Desert Mountain H. S. Math Department Summer Work Packet

Transcription

1 Corse #50-51 Desert Montain H. S. Math Department Smmer Work Packet Honors/AP/IB level math corses at Desert Montain are for stents who are enthsiastic learners of mathematics an whose work ethic is of the highest stanar. These stents are epecte to arrive reay to go on the first ay of school. The attache packet is esigne to help yo review concepts with which yo shol alreay e familiar. It is recommene that yo complete some of the prolems from the packet at the eginning of the smmer when the concepts are still fresh, an then complete the remainer of the prolems near the eginning of the school year. If yo o not complete the prolems in the packet, yor grae will not e affecte irectly, however, the material in the packet has een taght in yor previos math classes an will e assme to e flly nerstoo y yo. I, the teacher, strongly avise yo to work the prolems this smmer. The prolems will e collecte an reviewe after the first week of school once we have gone over any qestions yo have. If yo are new to the Scottsale Unifie School District an i not receive notice of this assignment ntil registration, these review prolems will e checke at the en of Agst. Some sggestions for the presentation an completion of mathematics assignments at DMHS are liste elow. If yo ahere to these gielines with yor smmer work, yo will e reay to meet the epectations of yor mathematics teacher ring the school year. Use noteook paper or plain white paper All working shol e neat an legile Neatly staple yor work or place complete work in a small iner or foler with ras Use pencil, erase completely when neee Work the prolems in orer an clearly inicate section an prolem nmers Begin new sections on a new piece of paper 1

2 Corse #50-51 Basic Differentiation Rles (Memorize all of these, or else!) 1.. c c. v v v 4. v v L v v NM O vqp v 5. c 0 6. n n n ln 10. sin tan cosg 1. csec h 14. g 16. sec sec tan e cos cot e g sin c csc h csc csc cot g 17. arcsin arccos arctan 1 0. arc cot 1 1. arc sec 1. arc csc 1. a a ln a log 4. 1 ln ** Be reay for a pop qiz on these as early as the first ay of school. Hee hee =)

3 Corse #50-51 Linear Eqations y m y Write the following eqations in point-slope form 1. The line containing the point, 7. The line containing the point, an having a slope of 5. 0 an perpeniclar to 4y.. The line containing the point,9 an having a slope of The perpeniclar isector of the segment etween 5, an, 1. Compositions of Fnctions Given f 4 1 an g 6 5. g f 6. f g 7. f f, fin the following compositions. Basic Factoring Factor each of the following as completely as possile y 5y y 4y 7y 1

4 Corse #50-51 Fnction Analysis Determine the omain an zeros of the each of the following fnctions Then se those vales on a sign chart (nmer line) to etermine intervals where the fnction is positive an negative. 11. P C f 14. T 10 Mie Review Prolems 15. Fin all roots of Solve y han: P sing factor y groping. log Epress as a single logarithm: log log 18. Solve 4y 9 5y Solve log 4 log.. 0. Simplify 1 y y 1 y y. 1. Determine the amplite an perio of y sin an sketch the graph.. Simplify tan cos tan sin sin.. Given 4 sin an, fin sin,cos, an tan Solve sin 1 0. on, 5. Solve cos sin on0,. (hint: se the ole-angle ientify first an on t cancel) 4

5 Corse #50-51 Trigonometry Yo shol complete these prolems withot the se of a calclator. 6. Evalate. 5 a. sin 10. cos 4 c. tan 60. sec e cot f. csc 7. Sketch a complete graph of y cos. Lael important places (like -intercepts). 8. State the omain of y sin an y csc. 9. Given that 5 sin in the r qarant, fin the vales of the other 5 trig. fnctions. 1 Solve for. 0. sin sin sin 5

6 Corse #50-51 Calcls: These are some of the most important qestions, so on t wait ntil the last minte, an on t ecie to leave them lank. That wol make me ma. Make sre yo spen time actally thinking aot them efore yo write anything own. Rea them now an consier them as yo work throgh the packet. Yo proaly can t answer them all right now. 1. A limit is a statement that states specific facts aot how inpt vales an otpt vales of a fnction or epression are relate. a) Eplain the meaning of lim f( ) 10 5 ) Eplain the meaning of lim f( ) 10. c) Eplain what the epression lim f( ) is asking s to fin. c. What types of things col case a limit to not eist?. If the limit of a fnction eists at = c, then mst the fnction mst e efine at = c? Eplain why or why not. 4. There are two special trig limits. State them. 5. There are at least three ways to fin a limit. State them. 6. Some fnctions are not continos at = c ecase they are not efine at = c, while some fnctions are not continos at = c ecase the limit oes not eist there. What mst e tre aot a fnction at = c in orer for it to e continos at = c? 7. What is the ifference etween removale an non-removale iscontinities? How is that relate to limits? 8. Is it possile for a fnction to e continos, t not ifferentiale? If so, give an eample. 9. Is it possile for a fnction to e ifferentiale, t not continos? If so, give an eample. 10. What oes f () tell yo aot f ()? 11. Let f ( ) e. Fin the inverse of f an call it g. a) Fin an compare f (1) an g (e). ) Fin an compare f () an g ( e ). c) Use yor answers to (a) an () to iscss the relationship etween the slope on a fnction an the slope on its inverse. 6

7 Corse # What eactly oes velocity measre? If the velocity of an oject is negative, what oes that mean? If the velocity of an oject is negative, oes that also mean that the oject is slowing own? Eplain why an/or why not. 1. When it is sai that the erivative of f() is positive at = c, what oes that really mean aot f()? f 14. Let f ( ). Fin lim ( ) f ( ) 0 know aot erivatives. an interpret yor answer knowing what yo 15. Determine whether the statement is tre or false. If it is false, eplain why or give an p( ) eample that shows it is false. If p() is a polynomial, then f ( ) has a vertical 1 asymptote at = 1. For prolems 16 an 17, se the graph sown in the figre. 16. Ientify or sketch each of the qantities on the figre. a) f(1) an f(4) ) f(4) - f(1) f ( 4) f ( 1) c) y 1g f ( 1) Insert the proper ineqality symol (< or >) etween the given qantities. a) f ( 4) f ( 1) f ( 4 ) f ( ) ) f ( 4 ) f ( 1 ) f ( 1 ) y at ( -1, ) a) Fin an eqation of the tangent line to the graph of f at the inicate point. ) Use a graphing tility to graph the fnction an its tangent line at the point. c) Use the erivative featre of a graphing tility to confirm yor reslts. 19. Determine the points if any at which the graph of the fnction has a horizontal tangent line. 4 y 8 For 0 an 1, etermine whether the statement is tre or false. If it is false, eplain why or give an eample that shows it is false. 0. If f () = g (), then f() = g(). 1. If y, then y/ =. 7

8 Corse # Fin f ( ) an f ( c) if f ( ) cos an c = 4. Fin the erivative: f ( t) t sin t Fin f ( ) for the fnctions in #4-7 given the following, g() = an g () = - h() = -1 an h () = 4 g( ) 4. f ( ) g( ) h( ) 5. f ( ) 4 h( ) 6. f ( ) 7. f ( ) g( ) h( ) h( ) For 8 an 9, etermine whether the statement is tre or false. If it is false, eplain why or give an eample that shows it is false. 8. If y f ( ) g( ), then y t f '( ) g'( ). g ( ) n1 9. If f() is an nth-egree polynomial, then f Fin the erivative of the fnction. 0 g 1. y 0. y y sin(cos ) 4. y ln( e ). f ( ) 1 sin 4 5. f ( ) ln F HG I K J 1 6. The relationship etween f an g is given. Fin g'( ) if g( ) f ( ) 7. Given that g(5) = -, g (5) = 6, h(5) =, an h (5) = -, fin f (5) (if possile) for each of the following. If it is not possile, state what aitional information is reqire. a) f ( ) g( ) h( ) ) f ( ) g( h( )) g( ) c) f ( ) ) f ( ) g( ) h( ) 8

9 Corse # Fin y/ y implicit ifferentiation. a) y 6 ) e y 10 y 0 9. Using the graph at the right, a) etermine whether y/t is positive or negative given that /t is negative, an ) etermine whether /t is positive or negative given that y/t is positive. 9