f @70'4 g !7'4 h 7'4 i 7'4 j 7'4 k 07 '4 l 7'4 m 7'4 n 7'4 o 7'4 p 7'4 q P 7@'4 r @'04 s !'4 t '4 u '4 v '4 w 0' 4 x '4 y '4 z '4 { '4 | '4 } P '@4 ~ @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  F64  '4  4  4  4  6&4  4  4  4  4  4  V F4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  F64  '4  4  4  4  6&4  4  4  4  4  4  V F4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @04  !4  4  4  4  0 4  4  4  4  4  4  P @4  @0w4  !w4  w4  w4  w4  0 w4  w4  w4  w4  w4  w4  P @w,t [ # #"  xw4  {4  ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4   {k4   k[,t [  # #" r hw4   {4   ;+4  4  {k4  k[4  [K4  K;4  + 4    4    4    4    4    4   4  4  4  4  {4  {k4  k[,t [  # #" b Xw4 ! {4 " ;+4 # 4 $ {k4 % k[4 & [K4 ' K;4 ( + 4 )   4 *   4 +   4 ,   4 -   4 .  4 / 4 0 4 1 4 2 {4 3 {k4 4 k[,t [ 5# #" R Hw4 6 {4 7 ;+4 8 4 9 {k4 : k[4 ; [K4 < K;4 = + 4 >   4 ? 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