Name w s2q0f1q7r XKkuxt[az usrodfxtdw^atruev hlglucz.s r katldli SrCifgshPtMsw tryems`e_rgviesdr.

Transcription

1 Precalculus Name w sq0f1q7r XKkut[az usrodftdw^atruev hlglucz.s r katldli SrCifgshPtMsw tryems`e_rgviesdr. Spring Final Review Solve each triangle. Round our answers to the nearest tenth. 1) ) B A 7 17 mi 1 d A 35 C C 19 d 37 B Find the area of each triangle to the nearest tenth. 3) d E 1. d D 1 d F Find the following information for each vector: Graph, component form, linear combination, magnitude and direction angle. ) AB where A = (0, ) B = (-, 0) Find the following information for each vector, if not provided in the question: Graph, component form, linear combination. 5) n =, 5 m BS0M1H7z ^KuhtaA ASIoqfitSwIaErFe\ BLCLVCi.M A naeldlh jrpiugshvtwsb DrTetsgehrzvUekd`.f T IMVardIek bwgietihj UITntfgivnzintkeS lporpevckaglcpuklmu]st. -1- Worksheet b Kuta Software LLC

2 Divide. Write our answer in fraction form. ) ( + 1-9) ( + ) Find the remainder when f () is divided b - k. 7) f () = k = - Write a polnomial function of least degree with integral coefficients that has the given zeros. ) 3, 0, -3 Find all zeros. 9) f () = For each function: (1) state the maimum number of turns the graph could make, () determine the real zeros and state the multiplicit of an repeated zeros, (3) list the -intercepts where the graph crosses the -ais and those where it does not cross the -ais, () describe the end behavior, and (5) sketch the graph. 10) f () = For each function, identif an holes, intercepts, asmptote, domain, range and graph the function. Give the coordinate of an possible holes and an intersections with the horizontal asmptote. 11) f () = Case 1. Find the partial fraction decomposition of each. 1) ( + )(5-3)( + 3) Case. Find the partial fraction decomposition of each. 13) Case 3. Find the partial fraction decomposition of each. 1) Case. Find the partial fraction decomposition of each. 15) ( + )( + 5) Find the net three terms in each sequence. 1) -9, -1, -13, -5, 3,... i ni01o7l okiuotna` fsiopfntawpanrbek gllmce.a h maalolf brriyghitksu brhezse\rsvcexdq.m I FMAaTdJe\ uwgiztkh[ ICnOfUipnFiqt[ee RPprnepczaalscpuTlDu[sB. -- Worksheet b Kuta Software LLC

3 Find the first four terms in each sequence. 17) a n = - + 5n 1) a n = a n a 1 = -0. Write the eplicit formula for each sequence. 19) 3, 3, 3, 3, 3,... Write the recursive formula for each sequence. 0) -30, -1, -, -, 0,... Determine if each sequence converges or diverges. 1) a n = (n - 1) ) a n = a n - 1 a 1 = -1.5 Rewrite each series as a sum. 3) Sn (0 - n) Evaluate each series. ) Sm (3m + 1) 5) Sk = (k + 3) Rewrite each series using sigma notation. ) Determine if the sequence is arithmetic. If it is, find the common difference, the term named in the problem, the eplicit formula, and the three terms in the sequence after the last one given. 7) -3, -, -, -1,... Find a 3 Given the eplicit formula for an arithmetic sequence find the first five terms and the term named in the problem. ) a n = 3 + (n - 1) 00 Find a Given the recursive formula for an arithmetic sequence find the first five terms, the term named in the problem, and the eplicit formula. 9) a n = a n a 1 = -33 Find a 3 Given two terms in an arithmetic sequence find the eplicit formula. 30) a 0 79 and a 3 = 379 s dk0d1c7e mkouotsa BSKoofGtHwnaCrXep HLlLUCz.\ n CANlMlm MrhiWgDhLt[sj hrwexspe^rmvxetds.m D `MUaGdheJ LwAiotNhd JIPnufTiqnNiktTeg lpjreexckaqlrciuflrudst. -3- Worksheet b Kuta Software LLC

4 Given a term in an arithmetic sequence and the common difference find the eplicit formula. 31) a = 33, d 0 Find the missing term or terms in each arithmetic sequence. 3)..., -5,,,,, -15,... Evaluate the related series of each sequence. 33) 13, 0, 7, 3, 1, Evaluate each arithmetic series described. 3) Sn 10 (10n - 13) 35) Si = 3 1 (3i + ) 3) , n Determine the number of terms n in each arithmetic series. 37) a 1 = 5, a n, S n = 97 Determine if the sequence is geometric. If it is, find the common ratio, the term named in the problem, the eplicit formula, and the three terms in the sequence after the last one given. 3) 3, -, 1, -,... Find a 10 Given the eplicit formula for a geometric sequence find the first five terms and the term named in the problem. 39) a n = 3 n - 1 Find a 10 Given the recursive formula for a geometric sequence find the first five terms and the term named in the problem. 0) a n = a n a 1 Find a 11 Find the eplicit formula. 1),, 1, 3,... Given a term in a geometric sequence and the common ratio find the eplicit formula. ) a = -1500, r = -5 Find the missing term or terms in each geometric sequence. 3)...,,,,, 500,... K ww01n7h ^KIu]ttaW bskorfytlwjawrlek elulcs.q gaflcl[ BrkiBgWhzt`sz YrjeksNezrgvleidG.X w RMvaodeZ WwWifthc RIintfTiAnJiStQeX cpr`eicxaslacuuvlhuvs\. -- Worksheet b Kuta Software LLC

5 Evaluate each geometric series described. ) , n = 7 9 5) Sm - m - 1 ) a 1 = -, r = 3, n = Determine the number of terms n in each geometric series. 7) a 1 =, r =, S n = Evaluate each infinite geometric series described. ) Sk 3 ( - 1 k - 1 ) 9) Determine the common ratio of the infinite geometric series. 50) a 1 = -, S = -9 Use the information provided to write the standard form equation of each circle. 51) Center: (-5, 15) Radius: 5) = 0 Use the information provided to write the general conic form equation of each circle. 53) ( - 3) + ( - 3) 9 Use the information provided to write the standard form equation of each circle. 5) Center: (17, 5) Point on Circle: (15, 5) Identif the center and radius of each. Then sketch the graph. 55) = 0 5) ( - 3) + ( - ) I H\0R1N7v ZKCult\aP OSCocfAtbwhagrreA BLlL_CG._ E SAclOlR IrciigThStWs_ ZrTe]soeLrMvneEdl.^ D \MlaTdbet YwXiVtDho KIlnSfaiun]ietJeG XPursegcBaIlYciu\lVuDsG. -5- Worksheet b Kuta Software LLC

6 Identif the center, vertices, co-vertices, and foci of each. Then sketch the graph. 57) ( - 1) 1 + ( - 1) Identif the center, vertices, co-vertices, foci, length of the major ais, length of the minor ais, and eccentricit of each. 5) ( + ) 11 + ( - ) 5 Use the information provided to write the standard form equation of each ellipse. 59) = 0 0) Vertices: (3, ), (-15, ) Co-vertices: (-, ), (-, 0) 1) Vertices: (7, ), (7, -) Foci: (7, ), (7, -) Use the information provided to write the standard form equation of each hperbola. ) Vertices: (5, -), (5, -1) Distance from Center to Focus = 5 3) = 0 Use the information provided to write the general conic form equation of each hperbola. ) ( - 9) 1 - Use the information provided to write the standard form equation of each hperbola. 5) Center at (-5, 0) Verte at (-, 0) Eccentricit = 5 3 g WS0k1G7T ekzugtcao msdoifqtmwiafrtet LjLdC].n g _ArlKld drgiqghitfsu mraevsbe[ravleidh._ m `MAahd[eE WwciRtchD wijncffihntibtrez PParjescZaIldcYuXlduisd. -- Worksheet b Kuta Software LLC

7 Identif the vertices, foci, asmptotes, and eccentricit of each. Then sketch the graph. ) ( - 3) - ( - ) ) = Evaluate each limit. ) lim ) lim -1 ( ) f() L Gi0v1o7u ]KPutJa_ FSOo[f\towkaCrNef CLvLrCo.K g easlula SraivgOhYtwsf ArmedsjeurEvXeOdG.R Z nmzandzel FwiJtahq miwnofqisnviiteex DPIrGeJcLaNlBcNuZl`uzsU. -7- Worksheet b Kuta Software LLC

8 70) lim - f (), f () = f() {- + 1, , > 71) lim f() ) lim f() 73) lim 0 ( - 3) ) lim ) lim ) lim For each problem, find the instantaneous rate of change of the function at the given value. 77) f () = + 1; For each problem, find the equation of the tangent line to the function at the given point. 7) f () = ; ( 1, - 1 ) Use the definition of the derivative to find the derivative of each function with respect to. 79) f () = + - 0) f () = + P W0Y1w7O akfuktaq ws]o^fbt`wdaxrheg jltlqci.b f `ANlgll TrNiIgDhEtbsV lretsiehr_vjeide.j H UMpaedkeS MwuigtkhW OIBngfZikn^iUtPeh FPLrIeTcBaClSccuSlcuzsN. -- Worksheet b Kuta Software LLC