Summer Assignment S v2j0k1s1g lknu3tga7 8SioTf8tZwYatrdeL 6LrLZCe.M i NAclulu MrciXgBhGt8sH JrTers1eOrgvge7da.Y

Size: px

Start display at page:

Download "Summer Assignment S v2j0k1s1g lknu3tga7 8SioTf8tZwYatrdeL 6LrLZCe.M i NAclulu MrciXgBhGt8sH JrTers1eOrgvge7da.Y"

Morgan Eaton
5 years ago
Views:

1 -- U a0dro YKubtUa wshopfqtewcakrfev qlhlpc. f PAAlOl0 QrViWgThqtgsv brwetservrezdi.k K BMavdmej EwnitMht GIntfVinnRivtceM 0AXlNgreBbrOaG 79. Worksheet b Kuta Software LLC Honors Precalculus Summer Assignment S vj0ksg lknutga7 SioTftZwYatrdeL LrLZCe.M i NAclulu MrciXgBhGtsH JrTerseOrgvge7da.Y ) Dear prospective Honors Precalculus student, This summer packet is designed to help ou practice the concepts ou learned in Algebra II so that ou are prepared to stud Honors Precalculus this fall. The content and philosoph of this summer packet is consistent with the math department goals and will enable ou to: () value mathematics, () become confident in our abilit to do mathematics, () become mathematical problem solvers, () communicate mathematicall, and () reason mathematicall. You are responsible for knowing how to do all the eercises noted before the first da of classes. If ou do not know how to solve a problem ou are epected to use the sources available to ou (notes, handouts, books, Internet, etc.) to figure it out independentl. The best stud routine during thesummer months is to constantl review topics and do a few problems each da, not attempt to do the entire packet the da before school starts. For our convenience, the answers to all of the eercises are included at the end of the document. Unless specificall stated or unless ou are to give a decimal approimation to a square root, ou should not use a calculator to do these eercises. You ma, however, use our calculator to check our answers. Use separate sheets as necessar to show our work in a neat and organized wa. Do not tr to show all work on these worksheets; there isn t enough room! This summer assignment will not be collected. You are responsible for knowing how tosolve ever single problem, but this does not mean ou need to do ever single eercise. At a minimum, we suggest doing half of the problems so that our summer workload is manageable and ou review some problems involving each topic. There will be a ver brief review of these topics during the first week of class and then ou will be formall evaluated on our knowledge of these topics. This eam will count as 0% of our first quarter grade. The prepared Honors Precalculus student should easil score over 90% on such an eam. If ou have an questions, please alfonso.gonzalez@asfg.m or leticia.garcia@asfg.m Enjo our summer and do our best! Sincerel, The ASFG Math Department

2 -- S Op0moc KKGuotma0 oskojfgtwagr7eq 0LFLzCb.J o dazlvli ZrvigAhJtTso FrOeuserKvtemdd.j q bmhaadieb zweivtqhp BIunBfQiBnbiMtZer jajlrgkefbkrdar Qz. Worksheet b Kuta Software LLC Solve each equation. ) n + + = ) + + = 0 ) a = 77 ) + 9 v = 77 Solve each inequalit and graph its solution. ) 0 + > 9 7) > ) a 9) k < Graph each equation. 0) = + ) = Solve each equation b completing the square. ) n + n + = 9 ) m m + = ) + = 0 ) 9r r 70 = Simplif. ) i + i ( i) 7) i ( i) ( i)

3 -- b PE0Twn KUuWt7al rsfodfqtywuaqrlek LULTCn.O d qahl0lv NrVicg0hetMsP FrTepsBedrvvVewdg.C b AMcaVdeq twriztwhv jihnmfiiqnkiqt9e IAYltggezbhraX sf.f Worksheet b Kuta Software LLC ) ( + i)(7 i) i + i 9) i( + i)( i) 0) + i 0 i ) 9 + i 7 9i ) 7 ) Use the information provided to write the verte form equation of each parabola. ) = + ) = + 9 ) Verte: (, ), -intercept: 9 7) Verte: (, ), -intercept: Use Cramer's Rule to solve each sstem. ) z = z = = 9) + z = + = z = Long Division 0) (r + 7r 7r 7) (7r ) ) (0b + 7b + b + ) (b + ) Snthetic division ) ( 9 + ) ( 7) ) (n n + n n + ) (n )

4 -- l er0saj ZK0utDa 9SXoSft9wZarLej LoLhCn.b c iajlilj mriagehtqsp Yrze9s0eUrUvefdg.B l M0aTdqeZ DwitFhj 9InAfXiSnCiWtIe vaelbgweabrda 0V.R Worksheet b Kuta Software LLC Sketch the graph of each function. ) = ) = + Solve each equation. ) = 7) ( = ) Solve each equation. Round our answers to the nearest ten-thousandth. ) a + = 7 9) k = 00 Solve each equation. 0) log log 0 = ) log ( 0) + log = ) log (n + 7) = log ( n 0) ) log ( m 7) = log ( m ) Factor each and find all roots. ) = 0 ) = 0 Solve each equation b completing the square. ) n + n 70 = 0 7) b + 0b + 7 = 9

5 -- D SI0Pk KHutlaS dso0fftnwcaxrbe LaLhCU.k X 9AIlrle vr9ikgnhltesq LrEeSsZeJrqvteXdj.r J KMaPdTeA Zwliatsh eilntfmionigt7ez AtlPgwebrla WV.l Worksheet b Kuta Software LLC Solve each equation b factoring. ) v = v 9) + = 0) n + n + 7 = ) a + a + 0 = Solve each equation. Remember to check for etraneous solutions. ) k = k ) = Solve each equation. ) + = ) n + = 7 Solve each equation. Remember to check for etraneous solutions. ) p = p + 0 p 0 p 7) m + = m + m + m + ) n = n 9) + = +

6 -- H Ml0gZn KuMtgaX HSkovfptawgaLre0 LLOLSC.i Y lawlnlh hrkignhhtst mruejsqetrqvdeddw.a J EMFaHdez zwziotoh XIqnRfDiniVtzel RAjlXgFeubrIap wk.d Worksheet b Kuta Software LLC Sketch the graph of each function. 0) = ) = Simplif. Your answer should contain onl positive eponents with no fractional eponents in the denominator. ) ( )0 ) m n mn 0 (n ) Factor each completel. ) 0v v v + ) a a a + State the number of comple roots, the possible number of real and imaginar roots, and the possible rational roots for each equation. Then factor each and find all roots. ) + 9 = 0 7) = 0 Factor each completel. ) m + m 9) n + n + 7n 70) n + n 0 7) b b b

7 -7- n IW0RbB UKlurtVa DSVokfOtnwZaRrBep clilcz. u walluli GrRiQgNhMtpsV lrwepserqvbefdl.f O vmmaddew iwoiqtnhm OIJnpfJin9itZed SAkljgleObgrMaJ mh.n Worksheet b Kuta Software LLC 7) 9n n + 7) r + r + 7) 9m 7) n 9 7) ) m + Find all roots. 7) ( )( + )( ) = 0 79) ( )( + )( 9) = 0 Find the inverse of each function. 0) f (n) = n ) g() = + Perform the indicated operation. ) h(a) = a + g(a) = a Find (h g)(a) ) g(t) = t + h(t) = t Find (g h)(t) State the number of comple zeros, the possible number of real and imaginar zeros, and the possible rational zeros for each function. Then find all zeros. One zero has been given. ) f () = + 0; ) f () = + 7 ; Sketch the graph of each line. ) 0 = 7) = 0 0

8 -- i c0pab pksutfam SoMfgthwqairWeI zlnlccb.o l mazlolo RrEiHgehWtnsH ErWeUsiegrvJeDds.T q hmnaidke wlistrh fignqfsivnuimtlel AplEgCesbzras rn. Worksheet b Kuta Software LLC Graph each function. ) f () = + 9) f () = Identif the holes, vertical asmptotes, -intercepts, horizontal asmptote, and domain of each. Then sketch the graph. 90) f () = + 9) f () = Epand each logarithm. 9) log ( ) 9) log a b c Condense each epression to a single logarithm. 9) log 7 log 7 0log 7 9) log + log + log 7 + log

9 -9- of0hz AKruwtkaq lso7fdtvwpabrseo TLdLeCu.q e lanlplw 7rPi7gshYtosr lrelsveirqvkeadk.z H QMQa0deM HwSithhC EIqnfOiXnWieteJ haglqg7eaberian Ew.H Worksheet b Kuta Software LLC Rewrite each equation in logarithmic form. 9) ( 7) = 7 97) = 9 9) = 99) = 9 Sketch the graph of each function. 00) f () = 0) f () = + Sketch the graph of each function. Approimate each real zero to the nearest tenth. Approimate the relative minima and relative maima to the nearest tenth. 0) f () = + 0) f () = Simplif. Use absolute value signs when necessar. 0) hj k 0) 79 z

10 -0- i Rv0fc AKGuqtMa SCoIfVtwa0ren mlvlmco.f i RArlVlG UrTiZghtYsA nrdehsiervoesda.s u omzagdel rwbiftkhm InvfIihniktbew laqlhgvembgrwaz W. Worksheet b Kuta Software LLC Simplif each epression. 0) v v + v 07) 7b b b + Evaluate each function at the given value (remainder theorem). 0) f () = at = 09) f (n) = n + n 0n + at n = 0) Moll traveled to the ferr office and back. It took one hour less time to get there than it did to get back. The average speed on the trip there was 0 mph. The average speed on the wa back was mph. How man hours did the trip there take? ) Imani drove to her friend's house and back. On the trip there she drove 0 km/h and on the return trip she went 0 km/h. How long did the trip there take if the return trip took five hours? ) How man oz of cane molasses which costs $/oz must be added to oz of beet molasses which costs $/oz to make Anjali's Premium Molasses which costs $/oz? ) How man lb of peanuts which cost $/lb must be added to lb of spices which cost $/lb to make Stefan's Red Hot Peanuts which cost $/lb? Solve each question. Round our answer to the nearest hundredth. ) Moll can pick fort bushels of apples in 9 hours. One da her friend Mike helped her and it onl took.9 hours. Find how long it would take Mike to do it alone. ) It takes Arjun hours to pick fort bushels of apples. Trevon can pick the same amount in 0 hours. Find how long it would take them if the worked together. ) The frequenc of a vibrating guitar string varies inversel as its length. Suppose a guitar string 0. meters long vibrates. times per second. What frequenc would a string 0. meters long have? 7) If the fied costs are $00 if the average variable cost is $, and if the selling price is $.0 per unit then: a) the total cost of producing q units is given b the cost function ; b) the revenue from selling q units is given b the revenue function ; c) the profit from producing and selling q units is given b the profit function

11 -- 0 no0vvz qkgujtzaf ASkoJfOtWwKarNeT LiLLCf.V e 9ANlRlI VrrigRhgtms RrUeTserrKv9edf.O L 9MOagd7eC VwditohP IDn7fpinn7iOtveu hael7gseb9rla kb.y Worksheet b Kuta Software LLC ) A rectangular piece of cardboard is inches longer than it is wide. If -inch squares are cut from each corner, and the remaining piece folded up to form a bo, the volume of the bo is 0 cubic inches. Find the dimensions of the piece of cardboard 9) A rectangular shipping container has a volume of 00 cm. The container is times as wide as it is deep, and cm taller than it is wide. What are the dimensions of the container? Answer from the graph. 0) "A rectangle garden, meters squared in area, will be fenced to keep out rabbits and skunks. Find the dimensions that will require the least amount of fencing if a barn alread protects one side of the garden." ) This word problem has got me stumped. An help ou can provide would be appreciated. The percent of deaths caused b smoking is modeled b the rational funtion defined b: P(X)=X-/X where is the number of times a smoker is more likel to die of lung cancer than a nonsmoker. is equal to 0. Please help me find: a. p() if is 0 b. For what values of is p() = 0%

12 V Uz0Sru dksutza HSboVfrthwga9rbeb XLOLbC7. MAplbln ArWifgNhet7sl rkehsxelrivsedd.x I JMoaKdfel ZwviQtchP TIznIf0injiStEe7 hajllgesbrrva MV.v -- Worksheet b Kuta Software LLC Answers to Summer Assignment ) The dot net to the choice indicates that it is the answer. ) { 7 }, ) No solution. ) {, 0} ) < or > 0 : 0 0 ) {, } 7) < 0 or > : 0 7 ) { All real numbers. } : 0 9) < k < 9 : 0 0) ) ) { +, } 0 0 ) { + i, i } ) {, 7} ) { +, } ) + 0i 7) + 0i ) 0 + i 9) i 77i 9 i 0) ) ) 7 ) ) = ( + ) + 9 ) = ( 9) 7 ) = ( + ) 7) = ( ) ) (0,, ) ) b + 0b + b + ) 7) { } 9) ( 9, 9, 9 9) 0) r + 9r + ) ) ) { 9 } ) { 7 7 } 7 ) { } ) Factors to: ( + )( + )( )( + + ) = 0 Roots: {, + i 7 7r ) n 7n + n 0 + n ) 0. 9).07 0) { 0}, i,, + i, i ) { } }

13 d aq0yjn akwuutqak csbonfotwvarrweu RL0L0C. q 0AqldlH ArmibgNh7tfsp HrJeesreQrDvveudk.i j mmaadeq mwsibtrhh IpnhfRinjiltPe jaflagkevbbrjao br.p -- Worksheet b Kuta Software LLC ) Factors to: ( + )( + )( )( + + ) = 0 Roots: {, + i, i,, + i, i } ) {, 0} 7) {, } ) {, } 9) {, 7} ) No solution. ) No solution. 0) {, 7 } ) {, } ) {9} ) {, } ) {} ) {} 9) { } 0) 0 0 7) { } ) 0 0 ) 0 ) m 9 n 0 ) (v 7)(v ) ) (a )(a ) ) # of comple roots: Possible # of real roots: or 0 Possible # of imaginar roots: or 0 Possible rational roots: 7) # of comple roots: Possible # of real roots:,, or Possible # of imaginar roots:,, or 0 Possible rational roots: ±, ±, ± 9, ±, ±, ± 9 Factors to: ( )( + ) = 0 Roots: {, } ) m (m + 7) 9) n(n + )(n + ) ±, ±, ±, ±, ±, ±, ±, ± Factors to: ( )( + )( + ) = 0 i Roots: {, i, i,, i } 70) (n + 0)(n ) 7) b(b )(b + ) 7) (n ) 7) (r + ) 7) (m + )(m ) 7) (n + )(n ) 7) ( + )( 0 + ) 77) (m + )(m m + )

14 n Az0wIm BKguZtYaR Swo7fUtnwbasrBeI OLDLJCF.F U batldlb hreipgchbtvs FrqesKevrEvkeCds.q F CMmaNdXee lwuiytrhb PIKnfei0nuiutweg EAwlgMenbfrtaU tq. -- Worksheet b Kuta Software LLC 7) {, i, i,, } 79) {, i, i,, } 0) f (n) = n + ) g () = ) a 7 ) t t + 0 ) # of comple zeros: Possible # of real zeros: or Possible # of imaginar zeros: or 0 Possible rational zeros: ±, ±, ±, ±, ± 0, ± 0 Zeros: { + i, i, } ) 9) 9) 0 7) 90) Vertical Asm.: =, = Holes: None Horz. Asm.: = X-intercepts:, Domain: All reals ecept, 9) log a 9) log 7 00) + log b + log c 7 = 97) log 9 = 0 ) # of comple zeros: Possible # of real zeros: or Possible # of imaginar zeros: or 0 Possible rational zeros: ±, ±, ± 7, ± Zeros: { +,, } ) Vertical Asm.: = Holes: None Horz. Asm.: None X-intercepts:, Domain: All reals ecept 9) log + log 9) log ( ) 9) log 7 0 0) 9) log = 99) log 9 =

15 t Ep0DLg UKnultKaV JSboOfttXwhaprwen TLdLiCp.Q q galilv YrtiPghmtUsK Xr0eWsOerTvveid7.9 i MRahdGe gwzictuhd sionbfbinnpiwte jazlwgjewbbrfa b.i -- Worksheet b Kuta Software LLC 0) Real Zeros:.,, Minima: ( 0.,.) (.,.) Maima: (.,.) (0.,.) 0) j k h 0) z 9z 0) Real Zeros:., 0. Minima: (.7,.) ( 0.,.) Maima: (, ) 0) v 7v 0 (v )(v ) 07) 7b b + (b )(b + ) 0) 09) 7 0) hours ) hours ) ozs ) lbs ) hours ) hours ) The dot net to the choice indicates that it is the answer. 7) The dot net to the choice indicates that it is the answer. ) The dot net to the choice indicates that it is the answer. 9) The dot net to the choice indicates that it is the answer. 0) The dot net to the choice indicates that it is the answer. ) The dot net to the choice indicates that it is the answer.

SUMMER ASSIGNMENT STUDY PACKET Calculus

SUMMER ASSIGNMENT STUDY PACKET Calculus Dear Calculus student, This summer assignment will enable ou to be successful in knowing prerequisites for our net course. The content and philosoph of this summer