Factor each completely.

Transkrypt

1 Math 2 Final Exam Packet Part I Name ID: 1 Date Block Factor each completely. 1) p 2 + p 28 A) ( p + 7)( p + 4) B) Not factorable C) ( p + 7)( p 4) D) ( p + 2)( p 14) 2) r 2 14r + 45 A) (r 5)(r + 9) B) (r 5)(r 9) C) (r + 5)(r + 9) D) (r + 5)(r 9) ) 21k 2 k A) k(7k + 1) B) None of these C) 21k(k 1) D) k(7k 1) 4) 21x + 177x x A) (7x + 12)(x + 2) B) None of these C) (x + )(7x 8) D) x(7x + )(x + 8) 5) 7a 55a a A) Not factorable B) a(7a 6)(a 7) C) (7a + 6)(a 7) B X2\0A1d9h \Kiuctzau vsoo]fktcwva]rjeg PLILlC\.j E YAClZlF ErriXgLhZthsm MrIeisqeerrv]eedp.N \ zmaaodmew Uw\iBtohb ui`nwfdiqneilteeq maalwgbejbdraam K2m. -1-

2 Solve each equation by factoring. 6) (4x 1)(5x 1) = 0 A) { 1 4, } B) { 1 4, 1 5 } C) { 1 4, 2 } 7) (5n + 4)(n + 4) = 0 A) { 1, 2 } B) { 1, } C) { 4 5, 4 } D) { 5, 4 } 8) 6b 2 84 = 0b A) None of these B) {, 0} C) {6, 2} D) {4, 2} 9) n n = 0 A) {5, 6} B) {, 6} C) { 5, 6} 10) 15n 2 18 = + 16n A) { 5, 5 } B) { 7 5, 2 } C) { 5, 4 } D) { 5, 5 } 11) 5x 2 = 4x 24 A) { 4 5, 7 } B) { 8 7, 6 } C) { 8 5, 4 } D) { 4 5, 6 } A H2p0k1S9b oktuntza_ tsvo]fhtyweamroet cluldck.l K HA\lQlF `reiigjhltrs^ TrKemsdeCrTvxeedK.H d XMHaudaeE FweiZtBhO yi[njfei\npiztsel DAulBgTeCbHrtaB f2k. -2-

3 Solve each equation by completing the square. 12) x x + = 0 A) {2.055, } B) None of these C) {6, 10} D) {, 11} 1) a 2 10a 24 = 0 A) {8, 4} B) {12, 2} C) {9.099, 1.099} D) {21.16, 1.16} 14) r 2 6r 51 = 6 A) {8 + 17, 8 17 } B) { + 6, 6 } C) { , } D) { , } 15) r 2 20r + 22 = 6 A) { , } B) {4, 2} C) { , } D) {2 + 2, 2 2 } 16) x 2 6x 66 = 6 A) {12, 6} B) { , } C) {6, 4} D) { , 7 15 } G e2a0c1b9v YKKuvtFa^ dstotfktqwdasrwe] KLKLtCU.i ] bawlnlx MrDixgehStJsZ nrnexshe`rgvleldn.b O hm_aldoev PwxiKtFh\ niinlf[iynhivtbeb zamligcetbdrhat t2g. --

4 Solve each equation with the quadratic formula. 17) n 2 + 5n 24 = 0 A) {4, 1} B) {1, 0.5} C) {0.618, 1.618} D) {, 8} 18) 2x 2 + x = A) {, 2 2 } B) { 5, 11 2 } C) {7, } 19) k 2 = 9 + 6k A) { 1 + i 17 2 B) {} C) { }, 1 i 17 2 } D) { , } Find the discriminant of each quadratic equation then state the number and type of solutions. 20) v 2 + 6v 9 = 6 A) 81; two real solutions B) 0; two real solutions C) 0; two imaginary solutions D) 0; one real solution 21) 7x 2 + x + 2 = 8 A) 177; two real solutions B) None of these C) 299; two real solutions D) 159; one real solution e K2K0r1y9Y ZK^uIt`aO FSlolfHtuwCaRrveP GLiLVCS.b n zanlzle zrfingbhqtdso Yr]eysaeSrIvfeXdt.f K VMvaJdFeo MwniOt_hx _IOn^fBi^neiytneS paelrg`ecbkrhae S2k. -4-

5 22) a 2 a 1 = a A) 0; one rational solution B) 196; two rational solutions C) 296; two irrational solutions D) 52; two irrational solutions 2) 4b 2 + 7b + 1 = 2b A) 97; two rational solutions B) 14; two imaginary solutions C) 65; two irrational solutions D) 65; one rational solution Simplify each expression. 24) (12p 4 7p + 11p) (6p 8p p) A) 4p 4 1p + 4p B) 20p 4 1p + 4p C) 4p p D) 4p 4 + 4p 25) (4p 10p + 4) + (14p + 5p + 8) A) 15p + 9p + 12 B) 15p + 5p + 22 C) 4p + 9p + 12 D) 15p + 5p + 12 Find each product. 26) (2v + )(5v + 8) A) 6v 2 9 B) 6v 2 15v 9 C) 10v 2 v 24 D) 10v 2 + 1v ) ( 4n + 6)( 6n 7) A) 24n 2 42 B) 16n 2 4n 20 C) 24n 2 64n + 42 V Y2J0T1m9I PK^uYtqaz `SkoifmtzwaaTrcew xlwlwcx.d r JAylTlo druibg]hctksv Drte^szekrqvNehd_.D Q gmjaxdfes WwNiytqhm iiznyf\iznwiktjed qarllgnetbyroa_ j2a. -5-

6 Factor each completely. 28) 6xy + 147x y + 42x A) 14x(y + 2) B) (7x + 2)(y + 7x) C) (7x + 2)(y + 2) 29) 28xy 5x 2 4y + 5x A) (7x + 1)(4y + 5x) B) None of these C) 2x(4y + 1) D) (7x 1)(4y 5x) Describe the end behavior of each function. 0) f (x) = 2x 2 + 4x + 4 A) f (x) + as x - f (x) + as x + B) f (x) - as x - f (x) - as x + C) f (x) + as x - f (x) - as x + D) f (x) - as x - f (x) + as x + 1) f (x) = x 2 6x + A) f (x) + as x - f (x) + as x + B) f (x) + as x - f (x) - as x + C) f (x) - as x - f (x) - as x + D) f (x) - as x - f (x) + as x + Simplify. 2) 5 6x y A) 64x 2 2y B) None of these C) 0xy xy D) 48y 5x ) 294ab 4 A) 21b 2 6a B) 10a 2 b C) 5a 2 b 2 D) 40a 2 b 2 2 l K2c0r1d9S TKEumtVaZ XS]otfpt^wHaDrSeJ jlhlscy.n X laulglv `rjiogkhhtusg PrceYsYeTrBvoeqdK.C p QMBaOdHe` rwiiwtshh diznffki_nfiotveg oadl]gjecberraq Y2W. -6-

7 4) A) 9 6 B) C) None of these D) 6 5) A) B) C) D) ) 4 15( ) A) 0 + B) C) 40 D) 8 7) 5( ) A) B) 29 C) 12 + D) Write each expression in exponential form. 8) ( x) 2 A) (5x) C) (x) 2 5 B) (10x) D) (5x) 7 4 9) 2n 1 2 A) (2n) C) n 5 6 B) n 1 o \2x0b1W9J HKyuStbaU [SWouf\thwXarrueV ]LsLQCW.n U SAelZlE IrFiHgehpt^sP LrBejsaeCrgvHeKds._ x mmkawdqey CwniqtNhf nihnyfuiinuintgej UATlZgieVbGrNaL K2s. -7-

8 Write each expression in radical form. 40) v 8 5 A) ( 5 v) 8 B) ( 2v) 5 C) 7v D) ( v) 4 41) r A) 4 4 r B) ( r) 4 C) ( 4r) 4 D) ( r) Identify the vertex, axis of symmetry, and min/max value of each. 42) f (x) = x x 104 A) None of these B) Vertex: ( 8, 2) Axis of Sym.: y = 2 Min value = 8 C) Vertex: (10, 4) Axis of Sym.: x = 10 Max value = 4 D) Vertex: (12, 5) Axis of Sym.: x = 12 Min value = 5 4) f (x) = x 2 + 4x 1 A) None of these B) Vertex: (2, ) Axis of Sym.: x = 2 Max value = C) Vertex: (, 2) Axis of Sym.: y = 2 Min value = D) Vertex: ( 2, ) Axis of Sym.: y = Min value = 2 f X2\0I1Z9I HKZuPtVaq lskogfktxwtaorve^ FLGLiCL.o J zaklelk IrpixgphQtvsO nrkemsbearovkeed].s Y GMvaWdweY ZwNimtYh_ GIHnWfIihnliOtRe] IAilogAeGbjrgac y2i. -8-

9 Use the information provided to write the vertex form equation of each parabola. 44) f (x) = x 2 8x 14 A) f (x) = (x 4) 2 2 B) f (x) = (x + 4) C) f (x) = (x 4) ) f (x) = x 2 10x 25 A) f (x) = x B) f (x) = (x + 5) 2 C) f (x) = (x + 8) 2 D) f (x) = (x + 5) 2 Use the information provided to write the standard form equation of each parabola. 46) f (x) = 1 1 x2 + 4 A) None of these B) f (x) = 4 1 x2 + 4 C) f (y) = 1 1 y y ) f (x) = (x 9) 2 A) f (x) = x x 81 B) f (x) = x x 81 C) f (x) = x 2 18x + 81 D) f (x) = 2x 2 9 D) f (x) = 2 1 x2 + 4 o J2I0F1c9n gk]udt[aa ksqoifntmwlazrbek olalwch.n q \A[lWl] br_ifgghdtqsx grgedseexrgvdeed].] [ AM_aqdleQ uwkittchi wignhfzitnfiwteeh NAel_g\eBbOrraM P2V. -9-

10 Determine whether the scenario involves independent or dependent events. Then find the probability. 48) A basket contains four apples and four peaches. You randomly select a piece of fruit and then return it to the basket. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach. A) Dependent; B) Dependent; C) Dependent; ) A cooler contains thirteen bottles of sports drink: five lemon-lime flavored, five orange flavored, and three fruit-punch flavored. You randomly grab a bottle. Then you return the bottle to the cooler, mix up the bottles, and randomly select another bottle. Both times you get a lemon-lime drink. A) Dependent; B) Independent; C) Independent; D) Independent; = 0.25 Find the probability. 50) There are seven nickels and five dimes in your pocket. Four of the nickels and two of the dimes are Canadian. The others are US currency. You randomly select a coin from your pocket. It is a nickel or is Canadian currency. A) B) 4 = 0.75 C) 1 D) U c2e0d1c9z xk`u\tnal wstoofctjw`aeraev ilel`ch.v N SAflilC yrniwgyhmtasb WrwemsieDryvAemdv.C j ]MiaFdneE ]w[irtbhr OIen]fAiwnDiatVeN XAalJgSe^barfaj l2u. -10-

11 Answers to Part I (ID: 1) 1) C 2) B ) D 4) D 5) B 6) B 7) C 8) A 9) C 10) A 11) D 12) D 1) B 14) B 15) C 16) A 17) D 18) B 19) B 20) D 21) B 22) A 2) C 24) B 25) C 26) D 27) D 28) B 29) D 0) B 1) A 2) C ) A 4) C 5) B 6) B 7) A 8) C 9) A 40) A 41) B 42) C 4) B 44) B 45) B 46) A 47) B 48) D 49) C 50) B l a2n0h1z9c EK]uOtUao msxoifst_wnarrxem ulgldcv.e i madlgln kruiagihktzsc zrqensae`rjvxepdi.x Y fmuaddeei AwViJtah` OIonhfrienwi_t]ep XAulOgqegbyrZa\ j2t. -11-

12 Math 2 Final Exam Packet Part I Factor each completely. 1) x 2 + 4x 12 A) (x + 12)(x 1) B) None of these C) Not factorable D) (x + 2)(x + 6) Name ID: 2 2) x 2 + 5x 6 A) Not factorable B) (x + 4)(x 9) C) (x 4)(x 9) D) (x 4)(x + 9) Date Block ) 2x + 25x x A) x(2x + 9)(x 8) B) None of these C) x(2x + 9)(x + 8) D) 2x(x + 4)(x + 9) 4) 28n 4 16n + 96n 2 A) 4(7n + 24)(n + 1) B) 4n 2 (n 6)(7n + 4) C) 4n 2 (7n 6)(n 4) D) 4n 2 (7n + 6)(n 4) 5) a 2 + a 10 A) (2a + 5)(a 2) B) (a 5)(a 2) C) (a 5)(a + 2) D) (a + 2)(a 5) Y q2f0o1b9` pkfuitoah nsponfetvw\a^rrej GLsLnC[.\ e sawlvli FrZiggChMtMst lrie^stetrtvnesdl.y ^ BM\abdBeE qwkiltnhk cijngfeiynyiktyen rahlbgdegbxrpah T2D. -1-

13 Solve each equation by factoring. 6) (x 4)(x ) = 0 A) {2, } B) {4, } C) {2, 0} D) { 4 5, 0 } 7) (m 5)(m + 4) = 0 A) { 1, 1 } B) {5, 4} C) { 5, 4 } D) { 2, } 8) 2k 2 48 = 4k A) { 2, 6} B) { 4, 6} C) { 8, 7} D) {1, 4} 9) b = 7b A) { 2, 5} B) { 5, 0} C) { 6, 4} D) { 5} 10) 0b b = 5 A) { 7 5, 8 } B) { 7, 2 } C) { 7 5, 8 } D) { 5, } 11) 15b b = 4b A) { 2 7, 7 } B) { 4 7, 5 } C) { 8, 1 } D) { 7, 5 } d g2m0x1z9u vkpudtrac WSPoyf`tOw\axr^eB plqlocc.y f qawlcls mrcixgdhwtysu Pr`eksMewrBvGegdI.] ^ dmxaodzeq dw\ijthhz oijnlfbionwiitjex WAklugceTburTaQ A2O. -2-

14 Solve each equation by completing the square. 12) x 2 4x 60 = 0 A) {6.449, 1.551} B) {.196, 7.196} C) {15.48, 0.652} D) {10, 6} 1) n 2 10n 46 = 0 A) {1.426,.426} B) { 4, 8} C) {11.12, 2.877} D) {16, 2} 14) x 2 4x 5 = 8 A) { , } B) None of these C) {, 1} D) { 4, 16} 15) b b + 16 = A) {6, 2} B) {, 9} C) { 1, 1} D) { 6 + 7, 6 7 } 16) r 2 + 8r 1 = 7 A) { , } B) {2, 10} C) {5, 7} D) { , } n K2h0G1U9T gkouetoaq js]oefptvw[asrgex MLmLOCt.o J CA[lVld Er`iPgYhmtfst proebskeorhvneedn.r j WMoa[deeW qwbirtsht ]IgnzfhiInuiNt\eB FAvlVgJe[bUrCaz v2r. --

15 Solve each equation with the quadratic formula. 17) 2k 2 5k 25 = 0 A) {8, } B) {2.5, 5} C) {0.5, 1} D) {5, 2.5} 18) 10k 2 = A) { 1} B) { 1 + 2, 1 2 } C) {1} D) { i 0 10, i 0 10 } 19) 2n = n A) {, 2 2 } B) { 2, 5 } C) None of these D) { 1 + i 119, 1 i } Find the discriminant of each quadratic equation then state the number and type of solutions. 20) 5x 2 x + 15 = 7 A) 169; two real solutions B) 4; two imaginary solutions C) 169; one real solution D) 271; two imaginary solutions 21) x 2 + 6x 1 = 7 A) 4; two imaginary solutions B) 4; one real solution C) 261; two real solutions D) 4; two real solutions Q A2Z0i1f9W nkluqtjau BSEoPfktlwdaerSeQ tl_lmca.v o lajlelk urlifgzhwtlsb irhecseeyruvjekdc.w c RMaardeef twiimt\hd siwn]ftinnjimtued macllgsecbrroa] g2x. -4-

16 22) x = 10 A) 4; two imaginary solutions B) 4; two rational solutions C) 4; two imaginary solutions D) 4; two rational solutions 2) 12r 2 17r 17 = 10r r A) 1; one rational solution B) None of these C) 1; two rational solutions D) 1; two irrational solutions Simplify each expression. 24) (10x + 8x 5 + 2x ) ( 9x 5 + x + 5) A) 2x 5 1x + 10x 5 B) 10x 5 + x + 10x 5 C) 17x 5 + x + 10x 5 D) 2x 5 + x + 10x 5 25) ( 2x 2 8x 2x) + ( 1 + 5x + 10x) A) x 2x x 22 B) x 2x 2 + 8x 1 C) None of these D) x + 6x x 22 Find each product. 26) ( 8n + 1)( n 6) A) 8n 2 49n + 6 B) 8n n 6 C) 8n n + 6 D) 8n ) (7n 5)( 5n + 4) A) 42n n 8 B) 6n C) 5n 2 + 5n 20 D) 5n 2 + n + 20 G R2D0Y1o9D UKAufttaO [S^ojf]thwgacrSeY NLYLnCS.t c qa`leln BrCi]gPhTtysP ursess\etrqv_ekdm.z m dmaaideea DwCintqhp QI^nPfbiAniintDeT \AFlagveebHrhaL P2U. -5-

17 Factor each completely. 28) 8xy + x 24y 2 y A) (x y)(8y + 1) B) 5y(x + 1) C) 11y(x + y) D) 11y(x + 1) 29) 40xy + 16x + 25y + 10 A) (8x + 5)(5y + 2) B) None of these C) 2(8x + 5)(4x 1) D) 10(y + 1)(4x 1) Describe the end behavior of each function. 0) f (x) = x 2 + 8x 11 A) f (x) - as x - f (x) - as x + B) f (x) + as x - f (x) - as x + C) f (x) - as x - f (x) + as x + D) f (x) + as x - f (x) + as x + 1) f (x) = x 2 + 2x A) None of these B) f (x) + as x - f (x) - as x + C) f (x) + as x - f (x) + as x + D) f (x) - as x - f (x) + as x + Simplify. 2) 6 150x 4 y A) 64x y B) 98x 2 y 2y C) None of these D) 0x 2 y 6y ) 72x 2 y 4 A) 18y 2 x 2 B) 42y 2 2x C) 40x 2 y 6y D) 16x 2 y h g2_0x1t9j _KvuhtxaU isooyf^tgweahr]er KLnL`CY.Q C [AblGl_ PrTi[gvhftJsQ Nr`ersaevravIecdV.m P VMiaadLei owiiotwhb uianvfjienmiataeo eaulagce[b_rka^ b2w. -6-

18 4) A) None of these B) 2 5 C) D) 4 5) A) None of these B) 11 C) 9 D) 15 6) 5( ) A) B) C) None of these D) ) 15(2 + 6) A) B) C) D) Write each expression in exponential form. 8) 6p A) p 1 4 C) (6p) 1 B) None of these D) ( p ) 1 4 9) 7b 2 A) (7b) 1 B) (7b) C) None of these D) (6b 2 ) 1 P ]2X0l1l9A fkmurtaaf esno\fjtlweairnew ALVLzCe.e D MAClplR Ir]iIglhbttsG VrXeksjeprYveeLdb.n Z ZMOaNdYeN BwTictUh^ ri_nif[innai_tteu ganl\ghevbmrcah M2\. -7-

19 Write each expression in radical form. 1 40) (2v 6 ) A) ( 6v) B) ( 10v) 5 C) None of these D) 6 2v 2 41) (6n) A) ( 5 n) 7 B) 7n C) ( 6n) D) ( 4 5n) 7 Identify the vertex, axis of symmetry, and min/max value of each. 42) f (x) = x 2 14x 55 A) Vertex: ( 7, 6) Axis of Sym.: y = 6 Max value = 7 B) Vertex: (7, 6) Axis of Sym.: x = 7 Max value = 6 C) Vertex: ( 7, 6) Axis of Sym.: x = 7 Min value = 6 D) Vertex: ( 7, 6) Axis of Sym.: x = 7 Max value = 6 4) f (x) = 1 x2 + 4 x + 7 A) Vertex: ( 2, 1) Axis of Sym.: x = 2 Min value = 1 B) Vertex: ( 2, 1) Axis of Sym.: x = 2 Max value = 1 C) Vertex: ( 4, ) Axis of Sym.: x = 4 Max value = D) Vertex: ( 2, 1) Axis of Sym.: y = 1 Min value = 2 r O2F0A1K9c jk`uatiar pskosfntbwcaareey ELULLCA.\ ^ pazlzlj VrIiFgVhctCsZ droejsherrzvvedd\.o q KMRaYdZeY UwSiNtZhv GIsnqf_iDnjictCeG kaplagveybaraao j2e. -8-

20 Use the information provided to write the vertex form equation of each parabola. 44) f (x) = x x + 6 A) f (x) = (x + 6) 2 B) f (x) = x C) f (x) = (x + 6) 2 D) f (x) = (2x + 7) 2 45) f (x) = 6x 2 108x 494 A) f (x) = 6(x 9) 2 8 B) f (x) = 6(x + 7) 2 8 C) f (x) = 1 ( x + 9) Use the information provided to write the standard form equation of each parabola. 46) f (x) = (x 6) A) f (x) = x 2 66x + 55 B) f (x) = x 2 + 6x + 99 C) None of these D) f (x) = x 2 6x ) f (x) = 1 ( x + 7) 2 + A) None of these B) f (x) = 1 x x + 56 C) f (x) = 1 x2 14 x + 58 D) f (x) = 1 x x + 58 ^ \2O0x1s9n lkkutttao GSuoTflttwaaIrTeB qlblxc\.s X ZASlZlQ VrwicguhNtDsH ^rwehsieertvoeadt.v A RMjaZdse` uwzistmhj zitntf`iinsihtbem baolyghekbsruai \2R. -9-

21 Determine whether the scenario involves independent or dependent events. Then find the probability. 48) You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a two. A) None of these B) Independent; C) Independent; D) Dependent; ) A bag contains four red marbles and eight blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. Both marbles are red. A) None of these B) Independent; C) Independent; 1 4 = 0.25 D) Independent; Find the probability. 50) A spinner has an equal chance of landing on each of its six numbered regions. After spinning, it lands in region two or three. A) 1 0. B) None of these C) D) 7 10 = 0.7 f `2C0C1V9P HKJuEtiaD ^SOoGfntLwzasrueo rlcljcj.z c MArlwlP _rmi^gxhetusx \r]etsdehrpvpeedf.k B OMwaud_ez lwfijtkhn WIwnGfyiMnriCtfeH FAYlwgFeAb[ruaT N2U. -10-

22 Answers to Part I (ID: 2) 1) B 2) D ) C 4) C 5) C 6) B 7) C 8) B 9) A 10) C 11) D 12) D 1) A 14) C 15) C 16) B 17) D 18) D 19) C 20) A 21) D 22) B 2) C 24) C 25) B 26) B 27) C 28) A 29) A 0) A 1) A 2) D ) A 4) B 5) C 6) D 7) B 8) C 9) B 40) D 41) C 42) D 4) A 44) C 45) D 46) D 47) D 48) C 49) A 50) A g V2J0W1f9e vkruqttas FS`o`fut\wSa_rEee LL^LlCM.R E jabl[ld IrbiagphPt]sI [rhezsbeirdvfegd].f I XMIaKdBeH swuiotmht \I^nKfXiJn`iZt[eY LAElkgsebblrwaS K2U. -11-

23 Math 2 Final Exam Packet Part I Factor each completely. 1) x 2 x + 2 A) (x + 2)(x 1) B) None of these C) (x + 2)(x + 1) D) Not factorable Name ID: 2) x 2 9x + 18 A) (x + )(x 6) B) (x + 2)(x + 1) C) (x )(x 6) D) (x )(x + 6) Date Block ) 20x 2 + 6x A) 4x(5x 9) B) 4x(5x + 9) C) 4x(5x + 1) D) 20x(x + 9) 4) 15v 2 + 6v + 42 A) (5v + 2)(v 10) B) (5v 2 + 2v + 14) C) 15(v + 2) 2 D) (5v 2)(v 10) 5) 5r r 24 A) (5r + 24)(r 1) B) (5r + 4)(r 6) C) (5r 6)(r + 4) D) 2(5r + 2)(r + ) p `2E0V1U9k `K^unthal [SboyfytbwuaTrKeG VLFLGCR.R p UAIlslN srpimgnhwtlsp QrveVslekrMvOeHdi.z ] MMXagdOeR TwviZtvhr GIqnMfuifnCiNtoe_ jahl[gzewbirxa[ Y2B. -1-

24 Solve each equation by factoring. 6) (r 4)(r 1) = 0 A) None of these B) {4, 2} C) {4, 1} D) { 5 2, 1 2 } 7) (x 1)(5x + 1) = 0 A) { 4, 1 5 } B) { 4, 5} C) { 1, 1 5 } 8) 6b 2 54b = 84 A) { 7, 8} B) {2, 7} C) {2, 5} D) { 7, 7} 9) v 2 = 8 6v A) None of these B) { 4, 7} C) {, 7} D) {, 0} 10) 27x 2 19x 17 = 5 + 6x 2 A) { 5 2, 2 } B) None of these C) { 4, 7 } D) { 1 7, 5 } 11) 11x 2 = 8x 2 + 8x A) { 7, } B) { 5 4, } C) { 1, } D) { 7 2, 4 7 } V B2n0[1M9z JKauntXap gspolfftuwnamrvef vlclhcv.y Z vazlclc RrciMgAh_tSsy sr`epsieorvvdecdz.p h PMPaAdEey ]whigt]hl LITnFfjiwnAictvew qaqldgfe^bhrtay d2o. -2-

25 Solve each equation by completing the square. 12) x x 24 = 0 A) {11.08, 1.08} B) None of these C) {4.124, } D) {10, 2} 1) m m 50 = 0 A) None of these B) {6, 8} C) {5.55, 9.55} D) {2.95, 16.95} 14) n n + 87 = A) {1 + 67, 1 67 } B) { 6, 14} C) { , } D) { , 5 67 } 15) n 2 18n 70 = 7 A) {2 + 2, 2 2 } B) {21, } C) None of these D) {7 + 95, 7 95 } 16) m 2 + 8m + 10 = A) { 1, 7} B) {, 1} C) {4 +, 4 } Y P2\0^1e9J akdurtzat ^SUoZf\tkwqa`rdeS JLcLWCV.s o _AdlMlk Vr\itgUhLtFsz _r`e^spezrlvzeldx.w A LMdabdVev gwni[tdhm cisnafeivnjizteeg TAEl^gDeIbdrHad y2_. --

26 Solve each equation with the quadratic formula. 17) n 2 5n 24 = 0 A) {8, } B) {6, 4} C) {1.646,.646} D) {4, 6} 18) 7m = 4m A) None of these B) { 1 + i 7, 1 i } C) { 2 + i, 2 i 7 7 } D) { 1 + i, 1 i 2 2 } 19) x 2 + 2x = A) None of these 1 + 7i 2 1 7i 2 B) {, } C) { 1 + 7i 2, 1 7i 2 } D) {, 11 } Find the discriminant of each quadratic equation then state the number and type of solutions. 20) k 2 + k 11 = 2 A) 117; one real solution B) 99; two imaginary solutions C) 117; two real solutions D) 99; one real solution 21) n 2 6n + 12 = A) 0; one real solution B) 284; two real solutions C) 105; two real solutions D) 0; two real solutions a b2c0e1r9k nkpuwtbad TSqoEfztJwNajrMeU wl`lhcw.p x kadlhlf TriiegVhytVsT brye`svearkvcezde.e i pm\andcew Xwbiat[hs pign_fzianci]tsex ^A_l]gcenbqrDa^ I2u. -4-

27 22) 14x 2 5x 5 = 14x 6 + 1x 2 A) 77; one rational solution B) 77; two imaginary solutions C) 5; two imaginary solutions D) 77; two irrational solutions 2) 1x 2 5x + 14 = 2x A) 777; two imaginary solutions B) 777; two irrational solutions C) 679; two imaginary solutions D) 777; one rational solution Simplify each expression. 24) (11 n + 6n 2 ) + ( 14 14n 2 9n ) A) 16n 8n 2 n 2 B) 9n 8n 2 n C) 22n 8n 2 n 25) (5a 2 a + a 4 ) (11a 2 9a 12a 4 ) A) 1a 4 10a 6a 2 B) None of these C) 1a 4 6a 6a 2 D) 1a 4 + 2a 6a 2 Find each product. 26) (8x 7)(4x 5) A) 2x x 5 B) 2x 2 12x 5 C) 2x ) (7n 7)(n 4) A) 21n 2 7n 28 B) 21n 2 41n 10 C) 21n n + 10 t D2[0`1f9R QKtuPtWad ESBonfDtwwkaUrqeg al]llcc.l Y ha]lnlx JrTingwhxttsq NrYeCsfefr[v_eqdv.F h _MzakdCey rwticthhq nimnkftidniirtaey ]AIlsgUe[bArFaU Q2B. -5-

28 Factor each completely. 28) 21uv 18u 2 + 4v 2 A) (u + 4v)(v 6u) B) 9u(u 4v) C) u(u + 4v) 29) 8xy 14x 2 + 4y 7x A) (2x + 1)(4y + 1) B) (2x + 1)(4y + 7x) C) None of these D) 9x(2x 1) Describe the end behavior of each function. 0) f (x) = x 2 4x 2 A) f (x) + as x - f (x) - as x + B) f (x) - as x - f (x) + as x + C) f (x) + as x - f (x) + as x + 1) f (x) = x 2 6 A) f (x) + as x - f (x) - as x + B) f (x) - as x - f (x) - as x + C) f (x) - as x - f (x) + as x + D) f (x) + as x - f (x) + as x + Simplify. 2) 4 112xy 2 A) 16xy 2 B) 14y 2 x 5x C) 112xy 2y D) 16y 7x ) 2 108u 4 v A) 12u 2 v B) 8v 7uv C) 64uv 6u D) 24v 7u s J2E0p1o9y fkkujtxav CSuoXfytqwmaSrXel FLALlCg.` K RAQldl` QrZiDgMhLtEs\ erwe]s_emrdvpevdy.l l RM\aHdseg FwkiVt`hF AIGnrfziYnPiwtXeT ratlpgiezblrpag e2t. -6-

29 4) A) 8 B) None of these C) 7 D) ) 2 + A) 5 B) 2 C) D) 0 6) 6(5 + 2) A) B) C) None of these D) ) ( 5 + 5) A) 44 B) C) D) Write each expression in exponential form. 8) ( 4 v) 5 A) None of these B) v C) v 4 5 D) v ) ( 6m) A) m 2 C) (2m) B) (6m) D) (4m) 2 m R2^0R1]9v MKkuRtkaD ASOopfBtbwNaLrpec yldlicc.t L XATlila ir\imgqhmtvsl erve[soeerkvsegdk.c l AMsakdZeK VwbiKtzhO gi`nefkipnjiwtpep razlfguevbornal m2n. -7-

30 Write each expression in radical form ) (2k) A) ( 5 k) 7 B) ( 5 10k) 6 C) ( 5 2k) 8 D) ( 5 2k) ) (7p) A) p B) ( 2p) 4 C) ( 5 p 2 ) 2 D) ( 7p) 2 Identify the vertex, axis of symmetry, and min/max value of each. 42) f (x) = x x + 27 A) Vertex: ( 9, 6) Axis of Sym.: x = 9 Min value = 6 B) Vertex: ( 6, 9) Axis of Sym.: x = 6 Min value = 9 C) Vertex: (6, 9) Axis of Sym.: x = 6 Max value = 9 D) Vertex: ( 6, 9) Axis of Sym.: y = 9 Min value = 6 4) f (x) = x 2 16x + 71 A) None of these B) Vertex: (8, 7) Axis of Sym.: x = 8 Min value = 7 C) Vertex: ( 8, 7) Axis of Sym.: y = 7 Max value = 8 D) Vertex: ( 7, 8) Axis of Sym.: x = 7 Min value = 8 g s2l0b1[9c nksuxtmae ^Sionfrt\waaErjeS bljleci.w W SAqlZls FrLiCgphGtssg irwersje^rqvyehdx.m X WMOabdjen Nwni\tVhM SIAnafSiFnOintbei GAtlPgbeHbUrJa^ d2y. -8-

31 Use the information provided to write the vertex form equation of each parabola. 44) f (x) = 2x 2 20x 55 A) None of these B) f (x) = 2(x + 5) 2 5 C) f (x) = 2(x 5) D) f (x) = 2(x 7) ) f (x) = 4x 2 16x 10 A) f (x) = 4(x + 2) B) f (x) = 4(x 2) C) f (x) = 4(x + 2) D) f (x) = 4(x + 6) Use the information provided to write the standard form equation of each parabola. 46) f (x) = 6(x + 7) 2 10 A) f (x) = 6x x B) f (x) = 9x 2 84x + 05 C) f (x) = 6x 2 84x 04 47) f (x) = (x + 9) 2 8 A) f (x) = x 2 18x 89 B) f (x) = x x 89 C) f (x) = x 89 D) f (x) = 2x 2 + 6x v Q2w0f1q9^ BKDuZtsao ESqoZfEtBw\a\rkei dlvlscw.p Q YAolblq CrziggJhet]s[ pryezsweirbvdeldw.z \ kmdajdsek lwsiit_hv bion_fqifnyittte` HAHlhgieOb^rhaA V2U. -9-

32 Determine whether the scenario involves independent or dependent events. Then find the probability. 48) A box of chocolates contains five milk chocolates and seven dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. Both pieces are milk chocolate. A) Independent; 1 4 = 0.25 B) Dependent; C) Dependent; ) You flip a coin twice. The first flip lands tails-up and the second flip lands heads-up. A) Independent; B) Independent; C) Independent; 1 4 = 0.25 D) Dependent; Find the probability. 50) A spinner has an equal chance of landing on each of its four numbered regions. After spinning, it lands in region two or three. A) 1 0. B) C) None of these D) F u2i0q1t9^ ukyuwtsax LSRobfAtfwQavr^eT jlkljcv.o c MATlDlh Gr`itgAh^t\sQ hrkeysbebrdvtewdt.d [ _MRaAdReF Jw_ijtPhG MIEnBfaiCnAiWtTes XAAlLgCebbnr^ay `2\. -10-

33 Answers to Part I (ID: ) 1) B 2) C ) B 4) B 5) C 6) C 7) C 8) B 9) A 10) C 11) C 12) B 1) D 14) B 15) B 16) A 17) A 18) C 19) D 20) B 21) A 22) D 2) B 24) B 25) B 26) D 27) D 28) A 29) C 0) C 1) D 2) D ) A 4) D 5) B 6) B 7) C 8) B 9) B 40) D 41) D 42) B 4) B 44) B 45) C 46) C 47) A 48) B 49) C 50) C d d2w0t1r9m _K^uctEaY jsloufwtcwxagrkek CL_LNCF.u U QABlJlF zrdi]gqhttasz vrzecs\eerkvqejdc.s N lmcafdber KwRirtChr UILnvfyiHnViItpe\ UAdlagMekbVrVaU J2e. -11-

34 Math 2 Final Exam Packet Part I Factor each completely. 1) m 2 + m 0 A) (m 5)(m + 6) B) (m + 5)(m + 6) C) (m 5)(m 6) D) (m + 5)(m 6) Name ID: 4 2) v 2 + 2v 8 A) (v 9)(v + 1) B) (v 2)(v 4) C) (v + 2)(v 4) D) (v 2)(v + 4) Date Block ) 7n 4 + 4n A) 6(5n 7)(n + 10) B) n (7n + 4) C) n (n + 7) D) n (7n + 1) 4) 10n 2 48n + 2 A) 2(n 4)(5n + 4) B) (n 4)(5n 4) C) 2(5n 4)(n 4) D) 2(5n + 8)(n + 2) 5) 5v 2 + 8v A) (5v + )(v + 1) B) (5v )(v 1) C) Not factorable D) (v )(5v + 1) X a2p0u1g9s VKkuBthaZ YSZozfhtOwFaGrrel olglec^.h v ka^lllh nrvizg`hutzsj Wr`eusuePrRvce]dt.V B nmcaidaef MwPistjhu iignofuidnwiiteef MAplsg_eXburNau a2n. -1-

35 Solve each equation by factoring. 6) (x + )(x ) = 0 A) {, } B) { 2, } C) { 5 4, 2 } D) { 1, 2 5 } 7) (n + 2)(n 4) = 0 A) None of these B) { 2, 2 } C) {1, 0} D) { 2, } 8) x 2 + 7x = 8 A) {1, 0} B) {1, 8} C) {5, 8} D) {1, 5} 9) m 2 8m = 0 A) {8, 0} B) {2, 6} C) None of these D) { 5, 0} 10) 4b 2 b + 12 = 8b + 6 A) None of these B) { 4, 2 } C) { 5 7, } D) { 5, 2 5 } 11) a 2 24 = a A) { 7, 5 } B) None of these C) { 8, } D) { 2, 1 2 } L B2Q0b1F9c UKcuMt_ap vsaorfutmwrajrhez ELhLlCl.c e XAJlMlf _ryifgohytksr prde^sneqrevketdk.^ G IMFaydPeZ swii`tihu wianmfdi`nqivtcep oaqlagjefbyr\az S2`. -2-

36 Solve each equation by completing the square. 12) v 2 10v 9 = 0 A) { 1, 9} B) None of these C) { 5, 7} D) { 0.461, 19.59} 1) x x 51 = 0 A) {0.292, } B) {, 17} C) { 0.1, 9.69} D) { 0.151, } 14) n 2 10n + 16 = 5 A) {7, } B) {9, 1} C) None of these D) {7, 11} 15) m 2 + 8m 76 = 4 A) None of these B) { 1, 9} C) { , } D) {4, 18} 16) b b + 82 = 10 A) { , 2 22 } B) {2 + 74, 2 74 } C) { 6, 12} D) {14, 4} W B2^0V1O9Y DKPuxtUah ASyoffGtjwKaBrger ML[LpCA.^ z OAyljlK XrCiFgdhStPsh Yrke^sAetrKvuevd`.B i im`afdsei kwmiftdhm fiznbf`itnnidtvew nahlngve_bvrka[ z2o. --

37 Solve each equation with the quadratic formula. 17) n 2 + 5n + 6 = 0 A) {1, 2} B) {, 5} C) { 2, } D) {6, 1} 18) 2m 2 6m = 10 A) { + i, i} B) { + 29, } C) { 5 2, 1 2 } 19) 4a 2 12 = 8a A) {, 1} B) {1, 1} C) {1 + i 2, 1 i 2 } D) { 2 + 7, } Find the discriminant of each quadratic equation then state the number and type of solutions. 20) k 2 2k + 6 = 5 A) 8; two real solutions B) 0; one real solution C) 20; two imaginary solutions D) 9; two real solutions 21) 4x 2 x 4 = 8 A) 6; two imaginary solutions B) 160; two real solutions C) 15; two imaginary solutions D) 6; two real solutions C M2u0S1X9G DKQuptma] psvotfbtiwfayrqew ZLPLTCU.C o yaolqlx nriivgahqtasj ErheNsjeDryvEe]dz.V l umfaodoe] UwZiqtVhE RIGn_fKirn_ijt^ev xakleglebbyriae H2X. -4-

38 22) 2k 2 6k + = 8k 2 + 7k A) 167; two imaginary solutions B) None of these C) 20; two rational solutions D) 97; two irrational solutions 2) 11b 2 11 = 6b A) 448; two rational solutions B) 448; two irrational solutions C) 448; two imaginary solutions D) 520; one rational solution Simplify each expression. 24) ( 14p 7p 2 + 2p 5 ) ( 6p 2 + 4p 5 6p ) A) 2p 5 + 6p p 2 14p B) 4p 5 + 6p p 2 14p C) 4p 5 + 2p + 1p 2 14p D) 4p 5 + 2p p 2 14p 25) ( 1n 5 9n 8n 4 ) + (12n 5 8n 4 1n) A) n 5 5n 4 24n B) None of these C) n 5 16n 4 22n D) 9n 5 5n 4 24n Find each product. 26) (8a + 1)(a 6) A) 12a 2 + 7a + 49 B) 8a 2 47a 6 C) 12a a 49 D) 8a ) (n + 1)( 8n ) A) 42n n 12 B) 24n 2 n + C) None of these D) 24n 2 17n g y2p0u1y9l rkdukttaa csrogfntuwea\raeg vleltcg.f c paal\la SrAiZguhOtksl hrvemsteersvxe^dg.v ` FMcaDd\et hwuiitmhf [IRnLfDiLnAiLtBeA AAtlVgceQbfrBaZ y2x. -5-

39 Factor each completely. 28) 7uv + 2u + 42v + 12 A) (7v + 6)(u 2) B) (u + 6)(7v + 2) C) None of these D) (u + 6)(7v + 6) 29) 120uv 168u + 280v 92 A) None of these B) 8(u 7)(5v + 7) C) 8(u + 7)(5v 7) D) (u 7)(5v 7) Describe the end behavior of each function. 0) f (x) = x 2 8x 10 A) f (x) - as x - f (x) - as x + B) f (x) + as x - f (x) + as x + C) f (x) - as x - f (x) + as x + D) f (x) + as x - f (x) - as x + 1) f (x) = 2x 2 + 8x + 2 A) f (x) + as x - f (x) - as x + B) f (x) + as x - f (x) + as x + C) f (x) - as x - f (x) + as x + D) f (x) - as x - f (x) - as x + Simplify. 2) 92xy A) 40y 2 x 2 B) 42 2xy C) 84y x D) 24x 2 y 2 ) 100u v A) 24uv u B) 7u 2 v 2 5 C) 0uv uv M y2e0b1n9l IKAuctZad nssomfftwwtayrdex ^LGLOCt.V r MAmljli IrJiLgWhUtFsp trzeqsiebrevoendy.d a GMfafdReS OwjiYt^hA iivn\f_iwnfiktfef ]AVl\gPecbcryaa x2v. -6-

40 4) A) B) C) D) ) A) B) None of these C) D) ) 15( 6 + ) A) 25 B) 14 C) ) 15( + ) A) B) C) D) Write each expression in exponential form. 8) ( 5 b) 2 2 A) (4b) C) (6b) 2 4 B) (10b) D) b 2 5 9) a 1 A) (6a) C) (a) 1 2 B) a 4 5 o d2h0y1t9x YKNuFt[aZ BSRoHfLtcwUaVree\ _LILaCB.y ^ OAVlLlo jrcidgxhpthsq ]rqeis]ebryvpeady.z L kmga`dfeg Pwhistph^ yiznlf^isnoiqt\e[ eagldg[ewbireas o2u. -7-

41 Write each expression in radical form. 40) n A) 5 4 2n B) ( n) 5 C) ( n) 5 D) ( 5 n) ) (7v) A) None of these B) ( 5 v) 7 C) 7v D) ( 4 10v) 5 Identify the vertex, axis of symmetry, and min/max value of each. 42) f (x) = 6x 2 96x 91 A) Vertex: (7, 8) Axis of Sym.: x = 7 Max value = 8 B) Vertex: ( 8, 7) Axis of Sym.: x = 8 Max value = 7 C) Vertex: ( 8, 7) Axis of Sym.: y = 7 Min value = 8 D) Vertex: (8, 7) Axis of Sym.: x = 8 Max value = 7 4) f (x) = 2x 2 24x 7 A) Vertex: ( 6, 1) Axis of Sym.: y = 1 Min value = 6 B) Vertex: ( 5, ) Axis of Sym.: y = Min value = 5 C) None of these D) Vertex: ( 6, 1) Axis of Sym.: x = 6 Max value = 1 s N2v0q1y9k qkxuqtoaf lsaoff^tpwlayrheg alylccn.h O YAwlcl^ JrniOgDhct_sY ArgepsMepruvuePdz.x B XMyahdneQ lw^ihtbhp UIGnXf\iLnliStceP WAilwgCelbar_a\ v2r. -8-

42 Use the information provided to write the vertex form equation of each parabola. 44) f (x) = x x 297 A) f (x) = (x 10) 2 B) f (x) = (x 10) 2 + C) f (x) = (x + ) D) f (x) = (x 10) ) f (x) = x 2 + 2x 2 A) f (x) = 2(x + 1) 2 B) f (x) = (x + 1) 2 C) f (x) = (x + 1) 2 Use the information provided to write the standard form equation of each parabola. 46) f (x) = 1 2 ( x 1) 2 A) f (x) = 1 1 x2 x 5 B) None of these C) f (x) = 1 2 x2 x ) f (x) = (x + 8) 2 5 A) f (x) = x x + 59 B) f (x) = 2x 2 + 2x + 12 C) f (x) = 1 2 x2 + 8x + 27 D) f (x) = x 2 16x 69 D) f (x) = 1 2 x2 x 5 2 x N2k0R1C9d MKruXtuar ^SlowfdtbwYaor`eZ blplcc`.q n NAIlMlR ]ryijgqhctcsr DrFeTsWeIrGveeFdY.C ` NMDamdreg awniktwhr VI^nHfAiOnTintCet NArlsgaezbjrvaE n2i. -9-

43 Determine whether the scenario involves independent or dependent events. Then find the probability. 48) A bag contains three red marbles and five blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. The first marble is red and the second marble is blue. A) Independent; B) Dependent; C) Independent; 1 4 = 0.25 D) Dependent; ) You flip a coin twice. The first flip lands tails-up and the second flip also lands tails-up. 56 A) Independent; B) Dependent; C) Independent; 1 4 = 0.25 Find the probability. 50) A litter of kittens consists of two gray kittens, two black kittens, and three mixed-color kittens. You randomly pick one kitten. The kitten is gray or mixed-color. 7 A) 10 = 0.7 B) 9 10 = C) D) u b2q0c1m9i mk^uzt_ap xsoopfntbwlasryej rlilhcw.j F ZAClllv MrFiugvhGtYsX ]rjepsdedrlvueldt.[ H imuabdpen PwLiRt`hI BIWnLfZipn]iatheN `AllmgVembNrraJ u2e. -10-

44 Answers to Part I (ID: 4) 1) A 2) D ) B 4) C 5) B 6) A 7) A 8) B 9) A 10) B 11) C 12) B 1) B 14) A 15) C 16) C 17) C 18) D 19) A 20) B 21) A 22) D 2) C 24) A 25) C 26) B 27) D 28) B 29) C 0) A 1) B 2) B ) C 4) B 5) A 6) D 7) C 8) D 9) C 40) C 41) C 42) B 4) D 44) B 45) B 46) D 47) A 48) B 49) C 50) D J q2f0y1e9z iknuwtvah NSnoEfotBwTaQrYeC ]LgLXC`.\ u laflkll trpimgghdtost DrneKs]eTrIvGe[dw.L V rmnakdgej wwhiftkhz XIRnOfUienjiLtMea tablgghekbvriaf q2o. -11-