Keystone Algebra I Practice Workbook
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1 Kyo Algba I Pai Wokbook Haibug Shool Dii, Haibug, PA Nam:
2 2
3 Ifo I N F O G L O S S A R Y P a i C o u d R p o M O D 2 M O D 1 W i i g P a i C R 2 Opaio, Lia Equaio & Iqualii Lia Fuio & Daa Ogaizaio Fill I h Blak Wi Rpo (Modul 1 & 2) Gaph Ipaio Mixd Pai Gloay of Tm 3
4 I N F O Ifo 4
5 Abou hi wokbook I N F O Muh of h maial fom hi wokbook wa podud ud Fai U fom h PDE Kyo Exam Im ad Soig Sampl. Oh poblm w ad by h am o opid dily fom oh Kyo ppaaio wbi. Modul 1 & 2 ad h Coud Rpo io a PDE xampl of wha will b o h xam. Th fi poblm lid i h CR2 io w alo iud by h PDE, h w ad by h am. Pla mail ayo o h la pag wih oio, uggio o xampl ha you would lik o iludd i fuu diio. 5
6 I N F O Algba I Kyo Exam Quik Fa Am Aho Covd Numb of Mulipl Choi Quio Numb of Coud Rpo Quio Modul 1: Opaio ad Lia Equaio ad Iqualii Modul 2: Lia Fuio ad Daa Ogaizaio Toal Eimad im o ak h i 2.5 hou. 6
7 Coud Rpo Quio I N F O Th Algba I Kyo Exam will hav wo diff yp of oud-po quio. Boh yp of oud-po quio will b od o a al agig fom 0 4 poi. Saffoldig Complio Quio a oud-po quio ha lii woo-fou dii po fom a ud. Wh admiid oli, h po a loially d by h ud ad a objiv ad oi. Som xampl of ud po may b 5 gallo, vx a (5, 11), o y = 3x + 9. A digad aw pa/box will b povidd fo ah pa of h quio. No xaou wok o xplaaio will b od. To h ga x poibl, auomad oig will b ud o dmi h poi valu of h po. Wh appliabl, Ifd Paial Cdi Rubi ad Soig Guid will b ud o awad paial di o qualifyig po. Exdd Saffoldig Complio Quio a oud-po quio ha qui ud o pod wih xaou wok o xplaaio fo a la pa of h quio. Fo xampl, h ud may b akd o Show all of you wok, Explai why h uv i o a paabola, o Wha i h o i Jill aoig? Wh admiid oli, po a b ypd by h ud, bu oig will o b auomad. Quio-pifi oig guid will b ud by o o awad di, iludig paial di, fo po. 7
8 I N F O 8
9 M O D 1 Modul 1 Opaio, Lia Equaio & Iqualii Rubi: 1 poi fo ah o aw: mulipl hoi. 9
10 M O D A1.1.1 Opaio wih Ral Numb ad Expio 1 10
11 1. Whih of h followig iqualii i u fo all al valu of x? A. x3 x2 M O D B. 3x2 2x3 1 C. (2x)2 3x2 D. 3(x 2)2 3x A xpio i how blow. 2 Whih valu of x mak h xpio quival o 10? A. 5 B. 25 C. 50 D
12 3. A xpio i how blow. M O D 1 Fo whih valu of x hould h xpio b fuh implifid? A. x = 10 B. x = 13 C. x = 21 D. x = Two moomial a how blow. 450x2y5 3,000x4y3 Wha i h la ommo mulipl (LCM) of h moomial? A. 2xy B. 30xy C. 150x2y3 D. 9,000x4y5 12
13 5. Simplify: 2(2 ) 2 M O D A. 1 B. C. 16 D A hm pak hag $52 fo a day pa ad $110 fo a wk pa. La moh, 4,432 day pa w old ad 979 wk pa w old. Whih i h lo ima of h oal amou of moy paid fo h day ad wk pa fo la moh? A. $300,000 B. $400,000 C. $500,000 D. $600,000 13
14 M O D 1 7. A polyomial xpio i how blow. (mx 3 + 3) (2x 2 + 5x + 2) (8x x 4 ) Th xpio i implifid o 8x 3 + 6x x + 6. Wha i h valu of m? A. 8 B. 4 C. 4 D Wh h xpio x 2 3x 18 i faod omplly, whih i o of i fao? A. (x 2) B. (x 3) C. (x 6) D. (x 9) 14
15 9. Whih i a fao of h iomial x2 2x 15? A. (x 13) M O D B. (x 5) 1 C. (x + 5) D. (x + 13) 10. Simplify: A. ; x 4, 2 x B. x2 x C. D. 15
16 M O D 11. Simplify: A. x2 ; x 4, 2, 0 x 1 B. x3 x2 C. D. x 16
17 A1.1.2 Lia Equaio M O D 1 17
18 M O D Jy ha a job ha pay h $8 p hou plu ip (). Jy wokd fo 4 hou o Moday ad mad $65 i all. Whih quaio ould b ud o fid, h amou Jy mad i ip? A. 65 = B. 65 = 8 4 C. 65 = D. 65 = 8(4) O of h p Jami ud o olv a quaio i how blow. 5(3x + 7) = 10 15x + 35 = 10 Whih am dib h podu Jami ud i hi p ad idify h popy ha juifi h podu? A. Jami addd 5 ad 3x o limia h pah. Thi podu i juifid by h aoiaiv popy. B. Jami addd 5 ad 3x o limia h pah. Thi podu i juifid by h diibuiv popy. C. Jami muliplid 3x ad 7 by 5 o limia h pah. Thi podu i juifid by h aoiaiv popy. D. Jami muliplid 3x ad 7 by 5 o limia h pah. Thi podu i juifid by h diibuiv popy. 18
19 14. Faio puhad x ho dog ad y hambug a a baball gam. H p a oal of $10. Th quaio blow dib h laiohip bw h umb of ho dog ad h umb of hambug puhad. 3x + 4y = 10 M O D 1 Th odd pai (2, 1) i a oluio of h quaio. Wha do h oluio (2, 1) p? A. Hambug o 2 im a muh a ho dog. B. Faio puhad 2 ho dog ad 1 hambug. C. Ho dog o $2 ah ad hambug o $1 ah. D. Faio p $2 o ho dog ad $1 o hambug. 15. Aa bud 15 aloi p miu uig fo x miu ad 10 aloi p miu hikig fo y miu. Sh p a oal of 60 miu uig ad hikig ad bud 700 aloi. Th ym of quaio how blow a b ud o dmi how muh im Aa p o ah xi. 15x + 10y = 700 x + y = 60 Wha i h valu of x, h miu Aa p uig? A. 10 B. 20 C. 30 D
20 M O D Samaha ad Maia puhad flow. Samaha puhad 5 o fo x dolla ah ad 4 daii fo y dolla ah ad p $32 o h flow. Maia puhad 1 o fo x dolla ad 6 daii fo y dolla ah ad p $22. Th ym of quaio how blow p hi iuaio. 5x + 4y = 32 x + 6y = 22 Whih am i u? A. A o o $1 mo ha a daiy. B. Samaha p $4 o ah daiy. C. Samaha p mo o daii ha h did o o. D. Samaha p ov 4 im a muh o daii a h did o o. 20
21 A1.1.3 Lia Iqualii M O D 1 M O D U L E 1 21
22 17. A ompoud iqualiy i how blow. M O D 1 5 < 2 3y < 14 Wha i h oluio of h ompoud iqualiy? A. 4 > y > 1 B. 4 < y < 1 C. 1 > y > 4 D. 1 < y < Whih i a gaph of h oluio of h iqualiy 5? 22
23 19. Th oluio of a iqualiy i gaphd o h umb li blow. Th gaph how h oluio of whih iqualiy? M O D 1 A. 2x + 5 < 1 B. 2x C. 2x + 5 > 1 D. 2x A baball am had $1,000 o pd o uppli. Th am p $185 o a w ba. Nw baball o $4 ah. Th iqualiy b 1,000 a b ud o dmi h umb of w baball (b) ha h am a puha. Whih am abou h umb of w baball ha a b puhad i u? A. Th am a puha 204 w baball. B. Th miimum umb of w baball ha a b puhad i 185. C. Th maximum umb of w baball ha a b puhad i 185. D. Th am a puha 185 w baball, bu hi umb i ih h maximum o h miimum. 23
24 M O D 21. A ym of iqualii i how blow. y < x 6 y > 2x Whih gaph how h oluio of h ym of iqualii? 1 24
25 22. Tyk alway lav a ip of bw 8% ad 20% fo h v wh h pay fo hi di. Thi a b pd by h ym of iqualii how blow, wh y i h amou of ip ad x i h o of di. y > 0.08x y < 0.2x M O D 1 Whih of h followig i a u am? A. Wh h o of di ( x) i $10, h amou of ip ( y) mu b bw $2 ad $8. B. Wh h o of di ( x) i $15, h amou of ip ( y) mu b bw $1.20 ad $3.00. C. Wh h amou of ip ( y) i $3, h o of di ( x) mu b bw $11 ad $23. D. Wh h amou of ip ( y) i $2.40, h o of di ( x) mu b bw $3 ad $6. 25
26 M O D 2 Modul 2 Lia Fuio & Daa Ogaizaio Rubi: 1 poi fo ah o aw: mulipl hoi. 26
27 A1.2.1 Fuio M O D 2 27
28 23. Tim o h fi 5 im h playd a vido gam a lid blow. 4,526 4,599 4,672 4,745 4,818 M O D 2 Tim o follow a pa. Whih xpio a b ud o dmi hi o af h playd h vido gam im? A ,453 B. 73( + 4,453) C. 4, D. 4,526 28
29 24. Whih gaph how y a a fuio of x? M O D 2 29
30 25. Th gaph of a fuio i how blow. M O D 2 Whih valu i o i h ag of h fuio? A. 0 B. 3 C. 4 D. 5 30
31 26. A pizza aua hag fo pizza ad add a dlivy f. Th o (), i dolla, o hav ay umb of pizza (p) dlivd o a hom i dibd by h fuio = 8p + 3. Whih am i u? A. Th o of 8 pizza i $11. B. Th o of 3 pizza i $14. C. Eah pizza o $8 ad h dlivy f i $3. M O D 2 D. Eah pizza o $3 ad h dlivy f i $ Th abl blow how valu of y a a fuio of x. Whih lia quaio b dib h laiohip bw x ad y? A. y = 2.5x + 5 B. y = 3.75x C. y = 4x + 1 D. y = 5x 31
32 A1.2.2 Coodia Gomy M O D 2 32
33 28. Jff aua ll hambug. Th amou hagd fo a hambug ( h) i bad o h o fo a plai hambug plu a addiioal hag fo ah oppig ( ) a how i h quaio blow. h = Wha do h umb 0.60 p i h quaio? A. h umb of oppig M O D 2 B. h o of a plai hambug C. h addiioal o fo ah oppig D. h o of a hambug wih 1 oppig 33
34 29. A ball oll dow a amp wih a lop of. A o poi h ball i 10 f high, ad a aoh poi h ball i 4 f high, a how i h diagam blow. M O D 2 Wha i h hoizoal dia (x), i f, h ball avld a i olld dow h amp fom 10 f high o 4 f high? A. 6 B. 9 C. 14 D
35 30. A gaph of a lia quaio i how blow. M O D 2 Whih quaio dib h gaph? A. y = 0.5x 1.5 B. y = 0.5x + 3 C. y = 2x 1.5 D. y = 2x
36 31. A jui mahi dip h am amou of jui io a up ah im h mahi i ud. Th quaio blow dib h laiohip bw h umb of up (x) io whih jui i dipd ad h gallo of jui (y) maiig i h mahi. M O D 2 x + 12y = 180 How may gallo of jui a i h mahi wh i i full? A. 12 B. 15 C. 168 D
37 32. Th a plo blow how h o ( y) of goud hippig pakag fom Haibug, PA, o Miapoli, MN, bad o h pakag wigh ( x). M O D 2 Whih quaio b dib h li of b fi? A. y = 0.37x B. y = 0.37x C. y = 0.68 x D. y = 0.68 x
38 A1.2.3 Daa Aalyi M O D 2 38
39 33. Th daily high mpau, i dg Fahhi ( F), of a ow a odd fo o ya. Th mdia high mpau i 62 F. Th iquail ag of high mpau i 32. Whih i mo likly o b u? A. Appoximaly 25% of h day had a high mpau l ha 30 F. B. Appoximaly 25% of h day had a high mpau ga ha 62 F. M O D 2 C. Appoximaly 50% of h day had a high mpau ga ha 62 F. D. Appoximaly 75% of h day had a high mpau l ha 94 F. 34. Th daily high mpau i dg Fahhi i Allow, PA, fo a piod of 10 day a how blow Whih am oly dib h daa? A. Th mdia valu i 98. B. Th iquail ag i 16. C. Th low quail valu i 76. D. Th upp quail valu i
40 35. Vy akd 200 ud o l hi favoi po ad h odd h ul i h ba gaph blow. M O D 2 Vy will ak aoh 80 ud o l hi favoi po. Bad o h ifomaio i h ba gaph, how may mo ud of h x 80 akd will l bakball ah ha fooball a hi favoi po? A. 10 B. 20 C. 25 D
41 36. Th poi od by a fooball am a how i h m-ad-laf plo blow. M O D 2 Wha wa h mdia umb of poi od by h fooball am? A. 24 B. 27 C. 28 D
42 37. Joh odd h wigh of hi dog Spo a diff ag a how i h a plo blow. M O D 2 Bad o h li of b fi, wha will b Spo wigh af 18 moh? A. 27 poud B. 32 poud C. 36 poud D. 50 poud 24. A umb ub wih id labld 1 hough 6 i olld wo im, ad h um of h umb ha d fa up i alulad. Wha i h pobabiliy ha h um of h umb i 3? A. B. C. D. 42
43 Coud Rpo Fill I h Blak A1.1.1 o A1.2.3 C o u d R p o Rubi: 1 poi fo ah o aw. Ui a uually upplid fo h ud. Aw i uually a umb, quaio o dipio 43
44 C o u d R p o 44
45 C o u d R p o 45
46 C o u d R p o 46
47 C o u d R p o 47
48 C o u d R p o 48
49 C o u d R p o 49
50 C o u d R p o 50
51 C o u d R p o 51
52 C o u d R p o 52
53 C o u d R p o 53
54 C o u d R p o 54
55 C o u d R p o 55
56 C o u d R p o 56
57 C o u d R p o 57
58 C o u d R p o 58
59 C o u d R p o 59
60 C o u d R p o 60
61 C o u d R p o 61
62 C o u d R p o 62
63 C o u d R p o 63
64 C o u d R p o 64
65 C o u d R p o 65
66 C o u d R p o 66
67 C o u d R p o 67
68 C o u d R p o 68
69 Coud Rpo Mod 1: Wiig Pai A1.1.1 C R 2 Rubi: [4 poi] 1 poi fo o aw i h box. 1 addiioal poi fo o dipio, wh pompd. 69
70 1 Poi Wha h mai ida? A = L x W Daw h 3 fam: C R 1 Poi 2 Wha h mai ida? A = L x W Why am I doig hi p? 1 Poi Why am I doig hi p? 1 Poi Wha do h aw ma o h avag po? 70
71 1 Poi Wha h mai ida? Daw h 3 fam: 1 Poi C R 2 Wha h mai ida? Why am I doig hi p? Wha do h aw ma o h avag po? 71
72 EX: Shalama mad a pi i a la fom ik, pai, avd blok ad obj fom au. Pap iz i a la alway hav o id wih a lgh ha i 17/22 of h log id. X A: Wi a polyomial xpio, i implifid fom, whih p h aa of h pap. Wha h mai ida? C R 2 B: Shalama wa o mak a po ou of h a wok. Fom xpi, h kow ha i i b o o pi hi yp of a mo ha 4 im lag, a maud by aa. Wi xpio, i implifid fom, whih p h lgh ad widh of h lag po iz ha Shalama may pi, giv h lgh of a oigial id, X. [No: A pi mai popoioa i iz o h oigial.] Wha h mai ida? Why am I doig hi p? Why am I doig hi p? Wha do h aw ma o h avag po? 72
73 C: Th po i oo big fo h maqui i h hool hallway. So, Shalama mak aoh po whih i oly 2 ¼ im lag ha h oigial. Wha a h w dimio? [No: A pi mai popoioa i iz o h oigial.] Show all you wok. Explai why you did ah p. Wha h mai ida? Why am I doig hi p? C R Why am I doig hi p? 2 Wha do h aw ma o h avag po? 73
74 Coud Rpo C R Mod 2: Wiig Pai A Rubi: [4 poi] 1 poi fo o aw i h box. 1 poi fo a o gaph [2 poi ad li] 1 addiioal poi fo o dipio, wh pompd. 74
75 L look a h o way o aw a oud po: C R 2 75
76 gallo of ga i ak A1.2.1 Rpo So 1 Poi C R 2 Explai: 1 2 I lop gaiv o poiiv? Whih quaiy i iaig? mil div Whih quaiy i daig? Wha do hi ma o h avag po? 1 Thi i a ba miimum xplaaio oi ha i do o xplai ha h lop i gaiv o a h maig lik, You bu up ga a you div. Now, wi h xplaaio. U you ow wod ad xplai all 4 poi abov: Poi Now, ad pap wih a pa. Cil ad umb all 4 xplaaio poi fom abov. Add wha hy mid. 76
77 L y hi am poblm agai, ow ha w v paid: C R 2 77
78 gallo of ga i ak A1.2.1 Rpo So 1 Poi C R 2 Explai: 1 2 I lop gaiv o poiiv? Whih quaiy i iaig? 3 4 mil div Whih quaiy i daig? Wha do hi ma o h avag po? 1 Poi Now, ad pap wih a pa. Cil ad umb all 4 xplaaio poi fom abov. Add wha hy mid. 78
79 EX: Buup ha a faily oa amou of im i ak fo h o g io h a fom a hou, a h a ad h la o walk o h wokaio fom h a. A: Wh Buup div o wok, h pd 3 miu gig io h a fom h hou, 2 miu aig h a ad 5 miu walkig o h wok aio. If h avag pd i 30 mil p hou, h how log will i ak Buup o g o h wokaio if h liv 10 mil fom wok? Show all you wok. Explai why you did ah p. Wha h mai ida? Why am I doig hi p? B: Somim Buup vii a fid o go hoppig bfo wok. Wi a quaio, i implifid fom, ha p Buup avl im () o wok bad upo h dia (d) h mu avl. Aum h im o g io ad a h a, a wll a walk o h wok aio mai h am a i Pa A. Show all you wok. Explai why you did ah p. Wha h mai ida? C R 2 Why am I doig hi p? Wha do h aw ma o h avag po? 79
80 C: Rwi h quaio fom Pa B i h li povidd. U hi quaio o a a daa abl howig h laiohip bw im (i 5 miu im) ad dia o wok (i mil). Daw a gaph uig h daa o quaio. d Equaio: C R 2 Tim () Dia (d) m i l miu D: If Buup op a a Div-Thu o h way o wok, 10 miu i addd o h oal avl im. Wi a w quaio o xplai h ip o wok wh h op a a Div-Thu. Mak a w daa abl blow. Mak a od li o h abov gaph o p hi w xpio. Explai h ombid gaph. Tim () Dia (d) Nw Equaio: Wha do h aw ma o h avag po? 80
81 EX: Malik ad ok i hi im aou. Evy ad o $5 plu $1 fo vy $1,000 add. A: Wi a quaio o fid h o of a ok ad () fo a giv ad amou (). Explai h lop ad ip valu of you quaio. Wha do h aw ma o h avag po? Tad Amou () B: Mak a daa abl fo Malik ad bad upo h quaio you mad i Pa A. Gaph h daa. Tad Co () T a d C o $ C R 2 Tad Amou x $1,000 81
82 C: Rwi h quaio fom Pa A i h li povidd. U hi quaio o a a w daa abl howig h laiohip bw ad amou (hi im i $10,000 im) ad ad o (i dolla). Daw a gaph uig h daa o quaio. C R 2 Tim () Dia (d) T a d C o $ Equaio: D: Explai h gaph i Pa B & C. Tad Amou x $10,000 Explai: 1 2 I lop gaiv o poiiv? Whih quaiy i iaig? 3 4 Whih quaiy i daig? Wha do hi ma o h avag po? 82
83 Gaph Ipaio Wiig Pai Thi io ha gaph ha h ud may pai ipig. W i i g P a i Th ubi i povidd wih ah poblm a a guid o awig Kyo quio. 83
84 Explai: I lop gaiv o poiiv? 1 2 Whih quaiy i iaig? 3 4 Sp 1 : Explai h lop: + o -? Sp 2 & 3 : Sa how h vaiabl ia wih ah oh: iaig o daig? Sp 4 : Explai h gaph i a omahmaial way ha h avag po would udad. W i i g P a i To 4 h avag po, hi gaph ll u ha h fuh you div h amou of ga i you ga ak will da. 3 Thi ma ha a h x-valu (mil div) ia, h y-valu (gallo of ga i h ak) will da. 2 1 Aodig o h gaph, h lop will b gaiv bau h li i fallig o h igh. I hi poblm, I had o ip h gaph by udadig wha i ouig wih h li. Exampl fo Complig h Paagaph: Whih quaiy i daig? Wha do hi ma o h avag po? 84
85 S I a m C o S a l Daily Tmpau ⁰F T Explai h abov gaph: W i i g P a i Explai: 1 2 I lop gaiv o poiiv? Whih quaiy i iaig? 3 4 Whih quaiy i daig? Wha do hi ma o h avag po? 85
86 C o $ $ Mohly Eli Uag KWh E Explai h abov gaph. If o li i ud fo h moh, i h uom ill billd? Why? W i i g P a i Suppo h miimum mohly hag i aid $10 p moh. Gaph h w li abov. Explai: 1 2 I lop gaiv o poiiv? Whih quaiy i iaig? 3 4 Whih quaiy i daig? Wha do hi ma o h avag po? 86
87 Amy Siz x1,000 Explai: I lop gaiv o poiiv? Whih quaiy i iaig? Whih quaiy i daig? Wha do hi ma o h avag po? A Appoxima Amy Siz o Ru fom Moow D Explai h gaph. Wha happd o Napolo Amy o h u mah fom Moow? W i i g P a i Day Mahd Blow Fzig 87
88 Mixd Pai mulipl hoi: 100 poblm fo pai P a i 88
89 89 P a i
90 P a i 90
91 91 P a i
92 P a i 92
93 93 P a i
94 P a i 94
95 95 P a i
96 P a i 96
97 97 P a i
98 P a i 98
99 99 P a i
100 P a i 100
101 101 P a i
102 P a i 102
103 103 P a i
104 P a i 104
105 105 P a i
106 P a i 106
107 Gloay Adddum 107 G L O S S A R Y
108 G L O S S A R Y 108
109 109 G L O S S A R Y
110 G L O S S A R Y 110
111 111 G L O S S A R Y
112 G L O S S A R Y 112
113 113 G L O S S A R Y
114 G L O S S A R Y 114
115 115 G L O S S A R Y
116 G L O S S A R Y 116
117 117 G L O S S A R Y
118 G L O S S A R Y 118
119 119 G L O S S A R Y
120 Cdi & Kudo PDESAS hp:// Haibug Shool Dii Mah Wikipa hp://hbgdmah.wikipa.om/kyo+maial Noh Allghy Imdia High Shool hp:// Haibug Shool Dii Dia Hai, GEAR UP Mah Coah Bob Molad, SIG Mah Tafomaio Coula Coi Shao, GEAR UP Mah Coah Auum Calo, Spial Ed Tah Dav MaIi, Mah Tah Ei Coll, Mah Tah Quio o Comm: dhai@hbgd.k12.pa.u bmolad@hbgd.k12.pa.u 120
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