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Xivcs Cssissmi`x
an G`atlihdi c`h _gells
IVEX LI^ILMCXFIMCXEO_
Chme`esxirih Czrel 2::5
Oazuredfx 2::5, Xivcs Ihyocxea` Cdi`ou. Cll redfxs risir~ih. Rizrahyoxea` an cll ar zarxea`s an xfes targ es zrafebexihtexfayx ivzriss trexxi` zirmessea` nram xfi Xivcs Ihyocxea` Cdi`ou.
_XYHI@X @CMI
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MCXFIMCXEO_
Zcdi ?
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Zcdi 8
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Mcxfimcxeos Ofcrx
LI@DXF
Mixreo Oysxamcru
3 gelamixir = 3::: mixir 3 meli = 34>: ucrh
3 mixir = 3:: oi`xemixir 3 meli = 926: niix
3 oi`xemixir = 3: mellemixir 3 ucrh = ? niix
3 naax = 32 e`ofi
OCZCOEXU C@H ^ALYMI
Mixreo Oysxamcru
3 lexir = 3::: mellelexir 3 dclla` = 8 sycrx
3 dclla` = 326 nlyeh ay`oi
3 sycrx = 2 ze`x
3 ze`x = 2 oyz
3 oyz = 6 nlyeh ay`oi
MC__ C@H TIEDFX
Mixreo Oysxamcru
3 geladrcm = 3::: drcm 3 xa` = 2::: zay`h
3 drcm = 3::: melledrcm 3 zay`h = 3> ay`oi
XEMI
3 uicr = ?>9 hcu
3 uicr = 32 ma`xf
3 uicr = 92 tiig
3 tiig = 4 hcu3 hcu = 28 fayr
3 fayr = >: me`yxi
3 me`yxi = >: ioa`h
Oa`xe`yih a` xfi `ivx zcdi
Mixreo c`h oyxamcru rylir oc` bi nay`h a` xfi izcrcxi Mcxfimcxeo Ofcrx.
Xivcs Cssissmi`xan G`atlihdi c`h _gells
Zcdi 9
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Mcxfimcxeos Ofcrx
Ziremixir rioxc`dli Z = 2l ' 2t ar Z = 2&l ' t%
Oeroymniri`oi oeroli O = 2r ar O = h
Cric rioxc`dli C = lt ar C = bf
xrec`dli C = bf ar C =
xrczi{aeh C = &b3 ' b2%f ar C =
ridylcr zaluda` C = cZ
oeroli C = r 2
Z rizrii`x xfi Ziremixir an xfi Bci an c xfrii-hemi`ea`cl nedyri.
B rizrii`x xfi Cric an xfi Bci an c xfrii-hemi`ea`cl nedyri.
_yrncoi Cric oybi &xaxcl% _ = > 2
zrem &lcxircl% _ =Zf
zrem &xaxcl% _ =Zf ' 2B
zurcmeh &lcxircl% _ = Zl
zurcmeh &xaxcl% _ = Zl 'B
oule`hir &lcxircl% _ = 2rf
oule`hir &xaxcl% _ = 2rf ' 2r 2 ar _ = 2r&f ' r%
oa`i &lcxircl% _ = rl
oa`i &xaxcl% _ = rl ' r 2 ar _ = r&l ' r%
zfiri _ = 8r 2
^alymi zrem ar oule`hir ^=Bf
zurcmeh ar oa`i ^= Bf
zfiri ^= r ?
_zioecl Redfx Xrec`dli ?:, >:, 5: v, vQQ?, 2v
89, 89, 5: v, v, vQQ2
32
3?8?
bf
2
32
&b3 ' b2%f
2
Zuxfcdaric` Xfiarim c 2 ' b 2 = o 2
Hexc`oi Narmylc h = &v2 v3% 2 ' &u2 u3% 2
_lazi an c Le`i m =
Mehzae`x Narmylc M= & , %Sychrcxeo Narmylc v =
_lazi-E`xiroizx Narm an c` Isycxea` u = mv ' b
Zae`x-_lazi Narm an c` Isycxea` u u3 = m&v v3%
_xc`hcrh Narm an c` Isycxea` Cv 'Bu = O
_emzli E`xirisx Narmylc E=zrx
u2 u3v2 v3
v3
'v2
2
u3
'u2
2
b b 2 8co2c
32
32
32
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_CMZLI B
Ne`h xfi lazi an xfi le`i 2u = 6v ?.
C
B 8
O 6
H @ax firi
?2
Kc`eoi yi c rioxc`dylcr bav xa xari fir crxyzzlei. Xfi hemi`ea` an xfi rioxc`dylcrbav cri 22.9 e`ofi bu 38 e`ofi bu 33.9 e`ofi.Tfcx e xfi ~alymi an xfe bav e` oybeo e`ofi1
Rioarh uayr c`tir c`h nell e` xfi bybbli a`uayr c`tir haoymi`x. Bi yri xa yi xfioarriox zlcoi ~clyi.
HERIOXEA@_
Rich icof syixea`. Xfi` nell e` xfi oarrioxc`tir a` uayr c`tir haoymi`x. En coarriox c`tir e `ax firi, mcrg xfi lixxirnar @ax firi.
_CMZLI C
Zcdi 4
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Zcdi 6 DA A@
3 M. Ydclhi fc c` 6:-cori ncrm.
?6 cori cri yih nar zlc`xe`d oar`.
36 cori cri yih nar zlc`xe`d aubic`.
3: cori cri yih nar zlc`xe`d tficx.
Xfi rimce`e`d cori cri yih nar zlc`xe`d acx. Tfeof an xfi nallate`d drczf bix rizrii`x xfiihcxc1
C O
B H
Oar`
Acxs
Tficx
_aubic`s
Orazs Zlc`xih
Oar`Tficx
_aubic`s
Acxs
Orazs Zlc`xih
Tficx
_aubic`s
Oar`
Acxs
Orazs Zlc`xih
Oar`Acxs
Tficx
_aubic`s
Orazs Zlc`xih
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Zcdi 5 DA A@
2 Tfeof zae`x a` xfi `ymbir le`i bilat e ncrxfix ctcu nram QQ> 1
N Zae`x S
D Zae`xR
F Zae`x _
K Zae`x X
3 : 3 2 ? 8 9
S R _ X
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Zcdi 3: DA A@
? Tfeof drczf bix rizrii`x xfi rilcxea`fez e` xfi xcbli bilat1
C O
B H
u
v
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:
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Zcdi 33 DA A@
9 C rixcyrc`x alh c xaxcl an 836 lcrdi c`hmcll fcmbyrdir hyre`d a`i hcu. Xaxclfcmbyrdir cli tiri (3:44. Lcrdifcmbyrdir alh nar (?, c`h mcllfcmbyrdir alh nar (3.9:. Tfeof uximan le`icr isycxea` oc` bi yih xa ne`hl, xfi `ymbir an lcrdi fcmbyrdir alh, c`h
, xfi `ymbir an mcll fcmbyrdir alh1
C l '=
3:44?l ' 3.9: = 836
B l ' = 836?l ' 3.9: = 3:44
O 3.9:l ' ? = 836l ' = 3:44
H l ' = 8363.9:l ' ? = 3:44
8 En xfi drczf anu = 35v 2 ' ?3 e xrc`lcxih yz39 y`ex, tfeof an xfi nallate`d isycxea` tellbix hiorebi xfi riylxe`d drczf1
N u = ?8v 2 ' ?3
D u = ?8v 2 ' 8>
F u = 35v 2 ' 8>
K u = 35v 2 ' 3>
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Zcdi 3? DA A@
4 _oei`xex hi~ilazih xfi le`icr mahil bilat xa fat xfi rilcxea`fez bixtii` clxexyhi, ar ili~cxea`cba~i ic li~il &: niix%, c`h cer ximzircxyri.
Cooarhe`d xa xfi mahil, tfcx taylh bi xfi cer ximzircxyri cx c` clxexyhi an : niix1
C 3>N
B 89N
O 95N
H 44N
9
3:
39
2:
29
?:
?9
8:
89
4> 698?23: 5 3: 33 32 3? 38 39 3>
&9, 83%
&3:, 2?%
v
u
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&N%
Clxexyhi&xfaysc`hs an niix%
Ximzircxyri cx Henniri`x Clxexyhis
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Zcdi 38 DA A@
5 C xaxcl an 3499 oyxamir cx c` ilioxra`eoxari tiri cgih xa ehi`xenu tfeof exim xfiuzlc``ih xa zyrofci e` xfi `ivx ma`xf. Xfixcbli bilat fat xfi riylx an xfi yr~iu.
Cooarhe`d xa xfi e`narmcxea` cba~i, tfeof an
xfi nallate`d xcximi`x e xryi1
C Cbayx an xfi oyxamir zlc``ih xa
zyrofci c H^H zlcuir.
B Cbayx an xfi oyxamir zlc``ih xa
zyrofci c xili~eea`.
O Cbayx an xfi oyxamir zlc``ih xa
zyrofci c lczxaz oamzyxir.
H Mari xfc` an xfi oyxamir zlc``ih xa
zyrofci iexfir c oamzyxir ar c H^H
zlcuir.
32
2
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335
?2:
Risylxs an Oysxamir _yr~iu
Exim@ymbir an
Oysxamirs^ehia ocmirc
H^H zlcuir
Xili~esea`
Hisgxaz oamzyxir
Lczxaz oamzyxir
956
2>8
?29
?32
29>
6 Sychrelcxircl Y^TVe fat` bilat.
EnYUVc`h ^[Tcri emelcr, tfeof an xfinallate`d e olaix xa xfi cric an^[T1
N >3 om 2
D ?6 om 2
F ?: om 2
K 5 om 2
T
V
Y U [ ^
4.9 om
8.9 om >.49 om
> om
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Zcdi 39 DA A@
33 Hyre`d c cli cx c fai xari, cll fai tiri29) ann xfi arede`cl zreoi. Tfeof xcximi`xbix hiorebi xfi ny`oxea`cl rilcxea`fezbixtii` xfi cli zreoi an c zcer an fai c`hxfi arede`cl zreoi1
C Xfi cli zreoi e hizi`hi`x a` xfi arede`clzreoi.
B Xfi arede`cl zreoi e hizi`hi`x a` xfi clizreoi.
O Xfi cli zreoi c`h xfi arede`cl zreoi crie`hizi`hi`x an icof axfir.
H Xfi cli zreoi e hizi`hi`x a` xfi `ymbiran zcer an fai zyrofcih.
3: Tfeof isycxea` e xfi zcri`x ny`oxea` an xfi drczf fat` bilat1
N u = v
D u = QQv
F u = v 2
K u = v
u
v
9
8
>
4
6
5
?
2
3
:
3
2
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8
9
>
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6
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3 32?89>465 2 ? 8 9 > 4 6 5
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Zcdi 3> DA A@
3? M. Rahrdyi{ zlc` xa arhir nram 2: xa2> baag nar fir olc. Xfi zreoi an xfi baagfi zlc` xa arhir rc`di nram (8.59 xa (32.59icof. En xfi zyblefir ofcrdi c fezze`d nii an(:.9: zir baag arhirih, tfeof an xfi nallate`de `ax c rica`cbli zreoi nar xfi baag,e`olyhe`d fezze`d1
C (389
B (289
O (?89
H (889
32 Oeroli S fc c hecmixir TU. Zae x Telaocxih cx &?, 2%, c`h zae`x Ue laocxih cx&9, >%. Tfeof an xfi nallate`d arhirih zcerrizrii`x zae`x S, xfi oi`xir an xfi oeroli1
N &6, 6%
D &8, 8%
F &3.9, 3.9%
K &?, >%
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Zcdi 34 DA A@
38 Bcrbcrc drczf c ncmelu an isycxea` an xfi narmu = cv 2 ' 3. Fat hai icof `it drczf oamzcri xa xfi
zri~eay drczf c Bcrbcrc e`orici xfi ~clyi anc nram xa 3 xa 3 c`h ne cllu xa 21
N Icof `it drczf e cba~i xfi zri~eay drczf.
D Icof `it drczf e tehir xfc` xfi zri~eay drczf.
F Icof `it drczf e `crratir xfc` xfi zri~eay drczf.
K Icof `it drczf e xa xfi redfx an xfi zri~eay drczf.
32
32
39 Rioxc`dliZSR_ e fat` a` xfi dreh bilat.
Tfeof isycxea` bix rizrii`x c le`i xfcx e zcrcllil xaZR1
C u = 2v 9
B u = 2v ' 8
O u = v 2
H u = v ' 432
32
u
v
9
8
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4
6
5
3:
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2
3
:
3
2
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9
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3:
3 32?89>4653: 2 ? 8 9 > 4 6 5 3:
_
Z S
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Zcdi 35 DA A@
34 Icof sycri hied` bilat e mchi yz an rioxc`dli an isycl e{i. Icof rioxc`dli e xteoi c la`d c ex etehi.
Texfe` xfi cmi hied`, tfeof an xfi nallate`d e zaebli1
C C sycri texf c ehi li`dxf an >6 mchi yz an ?> rioxc`dli
B C sycri texf c ehi li`dxf an 6: mchi yz an 8: rioxc`dli
O C sycri texf c ehi li`dxf an 4> mchi yz an ?2 rioxc`dli
H C sycri texf c ehi li`dxf an 92 mchi yz an 28 rioxc`dli
32 e`. 2: e`. 26 e`.
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Zcdi 2: DA A@
36 Xfi ny`oxea`u = ?v 6 e drczfih bilat.
E` xfi ny`oxea` cba~i, xfi lazi tell bi mylxezleih bu 2, c`h xfiu-~clyi an xfiu-e`xiroizx tell bie`oricih bu 2 y`ex. Tfeof an xfi nallate`d drczf bix rizrii`x xfi `it ny`oxea`1
N F
D K
u
v
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v
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v
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3 32?89>465 2 ? 8 9 > 4 6 5
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v
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Zcdi 23 DA A@
35 Tiliu c`h Hilec cri zlcue`d c mcxf dcmi.Tiliu de~i Hilec xfii xiz xa nallat.
_xiz 3 Mylxezlu c ymbir bu > c`h xfi`ybxrcox 8.
_xiz 2 He~ehi xfi riylx bu 2.
_xiz ? Chh ? xa xfi riylx nram xfi
ioa`h xiz.
En Hilec ne`cl c`tir e 35, tfcx tc xfiarede`cl `ymbir1
Rioarh uayr c`tir c`h nell e` xfi bybbli a`uayr c`tir haoymi`x. Bi yri xa yi xfioarriox zlcoi ~clyi.
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Zcdi 22 DA A@
22 Xfi hecdrcm bilat fat c oeroli e`orebih e`c` eaoili redfx xrec`dli.
Tfeof isycxea` bix rizrii`x xfi cric,C, anxfi fchih ridea`1
N C = v 2 u 2
D C = v 2 ' u 2
F C = v 2 u 2
K C = v 2 u 2
32
32
v
u
v
23 Gi~e` c~i 2:) an fe xaxcl tiiglu icr`e`dnram fe 2 zcrx-xemi kab. Fi icr` (9.49 zirfayr cx fe nerx kab c`h (>.99 zir fayr cx feioa`h kab. Gi~e` targ 2: fayr xfe tiig cxxfi nerx kab c`h 3: fayr xfe tiig cx xfiioa`h kab. Tfcx e xfi cmay`x xfcx fi tellc~i xfe tiig1
C (?>.3:B (?4.4:
O (?>.5:
H (?8.9:
2: Xta syc`xexei,v c`hu, cri e` c rilcxea`feze` tfeofu ~crei herioxlu texfv. Xfi drczf anxfe ny`oxea` oa`xce` xfi zae`x &3>, 26%.Tfeof an xfi nallate`d rizrii`x xferilcxea`fez1
N u = v
D u = v
F u = v
K u = v48
84
48
84
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Zcdi 2? DA A@
29 C oexu by oallioxih (46: e` ncri a` a`i hcu.Xfi zreoi an c ridylcr ncri tc (:.6:, c`h xfizreoi an c heoay`x ncri tc (:.8:. En c xaxcl an32:: ziazli zceh xfi ncri a` xfe by, fatmc`u ziazli zceh xfi ridylcr ncri1
C 3:::
B 359:
O >::H 49:
28 Xfi li`dxf an c rioxc`dli e 8r 2 9x ? y`ex, c`hxfi rioxc`dli cric e 2:r 9 4x 8 sycri y`ex. Enr :, :, c`h x :, tfeof an xfi nallate`dbix hiorebi xfi tehxf an xfi rioxc`dli1
N 9r ? 2x y`ex
D 9r 4 32x 4 y`ex
F 3>r?
2
x y`exK 28r 4 32x 4 y`ex
2? Hyre`d xfi ioa`h tiig an ymmir ~cocxea`,Riybi` zrcoxeoih fe dyexcr nar 3: me`yxili xfc` xteoi xfi cmay`x an xemi fizrcoxeoih xfi nerx tiig. En fi zrcoxeoihm me`yxi xfi nerx tiig, tfeof an xfinallate`d ivzriea` rizrii`x xfi `ymbiran me`yxi xfcx Riybi` zrcoxeoih hyre`d xfiioa`h tiig1
C 2
3:mB 3: 2m
O 2m 3:
H 3:m 2
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Zcdi 28 DA A@
2> Xfi hrcte`d bilat fat xfi `ix an c rioxc`dylcr zrem. Yi xfi rylir a` xfi Mcxfimcxeo Ofcrx xamicyri xfi hemi`ea` an xfi `ix xa xfi `icrix xi`xf an c oi`xemixir.
En xfi `ix e nalhih xa narm xfi rioxc`dylcr zrem, tfeof an xfi nallate`d e olaix xa xfi zrem~alymi1
N 34.? om ?
D 9.6 om ?
F 8.6 om ?
K 3:.6 om ?
24 Meofilli oillylcr-zfa`i oamzc`u annir czlc` xfcx cllat ?:: me`yxi an yi nar(25.59 zir ma`xf c`h ofcrdi (:.35 nar icofchhexea`cl me`yxi. Cll zreoi e`olyhi xcv c`hnii. Meofilli fc byhdixih (9: zir ma`xf narocll a` fir oillylcr zfa`i. Tfcx e xfimcvemym `ymbir an me`yxi xfcx fi oc` yi
fir oillylcr zfa`i icof ma`xf texfayxzi`he`d mari xfc` (9:1
C 8:9 me`
B 3:9 me`
O 8:> me`
H 3:> me`
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Zcdi 29 DA A@
25 C rfamby e fat` bilat.
En xfi fiedfx, f, e`xiriox xfi bci cx exmehzae`x, tfeof an xfii e olaix xa xfifiedfx an xfi rfamby1
C :.5 e`of
B :.4 e`of
O 3.8 e`ofi
H 3.4 e`ofi
3 e`of
>:
f
26 Tfeof isycxea` bix rizrii`x xfi le`idrczfih bilat1
N 4v ' 8u = ?9
D 8v 4u = ?9
F 8v ' 4u = ?9
K 4v 8u = ?9
u
v
9
8
>
4
6
5
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2
3
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Zcdi 2> DA A@
?: Xfi nedyri bilat fat c sycri zurcmeh texf c bci li`dxf an ?2 e`ofi c`h c lc`x fiedfx an?8 e`ofi.
Tfeof an xfi nallate`d sycri zurcmeh e emelcr xa xfi sycri zurcmeh cba~i1
N F
D K
36.4 e`.
34.> e`.
2:.8 e`.
35.2 e`.
2:.6 e`.
36.4 e`.
22.8 e`.
2?.6 e`.
?2 e`.
?8 e`.?: e`.
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Zcdi 24 DA A@
?3 Xfi ny`oxea` bilat fat c rilcxea`fezbixtii`v c`hu.
u = 4v ' ?
En xfi ~clyi anv e`orici bu 3, tfcx fczzi`xa xfi ~clyi anu1
C Xfi ~clyi anu e`orici bu ?.
B Xfi ~clyi anu e`orici bu 4.
O Xfi ~clyi anu e`orici bu 3:.
H Xfi ~clyi anu e`orici bu 23.
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Zcdi 26 DA A@
?2 Cx c` eoi-oricm faz, oyxamir oc` arhir c y`hci texf 3 xuzi an eoi oricm, 3 xuzi an cyoi, c`h 3 xuzian xazze`d. Xfi xuzi an eoi oricm, cyoi, c`h xazze`d annirih cri fat` bilat.
En icof xuzi an eoi oricm, cyoi, c`h xazze`d e isycllu legilu xa bi ilioxih, tfcx e xfi zrabcbelexu xfcxc oyxamir tell arhir c y`hci texf ~c`ellc eoi oricm, ocrcmil cyoi, c`h tcl`yx1
N
D
F
K3
32
333
38
3>:
Eoi Oricm _cyoi Xazze`d
Ofaoalcxi
_xrctbirru
^c`ellc
Ocrcmil
_xrctbirru
Ofaoalcxi
Byxxirsoaxof
Ofaoalcxi ofezs
Zic`yxs
Rcese`s
_xrctbirreis
Tcl`yxs
Ofaeois cx c` Eoi-Oricm _faz
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Zcdi 25 DA A@
?8 Ocrl tc cgih xa al~i xfi zrablim fat` e`xfi bav bilat.
Tfeof an xfi nallate`d oaylh Ocrl ha xa al~ixfi zrablim oarrioxlu1
N Chh xfi hemi`ea` de~i e` niix
D Mylxezlu icof hemi`ea` de~i` e` niix bu2 e`ofi
F Oa`~irx 2 e`ofi e`xa 28 niix
K Oa`~irx xfi hemi`ea` an xfi bav nramniix xa e`ofi
C oirxce` xuzi an oybi fcs 2-e`of ihdis.Tfcx es xfi mcvemym `ymbir an oybis
xfcx oc` bi zyx e`xa c bav xfcx micsyris2.4 niix bu ?.2 niix bu 8.3 niix1
?? CBO fc ~irxeoiC &2, 9%,B &2, 2%,c`h O &9, 2%.
EnCBO e rinlioxih cora xfi le`iu = v,tfeof an xfi nallate`d tell bi xfi oaarhe`cxianC1
C &2, 9%
B &9, 2%
O &2, 9%
H &9, 2%
u
v
9
8
?
2
3
3
2
?
8
9
:32?89 3 2 ? 8 9
C
BO
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Zcdi ?: DA A@
?9 Xfi nedyri bilat fat oeroliZ c`h oeroli S.ZS, SR, c`hR_ cri icof ? y`ex la`d.
Tfcx e xfi cric an xfi fchih ridea` e` xirman1
C ?>
B 42
O 32
H 46
ZS R
_
?> Tfeof an xfi nallate`d `ix narm c xrec`dylcrzurcmeh1
N
D
F
K
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Zcdi ?3 DA A@
?4 Xfi xcbli bilat fat fat mc`u xrec`dli cri narmih tfi` cll xfi hecda`cl cri hrct` nram a`i~irxiv e` henniri`x ridylcr zaluda`.
Bcih a` xfi xcbli, tfeof an xfi nallate`d xcximi`x e xryi1
C Cll xfi xrec`dli narmih e` icof ridylcr zaluda` cri oa`dryi`x.
B Cll xfi xrec`dli narmih e` icof ridylcr zaluda` cri eaoili.
O Xfi `ymbir an xrec`dli narmih e` c`u ridylcr zaluda` e 2 li xfc` xfi `ymbir an ehi e` xfizaluda`.
H Xfi `ymbir an xrec`dli narmih e` c`u ridylcr zaluda` e fcln xfi `ymbir an ehi e` xfi zaluda`.
@ymbir an_ehis
?
Ridylcr
Zaluda`
@ymbir anXrec`dlis
3
8
2
9
?
>
8
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Zcdi ?2 DA A@
8: Ofc` hrit xfi nallate`d hied`.
Fi xfi` yih xfi hied` xa oricxi xfi zcxxir`bilat.
Tfcx xuzi an xrc`narmcxea` heh Ofc` yi xaoricxi fe zcxxir`1
N Helcxea`
D Rinlioxea`
F Raxcxea`
K Xrc`lcxea`
?5 Tfeof an xfi nallate`d ivzriea` eisye~cli`x xa xfi ivzriea`9v&2v ' 4u% ' 4vu 8v&u ' ?%1
C 3:v 2 ' 4u ' ?vu ' ?
B 3:v 2 ' ?6vu ' 32v
O 3:v 2 ?2vu 32v
H 3:v 2 ?6vu ' 32v
?6 E` Nedyri 3 c oule`hir texf c hecmixir an32 oi`xemixir e nellih texf tcxir xa c fiedfxan 6 oi`xemixir.
E` Nedyri 2 c raog e ybmirdih e` xfioule`hir.
Tfeof an xfi nallate`d e olaix xa xfi ~alymian xfi raog1
N 3?5 om ?
D 836 om ?
F 3>48 om ?
K 3?2? om ?
33.4 om
Nedyri 2
32 om
6 om
32 om
Nedyri 3
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Zcdi ?8 DA A@
8? Tfcx e xfi alyxea` ix nar xfi isycxea`2v 2 3>v 5> = :1
C w8, 32}
B w8, 32}
O w8, 32}
H w8, 32}
8> Nar c ridylcr zi`xcda`cl zrem, tfcx e xfircxea an xfi `ymbir an ~irxeoi xa xfi `ymbiran ihdi1
N 2;?
D ?;2
F ?;9
K 9;?
89 Hi`ei oc` cimbli c ofcer e` :.49 fayr c`hc xcbli e` :.8 fayr. Tfeof e`isyclexu bixrizrii`x xfi `ymbir an ofcer, o, c`h xfi`ymbir an xcbli, x, xfcx Hi`ei oc` cimblie` a`i hcu en fi targ c mcvemym an6 fayr1
C &:.49 ' :.8%&o ' x% 6
B :.49o ' :.8x 6
O :.49o ' :.8x 6
H &:.49 ' o% ' &:.8 ' x% 6
88 Xfi ny`oxea` xcbli fat xfi ~clyi ann&`% narde~i` ~clyi an`.
Tfeof ny`oxea` bix rizrii`x xfirilcxea`fez bixtii` xfi syc`xexei e` xfixcbli1
N n&`% = ` '
D n&`% = 2`
F n&`% =
K n&`% =` ' ?
2
` ' 3
`
32
`
n&`%
3 2 ? 8
2 2.9 ? ?.9
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Zcdi ?9 DA A@
84 Xta ocr-ri`xcl oamzc`ei cri ch~irxee`d zioecl rcxi nar c mehe{i ocr. Ti`hill Maxar Ri`xcl ech~irxee`d c rcxi an (?9 c hcu zly (:.2: zir meli xrc~ilih, xcv e`olyhih. Mcre`c Ocr Ri`xcl ech~irxee`d c rcxi an (29 c hcu zly (:.8: zir meli xrc~ilih, xcv e`olyhih. Tfeof drczf oarrioxluoamzcri xfi oax an ri`xe`d c mehe{i ocr nar a`i hcu nram icof oamzc`u1
C O
B H
o
m
:
XaxclOasx
&hallcrs%
@ymbir an Melis Xrc~ilih
2: 8: >: 6: 3::
3:
2:
?:
8:
9:
>:
4:
_zioecl Rcxis nar
Mehse{i Ocr Ri`xcl
o
m
:
XaxclOasx
&hallcrs%
@ymbir an Melis Xrc~ilih
2: 8: >: 6: 3::
3:
2:
?:
8:
9:
>:
4:
_zioecl Rcxis nar
Mehse{i Ocr Ri`xcl
o
m
:
XaxclOasx
&hallcrs%
@ymbir an Melis Xrc~ilih
2: 8: >: 6: 3::
3:
2:
?:
8:
9:
>:
4:
_zioecl Rcxis nar
Mehse{i Ocr Ri`xcl
o
m
:
XaxclOasx
&hallcrs%
@ymbir an Melis Xrc~ilih
2: 8: >: 6: 3::
3:
2:
?:
8:
9:
>:
4:
_zioecl Rcxis nar
Mehse{i Ocr Ri`xcl
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Zcdi ?> DA A@
86 @efc oc` al~i c ix an 9 mcxf zrablim e`32 me`yxi. Cx xfe rcxi, fat la`d tell ex xcgifir xa al~i 2: ix an 4 mcxf zrablim1
N 96 me`yxi
D 9 fayr 3> me`yxi
F 86 me`yxi
K 9 fayr ?> me`yxi
85 Nar c`u `idcxe~i e`xidir m, `,z, c`h s,tfeof an xfi nallate`d e cltcu xryi enm` < zs1
C s 0 m
B m` 0 zs
O ` < z
H `s < mz
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Zcdi ?4 DA A@
9: Xfi nra`x c`h redfx-ehi ~eit an c nedyri mchi an ehi`xeocl oybi cri fat` bilat.
Tfeof ?-hemi`ea`cl nedyri e bix rizrii`xih bu xfi xta ~eit cba~i1
N F
D K
Nra`xRedfx
Nra`xRedfx
Nra`xRedfx
Nra`xRedfx
Nra`x
~eit
Redfx-sehi
~eit
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Zcdi ?6 DA A@
9? Xfi rioxc`dli bilat fc c ziremixir an 36 niixtexf c li`dxf an > niix.
C `it rioxc`dli e narmih bu hiorice`d xfitehxf an xfi arede`cl rioxc`dli bu 3 naax c`hgiize`d xfi li`dxf xfi cmi. Fat tell xfiziremixir an xfi `it rioxc`dli oamzcri texfxfi ziremixir an xfi arede`cl rioxc`dli1
C Xfi ziremixir an xfi `it rioxc`dli tell bi? niix farxir xfc` xfi ziremixir an xfiarede`cl rioxc`dli.
B Xfi ziremixir an xfi `it rioxc`dli tell bi2 niix farxir xfc` xfi ziremixir an xfiarede`cl rioxc`dli.
O Xfi ziremixir an xfi `it rioxc`dli tell bi3 naax farxir xfc` xfi ziremixir an xfiarede`cl rioxc`dli.
H Xfi ziremixir an xfi `it rioxc`dli tell bi
naax farxir xfc` xfi ziremixir an xfi
arede`cl rioxc`dli.
32
> nx
Z= 36 nx
92 Tfcx e xfi lazi an xfi le`icr isycxea`3:3v ' 9?u = 321
N 3:3
D
F
K32
3:3
3:39?
329?
93 Tfeof ivzriea` rizrii`x xfi ziremixir anxfi xrec`dli bilat1
C ?v ' 8
B
O 2v ' 2
H v 2 ' 2v
v 2 ' 2v2
v
v ' 2
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Zcdi ?5 DA A@
99 Kcli` `iih xa icr` c` c~ircdi an (32: c tiignram fe zcrx-xemi kab bu xfi i`h an fe 8xftiig. Fe nerx ? tiiglu zcuofiog tiri nar(59, (389, c`h (3?:. Tfeof isycxea` oc`Kcli` yi xa ne`h fat myof fi myx icr` e`xfi 8xf tiig e` arhir xa miix fe dacl1
C = 32:
B = 32:
O v ' 32: =
H = ?4:v ' 32:8
?4:?
v ' ?4:8
v ' ?4:?
98 Xfi xcbli bilat fat xfi ~clyi an c xirm e` cde~i` zaexea` e` c isyi`oi an `ymbir xfcxnallat c zcxxir`.
Tfeof ivzriea` bix rizrii`x xfi ~clyi anxfi `xf xirm1
N ?
D
F 8
K2` 2 34
>
?` 2
2
` 2 338
` 2
2
Zasexea` ^clyi an Xirm
3
2
?
8
9
`
2
3
3
9
5
1
32
32
3
2
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Zcdi 8: DA A@
9> Fat mc`u ~irxeoi hai xfi zalufihra` bilatfc~i1
N ?
D 9
F 6
K @ax firi
94 Nrc`oe, Lia`, c`h _filbu cri ry``e`d narzriehi`x an xfier ofaal xyhi`x oay`oel. Crc`ham yr~iu an >: xyhi`x tc xcgi` xahixirme`i tfam xfiu zlc``ih xa ~axi nar e`xfi ilioxea`. Xfi riylx cri fat` e` xfixcbli bilat.
Bcih a` xfi hcxc e` xfi xcbli, tfeof anxfi nallate`d e xfi bix zriheoxea` an xfi
`ymbir an xyhi`x tfa tell ~axi nar Lia`en 29:: xyhi`x ~axi1
C 32:6
B 252
O 53>
H 99:
_yr~iu Risylxs
Oc`hehcxi@ymbir an_xyhi`xs
Nrc`oes
Lia`
_filbu
25
22
5
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Zcdi 83 DA A@
96 Xfi drczf bilat rizrii`x xfi rilcxea`fez bixtii` xfi hi`exu an tcxir c`h xfi ximzircxyri antcxir.
Cooarhe`d xa xfi drczf, tfeof an xfi nallate`d e`xir~cl bix rizrii`x xfi ximzircxyri cx tfeof xfihi`exu an tcxir e dricxir xfc` 555.5 geladrcm zir oybeo mixir1
N Li xfc` 3O
D Bixtii` :O c`h 8O
F Bixtii` 8O c`h 6O
K Bixtii` 3O c`h 4O
:
Hi`sexuanTcxir
&gd!m?%
Ximzircxyri
&O%
Hi`sexu an Tcxir ~s.
Ximzircxyri
555.>
2 8 > 6 3:
555.4
555.6
555.5
3:::.:
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>: Xfi fiedfx e` oi`xemixir, f&v%, an c fymc`nimcli an Iyrazic` c`oixru oc` bi ixemcxihbu mylxezlue`d xfi li`dxf an xfi xebec e`oi`xemixir,v, bu 2.5: c`h xfi` chhe`d >3.9?xa xfi zrahyox. Tfeof an xfi nallate`d bixrizrii`x xfe rilcxea`fez1
N f&v% = &2.5: 'v%&>3.9?%
D f&v% = 2.5:&v ' >3.9?%
F f&v% = 2.5:v ' >3.9?
K f&v% = ' >3.9?v
2.5:
95 Xfi drczf anv ' 9u = 5 e fat` bilat.
Tfeof zae`x rizrii`x c alyxea` xa xfeisycxea`1
C &:, 3%
B &2, 3%
O &3, 2%
H &4, :%
u
v
9
8
>
4
6
5
3:
?
2
3
:
3
2
?8
9
>
4
6
5
3:
3 32?89>4653: 2 ? 8 9 > 4 6 5 3:
Zcdi 82
BI _YRI UAY FC^I RIOARHIH CLL AN UAYR C@_TIR_
A@ XFI C@_TIR HAOYMI@X.
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XCG_ IVEX LI^IL
MCXFIMCXEO_
CZREL 2::5
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Xivcs Cssissmi`x an G`atlihdi c`h _gells - C`stir Giu
Drchi; Ivex Li~il_ybkiox; McxfimcxeosChme`esxrcxea`; Czrel 2::5
Xfi lixxir e`heocxis xfcx xfisxyhi`x ivzioxcxea` lesxih es nram xfiCldibrc E XIG_.
Xfi lixxir e`heocxis xfcx xfi
sxyhi`x ivzioxcxea` lesxih es nram xfiDiamixru XIG_.
Exim Oarriox Abkioxe~i _xyhi`x
@ymbir C`stir Micsyrih Ivzioxcxea`s
Oazuredfx 2::5, Xivcs Ihyocxea` Cdi`ou. Cll redfxs risir~ih. Rizrahyoxea` an cll ar zarxea`s an xfes targ eszrafebexih texfayx ivzriss trexxi` zirmessea` nram Xivcs Ihyocxea` Cdi`ou.
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XCG_ Ivex Li~il Mcxfimcxeo
Abkioxe~i 3;
Abkioxe~i 2;
Nar c mari oamzlixi hiorezxea` an xfi abkioxe~i micyrih, zlici rinir xa xfi Ri~eih XCG_E`narmcxea` Baaglix nar Ivex Li~il Mcxfimcxeo cxfxxz;!!ttt.xic.xcxi.xv.y!xyhi`x.cimi`x!xcg!baaglix!e`hiv.fxml.
&C.3% Xfi xyhi`x y`hirxc`h xfcx c ny`oxea` rizrii`x c hizi`hi`oian a`i syc`xexu a` c`axfir c`h oc` bi hiorebih e` c ~creixu an tcu. Xfi xyhi`x e ivzioxih xa
&C% hiorebi e`hizi`hi`x c`h hizi`hi`x syc xexei e ny`oxea`cl rilcxea`fez7
&B% Wdcxfir c`h rioarh hcxc c`h] yi hcxc ix xa hixirme`i ny`oxea`cl rilcxea`fez bixtii`syc`xexei7
&O% hiorebi ny`oxea`cl rilcxea`fez nar de~i` zrablim exycxea` c`h trexi isycxea` are`isyclexei xa c`tir syixea` cree`d nram xfi exycxea`7
&H% rizrii`x rilcxea`fez cma`d syc`xexei ye`d Woa`orixi] mahil, xcbli, drczf, hecdrcm,~irbcl hiorezxea`, isycxea`, c`h e`isyclexei7 c`h
&I% e`xirzrix c`h mcgi hioeea`, zriheoxea`, c`h orexeocl kyhdmi x nram ny`oxea`cl rilcxea`fez.
&C.2% Xfi xyhi`x yi xfi zrazirxei c`h cxxrebyxi an ny`oxea`. Xfixyhi`x e ivzioxih xa
&C% ehi`xenu Wc`h gixof] xfi di`ircl narm an le`icr & c`h sychrcxeo & % zcri`x ny`oxea`7
&B% ehi`xenu mcxfimcxeocl hamce` c`h rc`di c`h hixirme`i rica`cbli hamce` c`h rc`di~clyi nar de~i` exycxea`, baxf oa`xe`yay c`h heorixi7
&O% e`xirzrix exycxea` e` xirm an de~i` drczf War oricxi exycxea` xfcx nex de~i` drczf]7 c`h
&H% Woalliox c`h] ardc`e{i hcxc, Wmcgi c`h] e`xirzrix ocxxirzlax &e`olyhe`d rioad`e{e`d zaexe~i,`idcxe~i, ar `a oarrilcxea` nar hcxc czzravemcxe`d le`icr exycxea`%, c`h mahil, zriheox, c`hmcgi hioeea` c`h orexeocl kyhdmi`x e` zrablim exycxea`.
&C.?% Xfi xyhi`x y`hirxc`h fat cldibrc oc` bi yih xa ivzridi`ircle{cxea` c`h rioad`e{i c`h yi xfi zatir an umbal xa rizrii`x exycxea`. Xfi
xyhi`x e ivzioxih xa
&C% yi umbal xa rizrii`x y`g`at` c`h ~crecbli7 c`h
&B% laag nar zcxxir` c`h rizrii`x di`ircle{cxea` cldibrceocllu.
&C.8% Xfi xyhi`x y`hirxc`h xfi emzarxc`oi an xfi gell risyerih xamc`ezylcxi umbal e` arhir xa al~i zrablim c`h yi xfi `ioicru cldibrceo gell risyerih xaemzlenu cldibrceo ivzriea` c`h al~i isycxea` c`h e`isyclexei e` zrablim exycxea`. Xfixyhi`x e ivzioxih xa
&C% ne`h zioeneo ny`oxea` ~clyi, emzlenu zalu`amecl ivzriea`, xrc`narm c`hal~i isycxea`, c`h ncoxar c `ioicru e` zrablim exycxea`7
%
Zcdi 3
u = v u = v
Xfi xyhi`x tell hiorebi ny`oxea`cl rilcxea`fez e` c ~creixu an tcu.
Nay`hcxea` nar ny`oxea`.
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an xfi zrazirxei c`h cxxrebyxi an
ny`oxea`.
Nay`hcxea` nar ny`oxea`.
Nay`hcxea` nar ny`oxea`.
Nay`hcxea` nar ny`oxea`.
2
http://www.tea.state.tx.us/student.assessment/taks/booklets/index.htmlhttp://www.tea.state.tx.us/student.assessment/taks/booklets/index.htmlhttp://www.tea.state.tx.us/student.assessment/taks/booklets/index.html7/30/2019 Math Texas TAKS With Answers 2009
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XCG_ Ivex Li~il Mcxfimcxeo &oa`xe`yih%
Abkioxe~i ?;
Abkioxe~i 8;
&B% yi xfi oammyxcxe~i, caoecxe~i, c`h hexrebyxe~i zrazirxei xa emzlenu cldibrceoivzriea`7 c`h
&O% oa``iox isycxea` `axcxea` texf ny oxea` `axcxea`, yof c
&C.9% Xfi xyhi x y`hirxc`h xfcx l e icr ny`oxea` oc` bi rizrii xih e` henniri xtcu c`h xrc`lcxi cma`d xfier ~creay rizrii`xcxea`. Xfi xyhi`x e ivzioxih xa
&C% hixirme`i tfixfir ar `ax de~i` exycxea` oc` bi rizrii`xih bu le`icr ny`oxea`7 c`h
&O% yi, xrc`lcxi, c`h mcgi oa``ioxea` cma`d cldibrceo, xcbylcr, drczfeocl, ar ~irbclhiorezxea` an le`icr ny`oxea`.
&C.>% Xfi xyhi x y`hirxc`h xfi mic`e d an xfi lazi c`h e xiroizx an xfi drczfan le`icr ny`oxea` c`h {ira an le`icr ny`oxea` c`h e`xirzrix c`h hiorebi xfi inniox an ofc`die` zcrcmixir an le`icr ny`oxea` e` ricl-tarlh c`h mcxfimcxeocl exycxea`. Xfi xyhi`x eivzioxih xa
&C% hi~ilaz xfi oa`oizx an lazi c rcxi an ofc`di c`h hixirme`i lazi nram drczf, xcbli,c`h cldibrceo rizrii`xcxea`7
&B% e`xirzrix xfi mic`e`d an lazi c`h e`xiroizx e` exycxea` ye`d hcxc, umbaleorizrii`xcxea`, ar drczf7
&O% e`~ixedcxi, hiorebi, c`h zriheox xfi inniox an ofc`di e` c`h a` xfi drczf an 7
&H% drczf c`h trexi isycxea` an le`i de~i` ofcrcoxirexeo yof c xta zae`x, c zae`x c`h clazi, ar c lazi c`h -e`xiroizx7
&I% hixirme`i xfi e`xiroizx an xfi drczf an le`icr ny`oxea` c`h {ira an le`icr ny`oxea` nramdrczf, xcbli, c`h cldibrceo rizrii`xcxea`7
&N% e`xirzrix c`h zriheox xfi inniox an ofc`de`d lazi c`h -e`xiroizx e` czzleih exycxea`7 c`h
&D% rilcxi heriox ~crecxea` xa le`icr ny`oxea` c`h al~i zrablim e`~al~e`d zrazarxea`cl ofc`di.
&C.4% Xfi xyhi x narmylcxi isycxea` c`h e`isyclexei bcih a` l e icr ny`oxea`,yi c ~creixu an mixfah xa al~i xfim, c`h c`clu{i xfi alyxea` e` xirm an xfi exycxea`. Xfixyhi`x e ivzioxih xa
&C% c`clu{i exycxea` e`~al~e`d le`icr ny`oxea` c`h narmylcxi le`icr isycxea` ar e`isyclexei xaal~i zrablim7
&B% e`~ixedcxi mixfah nar al~e`d le`icr isycxea` c`h e`isyclexei ye`d Woa`orixi] mahil,drczf, c`h xfi zrazirxei an isyclexu, iliox c mixfah, c`h al~i xfi isycxea` c`he`isyclexei7 c`h
&O% e`xirzrix c`h hixirme i xfi rica`cbli`i an alyxea` xa le`icr isycxea` c`h e`isyclexei.
= ' 3 c`h & % = ' 3.
Zcdi 2
m b u = mv ' b
u
u
u v n v v
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an le`icr ny`oxea`.
Le`icr ny`oxea`.
Le`icr ny`oxea`.
Xfi xyhi`x tell narmylcxi c`h yi le`icr isycxea` c`h e`isyclexei.
Le`icr ny`oxea`.
7/30/2019 Math Texas TAKS With Answers 2009
48/51
XCG_ Ivex Li~il Mcxfimcxeo &oa`xe`yih%
Abkioxe~i 9;
Abkioxe~i >;
&C.6% Xfi xyhi x narmylcxi uxim an l e icr isycxea` nram zrablim exycxea`,yi c ~creixu an mixfah xa al~i xfim, c`h c`clu{i xfi alyxea` e` xirm an xfi exycxea`. Xfixyhi`x e ivzioxih xa
&C% c`clu{i exycxea` c`h narmylcxi uxim an le`icr isycxea` e` xta y`g`at` xa al~izrablim7
&B% al~i uxim an le`icr isycxea` ye`d Woa`orixi] mahil, drczf, xcbli, c`h cldibrceomixfah7 c`h
&O% e`xirzrix c`h hixirme i xfi rica`cbli`i an alyxea` xa uxim an le`icr isycxea`.
&C.5% Xfi xyhi`x y`hirxc`h xfcx xfi drczf ansychrcxeo ny`oxea` cri cnnioxih bu xfi zcrcmixir an xfi ny`oxea` c`h oc` e`xirzrix c`h hiorebixfi inniox an ofc`di e` xfi zcrcmixir an sychrcxeo ny`oxea`. Xfi xyhi`x e ivzioxih xa
&B% e`~ixedcxi, hiorebi, c`h zriheox xfi inniox an ofc`di e` a` xfi drczf an = ' 7
&O% e`~ixedcxi, hiorebi, c`h zriheox xfi inniox an ofc`di e` a` xfi drczf an = ' 7 c`h
&H% c`clu{i drczf an sychrcxeo ny`oxea` c`h hrct oa`olyea`.
&C.3:% Xfi xyhi`x y`hirxc`h xfiri e mari xfc` a`itcu xa al~i c sychrcxeo isycxea` c`h al~i xfim ye`d czzrazrecxi mixfah. Xfi xyhi`x eivzioxih xa
&C% al~i sychrcxeo isycxea` ye`d Woa`orixi] mahil, xcbli, drczf, c`h cldibrceo mixfah7c`h
&B% mcgi oa``ioxea` cma`d xfi alyxea` &raax% an sychrcxeo isycxea`, xfi {ira an xfierrilcxih ny`oxea`, c`h xfi fare{a`xcl e`xiroizx &
&C.33% Xfi xyhi`x y`hirxc`h xfiri cri exycxea`mahilih bu ny`oxea` xfcx cri `iexfir le`icr `ar sychrcxeo c`h mahil xfi exycxea`. Xfi xyhi`xe ivzioxih xa
&C% yi Wzcxxir` xa di`ircxi] xfi lct an ivza`i`x c`h czzlu xfim e` zrablim-al~e`dexycxea`.
&D.8% Xfi xyhi`x yi c ~creixu an rizrii`xcxea` xa hiorebi diamixreorilcxea`fez c`h al~i zrablim. Xfi xyhi`x e ivzioxih xa
&C% iliox c` czzrazrecxi rizrii`xcxea` &Woa`orixi,] zeoxarecl, drczfeocl, ~irbcl, ar umbaleo% e`arhir xa al~i zrablim.
-e`xiroizx% an xfi drczf an xfi ny`oxea`.
Zcdi ?
c u cv o
o u cv o
v
Le`icr ny`oxea`.
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an sychrcxeo c`h axfir `a`le`icrny`oxea`.
Sychrcxeo c`h axfir `a`le`icr ny`oxea`.
Sychrcxeo c`h axfir `a`le`icr ny`oxea`.
Sychrcxeo c`h axfir `a`le`icr ny`oxea`.
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an diamixreo rilcxea`fez c`hzcxecl rica`e`d.
Diamixreo xryoxyri.
2
2
7/30/2019 Math Texas TAKS With Answers 2009
49/51
XCG_ Ivex Li~il Mcxfimcxeo &oa`xe`yih%
Abkioxe~i 4;
&D.9% Xfi xyhi`x yi c ~creixu an rizrii`xcxea` xa hiorebi diamixreorilcxea`fez c`h al~i zrablim. Xfi xyhi`x e ivzioxih xa
&C% yi `ymireo c`h diamixreo zcxxir` xa hi~ilaz cldibrceo ivzriea` rizrii`xe`d diamixreozrazirxei7
&B% yi `ymireo c`h diamixreo zcxxir` xa mcgi di`ircle{cxea` cbayx diamixreo zrazirxei,e`olyhe`d zrazirxei an zaluda`, rcxea e` emelcr nedyri c`h aleh, c`h c`dli rilcxea`feze` zaluda` c`h oeroli7
&O% yi zrazirxei an xrc`narmcxea` c`h xfier oamzaexea` xa mcgi oa``ioxea` bixtii`mcxfimcxeo c`h xfi ricl tarlh, yof c xiillcxea`7 c`h
&H% ehi`xenu c`h czzlu zcxxir` nram redfx xrec`dli xa al~i mic`e`dnyl zrablim, e`olyhe`dzioecl redfx xrec`dli &89-89-5: c`h ?:->:-5:% c`h xrec`dli tfai ehi cri Zuxfcdaric`xrezli.
&D.3:% Xfi xyhi`x czzlei xfi oa`oizx an oa`dryi`oi xakyxenu zrazirxei an nedyri c`h al~i zrablim. Xfi xyhi`x e ivzioxih xa
&C% yi oa`dryi`oi xrc`narmcxea` xa mcgi oa kioxyri c`h kyxenu zrazirxei an diamixreonedyri e`olyhe`d nedyri rizrii`xih a` c oaarhe`cxi zlc`i.
&D.>% Xfi xyhi`x c`clu{i xfi rilcxea`fez bixtii`xfrii-hemi`ea`cl diamixreo nedyri c`h rilcxih xta-hemi`ea`cl rizrii`xcxea` c`h yi xfii
rizrii`xcxea` xa al~i zrablim. Xfi xyhi`x e ivzioxih xa
&B% yi `ix xa rizrii`x Wc`h oa`xryox] xfrii-hemi`ea`cl diamixreo nedyri7 c`h
&O% yi arxfadrczfeo c`h eamixreo ~eit an xfrii-hemi`ea`cl diamixreo nedyri xa rizrii`xWc`h oa`xryox] xfrii-hemi`ea`cl diamixreo nedyri c`h al~i zrablim.
&D.4% Xfi xyhi`x y`hirxc`h xfcx oaarhe`cxiuxim zra~ehi oa`~i`ei`x c`h inneoei`x tcu an rizrii`xe`d diamixreo nedyri c`h yi xfimcooarhe`dlu. Xfi xyhi`x e ivzioxih xa
&C% yi a`i- c`h xta-hemi`ea`cl oaarhe`cxi uxim xa rizrii`x zae`x, le`i, rcu, le`iidmi`x, c`h nedyri7
&B% yi lazi c`h isycxea` an le`i xa e`~ixedcxi diamixreo rilcxea`fez, e`olyhe`d zcrcllille`i, zirzi`heoylcr le`i, c`h Wzioecl idmi`x an] xrec`dli c`h axfir zaluda`7 c`h
&O% hire~i c`h yi narmylc e`~al~e`d li`dxf, lazi, c`h mehzae`x.
&D.5% Xfi xyhi`x c`clu{i zrazirxei c`h hiorebirilcxea`fez e` diamixreo nedyri. Xfi xyhi`x e ivzioxih xa
&H% c`clu{i xfi ofcrcoxirexeo an zalufihrc c`h axfir xfrii-hemi`ea`cl nedyri c`h xfieroamza`i`x zcrx bcih a` ivzlarcxea` c`h Woa`orixi] mahil.
Zcdi 8
Diamixreo zcxxir`.
Oa`dryi`oi c`h xfi diamixru an e{i.
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an xta- c`h xfrii-hemi`ea`clrizrii`xcxea` an diamixreo rilcxea`fez c`h fczi.
Hemi`ea`clexu c`h xfi diamixru an laocxea`.
Hemi`ea`clexu c`h xfi diamixru an laocxea`.
Oa`dryi`oi c`h xfi diamixru an e{i.
7/30/2019 Math Texas TAKS With Answers 2009
50/51
XCG_ Ivex Li~il Mcxfimcxeo &oa`xe`yih%
Abkioxe~i 6;
Abkioxe~i 5;
&D.6% Xfi xyhi`x yi xaal xa hixirme`i micyrimi`x andiamixreo nedyri c`h ivxi`h micyrimi`x oa`oizx xa ne`h ziremixir, cric, c`h ~alymi e`zrablim exycxea`. Xfi xyhi`x e ivzioxih xa
&C% ne`h cric an ridylcr zaluda`, oeroli, c`h oamzaexi nedyri7
&B% ne`h cric an ioxar c`h cro li`dxf an oeroli ye`d zrazarxea`cl rica`e`d7
&O% Whire~i,] ivxi`h, c`h yi xfi Zuxfcdaric` Xfiarim7 c`h
&H% ne`h yrncoi cric c`h ~alymi an zrem, zurcmeh, zfiri, oa`i, oule`hir, c`hoamzaexi an xfii nedyri e` zrablim exycxea`.
&D.33% Xfi xyhi`x czzlei xfi oa`oizx an emelcrexu xa kyxenuzrazirxei an nedyri c`h al~i zrablim. Xfi xyhi`x e ivzioxih xa
&C% yi c`h ivxi`h emelcrexu zrazirxei c`h xrc`narmcxea` xa ivzlari c`h kyxenu oa`kioxyricbayx diamixreo nedyri7
&B% yi rcxea xa al~i zrablim e`~al~e`d emelcr nedyri7
&O% Whi~ilaz,] czzlu, c`h kyxenu xrec`dli emelcrexu rilcxea`fez, yof c redfx xrec`dli rcxea,Wxreda`amixreo rcxea,] c`h Zuxfcdaric` xrezli ye`d c ~creixu an mixfah7 c`h
&H% hiorebi xfi inniox a` ziremixir, cric, c`h ~alymi tfi` a`i ar mari hemi`ea` an c nedyricri ofc`dih c`h czzlu xfe ehic e` al~e`d zrablim.
&6.?% Xfi xyhi`x ehi`xenei zrazarxea`cl ar a`-zrazarxea`cl le`icr rilcxea`fez e` zrablim exycxea` c`h al~i zrablim. Xfi xyhi`x eivzioxih xa
&B% ixemcxi c`h ne`h alyxea` xa czzleocxea` zrablim e`~al~e`d ziroi`x c`h axfir zrazarxea`clrilcxea`fez, yof c emelcrexu c`h rcxi.
&6.33% Xfi xyhi`x czzlei oa`oizx an xfiarixeocl c`h ivziremi`xcl
zrabcbelexu xa mcgi zriheoxea`. Xfi xyhi`x e ivzioxih xa
&C% ne`h xfi zrabcbelexei an hizi`hi`x c`h e`hizi`hi x i~i`x7 c`h
&B% yi xfiarixeocl zrabcbelexei c`h ivziremi`xcl riylx xa mcgi zriheoxea` c`h hioeea`.
&6.32% Xfi xyhi`x yi xcxexeocl zraoihyri xa hiorebi hcxc. Xfixyhi`x e ivzioxih xa
&C% iliox xfi czzrazrecxi micyri an oi`xrcl xi`hi`ou ar rc`di xa hiorebi c ix an hcxc c`hkyxenu xfi ofaeoi nar c zcrxeoylcr exycxea`7 c`h
Zcdi 9
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an xfi oa`oizx c`h yi an
micyrimi`x c`h emelcrexu.
Oa`dryi`oi c`h xfi diamixru an e{i.
_emelcrexu c`h xfi diamixru an fczi.
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an ziroi`x, zrazarxea`cl
rilcxea`fez, zrabcbelexu, c`h xcxexeo e` czzleocxea` zrablim.
Zcxxir`, rilcxea`fez, c`h cldibrceo xfe`ge`d.
Zrabcbelexu c`h xcxexeo.
Zrabcbelexu c`h xcxexeo.
7/30/2019 Math Texas TAKS With Answers 2009
51/51
XCG_ Ivex Li~il Mcxfimcxeo &oa`xe`yih%
Abkioxe~i 3:;
&O% iliox c`h yi c` czzrazrecxi rizrii`xcxea` nar zrii`xe d c`h hezlcue`d rilcxea`fezcma`d oallioxih hcxc, e`olyhe`d le`i zlax, le`i drczf, Wxim c`h licn zlax,] oeroli drczf, bcrdrczf, bav c`h tfegir zlax, fexadrcm, c`h ^i`` hecdrcm, texf c`h texfayx xfi yi an
xiof`aladu.
&6.3?% Xfi xyhi`x i~clycxi zriheoxea` c`h oa`olyea` bcih a`xcxexeocl hcxc. Xfi xyhi`x e ivzioxih xa
&B% rioad e{i meyi an drczfeocl ar `ymireocl e`narmcxea` c`h i~clycxi zriheoxea` c`hoa`olyea` bcih a` hcxc c`clue.
&6.38% Xfi xyhi`x czzlei Drchi 6 mcxfimcxeo xaal~i zrablim oa``ioxih xa i~iruhcu ivzirei`oi, e`~ixedcxea` e` axfir heoezle`i, c`h coxe~exeie` c`h ayxehi an ofaal. Xfi xyhi`x e ivzioxih xa
&C% ehi`xenu c`h czzlu mcxfimcxeo xa i~iruhcu ivzirei`oi, xa coxe~exei e` c`h ayxehi an ofaal,texf axfir heoezle`i, c`h texf axfir mcxfimcxeocl xazeo7
&B% yi c zrablim-al~e d mahil xfcx e`oarzarcxi y`hirxc`he`d xfi zrablim, mcge`d c zlc`,ocrrue`d ayx xfi zlc`, c`h i~clycxe`d xfi alyxea` nar rica`cbli`i7 c`h
&O% iliox ar hi~ilaz c` czzrazrecxi zrablim-al~e`d xrcxidu nram c ~creixu an henniri`x xuzi,e`olyhe`d hrcte`d c zeoxyri, laage`d nar c zcxxir`, uximcxeo dyie`d c`h ofioge`d, coxe`dex ayx, mcge`d c xcbli, targe`d c emzlir zrablim, ar targe`d bcogtcrh xa al~i c zrablim.
&6.39% Xfi xyhi`x oammy`eocxi cbayx Drchi 6mcxfimcxeo xfraydf e`narmcl c`h mcxfimcxeocl lc`dycdi, rizrii`xcxea`, c`h mahil. Xfixyhi`x e ivzioxih xa
&C% oammy`eocxi mcxfimcxeocl ehic ye`d lc`dycdi, inneoei x xaal, czzrazrecxi y`ex, c`hdrczfeocl, `ymireocl, zfueocl, ar cldibrceo mcxfimcxeocl mahil.
&6.3>% Xfi xyhi`x yi ladeocl rica`e`d xa mcgioa`kioxyri c`h ~irenu oa`olyea`. Xfi xyhi`x e ivzioxih xa
&C% mcgi oa kioxyri nram zcxxir ar ix an ivcmzli c`h `a`ivcmzli7 c`h
&B% ~clehcxi fe!fir oa`olyea` ye`d mcxfimcxeocl zrazirxei c`h rilcxea`fez.
Zrabcbelexu c`h xcxexeo.
Xfi xyhi`x tell hima`xrcxi c` y`hirxc`he`d an xfi mcxfimcxeocl zraoii
c`h xaal yih e` zrablim al~e`d.
Y`hirlue`d zraoii c`h mcxfimcxeocl xaal.
Y`hirlue`d zraoii c`h mcxfimcxeocl xaal.
Y`hirlue`d zraoii c`h mcxfimcxeocl xaal.
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