taks math study guide

Upload: aehsgo2college

Post on 04-Apr-2018

224 views

Category:

Documents


0 download

TRANSCRIPT

  • 7/30/2019 TAKS Math Study Guide

    1/303

    @ X~snca~ `an G`idet Ksdnc

    I`~bci`~dhx

    Zcwdxcn J`xcn la ^CFX Zcgdacica~x

    Zcwdxcn :==;

  • 7/30/2019 TAKS Math Study Guide

    2/303

    Crd~ Ecwce

    I`~bci`~dhx

    @ X~snca~ `an G`idet Ksdnc

    X^SNT KSDNC

    ^cr`x @xxcxxica~ lg Fal{ecnkc `an Xfdeex

    Hl}tzdkb~ :==;% ^cr`x Cnsh ~dla @kcaht! @ee zdkb~x zcxczwcn! Zc}zlnsh~dla lg `ee lz }lz~dlax lg ~bdx {lzf dx }zlbdjd~cn

    {d~bls~ cr}zcxx {zd~~ca }czidxxdla gzli ~bc cr`x Cnsh`~dla @kcaht!

  • 7/30/2019 TAKS Math Study Guide

    3/303

    Hlwcz }bl~l hzcnd~x? Ecg~ Zlt`e~t)Gzcc,HLZJDX6 Zdkb~ Hb`zecx Ks}~la,HLZJDX6

    Jl~~li Zlt`e~t)Gzcc,HLZJDX

  • 7/30/2019 TAKS Math Study Guide

    4/303

    8

    Nc`z X~snca~ `an ]`zca~?

    ^bc ^cr`x @xxcxxica~ lg Fal{ecnkc `an Xfdeex "^@FX$ dx ` hli}zcbcaxdwc ~cx~dak}zlkz`i glz }sjedh xhblle x~snca~x da kz`ncx 800 ^@FX% dahesndak ^@FX"@hhliiln`~cn$ `an Edaksdx~dh`eet @hhliiln`~cn ^cx~dak "E@^$% b`x zc}e`hcn ~bccr`x @xxcxxica~ lg @h`ncidh Xfdeex "^@@X$ `an dx ncxdkacn ~l ic`xszc ~l {b`~

    cr~ca~ ` x~snca~ b`x ec`zacn% sanczx~lln% `an dx `jec ~l `}}et ~bc di}lz~`a~ hlahc}~x`an xfdeex cr}ch~cn `~ c`hb ~cx~cn kz`nc ecwce Da `nnd~dla% ~bc ~cx~ h`a }zlwdncw`es`jec gccnj`hf ~l x~snca~x% }`zca~x% `an xhbllex `jls~ x~snca~ }zlkzcxx gzli kz`nc~l kz`nc

    X~snca~x `zc ~cx~cn da i`~bci`~dhx da kz`ncx 8006 zc`ndak da kz`ncx 846 {zd~dak dakz`ncx > `an ;6 Cakedxb e`aks`kc `z~x da kz`ncx 0= `an 006 xhdcahc da kz`ncx 3% 2% 0=%`an 006 `an xlhd`e x~sndcx da kz`ncx 2% 0=% `an 00 Cwczt ^@FX ~cx~ dx ndzch~et edafcn~l ~bc ^cr`x Cxxca~d`e Fal{ecnkc `an Xfdeex "^CFX$ hszzdhsesi ^bc ^CFX dx ~bcx~`~c)i`an`~cn hszzdhsesi glz ^cr`x }sjedh xhblle x~snca~x Cxxca~d`e fal{ecnkc`an xfdeex ~`skb~ `~ c`hb kz`nc jsden s}la ~bc i`~czd`e ec`zacn da }zcwdlsx kz`ncxJt ncwcel}dak ~bc `h`ncidh xfdeex x}chdffcn da ~bc ^CFX% x~snca~x h`a jsden ` x~zlakglsan`~dla glz gs~szc xshhcxx

    ^bc ^cr`x Cnsh`~dla @kcaht b`x ncwcel}cn ~bdx x~snt ksdnc ~l bce} x~snca~xx~zcak~bca ~bc ^CFX)j`xcn xfdeex ~b`~ `zc ~`skb~ da he`xx `an ~cx~cn la ^@FX ^bcksdnc dx ncxdkacn glz x~snca~x ~l sxc la ~bcdz l{a lz glz x~snca~x `an g`idedcx ~l{lzf ~bzlskb ~lkc~bcz Hlahc}~x `zc }zcxca~cn da ` w`zdc~t lg {`tx ~b`~ {dee bce}x~snca~x zcwdc{ ~bc daglzi`~dla `an xfdeex ~bct accn ~l jc xshhcxxgse la ^@FX Cwcztksdnc dahesncx cr}e`a`~dlax% }z`h~dhc pscx~dlax% nc~`decn `ax{cz fctx% `an x~snca~`h~dwd~dcx @~ ~bc can lg ~bdx x~snt ksdnc dx `a cw`es`~dla glzi glz tls ~l hli}ec~c `ani`de j`hf {bca tls b`wc ffadxbcn ~bc ksdnc Tlsz hliica~x {dee bce} sx di}zlwcgs~szc wczxdlax lg ~bdx ksdnc

    ^bczc `zc ` asijcz lg zcxlszhcx `w`de`jec glz x~snca~x `an g`idedcx {bl {lsen edfcilzc daglzi`~dla `jls~ ~bc ^@FX ~cx~dak }zlkz`i Daglzi`~dla jllfec~x `zc `w`de`jecglz cwczt ^@FX xsjoch~ `an kz`nc Jzlhbszcx `zc `exl `w`de`jec ~b`~ cr}e`da ~bc X~snca~Xshhcxx Dad~d`~dwc }zlil~dla zcpsdzcica~x `an ~bc ac{ kz`ns`~dla zcpsdzcica~x glzcecwca~b)kz`nc x~snca~x ^l lj~`da hl}dcx lg ~bcxc zcxlszhcx lz ~l ec`za ilzc `jls~~bc ~cx~dak }zlkz`i% }ec`xc hla~`h~ tlsz xhblle lz wdxd~ ~bc ^cr`x Cnsh`~dla @kcaht{cjxd~c `~ {{{~c`x~`~c~rsx,x~snca~`xxcxxica~

    ^cr`x dx }zlsn lg ~bc }zlkzcxx lsz x~snca~x b`wc i`nc `x ~bct x~zdwc ~l zc`hb ~bcdz`h`ncidh kl`ex [c bl}c ~bc x~snt ksdncx {dee bce} glx~cz x~snca~ ec`zadak% kzl{~b%

    `an xshhcxx da `ee lg ~bc ^@FX xsjoch~ `zc`xXdahczcet%

    Kelzd` _txfl{xfdNc}s~t @xxlhd`~c Hliidxxdlacz glz X~snca~ @xxcxxica~^cr`x Cnsh`~dla @kcaht

    @ Ec~~cz gzli ~bc Nc}s~t @xxlhd`~c Hliidxxdlacz glz X~snca~ @xxcxxica~

  • 7/30/2019 TAKS Math Study Guide

    5/303

    >

    Hla~ca~x

    Da~zlnsh~dla ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3

    I`~bci`~dhx Hb`z~! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2

    Ljoch~dwc 0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 0=

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 8=

    Ljoch~dwc : ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 87

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 78

    Ljoch~dwc 8 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 7;

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 47

    Ljoch~dwc > ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 44

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 00:

    Ljoch~dwc 3 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 007

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 082

    Ljoch~dwc 7 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 0>0

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 07>

    Ljoch~dwc ; ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 072

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 027

    Ljoch~dwc 2 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 04=

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ::8

    Ljoch~dwc 4 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ::2

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :3:

    Ljoch~dwc 0= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :32

    ]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :;>

    I`~bci`~dhx @ax{cz Fct! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :2=

    I`~bci`~dhx

  • 7/30/2019 TAKS Math Study Guide

    6/303

    3

    I@^BCI@^DHXI@^BCI@^DHX

    [b`~ Dx ^bdx Jllfz :

    Wlesic }zdxi lz htedancz W9Jb

    }tz`idn lz hlac W9 Jb

    x}bczc W9 z 8

    X}chd`e Zdkb~ ^zd`akecx 8=% 7=% 4= r% r\\8% :r

    >3% >3% 4= r% r% r\\:

    0:

    08>8

    jb:

    0

    :

    "j0 & j:$b

    :

    ]t~b`klzc`a ^bclzci ` : & j : 9 h :

    Ndx~`ahc Glzise` n 9 "r: r0$ : & "t: t0$ :

    Xel}c lg ` Edac i 9

    Idn}lda~ Glzise` I9 " % $Ps`nz`~dh Glzise` r 9

    Xel}c)Da~czhc}~ Glzi lg `a Cps`~dla t 9 ir & j

    ]lda~)Xel}c Glzi lg `a Cps`~dla t t0 9 i"r r0$

    X~`an`zn Glzi lg `a Cps`~dla @r &Jt 9 H

    Xdi}ec Da~czcx~ Glzise` D9}z~

    t: t0r: r0

    r0 &r::

    t0 &t::

    j j : >`h:`

    0:

    0

    :

    0:

  • 7/30/2019 TAKS Math Study Guide

    11/303

    0=

    ^bc x~snca~ {dee ncxhzdjc gsah~dla`e zce`~dlaxbd}x da ` w`zdc~t lg {`tx!

    Ljoch~dwc 0

    Glz ~bdx ljoch~dwc tls xblsen jc `jec ~l zchlkadc ~b`~ ` gsah~dlazc}zcxca~x ` nc}cancahc lg lac ps`a~d~t la `al~bcz `an h`a jc

    ncxhzdjcn da ` asijcz lg {`tx

    [b`~ Dx ` Gsah~dla% js~ ndggczca~t)hllznda`~cx%8 `an :

    ^bdx kz`}b lg lznczcn }`dzx nlcx al~ zc}zcxca~ ` gsah~dla jch`sxc~{l }lda~x edc la ~bc x`ic wcz~dh`e edac

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    Da ` gsah~dla% ~bct)hllznda`~c dx ncxhzdjcn da ~czix lg ~bcr)hllznda`~c^bc w`esc lg ~bct)hllznda`~c nc}canx la ~bc w`esc lg ~bcr)hllznda`~c

  • 7/30/2019 TAKS Math Study Guide

    14/303

    Ljoch~dwc 0

    08

    ^zt D~Glz ` xhdcahc cr}czdica~ I`zd`a` ic`xszcx ~bc z`~c `~ {bdhb `edpsdn hllex Xbc ffanx ~b`~ glz ~bc ffzx~ gc{ idas~cx ~bc edpsdn hllex%d~x ~ci}cz`~szc h`a jc kdwca sxdak ~bc cps`~dla ~ :0; 02i% da{bdhb i zc}zcxca~x ~bc asijcz lg idas~cx ~bc edpsdn b`x jccahlledak `an ~ dx d~x ~ci}cz`~szc da H

    [bdhb w`escx `zc ~bc nc}canca~ `an danc}canca~ ps`a~d~dcx da ~bdxgsah~dla`e zce`~dlaxbd}< [bdhb w`escx `zc ~bc hlax~`a~x da ~bdx

    gsah~dla`e zce`~dlaxbd}=== ic~czx% ~bc cps`~dla b >=== >4~: ncxhzdjcx b% Xb`aalax`e~d~snc da ic~czx% da ~czix lg~% ~bc asijcz lg xchlanx sa~de xbcl}cax bcz }`z`hbs~c

    Dnca~dgt ~bc danc}canca~ `an nc}canca~ ps`a~d~dcx `an ~bchlax~`a~x da ~bdx cps`~dla

    ^bc asijcz lg xchlanx sa~de Xb`aala l}cax bcz }`z`hbs~c dx~bc danc}canca~ ps`a~d~t

    Xb`aalax `e~d~snc nc}canx la ~bc asijcz lg xchlanx xbc b`xjcca g`eedak6 d~ dx ~bc nc}canca~ ps`a~d~t

    Xb`aalax x~`z~dak `e~d~snc% >=== ic~czx% `an >4 `zc hlax~`a~xda ~bc gsah~dla jch`sxc ~bct nl al~ hb`akc

  • 7/30/2019 TAKS Math Study Guide

    15/303

    Bl{ H`a Tls Zc}zcxca~ ` Gsah~dla

    0

    2

    0>!!! !!!

    Nz`{ ` }dh~szc ~b`~xbl{x bl{ ~bc lznczcn}`dzx `zc glzicn!

    ]e`hc ~bc lznczcn }`dzxda ` ~`jec!

    v"

    0%

    >$% "=%

    0$% "8% 2$%"3% 0>$% yEdx~ ~bc lznczcn }`dzx!

    r t

    0 >

    = 0

    8 2

    3 0>

    Ljoch~dwc 0

    0>

  • 7/30/2019 TAKS Math Study Guide

    16/303

    Ljoch~dwc 0

    03

    ^l sxc gsah~dla al~`~dla ~l ncxhzdjc ` gsah~dla% kdwc ~bc gsah~dla `a`ic% ~t}dh`eet ` ec~~cz xshb `xg% k% lz b ^bca sxc `a `ekcjz`dhcr}zcxxdla ~l ncxhzdjc ~bct)hllznda`~c lg `a lznczcn }`dz

    Bczc `zc ~bzcc ic~blnx tls h`a sxc ~l nc~czidac {bc~bcz ~{l ndggczca~zc}zcxca~`~dlax lg ` gsah~dla `zc cpsdw`eca~

    Xs}}lxcg"r$ 0>r 3

    ^bdx gsah~dla dx zc`n `x glgrcps`ex 0> ~dicxr}esx 3

    Dg tls da}s~r% ~bc ls~}s~ {dee jc 0>r 3

    ^bct)hllznda`~c lg `at lznczcn }`dz glz ~bdx gsah~dla dx 0>r 3

    ^bc gsah~dla ncxhzdjcn jtg"r$ 0>r 3 dx ~bc x`ic `x ~bc gsah~dla

    ncxhzdjcn jtt 0>r 3 ^bczcglzc% `at lznczcn }`dz

    glz ~bdx gsah~dla h`a jc zc}zcxca~cn jt "r% 0>r 3$

    Nl tls xcc~b`~ ! ! !

    Ic~bln

    I`~hb ` edx~ lz ~`jec lg lznczcn}`dzx ~l ` kz`}b!

    I`~hb `a cps`~dla ~l ` kz`}b!

    I`~hb ` wczj`e ncxhzd}~dla ~l` kz`}b% `a cps`~dla% lz `acr}zcxxdla {zd~~ca da gsah~dlaal~`~dla!

    @h~dla

    Xbl{ ~b`~ c`hb lznczcn }`dzedx~cn i`~hbcx ` }lda~ la ~bckz`}b!

    Nc~czidac {bc~bcz ~bct `zcjl~b edac`z lz ps`nz`~dhgsah~dlax!

    Gdan }lda~x la ~bc kz`}b `anxbl{ ~b`~ ~bcdz hllznda`~cxx`~dxgt ~bc cps`~dla!

    Gdan }lda~x ~b`~ x`~dxgt ~bccps`~dla `an xbl{ ~b`~ ~bct`zc la ~bc kz`}b!

    Sxc ~bc wczj`e ncxhzd}~dla ~lffan lznczcn }`dzx jcelakdak~l ~bc gsah~dla `an ~bca xbl{~b`~ ~bct x`~dxgt ~bc kz`}b%

    cps`~dla% lz gsah~dla zsec! Gdan }lda~x la ~bc kz`}b lz

    lznczcn }`dzx x`~dxgtdak ~bccps`~dla lz zsec `an xbl{~b`~ ~bct x`~dxgt ~bc wczj`encxhzd}~dla!

  • 7/30/2019 TAKS Math Study Guide

    17/303

    Ljoch~dwc 0

    07

    @at cps`~dla da ~bc glzit ir j dx ` edac`z gsah~dla D~x kz`}b{dee jc ` edac

    @at cps`~dla da ~bc glzit `r: jr h% {bczc ` =% dx `ps`nz`~dh gsah~dla D~x kz`}b {dee jc ` }`z`jle`

    t

    r

    3

    >

    7

    ;

    2

    4

    0=

    00

    0:

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0=

    00

    0:

    0 0:8>37;240=000: : 8 > 3 7 ; 2 4 0= 00 0:

    t 9r: & :r 8

    t

    r

    3

    >

    7

    ;

    2

    4

    0=

    00

    0:

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0=

    00

    0:

    0 0:8>37;240=000: : 8 > 3 7 ; 2 4 0= 00 0:

    t 9 r & 08:

    r t

    8 =

    0 >

    = 80 =

    8 0:

    r t

    2 00

    : :

    = 0

    > ;

  • 7/30/2019 TAKS Math Study Guide

    18/303

    Ljoch~dwc 0

    0;

    Nlcx ~bc lznczcn }`dz ":% :=$ jcelak ~l ~bc gsah~dlab"r$ r"r 3$ 7!3 : 7!3= Tcx

    t 7!3

    t 0!3"3$ :3 t ;!3 : 4!3= Tcx

    t 4!3

    t 0!3"0=$ :0= t 03 : 0;!== Tcx

    t 0;

  • 7/30/2019 TAKS Math Study Guide

    21/303

    Nlcx ~bc kz`}b jcel{ zc}zcxca~ ~bc cps`~dlat :r: > dx ` ps`nz`~dhgsah~dla jch`sxc ~bczc dx `ar: ~czi da ~bc cps`~dla ^bc kz`}bdx ` }`z`jle` D~ ncxhzdjcx ` ps`nz`~dh gsah~dla Jl~b ~bccps`~dla `an ~bc kz`}b ncxhzdjc ` ps`nz`~dh gsah~dla

    Hbchf xcwcz`e }lda~x la ~bc kz`}b ~l xcc {bc~bcz ~bcdzhllznda`~cx x`~dxgt ~bc cps`~dlat :r: > Hbllxc }lda~x{d~b hllznda`~cx ~b`~ `zc c`xdet zc`n gzli ~bc kz`}b Da ~bdxh`xc% hbllxc ~bc }lda~x "8% 0>$% "0% :$% `an ":% >$

    Xsjx~d~s~c ~bcxc w`escx da~l ~bc cps`~dlat :r: > `annc~czidac {bc~bcz ~bc cps`~dla dx ~zsc

    ]

    l

    d

    a

    ~

    "

    8

    %

    0

    >

    $

    ]

    l

    d

    a

    ~

    "

    0

    %

    :

    $

    ]

    l

    d

    a

    ~

    "

    :

    %

    >

    $

    r 8 `ant 0> r 0 `ant : r : `ant >

    t :r: > t :r: > t :r: >0> :"8$: > : :"0$: > > :":$: >0> :"4$ > : :"0$ > > :">$ >0> 02 > : : > > 2 >0> 0> : : > >

    ^bc hllznda`~cx lg ~bc }lda~x "8% 0>$% "0% :$% `an ":% >$

    x`~dxgt ~bc cps`~dla

    t

    r

    0=

    2

    0:

    0>

    07

    02

    7

    >

    :

    =

    :

    >

    7

    2

    0 0:8> : 8 >

    "0% :$

    ":% >$

    "8% 0>$

    Ljoch~dwc 0

    :=

  • 7/30/2019 TAKS Math Study Guide

    22/303

    Ljoch~dwc 0

    :0

    Tls h`a `exl ffan xcwcz`e lznczcn }`dzx lg asijczx ~b`~ x`~dxgt~bc cps`~dla `an hlaffzi ~b`~ ~bct `zc }lda~x la ~bc kz`}b ]dhfw`escx ~b`~ `zc c`xt ~l xsjx~d~s~c% xshb `xr 0%r =% `an

    r : Gdan ~bc hlzzcx}landak w`escx glzt

    Xsjx~d~s~c ~bcr)w`escx da~lt :r:

    > `an nc~czidac ~bcw`esc glzt

    r 0 r = r :

    t :r: > t :r: > t :r: >t :"0$: > t :"=$: > t :":$: >t :"0$ > t :"=$ > t :">$ >t : > t = > t 2 >t : t > t >

    ^bc lznczcn }`dzx "0% :$% "=% >$% `an ":% >$ x`~dxgt ~bccps`~dla Nc~czidac {bc~bcz ~bcxc lznczcn }`dzx `zc }lda~x la

    ~bc kz`}b Tcx% `ee ~bzcc }lda~x `zc la ~bc kz`}b^bc kz`}b nlcx zc}zcxca~ ~bc gsah~dlat :r: >

    Nlcx ~bc kz`}b jcel{ zc}zcxca~ ~bc dacps`ed~tt :8r 0

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

  • 7/30/2019 TAKS Math Study Guide

    23/303

    Ljoch~dwc 0

    ::

    Hbchf `~ ec`x~ ~{l }lda~x la ~bc jlsan`zt lg ~bc kz`}b ~l xcc

    {bc~bcz ~bcdz hllznda`~cx x`~dxgt ~bc cps`~dlat :8r 0

    Hbllxc }lda~x {d~b hllznda`~cx ~b`~ `zc c`xdet zc`n gzli ~bc

    kz`}b Da ~bdx h`xc% hbllxc ~bc }lda~x "8% 0$ `an "7% 8$

    Xsjx~d~s~c ~bcxc w`escx da~l ~bc cps`~dlat :8r 0 `an

    nc~czidac {bc~bcz ~bc cps`~dla dx ~zsc

    ]

    l

    d

    a

    ~

    "

    8

    %

    0

    $

    ]

    l

    d

    a

    ~

    "

    7

    %

    8

    $

    t :8r 0 t

    :8r 0

    0 :8"8$ 0 8

    :8"7$ 0

    0 : 0 8 > 0

    0 0 8 8^bc edac dx ~bc hlzzch~ jlsan`zt D~ dx nl~~cn jch`sxc ~bc

    dacps`ed~t t :8r 0 nlcx al~ dahesnc ~bc }lda~x la ~bc edac

    t :8r 0

    Hbchf `~ ec`x~ lac }lda~ {d~bda ~bc xb`ncn zckdla ~l jc hcz~`da~bc hlzzch~ xdnc lg ~bc edac b`x jcca xb`ncn Tls h`a sxc ~bc}lda~ "7% =$

    ]

    l

    d

    a

    ~

    "

    7

    %

    =

    $

    t

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

  • 7/30/2019 TAKS Math Study Guide

    25/303

    Gdan ~{l }lda~x ~b`~ x`~dxgt ~bc cps`~dlat 8r : `an xcc {bc~bcz~bct `zc }lda~x la ~bc kz`}b

    Dgr 0% ~bca Dg r 0% ~bca

    t 8 \\\\\\\ \\\\\\\ t 8 \\\\\\\ \\\\\\\

    t \\\\\\\ \\\\\\\ t \\\\\\\ \\\\\\\

    t \\\\\\\ t \\\\\\\

    ^bc }lda~ "\\\\\\\% \\\\\\\$ ^bc }lda~ "\\\\\\\% \\\\\\\$x`~dxffcx ~bc cps`~dla x`~dxffcx ~bc cps`~dla

    ^bc }lda~x "\\\\\\\% \\\\\\\$ `an "\\\\\\\% \\\\\\\$ `zc jl~b }lda~xla ~bc kz`}b

    ^bc kz`}b zc}zcxca~x ~bc gsah~dlat 8r :

    ^bc cps`~dla dx ` edac`z gsah~dla jch`sxc d~ dx da ~bc glzitirj! D~x kz`}bisx~ jc ` edac! Xdahc ~bc kz`}b dx ` edac% d~ dx ` edac`z gsah~dla!

    Dgr = `ant :% Dgr : `ant >%dx ~bc cps`~dlat 8r : ~zsc< dx ~bc cps`~dlat 8r : ~zsc 8 : :

    : = : > 7 :

    : : > >

    Jl~b }lda~x la ~bc kz`}b x`~dxgt ~bc cps`~dla! Gdan ~{l }lda~x ~b`~ x`~dxgt ~bccps`~dlat 8r : `an xcc {bc~bcz ~bct `zc }lda~x la ~bc kz`}b!

    Dgr 0% ~bca Dgr 0% ~bca

    t 8 0 : t 8 0 :

    t 8 : t 8 :

    t 0 t 3

    ^bc }lda~ "0% 0$ ^bc }lda~ "0% 3$x`~dxffcx ~bc cps`~dla! x`~dxffcx ~bc cps`~dla!

    ^bc }lda~x "0% 0$ `an "0% 3$ `zc jl~b }lda~x la ~bc kz`}b! ^bc kz`}bzc}zcxca~x ~bc gsah~dlat 8r :!

    Ljoch~dwc 0

    :>

  • 7/30/2019 TAKS Math Study Guide

    26/303

    Bl{ H`a Tls Nz`{ Hlahesxdlax gzli ` Gsah~dla`e Zce`~dlaxbd}=r 0= @ zcgsan {lsenal~ jc `nncn ~l ~bc ~l~`e hlx~6 d~ {lsen jc xsj~z`h~cn$

    J ^bc ~l~ e asijcz lg blszx ~z`wcecn%t% `x ` gsah~dla lg ~bc`wcz`kc x}ccn da idecx }cz blsz%r% {bczc >= zc}zcxca~x ~bcasijcz lg idecx ~z`wcecn `an 0= zc}zcxca~x ~bc ndx~`ahc daidecx gzli ~bc x~`z~dak }lda~

    "^bdx h`aal~ jc ilncecn jtt >=r 0= ^dic w`zdcx

    dawczxcet {d~b x}ccn% `x xbl{a da ~bc cps`~dla ~ $

    H ^bc ~l~`e hlx~ lg oldadak ` ff~acxx hesj%t% `x ` gsah~dla lg ~bcasijcz lg ila~bx `~~cancn%r% {bczc >= zc}zcxca~x ~bc hlx~lg c`hb ila~b `an 0= zc}zcxca~x ~bc dad~d`e icijczxbd} gcc

    "^bdx h`a jc ilncecn jtt >=r 0=$

    N ^bc `zc` lg ` ~z`}cldn%t% `x ` gsah~dla lg lac lg ~bc j`xcx%{bczc ~bc l~bcz j`xc dx >= `an ~bc bcdkb~ lg ~bc ~z`}cldndx 0=

    "^bdx h`aal~ jc ilncecn jtt >=r 0= ^bc glzise` glz

    ~bc `zc` lg ` ~z`}cldn dx @ "j0

    j:$b$0

    :

    n

    z

  • 7/30/2019 TAKS Math Study Guide

    30/303

    Ljoch~dwc 0

    :4

    ^zt D~X`i {lzfx `~ `a cech~zladhx x~lzc ^bc kz`}b xbl{x ~bc hliidxxdlabc c`zax la ` x`ec `x ` gsah~dla lg ~bc hlx~ lg ~bc d~ci bc xceex

    [b`~ {dee X`ix `}}zlrdi`~c hliidxxdla jc dg bc xceex `a d~ci ~b`~hlx~x .7;3=

    2

    0:

    07

    0= := 8= >= 3= 7= ;= 2= 4=

    Hliidxxdla

    "nlee`zx$

    Hlx~ lg D~ci "nlee`zx$

    t

    r

    =

    >

    2

    0:

    07

    0= := 8= >= 3= 7= ;= 2= 4=

    Hliidxxdla"nlee`zx$

    Hlx~ lg D~ci "nlee`zx$

    t

    r

    Al{ }z`h~dhc {b`~ tlswc ec`zacn!

  • 7/30/2019 TAKS Math Study Guide

    31/303

    Ljoch~dwc 0

    8=

    Pscx~dla 0

    ^bc j`xfc~j`ee ~c`i dx lznczdak ^)xbdz~x ~l xceeglz ` gsan)z`dxcz! ^bc ~c`i }`dn .:;3 glz ~bcxbdz~x `an {dee xcee ~bci glz .0: c`hb! ^bczce`~dlaxbd} jc~{cca ~bc asijcz lg xbdz~x xlen`an ~bc ~c`ix }zlff~ gzli ~bc x`ec lg ~bc xbdz~xh`a jc zc}zcxca~cn jt ~bc gsah~dlag"a$ 0:a :;3% da {bdhb a zc}zcxca~x ~bcasijcz lg xbdz~x xlen! [b`~ dx ~bc nc}canca~ps`a~d~t da ~bdx gsah~dla`e zce`~dlaxbd} c`hb% {bdhb dacps`ed~t ilncex a% ~bcasijcz lg NWNx Ed`ak dx `jec ~l zca~a 0: 83

    J >a 0: 83

    H >8a

    3 0:

    N 83 >a 0:

    Pscx~dla 8

    [bdhb lg ~bc gleel{dak ~`jecx zc}zcxca~xt `x `gsah~dla lgr :

    0 8: >

    3 3

    r t

    : 4

    : 7

    : 8

    : =

    @

    J

    H

    N

    @ax{cz Fct? }`kc :2=@ax{cz Fct? }`kc :2=

    @ax{cz Fct? }`kc :2=

  • 7/30/2019 TAKS Math Study Guide

    32/303

    Ljoch~dwc 0

    80

    Pscx~dla >

    ^bc ~l~`e hlx~ lg `a d~ci `~ ` x~lzc dx ~bc }zdhc lg~bc d~ci }esx 7!3# x`ecx ~`r! Dgh% ~bc ~l~`e hlx~ lg~bc d~ci% dx ` gsah~dla lgr% ~bc }zdhc lg ~bc d~ci%{bdhb gsah~dla ilncex ~bdx xd~s`~dla dx ` ps`nz`~dh gsah~dla6 ~bczcglzc% d~x

    }`zca~ gsah~dla dx ~bc ps`nz`~dh }`zca~ gsah~dla%t r:

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    37

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t9

    r:

    ]`zca~gsah~dla

    t9r

    :&>

    :3

    Ncffad~dlaCr`i}ec

    v"=% 0$% ":% 7$% "8% 3$y

    Nli`da^bc xc~ lg `ee ~bcr)hllznda`~cx da~bc gsah~dlax lznczcn }`dzx

    v=% :% 8y

    Z`akc^bc xc~ lg `ee ~bct)hllznda`~cx da~bc gsah~dlax lznczcn }`dzx

    v0% 3% 7y

    Dnca~dgt ~bc nli`da `an z`akc lg ~bc gsah~dla jcel{

    v"8% >$% "0% :$% ":% >$% ">% 7$y

    ^bc nli`da dx ~bc xc~ lgr)hllznda`~cx da ~bc lznczcn }`dzx?v"8% >$% "0% :$% ":% >$% ">% 7$y ^bc nli`da dx v8% 0% :% >y

    ^bc z`akc dx ~bc xc~ lgt)hllznda`~cx da ~bc lznczcn }`dzx?v"8% >$% "0% :$% ":% >$% ">% 7$y ^bc z`akc dx v7% >% :% >y

    Xcc Ljoch~dwc 0%}`kc 0=% glz ilzcdaglzi`~dla `jls~

    gsah~dlax!

  • 7/30/2019 TAKS Math Study Guide

    41/303

    Ljoch~dwc :

    >=

    ^zt D~[b`~ `zc ~bc nli`da `an z`akc lg ~bc gsah~dla jcel{

    3

    0 : 8 > 3r

  • 7/30/2019 TAKS Math Study Guide

    44/303

    Ljoch~dwc :

    >8

    @ hlax~zsh~dla hli}`at sxcx x~cce e`nncz jc`ix glz xh`gglendak^bc kz`}b jcel{ zc}zcxca~x ~bc zce`~dlaxbd} jc~{ccar% ~bc {cdkb~lg ~bc jc`ix da }lsanx% `ant% ~bcdz ecak~b da gcc~

    [b`~ dx ` zc`xla`jec nli`da `an z`akc glz ~bdx gsah~dla=

    >3

    3=

    : > 7

    [cdkb~ "}lsanx$

    2 0= 0: 0> 07 02 := ::

    33

    7=

    73

    Ecak~b"gcc~$

    t

    r

  • 7/30/2019 TAKS Math Study Guide

    45/303

    Ljoch~dwc :

    >>

    ^zt D~@ zch~`akse`z hlsz~t`zn dx }e`aacn `x }`z~ lg ~bc ncxdka glz ` ac{jsdendak ^bc hlsz~t`zn xblsen jc 8 gcc~ elakcz ~b`a d~ dx {dnc ^bchlsz~t`zn isx~ jc `~ ec`x~ 0: gcc~ {dnc js~ al ilzc ~b`a :3 gcc~

    {dnc ^bc gsah~dlag"r$ r:

    8rncxhzdjcx ~bc `zc` lg ~bchlsz~t`zn da ~czix lg d~x {dn~b da gcc~% r [b`~ dx ` zc`xla`jec z`akcglz ~bdx gsah~dla> 87

    g"r$ 02=

    ^bc i`rdisi `zc` lg ~bc hlsz~t`zn {dee lhhsz {bcar :3!

    g"r$ r: 8r

    g"r$ ":3$: 8":3$

    g"r$ 7:3 ;3

    g"r$ ;==

    @ zc`xla`jec z`akc glz ~bdx gsah~dla dx 02= g"r$ ;==!

  • 7/30/2019 TAKS Math Study Guide

    46/303

    Ljoch~dwc :

    >3

    Bl{ H`a Tls Da~cz}zc~ ` ]zljeci Xd~s`~dla gzli ` Kz`}b{ 7= :{ 7

    7{ 77

    ^bc }czdic~cz lg ~bc acdkbjlzx }lle h`a jc zc}zcxca~cn jt ~bccr}zcxxdla 7{ 77

  • 7/30/2019 TAKS Math Study Guide

    53/303

    Ljoch~dwc :

    3:

    Bl{ Nl Tls Zc}zcxca~ ]`~~czax da N`~` @ekcjz`dh`eet 8

    8 4 2

    > 07 03

  • 7/30/2019 TAKS Math Study Guide

    54/303

    Ljoch~dwc :

    38

    Wczdgt ~b`~ c`hb lg ~bc n`~` }lda~x "lznczcn }`dzx$ x`~dxffcx ~bccps`~dlat r: 0

    Zc}e`hct {d~bg"r$ ^bc zsec cr}zcxxcn da gsah~dla al~`~dladxg"r$ r: 0

    ^bc zsecg"r$ r: 0 zc}zcxca~x ~bdx zce`~dlaxbd}

    r g"r$ r: 0 t Tcx,Al

    g"0$ "0$: 00 g"0$ 0 0 = Tcx

    g"0$ =

    g":$ ":$: 0: g":$ > 0 8 Tcx

    g":$ 8

    g"8$ "8$: 08 g"8$ 4 0 2 Tcx

    g"8$ 2

    g">$ ">$:

    0> g">$ 07 0 03 Tcxg">$ 03

    Nl tls xcc

    ~b`~ ! ! !

  • 7/30/2019 TAKS Math Study Guide

    55/303

    Ljoch~dwc :

    3>

    Ellf `~ ~bc }`~~cza lg asijczx jcel{

    8% ;% 08% :0%

    Nlcx ~bc cr}zcxxdla a: a 0 zc}zcxca~ ~bc a~b asijcz da ~bdx}`~~cza : 0 ;

    88: 8 0

    08 Tcx4 8 0 08

    >>: > 0

    :0 Tcx07 > 0 :0

  • 7/30/2019 TAKS Math Study Guide

    56/303

    Ljoch~dwc :

    33

    X~snca~x da ` i`~b he`xx sxcn ` }`~~cza ~l hlax~zsh~ ` xczdcx lgdahzc`xdaket e`zkcz ps`nzde`~cz`ex% `an ~bca ~bct ic`xszcn ~bc}czdic~czx lg ~bc ps`nzde`~cz`ex ^bc }czdic~czx `zc kdwca da ~bc~`jec jcel{

    Ps`nzde`~cz`e

    Dg ~bc }`~~cza hla~dascx% {b`~ cr}zcxxdla h`a jc sxcn ~l zc}zcxca~~bc }czdic~cz lg ~bc a~b ps`nzde`~cz`e da ~bdx xczdcx ilzc ~b`a ~bc xps`zc lg d~x}lxd~dla asijcz da ~bc xczdcx ^bc }czdic~cz lg ~bc a~bps`nzde`~cz`e xblsen jc a: >

    Xcc {bc~bcz ~bdx cr}zcxxdla {lzfx glz ~bc fal{a w`escx

    Dg ~bc }`~~cza hla~dascx% ~bc }czdic~cz lg ~bc a~b ps`nzde`~cz`ehlsen jc zc}zcxca~cn jt ~bc cr}zcxxdla a: >

    ]lxd~dlaXps`zc lg

    ]czdic~cz"a$

    }lxd~dla"hi$

    "a:$

    0 0 3

    : > 2

    8 4 08

    > 07 :=

    ]lxd~dla 0 : 8 >

    ]czdic~cz "hi$ 3 2 08 :=

    ]lxd~dla a: >]czdic~cz

    Tcx,Al"hi$

    0 0: > 0 > 3 3 Tcx

    : :: > > > 2 2 Tcx

    8 8: > 4 > 08 08 Tcx

    > >: > 07 > := := Tcx

  • 7/30/2019 TAKS Math Study Guide

    57/303

    Ljoch~dwc :

    37

    Bl{ Nl Tls Xdi}edgt @ekcjz`dh Cr}zcxxdlax

    ecak~b : "{ 3$ : { 4

    Gdan ~bc `zc` lg ~bc }lx~cz jl`zn jt ise~d}etdak ~bc ecak~b lg~bc jl`zn jt ~bc {dn~b

    @

    "{

    4$"{

    >$@ "{$"{$ >"{$ 4"{$ "4$">$

    @ {: >{ 4{ 87

    @ {: 08{ 87

    ^bc cr}zcxxdla {: 08{ 87 zc}zcxca~x ~bc `zc` lg ~bc }lx~czdahesndak ~bc jlzncz

    : da!

    : da!

    : da!: da!

    { & 3

    {

    : da!

    Wl~c glz

    Z`ia! : da!

    Xcc Ljoch~dwc 3%}`kc 0:4% glz ilzcdaglzi`~dla `jls~~bc GLDE ic~bln!

  • 7/30/2019 TAKS Math Study Guide

    60/303

    Ljoch~dwc :

    34

    Bl{ Nl Tls Xlewc @ekcjz`dh Cps`~dlax :"r 0$ :8

    ^bc xles~dla ~l ~bc cps`~dla dxr ;

    r > :"r 0$ :8

    r > :r : :8

    8r

    :

    :8: :

    8r :0

    88r

    :80

    r ;

    Xlewc ~bc cps`~dla :"i 0$ 3"i :$ 7

    :"i 0$ 3"i :$ 7

    :i : 3i 0= 7

    :i : 3i >

    :i :i

    : 8i >

    > >

    7 8i

    87

    88i

    : i

    ^bc xles~dla ~l ~bc cps`~dla dx i :

    Da ~bc ~czi 7r% 7 dxh`eecn ~bc hlcgffhdca~lgr!

  • 7/30/2019 TAKS Math Study Guide

    61/303

    Ljoch~dwc :

    7=

    Bl{ i`at ideeded~czx lg {`~cz isx~ jc `nncn ~l ` jc`fczhla~`dadak :== ideeded~czx lg ` xles~dla ~b`~ dx ;3# c~b`ale ~l}zlnshc ` xles~dla ~b`~ dx 3=# c~b`ale

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    @ax{cz Fct? }`kc :2:@ax{cz Fct? }`kc :2:

    @ax{cz Fct? }`kc :2:

  • 7/30/2019 TAKS Math Study Guide

    65/303

    Ljoch~dwc :

    7>

    @

    J

    H

    N

    Pscx~dla 03

    @x ~bc `kc lg ` h`z dahzc`xcx% d~x w`esc nchzc`xcx! [bdhb xh`~~cz}el~ jcx~ zc}zcxca~x ~bdxzce`~dlaxbd}!:3 }cz }lsan%`an `eilanx hlx~ .3!3= }cz }lsan! Dgr zc}zcxca~x~bc asijcz lg }lsanx lg `eilanx A`aht jlskb~%{bdhb cr}zcxxdla zc}zcxca~x ~bc ~l~`e hlx~ lg ~bcas~x xbc }szhb`xcn2!;3

    H 4!;3r >2!;3

    N 4!;3r :0!:3

    Pscx~dla 02

    @ }czxla`e ~z`dacz `~ ` elh`e kti hb`zkcx ~bcgleel{dak gccx glz ` lac)blsz ~z`dadak xcxxdla glz0 ~l > }cl}ec!

    [bdhb cps`~dla jcx~ zc}zcxca~x ~bc zce`~dlaxbd}jc~{cca a% ~bc asijcz lg }cl}ec% `an h% ~bc hlx~a 07

    N h 3a 0>

    Pscx~dla 04

    [bdhb `ekcjz`dh cr}zcxxdla jcx~ zc}zcxca~x ~bczce`~dlaxbd} jc~{cca ~bc ~czix da ~bc gleel{dakxcpscahc `an ~bcdz }lxd~dla% a% da ~bc xcpscahc2%

    @ a :

    J :a: :

    H :a :

    N a: :

    @ax{cz Fct? }`kc :28@ax{cz Fct? }`kc :2:

    @ax{cz Fct? }`kc :2:

    Asijcz lg ]cl}ec 0 : 8 >

    Hlx~ ".$ := :> :2 8:

    Tc`z@wcz`kc^sd~dla

    042= .823

    0423 .30=

    044= .7=3

    0443 .;8=

    :=== .2:3

    :==3 .43=

    @ax{cz Fct? }`kc :28

  • 7/30/2019 TAKS Math Study Guide

    67/303

    Ljoch~dwc :

    77

    Pscx~dla :=

    J`zj`z` dx 8 ~dicx `x len `x I`zf! Dg ~bc xsi lg~bcdz `kcx dx 3:% {bdhb cps`~dla h`a jc sxcn ~lffan ~bcdz `kcxr 3:

    N 8r > 3:

    Pscx~dla :0

    [bdhb lg ~bc gleel{dak cr}zcxxdlax dx cpsdw`eca~~l >"a 8$"a :$a: >a :>

    J >a: >a :>

    H >a: :>

    N >a: >a :>

    @ax{cz Fct? }`kc :28 @ax{cz Fct? }`kc :28

  • 7/30/2019 TAKS Math Study Guide

    68/303

    7;

    ^bc x~snca~ {dee ncilax~z`~c `a sanczx~`andak lg edac`z gsah~dlax!

    Ljoch~dwc 8

    Glz ~bdx ljoch~dwc tls xblsen jc `jec ~l

    zc}zcxca~ edac`z gsah~dlax da ndggczca~ {`tx `an ~z`axe`~c `ilak~bcdz w`zdlsx zc}zcxca~`~dlax6 `an

    da~cz}zc~ ~bc ic`adak lg xel}c `an da~czhc}~x lg ` edac`z gsah~dla`an ncxhzdjc ~bc cggch~x lg hb`akcx da xel}c `ant)da~czhc}~ dazc`e){lzen `an i`~bci`~dh`e xd~s`~dlax

    [b`~ Dx ` Edac`z Gsah~dla

    03

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0=

    00

    0:

    080>

    03

    0 0:8>37;240=000:080>03 : 8 > 3 7 ; 2 4 0= 00 0: 08 030>

    r t

    2 08

    = 8

    0 3

    8 4

    Xcc Ljoch~dwc 0%

    }`kc 0=% glz ilzcdaglzi`~dla `jls~gsah~dlax!

  • 7/30/2019 TAKS Math Study Guide

    69/303

    Ljoch~dwc 8

    72

    ^zt D~^bc ~`jec jcel{ ncxhzdjcx ` edac`z zce`~dlaxbd}

    Nlcx ~bc cps`~dlar :t > zc}zcxca~ ~bc x`ic edac`z gsah~dla zc}zcxca~x ~bc x`ic edac`zgsah~dla `x ~bc ~`jec% xsjx~d~s~c ~bc lznczcn }`dzx gzli ~bc ~`jec da~l~bc cps`~dla

    ^bc ~`jec `an ~bc cps`~dla ncxhzdjc ~bc x`ic gsah~dla

    r t

    : 8

    > =

    2 :

    r t Nlcxr :t >< Tcx,Al

    \\\\\\\\ :" \\\\\\\\ $ >

    : 8 \\\\\\\\ \\\\\\\\ >

    \\\\\\\\ >

    \\\\\\\\ :" \\\\\\\\ $ >

    > = \\\\\\\\ \\\\\\\\ >

    \\\\\\\\ >

    \\\\\\\\ :" \\\\\\\\ $ >

    2 : \\\\\\\\ \\\\\\\\ >

    \\\\\\\\ >

    r tNlcx

    Tcx,Alr :t >> = > = > Tcx

    > >

    2 :":$ >2 : 2 > > Tcx

    > >

  • 7/30/2019 TAKS Math Study Guide

    70/303

    Ljoch~dwc 8

    74

    [b`~ Dx Xel}c

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    r 9 :

    Sancgdacn xel}c^bc edac dx wcz~dh`e!

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    t 9 :

    _czl xel}c^bc edac dx blzdla~`e!

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    t9r

    Ack`~dwc xel}c^bc edac g`eex gzli ecg~ ~l zdkb~!

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    t9r

    ]lxd~dwc xel}c^bc edac zdxcx gzli ecg~ ~l zdkb~!

    Nl tls xcc

    ~b`~ ! ! !

  • 7/30/2019 TAKS Math Study Guide

    71/303

    Ljoch~dwc 8

    ;=

    Da ~bc kz`}b jcel{ tls h`a ffan ~bc xel}c jt hlsa~dak ~bc hb`akcdat)w`escx `an ~bc hb`akc dar)w`escx jc~{cca `at ~{l }lda~x

    ^bct)w`esc hb`akcx : sad~x glz cwczt 8 sad~x ~bc r)w`esc hb`akcx@x tls kl gzli ecg~ ~l zdkb~% ~bc edac }lda~x nl{a% xl ~bc xel}c dxack`~dwc ^bc z`~c lg hb`akc dx kdwca jt ~bc z`~dl jcel{

    zzdsxac

    :8

    ^bc xel}c lg ~bc kz`}b dx :8

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    8 sad~x

    : sad~x

    [b`~ dx ~bc xel}c lg ~bc edac }`xxdak ~bzlskb ~bc }lda~x "2% 8$ `an"7% :$

    ^zt D~Gdan ~bc xel}c `ant)da~czhc}~ lg ~bc kz`}b lg ~bc gsah~dla7r :t 0:

    ^l nc~czidac ~bc xel}c `ant)da~czhc}~% ~z`axglzi ~bc cps`~dla7r :t 0: da~l xel}c)da~czhc}~ glzi%t ir j

    7r :t 0:

    \\\\\\\\ \\\\\\\\

    :t \\\\\\\\ 0:

    :t

    7r

    0:

    t \\\\\\\\ r \\\\\\\\

    Zc`n ~bc w`escx lg \\\\\\\\ `an \\\\\\\\ gzli ~bc zcwdxcn cps`~dla

    Glz ~bdx gsah~dla% i \\\\\\\\ `an j \\\\\\\\

    ^bc xel}c lg ~bc kz`}b lg ~bc gsah~dla dx \\\\\\\\

    ^bct)hllznda`~c lg ~bct)da~czhc}~ lg ~bc kz`}b lg ~bc gsah~dla

    dx \\\\\\\\

    7r :t 0:

    7r 7r

    :t 7r 0:

    ::t

    :7r

    0::

    t 8r 7

    Zc`n ~bc w`escx lgi `anj gzli ~bc zcwdxcn cps`~dla! Glz ~bdx gsah~dla%i 8 `anj 7! ^bc xel}c lg ~bc kz`}b lg ~bc gsah~dla dx 8! ^bct)hllznda`~c lg ~bct)da~czhc}~ lg ~bc kz`}b lg ~bc gsah~dla dx 7!

  • 7/30/2019 TAKS Math Study Guide

    76/303

    Ljoch~dwc 8

    ;3

    Gsah~dla 0 Gsah~dla : Cggch~

    Xdahc : 08% ~bc kz`}b lg

    gsah~dla : dx x~cc}cz ~b`a ~bc kz`}b

    lg gsah~dla 0!

    Xdahc 0 8% ~bc kz`}b lggsah~dla : dx ecxx x~cc} ~b`a ~bc

    kz`}b lg gsah~dla 0!

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t98r:

    t9r:

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t9 r0

    8

    t9:r

    [b`~ @zc ~bc Cggch~x la ~bc Kz`}b lg ` Edac`z Gsah~dla Dg ~bc W`escxlgi`an j@zc Hb`akcn da ~bc Cps`~dla t9 ir& j

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t98r

    &3

    t9

    r&3

    Nl tls xcc~b`~ ! ! !

  • 7/30/2019 TAKS Math Study Guide

    78/303

    Ljoch~dwc 8

    ;;

    Hb`akc dat)Da~czhc}~% j

    Gsah~dla 0 Gsah~dla : Cggch~

    Gsah~dla : hzlxxcx ~bct)`rdx `~ ` }lda~7 sad~x bdkbcz ~b`a gsah~dla 0 jch`sxc3 "0$ 7!

    Gsah~dla : hzlxxcx ~bct)`rdx `~ ` }lda~8 sad~x el{cz ~b`a gsah~dla 0 jch`sxc0 > 8!

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 r & >0:

    t 9 r & 00:

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 :r 0

    t 9 :r & 3

    t :r 0 t :r 3

    t 0:r > t

    0:r 0

  • 7/30/2019 TAKS Math Study Guide

    79/303

    Ljoch~dwc 8

    ;2

    Dg ~bct)da~czhc}~ lg ~bc gsah~dlat 8:r > {czc nchzc`xcn jt 8%

    {b`~ {lsen jc ~bc cps`~dla lg ~bc ac{ gsah~dla

    Dg ~bct)da~czhc}~ lg ~bc gsah~dla {czc nchzc`xcn jt 8% d~ {lsenjc > 8 0 ^bc ac{ w`esc glz j {lsen jc 0

    ^bc cps`~dla lg ~bc ac{ gsah~dla {lsen jc t 8:r 0

    ^bc gsah~dlat 3r : {`x hb`akcn ~lt 3r : Bl{ {lsen~bc kz`}b lg ~bc ac{ gsah~dla hli}`zc {d~b ~bc kz`}b lg ~bclzdkda`e gsah~dla% ~bc kz`}b lgt 3r : dx > sad~x jcel{ ~bckz`}b lgt 3r :

    t

    r

    3

    >

    7

    ;

    24

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 3r & :

    t 9 3r :

  • 7/30/2019 TAKS Math Study Guide

    80/303

    Ljoch~dwc 8

    ;4

    Xel}cx lg edacx h`a ~cee tls {bc~bcz ~bc edacx `zc }`z`eece lz }cz}candhse`z

    Dg ~{l edacx `zc }`z`eece% ~bca ~bct b`wc ~bc x`ic xel}c% `an ~bcdzcps`~dlax b`wc ~bc x`ic w`esc glz i

    Ellf `~ ~bc kz`}bx lg ~bcxc ~{l cps`~dlax?t :r > `ant :r 8

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 :r >t 9 :r & 8

    ]`z`eece edacx

    ^zt D~Dg ~bc xel}c lg ~bc gsah~dlat =3r > dx dahzc`xcn jt 8% bl{ {dee~bc kz`}b lg ~bc ac{ gsah~dla hli}`zc {d~b ~bc kz`}b lg ~bclzdkda`e gsah~dla! Dg ~bc xel}c dx dahzc`xcn jt 8% ~bc ac{ xel}c jchlicx =!3 8 8!3! ^bcac{ edac {dee b`wc ~bc x`ic t)da~czhc}~ `x ~bc lzdkda`e edac!Xdahc u8!3u u=!3u% ~bc kz`}b lg ~bc ac{ edac {dee jc x~cc}cz ~b`a ~bc lzdkda`eedac!

  • 7/30/2019 TAKS Math Study Guide

    81/303

    Ljoch~dwc 8

    2=

    Dg ~{l edacx `zc }cz}candhse`z% ~bca ~bct b`wc ack`~dwc zchd}zlh`exel}cx% `an ~bcdz cps`~dlax b`wc ack`~dwc zchd}zlh`e w`escx glz i

    Ellf `~ ~bc kz`}bx lg ~bcxc ~{l cps`~dlax?t :8r : `an

    t 8:r :

    Bl{ Nl Tls [zd~c Edac`z Cps`~dlax

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    ]cz}candhse`z edacx

    t 9 r & :t 9 r & :

    8

    :

    :

    8

    [b`~ dx ~bc cps`~dla lg ~bc edac {d~b ` xel}c lg > `an ` t)da~czhc}~lg:% ~bca i >

    Dg ~bct)da~czhc}~ dx :% ~bca j :

    ^bc cps`~dla lg ~bc edac dx?

    t ir j

    t >r :

    ^{l asijczx `zc ack`~dwczchd}zlh`ex lg c`hb l~bczdg ~bcdz }zlnsh~ dx 0!

    Glz cr`i}ec% :8 `an

    :8

    `zc ack`~dwc zchd}zlh`ex

    xdahc :8

    :8

    770!

  • 7/30/2019 TAKS Math Study Guide

    82/303

    Ljoch~dwc 8

    20

    Kdwca ~bc xel}c `an ` }lda~ la ~bc kz`}b

    Xsjx~d~s~c ~bc kdwca w`escx "~bcr) `ant)hllznda`~cx lg ~bc kdwca}lda~ `an i% ~bc xel}c$ da~l ~bc xel}c)da~czhc}~ glzi lg ~bc

    cps`~dla%t ir j Xlewc ~bc cps`~dla glz j

    Xsjx~d~s~c ~bc w`escx glz i `an j da~l ~bc xel}c)da~czhc}~ glzi%t ir j

    ^zt D~[zd~c ~bc cps`~dla lg ~bc edac {d~b ` xel}c lg

    03 `an `t)hllznda`~c

    lg ~bct)da~czhc}~ lg 2

    Dg ~bc xel}c dx 03% ~bca i \\\\\\\\

    Dg ~bct)hllznda`~c lg ~bct)da~czhc}~ dx 2% ~bca j \\\\\\\\^bc cps`~dla lg ~bc gsah~dla dx?

    t ir j

    t \\\\\\\\r \\\\\\\\

    Dg ~bc xel}c dx 0

    3% ~bcai 0

    3! Dg ~bct)hllznda`~c lg ~bct)da~czhc}~ dx 2%~bcaj 2!

    ^bc cps`~dla lg ~bc gsah~dla dx?

    t irj

    t 03r 2

    [b`~ dx ~bc cps`~dla lg ~bc edac {d~b ` xel}c lg 08 ~b`~ }`xxcx

    ~bzlskb ~bc }lda~ "8% 7$ 3":$ j

    7 0= j 0> 0= j

    0= 0= 0= 0=

    > j > j

    Tls al{ fal{ ~bc w`escx lgi `an j6 xsjx~d~s~c ~bci da~l ~bcxel}c)da~czhc}~ glzi lg ~bc cps`~dla

    t ir j

    t 3r >

    ^bc cps`~dla lg ~bc edac }`xxdak ~bzlskb ~bc }lda~x ":% 7$ `an

    ":% 0>$ dxt 3r >

    Kdwca ~{l }lda~x la ~bc kz`}b

    Sxc ~bcr)hllznda`~cx `ant)hllznda`~cx lg ~bc ~{l kdwca }lda~x~l ffan ~bc xel}c% i% lg ~bc edac

    Xsjx~d~s~c ~bc hllznda`~cx lg lac lg ~bc fal{a }lda~x `an ~bcxel}c tls osx~ glsan da~l ~bc xel}c)da~czhc}~ glzi lg ~bccps`~dla%t ir j

    Xlewc ~bc cps`~dla glz j

    Xsjx~d~s~c i `an j da~l ~bc xel}c)da~czhc}~ glzi%t ir j!

  • 7/30/2019 TAKS Math Study Guide

    86/303

    Ljoch~dwc 8

    23

    ^zt D~[zd~c ~bc cps`~dla lg ~bc edac`z gsah~dla ~b`~ hla~`dax ~bc }lda~x":% 3$ `an "8% 03$

    Jckda jt ffandak ~bc \\\\\\\\\\\\\\\\ lg ~bc kz`}b^bc edac }`xxcx ~bzlskb ~bc }lda~x "\\\\\\\\% \\\\\\\\$ `an

    "\\\\\\\\% \\\\\\\\$

    i t

    r:

    :

    t

    r0

    0 \\\\\\\\

    ^bc xel}c lg ~bc edac dx \\\\\\\\

    Acr~% xsjx~d~s~c ~bc hllznda`~cx lg lac lg ~bc kdwca }lda~x%

    ":% \\\\\\\\$% `an ~bc xel}c tls osx~ glsan% \\\\\\\\% da~l ~bcxel}c)da~czhc}~ glzi lg ~bc cps`~dla lg ` edac ~l ffan ~bc w`esc lgj

    t ir j

    \\\\\\\\ \\\\\\\\ \\\\\\\\ j

    3 \\\\\\\\ j

    > >

    \\\\\\\\ j

    Gda`eet% xsjx~d~s~c ~bc w`escx lgi `an j da~l ~bc xel}c)da~czhc}~

    glzi

    t \\\\\\\\r \\\\\\\\

    Jckda jt ffandak ~bc xel}c lg ~bc kz`}b! ^bc edac }`xxcx ~bzlskb ~bc }lda~x":% 3$ `an "8% 03$!

    i t

    r:

    :

    t

    r0

    0

    038

    3:

    0=3 :

    ^bc xel}c lg ~bc edac dx :!

    Acr~% xsjx~d~s~c ~bc hllznda`~cx lg lac lg ~bc kdwca }lda~x% ":% 3$% `an ~bcxel}c tls osx~ glsan% :% da~l ~bc xel}c)da~czhc}~ glzi lg ~bc cps`~dla lg `edac ~l ffan ~bc w`esc lgj!

    t irj

    3 : : j

    3 > j

    > >

    4 j

    Gda`eet% xsjx~d~s~c ~bc w`escx lgi `anj da~l ~bc xel}c)da~czhc}~ glzi!

    t :r 4

  • 7/30/2019 TAKS Math Study Guide

    87/303

    Ljoch~dwc 8

    27

    Bl{ Nl Tls Gdan ~bc r)Da~czhc}~ `an t)Da~czhc}~ glz ~bc Kz`}b lg `aCps`~dla :r

    ^bct)da~czhc}~ lg ~bc kz`}b dx : ^bc kz`}b da~czxch~x ~bct)`rdx`~ "=% :$

    Gdan ~bcr) `ant)da~czhc}~x lg 8r 7t 0:

    ^l ffan ~bcr)da~czhc}~% xsjx~d~s~ct = da~l ~bc cps`~dla `anxlewc glzr

    8r 7t 0:

    8r 7"=$ 0:8r = 0:

    8r 0:

    r >

    ^bcr)da~czhc}~ dx > ^bc kz`}b da~czxch~x ~bc r)`rdx `~ ">% =$

    Gdan ~bct)da~czhc}~ jt{zd~dak ~bc cps`~dla daxel}c)da~czhc}~ glzi

    8r 7t 0:

    8r 8r

    7t 8r 0:

    7

    7

    t

    78r

    07:

    t 0:r:

    ^bct)da~czhc}~ dx : ^bckz`}b da~czxch~x ~bct)`rdx `~"=% :$

    Lz% ffan ~bct)da~czhc}~ jtxsjx~d~s~dakr = da~l ~bccps`~dla

    8r 7t 0:

    8"=$ 7t 0:

    = 7t 0:

    7t 0:

    t :

    ^bct)da~czhc}~ dx : ^bckz`}b da~czxch~x ~bct)`rdx `~"=% :$

    [zd~c ~bc cps`~dla da ~bcglzit ir j

    ;t 0> :r

    0> 0>

    ;t :r0>

    ;

    ;

    t

    :;r

    0;>

    t :;r :

    ^bczcglzc% j :

    Xsjx~d~s~cr = `an xlewcglzt

    ;t 0> :r

    ;t 0> :"=$

    ;t 0> =

    0> 0>

    ;t 0>

    ;

    ;

    t

    0;>

    t :

  • 7/30/2019 TAKS Math Study Guide

    89/303

    Ljoch~dwc 8

    22

    Zll~x lg Cps`~dlax _czlx lg Gsah~dlax r)Da~czhc}~x lg Kz`}bx

    Glz `at cps`~dla% xshb `xt r 2% ` zll~ dx ` w`esc lgr~b`~ i`fcx

    t = Glz `at gsah~dla% ` w`esc lgr~b`~ i`fcxg"r$ cps`e ~l czl dx h`eecn

    ` czl lg ` gsah~dla Jl~b ~bc zll~ lg `a cps`~dla `an ~bc czl lg ` gsah~dla

    h`a jc glsan jt elh`~dak ~bcr)hllznda`~c lg ~bcr)da~czhc}~ lg ~bc kz`}b lg

    ` gsah~dla% ~bc }lda~ `~ {bdhb ~bc kz`}b da~czhc}~x ~bc r)`rdx

    >8

    t r 2>8

    t r 2>8

    = r 2

    2 2

    2 r

    " $ "2$ " $ " $r

    7 r

    r 7

    >8

    8>

    8>

    >8

    >8

    ^bc zll~ lg

    t r 2

    dx 7!

    >8

    g"r$ r 2>8

    ^bc czl lg

    g"r$ r 2

    dx 7!

    >8

    ^bc hllznda`~cx lg ~bcr)da~czhc}~ lg

    t r 2

    `zc "7% =$!

    >8

    t

    r

    3

    >

    7

    ;

    2

    4

    0=

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0=

    0 0:8>37;240= : 8 > 3 7 ; 2 4 0=

    "7% =$

    = r 2

    2 2

    2 r

    " $ "2$ " $ " $r

    7 r

    r 7

    >8

    8>

    8>

    >8

    >8

  • 7/30/2019 TAKS Math Study Guide

    90/303

    Ljoch~dwc 8

    24

    Bl{ Nl Tls Da~cz}zc~ ~bc Ic`adak lg Xel}cx `an Da~czhc}~x=

    3=

    7=

    ;=

    0 : 8 > 3 7 ; 2 4

    t

    r

    ^dic "xchlanx$

    Wlesic

    "da!8$

    =

    0%===

    :%===

    8%===

    >%===

    3%===

    7%===

    ;%===

    2%===

    0=%===

    4%===

    : > 7 2 0= 0: 0> 07 02 := :: :>r

    ^dic "xchlanx$

    @e~d~snc

    "gcc~$

  • 7/30/2019 TAKS Math Study Guide

    92/303

    Ljoch~dwc 8

    40

    ^bc nlicx~dh }zlnsh~dla lg hzsnc lde da ~bc Sad~cn X~`~cx gzli0423 ~l :==: h`a jc `}}zlrdi`~cn jt ~bc gleel{dak kz`}b

    [b`~ nl ~bc xel}c `ant)da~czhc}~ lg ~bdx kz`}b ~cee tls `jls~ ~bc`wcz`kc SX }zlnsh~dla lg hzsnc lde nszdak ~bdx ~dic }czdln =0>

    ^bc xel}c lg=0> zc}zcxca~x ` nchedac da `wcz`kc lde }zlnsh~dlalg=0> ideedla j`zzcex }cz n`t }cz tc`z "lz `}}zlrdi`~cet0>=%=== j`zzcex }cz n`t gc{cz c`hb tc`z$

    =

    2

    4

    0=

    00

    : > 7 2 0= 0: 0> 07 02 :=

    t

    rTc`zx Xdahc 0423

    Nlicx~dh ]zlnsh~dla lgHzsnc Lde% 0423:==:

    Ideedlax lgJ`zzcex}cz N`t

  • 7/30/2019 TAKS Math Study Guide

    93/303

    Ljoch~dwc 8

    4:

    ^zt D~^bc kz`}b jcel{ ncxhzdjcx ~bc asijcz lg kz`ix lg }l~`xxdsi dlndnc~b`~ {dee ndxxlewc da 0== kz`ix lg {`~cz da ~czix lg ~bc ~ci}cz`~szclg ~bc {`~cz da nckzccx Hcexdsx

    [b`~ nlcx ~bc xel}c lg ~bdx kz`}b ~cee tls `jls~ ~bc xlesjded~t lg}l~`xxdsi dlndnc=

    7=

    2=

    0==

    0:=

    0>=

    07=

    02=

    :==

    ::=

    :>=

    0= := 8= >= 3=

    Xlesjded~t lg]l~`xxdsi Dlndnc

    7= ;= 2= 4= 0==

    t

    r

    ^ci}cz`~szc "H$

    Xlesjded~t

    "kz`ix,0== kz`ixlg {`~cz$

  • 7/30/2019 TAKS Math Study Guide

    94/303

    Ljoch~dwc 8

    48

    @ h`jec)~cecwdxdla hli}`at hb`zkcx ` .83 dad~d`e dax~`ee`~dla gcc `an~bca .>3 }cz ila~b glz h`jec xczwdhc ^bc kz`}b jcel{ ncxhzdjcx ~bc~l~`e hlx~ lg ~bdx h`jec xczwdhc da ~czix lg ~bc asijcz lg ila~bx d~ dxsxcn

    Dg ~bc hli}`at ndxhlsa~cn ~bc hb`zkc ~l .84 }cz ila~b% bl{ {lsen~bdx hb`akc `ggch~ ~bc xel}c `ant)da~czhc}~ lg ~bc kz`}b3 ~l .84 {deenchzc`xc ~bc xel}c lg ~bc kz`}b ^bdx hb`akc {lsen i`fc ~bc kz`}becxx x~cc}

    ^bc ndxhlsa~ nlcx al~ `ggch~ ~bc dax~`ee`~dla gcc ^bc t)da~czhc}~ lg

    ~bc kz`}b {lsen zci`da `~ .83

    =

    3=

    0==

    03=

    :==

    :3=

    8==

    83=

    >==

    >3=

    3==

    0 : 8 > 3 7 ; 2 4 0=

    t

    r

    Ila~b

    ^l~`eHlx~ ".$

    Bl{ Nl Tls ]zcndh~ ~bc Cggch~x lg Hb`akdak Xel}cx `an t)Da~czhc}~x da@}}edcn Xd~s`~dlax

    Bl{ Nl Tls Xlewc ]zljecix Dawlewdak Ndzch~ W`zd`~dla lz ]zl}lz~dla`eHb`akc37;24 : 8 > 3 7 ; 2 4

    r 3 8 = 0 >

    t > = 8: 0

    0:

    @ax{cz Fct? }`kc :28

    @ax{cz Fct? }`kc :28

    @ax{cz Fct? }`kc :2>

  • 7/30/2019 TAKS Math Study Guide

    98/303

    Ljoch~dwc 8

    4;

    Pscx~dla :3

    ^bc kz`}b jcel{ xbl{x ~bc zce`~dlaxbd} jc~{cca~bc asijcz lg ~lax lg cec}b`a~ glln zci`dadak da~bc llx glln x~lz`kc jda `an ~bc asijcz lgn`tx xdahc ~bc glln {`x e`x~ }szhb`xcn!

    Bl{ i`at ~lax lg cec}b`a~ glln {czc da ~bc jdadiicnd`~cet `g~cz ~bc e`x~ }szhb`xc lg glln {`x}e`hcn da ~bc jda= ~lax

    H 7= ~lax

    N 3= ~lax

    Pscx~dla :7

    ^bc osadlz he`xx {dee x}can .3== la nchlz`~dlaxglz ` xhblle }`z~t! ^bc osadlzx {dee }szhb`xcr h`xcx lg j`eellax `ant h`xcx lg x~zc`iczx!J`eellax hlx~ .:3 glz c`hb h`xc% `an x~zc`iczxhlx~ .0:3 glz c`hb h`xc! Dg ~bdx daglzi`~dla dxkz`}bcn `x ` edac`z cps`~dla% {b`~ dx ~bc

    r)da~czhc}~ lg ~bc edac37;24 : 8 > 3 7 ; 2 4

    =

    :=

    >=

    7=

    2=

    := >= 7= 2=

    t

    r

    Asijcz lg N`tx

    ^laxlg

    Glln

    @ax{cz Fct? }`kc :2>@ax{cz Fct? }`kc :2>

    @ax{cz Fct? }`kc :2>

    @ax{cz Fct? }`kc :2>

  • 7/30/2019 TAKS Math Study Guide

    99/303

    Ljoch~dwc 8

    42

    Pscx~dla :4

    [bdhb dx ~bc cps`~dla lg ~bc edac ~b`~ hla~`dax~bc }lda~x "0% 3$ `an ":% 0$r

    0:

    N t >r 4

    Pscx~dla 8=

    Olxb ffeex bdx x{diidak }lle `~ ~bc z`~c lg :===k`eelax }cz blsz! ^bczc {czc 8=== k`eelax lg{`~cz da ~bc }lle {bca bc x~`z~cn ffeedak d~! ^bc~l~`e asijcz lg k`eelax lg {`~cz da ~bc }lle `g~czOlxb ffeex d~ glzr blszx h`a jc zc}zcxca~cn jt ~bccps`~dlat :===r 8===! Dg Olxb `nnx `xchlan blxc% bc h`a ffee ~bc }lle ~{dhc `x g`x~!Bl{ {dee ~bdx `ggch~ ~bc kz`}b lg ~bc cps`~dla

    @ax{cz Fct? }`kc :2>

  • 7/30/2019 TAKS Math Study Guide

    100/303

    ^bc x~snca~ {dee glzise`~c `an sxc edac`z cps`~dlax `an dacps`ed~dcx!

    Ljoch~dwc >

    44

    Glz ~bdx ljoch~dwc tls xblsen jc `jec ~l

    glzise`~c edac`z cps`~dlax `an dacps`ed~dcx gzli }zljeci

    xd~s`~dlax% sxc ` w`zdc~t lg ic~blnx ~l xlewc ~bci% `an `a`etc~bc xles~dlax6 `an

    glzise`~c xtx~cix lg edac`z cps`~dlax gzli }zljeci xd~s`~dlax% sxc` w`zdc~t lg ic~blnx ~l xlewc ~bci% `an `a`etc ~bc xles~dlax

    Bl{ Nl Tls Xlewc ]zljecix Sxdak Edac`z Cps`~dlax lz Dacps`ed~dcxr 0:

    >

    >

    r

    0:

    >

    r 8

    ^bc dacps`ed~t xtijle zcwczxcn6 d~ {ca~ gzli ~l

    Sxc ~bc xles~dla lg ~bc cps`~dla lz dacps`ed~t ~l ffan ~bc `ax{cz~l ~bc pscx~dla `xfcn

    Xcc {bc~bcz tlsz `ax{cz dx zc`xla`jec

    Ndwdnc jl~b xdncx jt ` ack`~dwc asijcz

    @a `ekcjz`dh xca~cahc

    {zd~~ca sxdak ~bc xtijle5% % 1% lz dx h`eecn`a dacps`ed~t!

    Nl tls xcc~b`~ ! ! !

  • 7/30/2019 TAKS Math Study Guide

    101/303

    Ljoch~dwc >

    0==

    @ hli}`at ~b`~ i`asg`h~szcx k`icx x}canx .0:== }cz ila~b ~li`da~`da d~x lgffhcx `an }zlnsh~dla g`hded~dcx ^bc k`icx hlx~ .> c`hb~l }zlnshc ^bc k`icx `zc xlen glz .2 c`hb Bl{ i`at k`icx isx~~bc hli}`at i`fc `an xcee c`hb ila~b ~l i`fc ` }zlff~ lg `~ ec`x~.0=== }cz ila~brzc}zcxca~x ~bc ~l~`e hlx~ lg }zlnshdak

    rk`icx

    ^bc cr}zcxxdla 2rzc}zcxca~x ~bc `ilsa~ c`zacn gzli xceedakrk`icx

    ^bc hli}`atx ila~bet }zlff~ dx cps`e ~l ~bc `ilsa~ lg ilact~bc hli}`at c`zax da ` ila~b "d~x zcwcasc$ idasx jl~b ~bclwczbc`n hlx~ `an ~bc hlx~ lg }zlnshdak ~bc k`icx

    ]zlff~ zcwcasc lwczbc`n }zlnsh~dla hlx~x

    ]zlff~ 2r 0:== >r

    ^bc }zlff~ isx~ jc `~ ec`x~ .0=== ^bdx ic`ax ~bc }zlff~ isx~ jckzc`~cz ~b`a lz cps`e ~l .0=== Sxc `a dacps`ed~t ~l zc}zcxca~~bdx xd~s`~dla

    2r 0:== >r 0===

    Ocaadgcz {lzfx `~ ` {`zcblsxc Xbc dx }`hfdak ` jlr lg hllfjllfx`an X}`adxb jllfx ~l xbd} ~l ` jllfx~lzc ^bc jlrcx Ocaadgcz sxcxh`a blen al ilzc ~b`a 83 }lsanx lg jllfx c`hb ^bc hllfjllfx{cdkb : }lsanx c`hb% `an ~bc X}`adxb jllfx {cdkb 03 }lsanxc`hb [zd~c `a dacps`ed~t ~b`~ zc}zcxca~x ~bc asijcz lg hllfjllfx%

    r% `an X}`adxb jllfx%t% ~b`~ Ocaadgcz h`a }`hf da lac jlr

    Zc}zcxca~ ~bc ps`a~d~dcx dawlewcn {d~b w`zd`jecx lz cr}zcxxdlax^bc asijcz lg hllfjllfx dx zc}zcxca~cn jtr ^bc hllfjllfx{cdkb : }lsanx c`hb ^bc cr}zcxxdla :rzc}zcxca~x ~bc ~l~`e{cdkb~ lg ~bc hllfjllfx

    ^bc asijcz lg X}`adxb jllfx dx zc}zcxca~cn jt t ^bc X}`adxbjllfx {cdkb 03 }lsanx c`hb ^bc cr}zcxxdla 03t zc}zcxca~x~bc ~l~`e {cdkb~ lg ~bc X}`adxb jllfx

    [zd~c `a dacps`ed~t xbl{dak ~b`~ ~bc ~l~`e {cdkb~ h`aal~ jcilzc ~b`a 83 }lsanx

    :r 03t 83

    ^bc dacps`ed~t :r 03t 83 h`a jc sxcn ~l ffan ~bc asijcz lgc`hb ~t}c lg jllf Ocaadgcz h`a }`hf da lac jlr

  • 7/30/2019 TAKS Math Study Guide

    102/303

  • 7/30/2019 TAKS Math Study Guide

    103/303

    Ljoch~dwc >

    0=:

    Ciic~~x ac{ bljjt dx jccfcc}dak Bc fal{x ~b`~ da lzncz glz ~bcjccx ~l i`fc blact% ~bct isx~ b`wc `w`de`jec ~l ~bci ` xsgffhdca~asijcz lg l{czdak }e`a~x Ciic~~ dx cr}ch~dak ` xbd}ica~ lg2== jccx `an accnx ~l fal{ bl{ i`at l{czdak }e`a~x ~bct {deezcpsdzc

    ^bc jcc hli}`at dahesncn ~bc kz`}b jcel{ ~l bce} hsx~liczxnc~czidac ~bc asijcz lg l{czdak }e`a~x accncn Sxc ~bc kz`}b ~lnc~czidac ~bc asijcz lg }e`a~x Ciic~~ xblsen }szhb`xc xl ~b`~bc {dee b`wc calskb }e`a~x glz ~bc 2== jccx bc dx cr}ch~dak

    ^bcr)`rdx zc}zcxca~x ~bc asijcz lg jccx% `an ~bc t)`rdx zc}zcxca~x~bc asijcz lg }e`a~x accncn Gdan ~bc }lda~ la ~bcr)`rdx ~b`~

    zc}zcxca~x 2== jccx Kl s} ~l ~bc kz`}b lg ~bc edac Zc`n ~bchlzzcx}landakt)w`esc lg ~bdx }lda~ Dg tls h`a~ ffan `a cr`h~ w`escla ~bc kz`}b glzt% zlsan s} xl ~b`~ Ciic~~ dx xszc ~l b`wccalskb }e`a~x ^bct)hllznda`~c dx `}}zlrdi`~cet ;7 Ciic~~xblsen }szhb`xc `~ ec`x~ ;7 }e`a~x

    =

    2

    07

    :>

    8:

    >=

    >2

    37

    :== >== 7== 2==

    7>

    ;:

    2=

    22

    47

    Asijczlg

    Gel{czdak]e`a~x

    Asijcz lg Jccx

    r

    t

  • 7/30/2019 TAKS Math Study Guide

    104/303

  • 7/30/2019 TAKS Math Study Guide

    105/303

  • 7/30/2019 TAKS Math Study Guide

    106/303

    ^zt D~@ zch~`akec b`x ` }czdic~cz lg 3= dahbcx ^bc ecak~b lg ~bc zch~`akecdx xdr dahbcx ecxx ~b`a ~bzcc ~dicx ~bc {dn~b [zd~c ` xtx~ci lgcps`~dlax ~b`~ hlsen jc sxcn ~l ffan ~bc ecak~b `an ~bc {dn~b lg ~bc

    zch~`akec^bc }zljeci dawlewcx ~{l ps`a~d~dcx% ~bc \\\\\\\\\\\\\\\\\\\\ `an

    ~bc \\\\\\\\\\\\\\\\\\\\ lg ~bc zch~`akec

    Zc}zcxca~ ~bc ecak~b lg ~bc zch~`akec {d~b e `an ~bc {dn~b {d~b {

    [zd~c `a cps`~dla xbl{dak ~b`~ ~bc }czdic~cz lg ~bc zch~`akec dx

    \\\\\\\\\\ dahbcx

    \\\\\\\\\\ \\\\\\\\\\ \\\\\\\\\\ \\\\\\\\\\ \\\\\\\\\\

    [zd~c `a cps`~dla xbl{dak ~b`~ ~bc ecak~b lg ~bc zch~`akec dx xdr

    dahbcx ecxx ~b`a ~bzcc ~dicx d~x {dn~becak~b "8 {dn~b$ 7

    e \\\\\\\\\\ \\\\\\\\\\ \\\\\\\\\\

    ^bc xtx~ci lg cps`~dlax

    \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

    \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

    hlsen jc sxcn ~l ffan ~bc ecak~b `an ~bc {dn~b lg ~bc zch~`akec

    ^bc }zljeci dawlewcx ~{l ps`a~d~dcx% ~bc ecak~b `an ~bc {dn~b lg ~bczch~`akec!

    [zd~c `a cps`~dla xbl{dak ~b`~ ~bc }czdic~cz lg ~bc zch~`akec dx 3= dahbcx!

    : e : { 3=

    [zd~c `a cps`~dla xbl{dak ~b`~ ~bc ecak~b lg ~bc zch~`akec dx xdr dahbcx ecxx~b`a ~bzcc ~dicx d~x {dn~b!

    e 8 { 7

    ^bc xtx~ci lg cps`~dlax

    :e :{ 3=

    e 8{ 7

    hlsen jc sxcn ~l ffan ~bc ecak~b `an ~bc {dn~b lg ~bc zch~`akec!

    Ljoch~dwc >

    0=3

  • 7/30/2019 TAKS Math Study Guide

    107/303

  • 7/30/2019 TAKS Math Study Guide

    108/303

    Xlewc ~bdx xtx~ci lg cps`~dlax sxdak ~bc kz`}bdh`e ic~bln

    rt 0

    8rt 8

    ^bc ~{l cps`~dlax `zc kz`}bcn jcel{

    ^bc }lda~ {bczc ~bc ~{l edacx da~czxch~% ":% 8$% zc}zcxca~x ~bcxles~dla lg ~bc xtx~ci lg cps`~dlax D~x hllznda`~cx x`~dxgt jl~bcps`~dlax

    ^bc xles~dla ~l ~bc xtx~ci lg cps`~dlax dx ":% 8$

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    t9r&0

    t98r

    8

    r : rt 0 8rt 8`an ":$ 8 0 8":$ 8 8

    t 8 0 0 7 8 88 8

    Ljoch~dwc >

    0=;

  • 7/30/2019 TAKS Math Study Guide

    109/303

    Ljoch~dwc >

    0=2

    Xlewc ~bc gleel{dak xtx~ci lg cps`~dlax sxdak ~bc xsjx~d~s~dlaic~bln

    i a 83

    >i :a :=

    ^bdx xtx~ci lg cps`~dlax ecanx d~xceg ~l jcdak xlewcn sxdakxsjx~d~s~dla jch`sxc ~bc ffzx~ cps`~dla h`a jc xlewcn c`xdet glzi da ~czix lga

    ^l xlewc ~bc ffzx~ cps`~dla glz i% xsj~z`h~ a gzli jl~b xdncx

    i a 83 a a

    i 83 a

    Al{ xsjx~d~s~c "83 a$ glz i da ~bc xchlan cps`~dla^bc zcxse~ {dee jc ` edac`z cps`~dla {d~b osx~ lac w`zd`jec

    Xlewc ~b`~ cps`~dla

    >i :a :=

    >"83 a$ :a :=

    0>= >a :a :=

    0>= 7a :=

    0>= 0>=

    7a 0:=

    a :=

    Al{ ~b`~ tls fal{ ~bc w`esc lga% tls h`a sxc ~bdx w`esc ~l ffan~bc w`esc lgi jt xsjx~d~s~dak ~bc w`esc lga da~l cd~bcz lg ~bc ~{llzdkda`e cps`~dlax

    Da ~bdx xtx~ci% ~bc ffzx~ cps`~dla dx ~bc c`xdcz cps`~dla ~l sxc

    i a 83

    i := 83

    i 03

    ^bc xles~dla ~l ~bc xtx~ci lg cps`~dlax dx i 03 `an a :=% lz"03% :=$

    [bca tls sxc ~bc xsjx~d~s~dla ic~bln ~l xlewc ` xtx~ci lg cps`~dlax%xlewc lac cps`~dla glz lac lg ~bc ~{l w`zd`jecx ^bca xsjx~d~s~c da~l~bc xchlan cps`~dla

  • 7/30/2019 TAKS Math Study Guide

    110/303

    Xlewc ~bc x`ic xtx~ci lg cps`~dlax sxdak ~bc cedida`~dla ic~bln

    i a 83

    >i :a :=

    Da ~bc kdwca xtx~ci lg cps`~dlax% dg tls ise~d}et jl~b xdncx lg ~bcffzx~ cps`~dla jt :% tls kc~ ~bc gleel{dak cps`~dla?

    :i :a ;=

    ^bc w`zd`jec a b`x ` hlcgffhdca~ lg : da ~bc ac{ ffzx~ cps`~dla `an` hlcgffhdca~ lg: da ~bc lzdkda`e xchlan cps`~dla [bca tls `nn~blxc ~{l cps`~dlax% ~bc w`zd`jec a {dee ndx`}}c`z jch`sxc d~ {dee

    b`wc ` = hlcgffhdca~

    :i :a ;=

    >i :a :=

    7i 4=

    i 03

    ^l ffan a% xsjx~d~s~c 03 glz i da~l ~bc ffzx~ cps`~dla

    i a 83

    03 a 83

    a :=

    ^bc xles~dla ~l ~bc xtx~ci lg cps`~dlax dx i 03 `an a :=%lz "03% :=$ ^bdx dx ~bc x`ic xles~dla lj~`dacn jt sxdak ~bcxsjx~d~s~dla ic~bln

    Nl tls xcc~b`~ ! ! !

    ^bc cedida`~dla ic~bln dx `exl h`eecn ~bc `nnd~dla ic~bln jch`sxc tlscedida`~c lac lg ~bc w`zd`jecx jt `nndak Jcglzc tls `nn% tls i`t accn~l ise~d}et lac lz jl~b cps`~dlax xl ~b`~ lac lg ~bc w`zd`jecx b`xl}}lxd~c hlcgffhdca~x

    Ljoch~dwc >

    0=4

  • 7/30/2019 TAKS Math Study Guide

    111/303

  • 7/30/2019 TAKS Math Study Guide

    112/303

  • 7/30/2019 TAKS Math Study Guide

    113/303

  • 7/30/2019 TAKS Math Study Guide

    114/303

    Ljoch~dwc >

    008

    Pscx~dla 8>

    ^bc Xc`xbcee Bl~ce hb`zkcx ` ndggczca~ z`~c glzd~x e`zkc zllix ~b`a glz d~x xi`ee zllix! [bca:= e`zkc zllix `zc lhhs}dcn% ~bc ~l~`e `ilsa~ lgilact hleech~cn gzli ~bc e`zkc zllix dx .02==![bca 0= e`zkc zllix `an :0 xi`ee zllix `zclhhs}dcn% ~bc bl~ce hleech~x .:8;=! Bl{ ishbnlcx ~bc bl~ce hb`zkc glz c`hb xi`ee zlli$

    H "0>% 2$

    N "0=% 0>$

    Pscx~dla 8;

    @anzc` dx i`fdak hllfdcx ~b`~ hla~`da jl~b}c`as~ js~~cz hbd}x `an hblhle`~c hbd}x! Xbcsxcn ` ~l~`e lg 07 lsahcx lg hbd}x! ^bczc `zc 2hblhle`~c hbd}x da c`hb lsahc lg hblhle`~c hbd}x%`an 0: }c`as~ js~~cz hbd}x da c`hb lsahc lg

    }c`as~ js~~cz hbd}x! Dg @anzc` sxcn ` ~l~`e lg8== hbd}x da bcz hllfdcx% {bdhb xtx~ci lg edac`zcps`~dlax hlsen jc sxcn ~l ffan ~bc asijcz lglsahcx lg hblhle`~c hbd}x% h% `an ~bc asijcz lglsahcx lg }c`as~ js~~cz hbd}x%}% @anzc` sxcn

    00>

    @ax{cz Fct? }`kc :27

    @ax{cz Fct? }`kc :2;

    Pscx~dla 82

    Osedc dx }e`aadak ~l }s~ ` gcahc `zlsan ` zch~`akse`z k`znca! ^bc ecak~b lg ~bc k`znca dx 8 gcc~ ilzc~b`a 0!3 ~dicx d~x {dn~b! Dg Osedc sxcx ` ~l~`e lg 87 gcc~ lg gcahdak `zlsan ~bc cnkc lg ~bc k`znca% {b`~

    dx ~bc ecak~b lg ~bc k`znca

    7

    ;

    2

    4

    8

    :

    0=

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    :8

  • 7/30/2019 TAKS Math Study Guide

    116/303

    Ljoch~dwc >

    @ax{cz Fct? }`kc :2; @ax{cz Fct? }`kc :2;

    003

    Pscx~dla >=

    [bdhb dx ~bc hlzzch~ xles~dla lg ~bc xtx~ci lgedac`z cps`~dlaxt 7

    7r 0:t 02

    @ "=% 8:$

    J "0% 3$

    H ^bczc `zc `a daffad~c asijcz lg xles~dlax!

    N ^bczc dx al xles~dla!

    Pscx~dla >0

    ^bc xtx~ci lg edac`z cps`~dlax jcel{ b`x bl{i`at xles~dlax

    =0:8> 0 : 8 >

    t 9r:

    007

  • 7/30/2019 TAKS Math Study Guide

    118/303

    Ljoch~dwc 3

    00;

    ^bc kz`}b lg ~bc ps`nz`~dh gsah~dlat r: > dx xbl{a jcel{

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    t)da~czhc}~

    }lda~ {bczc ~bc kz`}b

    da~czxch~x ~bc t)`rdx

    `rdx lg xtiic~zt

    zll~x

    ~bc xles~dlax ~l ~bc

    ps`nz`~dh cps`~dla

    r: > 9 =!

    r)da~czhc}~"x$ }lda~"x$ {bczc ~bc

    kz`}b da~czxch~x

    ~bc r)`rdx

    wcz~cr

    idadisi lz i`rdisi w`esc

    ^bc hb`z`h~czdx~dhx lg ~bc kz`}b lgt r: > `zc xbl{a jcel{

    t

    r

    3

    >

    7

    ;

    2

    4

    0=

    8

    :

    0

    =

    0

    :

    8>

    3

    7

    ;

    2

    4

    0=

    0 0:8>37;240= : 8 > 3 7 ; 2 4 0=

    Wcz~cr

    @rdx lg Xtiic~zt

    t)da~czhc}~

    r)da~czhc}~x

    _czlx

    "=% >$

    r 9 =

    Zll~x r 9 : `anr 9 :

    "=% >$

    ":% =$ `an ":% =$

    r 9 : `anr 9 :

  • 7/30/2019 TAKS Math Study Guide

    119/303

  • 7/30/2019 TAKS Math Study Guide

    120/303

  • 7/30/2019 TAKS Math Study Guide

    121/303

    Ljoch~dwc 3

    0:=

    [bdhb lg ~bcxc ~bzcc gsah~dlax }zlnshcx ~bc {dncx~ kz`}br:

    Hli}`zc ~bc `jxles~c w`escx lg ~bc ~bzcc hlcgffhdca~x lgr:

    ^bc ~bzcc hlcgffhdca~x lgr: `zc 8% 3% `an 8>

    ^bc `jxles~c w`escx lg ~bc hlcgffhdca~x `zc 8% 3% `an 8>

    ^bc hlcgffhdca~ 3 b`x ~bc kzc`~cx~ `jxles~c w`esc

    ^bc gsah~dlat 3r: b`x ~bc a`zzl{cx~ kz`}b

    ^bc hlcgffhdca~

    8

    >

    b`x ~bc ec`x~ `jxles~c w`esc^bc gsah~dlat

    8>r: b`x ~bc {dncx~ kz`}b

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 3r:

    t 9 8r:

    t 9 r:8

    >

    Dg ~{l ps`nz`~dh gsah~dlax lg ~bc glzit `r: b`wc ndggczca~ hlcgffhdca~xlgr:% ~bca lac kz`}b {dee jc {dncz ~b`a ~bc l~bcz ^bc xi`eecz ~bc`jxles~c w`esc lg`% ~bc hlcgffhdca~ lgr:% ~bc {dncz ~bc kz`}b

    Xcc Ljoch~dwc 8%}`kc ;3% glz ilzcdaglzi`~dla `jls~`jxles~c w`esc!

  • 7/30/2019 TAKS Math Study Guide

    122/303

    Ljoch~dwc 3

    Dg ~bc hlcgffhdca~ lgr: da ~bc gsah~dlat 08r: dx hb`akcn ~l :% bl{

    nlcx ~bc ac{ kz`}b hli}`zc {d~b ~bc lzdkda`e kz`}b

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 :r:

    t 9 r:0

    8

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8>

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9 r:

    t 9 r:08

    0

    8

    0:0

  • 7/30/2019 TAKS Math Study Guide

    123/303

    ^zt D~Dg ~bc kz`}bx lgt r:% t

    0>r:% `ant

    0>r: `zc kz`}bcn la

    ~bc x`ic hllznda`~c kzdn% {bdhb ~{l kz`}bx {dee jc hlakzsca~r: `zc zcch~dlax lg c`hb l~bcz! ^bcdz kz`}bx {dee jc hlakzsca~!

    ^bc hlcgffhdca~x lgr: da ~bc ~bzcc cps`~dlax `zc 0% 0> % `an

    0>! ^bc `jxles~c

    w`escx lg ~bc hlcgffhdca~x lgr: `zc 0% 0> % `an

    0>! ^bc hlcgffhdca~ 0 b`x ~bc

    kzc`~cx~ `jxles~c w`esc! ^bczcglzc% ~bc kz`}b lgt r: {dee jc ~bc a`zzl{cx~!

    Ljoch~dwc 3

    0::

  • 7/30/2019 TAKS Math Study Guide

    124/303

  • 7/30/2019 TAKS Math Study Guide

    125/303

    Ljoch~dwc 3

    0:>

    Bl{ Nl Tls Nz`{ Hlahesxdlax gzli ~bc Kz`}bx lg Ps`nz`~dhGsah~dlax

    3

    7

    ;

    0 : 8 > 3

    t

    r

    Xceedak ]zdhc"nlee`zx$

    ^l~`e]zlgd~

    "bsanzcnxlg

    nlee`zx$

    Xdahc ` 0 da jl~b gsah~dlax% ~bc ~{l kz`}bx `zc hlakzsca~

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    37

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9r: 3

    t 9r: & 0

  • 7/30/2019 TAKS Math Study Guide

    126/303

    Ljoch~dwc 3

    0:3

    Glz {b`~ `ilsa~ xblsen ~bc hesj xcee ~bc b`ijszkczx da lzncz ~li`rdidc d~x }zlff~% =$ `an":% =$ ^bcr)hllznda`~cx lg ~bcxc }lda~x `zc > `an :

    ^bc czlx lg ~bc gsah~dlat r: :r 2 `zc > `an :

    ^bczcglzc% ~bc zll~x lg ~bc cps`~dlar: :r 2 = `zc >`an : ^bc xles~dla xc~ dx v>% :y

    Tls h`a wczdgt ~b`~ ~bcxc asijczx `zc xles~dlax jt zc}e`hdakr{d~b~bcdz w`esc da ~bc ps`nz`~dh cps`~dla

    Xsjx~d~s~cr > Xsjx~d~s~cr :

    r: :r 2 = r: :r 2 =

    ">$: :">$ 2 = ":$: :":$ 2 =

    07 2 2 = > > 2 =

    = = = =

    Jl~b asijczx% > `an :% i`fc ~bc cps`~dla ~zsc Jl~b `zc

    xles~dlax

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    24

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    0:;

  • 7/30/2019 TAKS Math Study Guide

    129/303

  • 7/30/2019 TAKS Math Study Guide

    130/303

    Ljoch~dwc 3

    Bl{ H`a Tls Xlewc ` Ps`nz`~dh Cps`~dla jt G`h~lzdak

    :

    r

    7

    r

    7

    r

    7

    r:

    \\\\\\\ `anr:

    \\\\\\\7 7

    ^bc `}}zlrdi`~c zll~x lg ~bc cps`~dla `zc \\\\\\\ `an \\\\\\\

    [zd~c ~bc ps`nz`~dh cps`~dla da x~`an`zn glzi!8r: :r 3 =

    Da ~bc cps`~dla `jlwc%

    ` 8 j : h 3

    r

    r":$ ":$: > 8 3

    : 8

    j j: >`h

    :`

    j j: > h

    :`

    Ljoch~dwc 3

    088

  • 7/30/2019 TAKS Math Study Guide

    135/303

    @ee w`zd`jecx b`wc `acr}laca~! [bca `acr}laca~ dx al~ kdwca% d~dx sanczx~lln ~l jc 0!

    r9r0

    Ljoch~dwc 3

    08>

    r

    r

    r :

    72

    r :

    72

    0!7; `anr : 7

    2 0

    ^bc `}}zlrdi`~c zll~x lg ~bc cps`~dla `zc 0!7; `an 0!

    : 7>

    7

    : > 7=

    7

    Bl{ Nl Tls @}}et ~bc E`{x lg Cr}laca~x da ]zljeci)XlewdakXd~s`~dlax:$ r7

    "r r r r$ "r r$ r r rr r rr7

    [bca ndwdndak ~czix {d~b edfc j`xcx% xsj~z`h~ ~bc cr}laca~x

    rr

    `

    j r"`j$

    Cr`i}ec? rr

    2

    8 r"28$

    r3

    r r rrrrrrr r r r3

    Xlic~dicx ndwdndak w`zd`jecx {d~b cr}laca~x }zlnshcxack`~dwc cr}laca~x

    Cr`i}ec? rr

    8

    3 r"83$

    r:

    rrr

    rr

    rr r

    r0: r:

    @ ~czi {d~b ` ack`~dwc cr}laca~ dx cps`e ~l ~bc zchd}zlh`e lg~b`~ ~czi {d~b ` }lxd~dwc cr}laca~

    r` r0`

    Cr`i}ec? r3 r03

  • 7/30/2019 TAKS Math Study Guide

    136/303

    Ljoch~dwc 3

    [bca z`dxdak ` ~czi {d~b `a cr}laca~ ~l ` }l{cz% ise~d}et ~bccr}laca~x

    "r`$j r`j

    Cr`i}ec? "r:$; r:;

    r0>

    "r:

    $;

    "r r$ "r r$ "r r$ "r r$ "r r$ "r r$ "r r$"r:$; "r r r r r r r r r r r r r r$

    "r:$; r0>

    @at j`xc l~bcz ~b`a czl z`dxcn ~l ~bc czl }l{cz cps`ex lac

    r= 0

    Cr`i}ec? 2= 0

    Xdi}edgt ~bc cr}zcxxdla 7r>

    8r3

    7r> 8r3 "7 8$ "r> r3$

    02 r"> 3$

    02 r4

    02r4

    Xdi}edgt ~bc cr}zcxxdla ">`3j:$8 [zd~c tlsz `ax{cz sxdak laet}lxd~dwc cr}laca~x

    Lac {`t ~l xlewc ~bdx }zljeci dx~l ffzx~ hb`akc ack`~dwccr}laca~x ~l }lxd~dwccr}laca~x

    Xdahc `3 `03% d~ gleel{x

    ~b`~ >`3j: >`j3

    :

    ^bc cr}zcxxdla h`a jcxdi}edffcn `x gleel{x

    ">`3

    j:

    $8

    "

    >

    `

    j3

    :

    $

    8

    7`>0

    j3

    7

    @al~bcz {`t ~l xlewc ~bdx}zljeci dx ~l z`dxc ~bccr}zcxxdla ~l ` }l{cz `an ~bcahb`akc ack`~dwc cr}laca~x ~l}lxd~dwc cr}laca~x

    ">`3j:$8 ">8`3 8j:

    8$

    7>`03j7

    Xdahc `03 `003% ~bc cr}zcxxdla

    7>`03j7 dx {zd~~ca {d~b `ee

    }lxd~dwc cr}laca~x `x gleel{x

    7>`03j7

    7`>0

    j3

    7

    7> j7

    `03

    7> j7

    `03

    >8 j: 8

    `3 8

    083

  • 7/30/2019 TAKS Math Study Guide

    137/303

    Ljoch~dwc 3

    087

    Xdi}edgt ~bc gleel{dak cr}zcxxdla

    Gdzx~ xdi}edgt ~bc cr}zcxxdlax ~b`~ `zc z`dxcn ~l ` }l{cz

    Sxc ~bc cr}laca~ ise~d}edh`~dla zsec ~l hlijdac edfc w`zd`jecx {d~bcr}laca~x da ~bc asicz`~lz

    Ndwdnc edfc w`zd`jecx {d~b cr}laca~x

    3r

    >:tr:

    8

    t2

    24

    03>

    rr

    8

    : tt

    2

    :

    4

    2

    3>r"8 :$t"2 :$"4 2$

    3>rt7

    ^bc xdi}edffcn cr}zcxxdla dx 3>rt7

    3>r8t24

    r:t:2

    :; : r8 t7 : 4

    r:t:2:;r8t7 :t:4

    r:t:2

    :;r8t7:t:4

    r:t:2

    :;r8t:8

    :t:4

    r:t:>:

    "8$8"r$8"t:$8":t:4$

    "r$:"t$:">$:"8rt:$8":t:4$

    "rt>

    $:

    "8rt:

    $8

    ":t:4$

    "rt>

    $:

  • 7/30/2019 TAKS Math Study Guide

    138/303

    ^zt D~@ zch~`akse`z }zdxi b`x ecak~b :i0:a>% {dn~b 7i8}:% `an bcdkb~>ia3}8 Gdan ~bc wlesic lg ~bc }zdxi

    Xsjx~d~s~c ~bc kdwca cr}zcxxdlax glz ecak~b% {dn~b% `an bcdkb~ da~l~bc glzise` glz ~bc wlesic lg ` zch~`akse`z }zdxi% W Jb e{b%`an ~bca xdi}edgt ~bc cr}zcxxdla

    W ecak~b {dn~b bcdkb~

    W \\\\\\\\\\ \\\\\\\\\\ \\\\\\\\\\

    Xdi}edgt ~bc cr}zcxxdla

    W \\\\\\ \\\\\\ \\\\\\ i a }

    W \\\\\\ i a }

    W \\\\\\\\\\\\\\\\\

    W :i0:a> 7i8}: >ia3}8

    W : 7 > i0: 8 0 a> 3 }: 8

    W >2 i07 a4 }3

    W >2i07a4}3

    Al{ }z`h~dhc {b`~ tlswc ec`zacn!

    Ljoch~dwc 3

    08;

  • 7/30/2019 TAKS Math Study Guide

    139/303

    Ljoch~dwc 3

    082

    Pscx~dla >:

    [bdhb lg ~bc gleel{dak jcx~ ncxhzdjcx ~bc kz`}blg ~bc gsah~dla t `r: {bca ` 5 =8

    ^bc kz`}b lgt r: 8 `an d~x kz`}b ~z`axe`~cns} ; sad~x `zc xbl{a jcel{!

    [b`~ dx ~bc cps`~dla lg Kz`}b J

    J t r: ;

    H t r: >

    N t >r: 8

    Pscx~dla >>

    ^bc kz`}b lg {bdhb gsah~dla dx al~ hlakzsca~ ~l~bc kz`}b lgt :r: 03

    @ j`ee {`x }zloch~cn da~l ~bc `dz {d~b `a dad~d`es}{`zn wcelhd~t lg ;: gcc~ }cz xchlan! ^bcps`nz`~dh gsah~dla b ;:~ 07~: ncxhzdjcx~bc bcdkb~% b% lg ~bc j`ee ~ xchlanx `g~cz d~ {`x}zloch~cn da~l ~bc `dz!

    J`xcn la ~bc kz`}b% {bdhb lg ~bc gleel{dak dx~zsc xchlanx!

    H ^bc bcdkb~ :!3 xchlanx `g~cz ~bc j`ee {`x}zloch~cn {`x 7> gcc~!

    N ^bc bcdkb~ 8!3 xchlanx `g~cz ~bc j`ee {`x}zloch~cn {`x 37 gcc~!

    =

    0=

    :=

    8=

    >=

    3=

    7=

    ;=

    2=

    4=

    0 : 8 >

    b

    ~

    ^dic "xchlanx$

    Bcdkb~"gcc~$

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t 9r: 8

    J

    @ax{cz Fct? }`kc :2;

    @ax{cz Fct? }`kc :2;

    @ax{cz Fct? }`kc :2;

    @ax{cz Fct? }`kc :22

  • 7/30/2019 TAKS Math Study Guide

    140/303

    Pscx~dla >7

    @ j`fczt nc~czidacx ~bc gleel{dak zce`~dlaxbd}jc~{cca ~bc }zdhc lg d~x h`fcx `an d~x n`det}zlff~x!

    [bdhb dx ~bc jcx~ hlahesxdla ~b`~ h`a jc nz`{agzli ~bc kz`}b;

    [b`~ dx ~bc xles~dla xc~ glz ~bc cps`~dlar r: >::% >:y

    N v7 ;% 7 ;y

    Pscx~dla >2

    @ htedancz {d~b ` bcdkb~ lg 0!3 dahbcx b`x ` ~l~`exszg`hc `zc` lg > xps`zc dahbcx! [b`~ dx d~x`}}zlrdi`~c z`ndsx!= da!

    H =!23 da!

    N : da!

    Pscx~dla >4

    @ ~zd`akec b`x `a `zc` lg :2 xps`zc dahbcx! ^bcj`xc lg ~bc ~zd`akec dx 7 dahbcx ecxx ~b`a ~{dhc~bc bcdkb~! [b`~ dx ~bc ecak~b lg ~bc j`xc lg ~bc~zd`akec da!

    H ; da!

    N 2 da!

    =

    03=

    :==

    :3=

    8==

    0 : 8 > 3 7 ; 2 4

    t

    r

    Xceedak ]zdhc ".$

    ]zlgd~x".$

    Ljoch~dwc 3

    084

    @ax{cz Fct? }`kc :22

    @ax{cz Fct? }`kc :22

    @ax{cz Fct? }`kc :22

    @ax{cz Fct? }`kc :22

  • 7/30/2019 TAKS Math Study Guide

    141/303

    Pscx~dla 3=

    ^bc gsah~dlat r: 3r : dx kz`}bcn jcel{!

    Lac lg ~bc zll~x lg ~bc cps`~dlar: 3r : =edcx jc~{cca {bdhb }`dz lg da~ckczx

    H > `an 3

    N : `an 0

    Pscx~dla 30

    ^bc xszg`hc `zc` lg ` x}bczc h`a jc glsan sxdak~bc glzise` X >z:!

    [bdhb cr}zcxxdla zc}zcxca~x ~bc xszg`hc `zc` lg` x}bczc {d~b ` z`ndsx lg 3r>t8 sad~x$`:

    8j">$>

    `3j$`4

    3

    h

    j2

    8

    H `7

    :

    h

    j7

    8

    N >`4h

    :j7

    8

    Pscx~dla 38

    ^bc kz`}b lgg"r$ r: 8r 2 dx xbl{ajcel{!

    [bdhb lg ~bc gleel{dak x~`~cica~x `}}c`zx ~l jc~zsc

    7

    ;

    2

    4

    0=

    00

    0:

    08

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0=

    00

    0:

    08

    0 0:8>37;240=000:08 : 8 > 3 7 ; 2 4 0= 00 0: 08

    0

    :

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    @ax{cz Fct? }`kc :24

    @ax{cz Fct? }`kc :24 @ax{cz Fct? }`kc :24

    @ax{cz Fct? }`kc :24

    Ljoch~dwc 3

    0>=

  • 7/30/2019 TAKS Math Study Guide

    142/303

    ^bc x~snca~ {dee ncilax~z`~c `a sanczx~`andak lg kclic~zdh zce`~dlaxbd}x `an

    x}`~d`e zc`xladak!

    Ljoch~dwc 7

    Glz ~bdx ljoch~dwc tls xblsen jc `jec ~l

    sxc ` w`zdc~t lg zc}zcxca~`~dlax ~l ncxhzdjc kclic~zdhzce`~dlaxbd}x `an xlewc }zljecix6

    dnca~dgt% `a`etc% `an ncxhzdjc }`~~czax ~b`~ ciczkc gzli ~{l)`an ~bzcc)ndicaxdla`e kclic~zdh ffkszcx6 `an

    `}}et ~bc hlahc}~ lg hlakzscahc ~l osx~dgt }zl}cz~dcx lg ffkszcx`an xlewc }zljecix

    Bl{ Nl Tls Xlewc Kclic~zdh ]zljecix0

    [zd~c `a cr}zcxxdla ~b`~ zc}zcxca~x ~bc `zc` lg ~bc xb`ncn }lz~dlalg ~bc >)dahb xps`zc da ~bc nd`kz`i jcel{

    ^bc `zc` lg ~bc xb`ncn }lz~dla dx cps`e ~l ~bc `zc` lg ~bc xps`zcidasx ~bc `zc` lg ~bc ~zd`akec

    Gdan ~bc `zc` lg ~bc xps`zc

    @ x:

    @ >:

    @ 07

    r

    > dahbcx

    > dahbcx

  • 7/30/2019 TAKS Math Study Guide

    143/303

  • 7/30/2019 TAKS Math Study Guide

    144/303

    Da ~bc nd`kz`i jcel{% GZX dx xdide`z ~l GCN

    [zd~c `a cps`~dla ~b`~ hlsen jc sxcn ~l ffan ~bc ecak~b lgGX da~czix lgr

    ^bc ecak~bx lg hlzzcx}landak xdncx lg ~bc ~zd`akecx `zc

    }zl}lz~dla`e ^l bce} tls xcc {bdhb xdncx lg ~bc ~zd`akec `zc hlzzcx}landak%

    tls idkb~ nz`{ ~bc ~{l ~zd`akecx xc}`z`~cet

    GGCZNX

    GG

    ZC

    GGNX

    CZ

    NX

    Xsjx~d~s~c fal{a w`escx

    :737

    3r

    77r 3 :3

    77r 0:3

    ^bc cps`~dla :737

    3r% lz ~bc cps`~dla 77r 0:3% hlsen jc sxcn

    ~l ffan ~bc ecak~b lgG

    X

    G X

    Z

    C

    N

    G

    G Xr

    Z

    C

    N

    3

    0=3

    8

    3=

    7!7

    3=

    :!3

    :3

    Xcc Ljoch~dwc 2%}`kc :0:% glz ilzcdaglzi`~dla `jls~xdide`z gdkszcx!

    Ljoch~dwc 7

    0>8

  • 7/30/2019 TAKS Math Study Guide

    145/303

  • 7/30/2019 TAKS Math Study Guide

    146/303

    ]lda~ L dx ~bc hca~cz lg ~bc hdzhec jcel{ DgiL@J >=% ffan ~bcic`xszc lg@J

    ^bc ic`xszc lg@J dx ~bc x`ic `x ~bc ic`xszc lg hca~z`e `akec@LJ

    Sxc ~bc g`h~ ~b`~ ~bc xsi lg ~bc `akecx lg ` ~zd`akec dx `e{`tx 02=~l ffan ~bc ic`xszc lg@LJ

    Xdahc L@`an LJ `zc jl~b z`ndd lg ~bc hdzhec% L@ LJ^bczcglzc% @LJ dx `a dxlxhcecx ~zd`akec {d~biL@J iLJ@Xdahc iL@J >=% iLJ@ >=

    Ec~ i@LJ r

    iL@J iLJ@ i@LJ 02=>= >= r 02=

    2= r 02=r 0==

    Xdahc i@LJ 0==% ~bc ic`xszc lg@J `exl cps`ex 0==

    @

    L

    J

    >= Xcc Ljoch~dwc 2%}`kc 043% glz ilzcdaglzi`~dla `jls~`zhx!

    Ljoch~dwc 7

    0>3

  • 7/30/2019 TAKS Math Study Guide

    147/303

    Ljoch~dwc 7

    0>7

    Bl{ H`a Tls @a`etc `an Ncxhzdjc ]`~~czax da Kclic~zdh Gdkszcx2 hca~dic~czx Dg ~bc }zlhcxxlg glzidak xi`eecz ~zd`akecx da ~bdx {`t hla~dascx% {b`~ dx ~bc}czdic~cz lg ~bc ffg~b ~zd`akec da ~bdx xczdcx2 hi

    C`hb xdnc da ~bc acr~ xi`eecz ~zd`akec dx 0: ~bc ecak~b lg ~bc

    hlzzcx}landak xdnc da ~bc e`zkcz ~zd`akec Xl ~bc }czdic~cz lg ~bc

    xchlan ~zd`akec dx 0: ~bc }czdic~cz lg ~bc ffzx~ ~zd`akec

    ]xchlan 0: >2

    ]xchlan

    :>

    gdzx~

    ~zd`akec

    xchlan~zd`akec

  • 7/30/2019 TAKS Math Study Guide

    148/303

  • 7/30/2019 TAKS Math Study Guide

    149/303

    Ljoch~dwc 7

    0>2

    ^bc zckse`z }letklax jcel{ glzi ` }`~~cza

    [b`~ dx ~bc }czdic~cz lg ~bc xcwca~b ffkszc da ~bc }`~~czax 0:

    x 8C`hb xdnc lg ~bc xps`zc b`x ` ecak~b lg 8 dahbcx

    ^bc }czdic~cz lg ~bc }ca~`kla dx := dahbcx

    3x :=x >

    C`hb xdnc lg ~bc }ca~`kla b`x ` ecak~b lg > dahbcx

    ^bc }czdic~cz lg ~bc bcr`kla dx 8= dahbcx

    7x 8=

    x 3C`hb xdnc lg ~bc bcr`kla b`x ` ecak~b lg 3 dahbcx

    ]czdic~cz 9 7 da! ]czdic~cz 9 0: da! ]czdic~cz 9 := da! ]czdic~cz 9 8= da!

    Nl tls xcc~b`~ ! ! !

  • 7/30/2019 TAKS Math Study Guide

    150/303

    I`fc ` ~`jec ~l xbl{ ~bc }`~~cza da ~bcxc ffkszcx

    ^bc }czdic~cz lg ~bc xcwca~b ffkszc da ~bc }`~~cza dx ;: dahbcx

    H`a ~bc dxlxhcecx ~zd`akec xbl{a jcel{ jc sxcn `elac ~l glzi `~cxxcee`~dla 8 > 8 0:

    8 Zckse`z }ca~`kla 3 > 3 > :=

    > Zckse`z bcr`kla 7 3 7 3 8=

    3 Zckse`z bc}~`kla ; 7 ; 7 >:

    7 Zckse`z lh~`kla 2 ; 2 ; 37

    ; Zckse`z ala`kla 4 2 4 2 ;:

    [b`~ Dx ` ^cxxcee`~dla4

  • 7/30/2019 TAKS Math Study Guide

    151/303

    Ljoch~dwc 7

    03=

    Js~ tls h`a hzc`~c ` ~cxxcee`~dla jt sxdak ~bc dxlxhcecx ~zd`akec~lkc~bcz {d~b d~x zl~`~cn di`kc

    H`a ~bc dxlxhcecx ~z`}cldn xbl{a jcel{ jc sxcn ~l kcacz`~c `~cxxcee`~dla% :7y dx`exl ` ]t~b`klzc`a ~zd}ec

    ^bc xdnc ecak~bx lg ~bc zdkb~ ~zd`akec da ~bc nd`kz`i `zc cps`e ~l~{l lg ~bc w`escx da ~bc xc~ v0=% :>% :7y

    ^bc ~bdzn xdnc ecak~b lg ~bc zdkb~ ~zd`akec dx cps`e ~l ~bczci`dadak w`esc da ~bc xc~ v0=% :>% :7y

    Xdnc j b`x ` ecak~b lg :> gcc~

    0= g~:7 g~

    j

    X}chd`e Zdkb~ Xdnc Zce`~dlaxbd}x Cr`i}ec^zd`akec

    >3)>3)4= ^bc ecak~bx lg ~bc ~{l eckxzd`akec `zc cps`e!

    "Dxlxhcecx Zdkb~$ ^bc ecak~b lg ~bc bt}l~casxcdx ~bc ecak~b lg ` eck ~dicx :!

    8=)7=)4= ^bc ecak~b lg ~bc bt}l~casxczd`akec dx ~{dhc ~bc ecak~b lg ~bcxblz~cz eck!

    ^bc ecak~b lg ~bc elakcz eckdx cps`e ~l ~bc ecak~b lg ~bcxblz~cz eck ~dicx 8!

    >

    >>3

    >3

    > :

    8=

    7=

    0=

    3

    3 8

    r

    r>3

    >3

    r :

    8=

    7=

    :r

    r

    r 8

    Zcicijcz% da ` zdkb~~zd`akec% ~bc kzc`~cx~asijcz zc}zcxca~x~bc ecak~b lg ~bc

    bt}l~casxc!

  • 7/30/2019 TAKS Math Study Guide

    155/303

    Ljoch~dwc 7

    03>

    ^bc `akec lg nc}zcxxdlagzli }lda~@ ~l }lda~ Jdx ~bc `akec@J i`fcx{d~b ~bc blzdla~`e edac~bzlskb }lda~@!

    @

    J

    @akec lg nc}zcxxdla

    Hb`zecx dx ellfdak ls~ ` {danl{ gzli ` }lda~ 3= gcc~ `jlwc ~bckzlsan [bca Hb`zecx ellfx nl{a `~ `a `akec lg nc}zcxxdla lg 8=%bc xccx bdx nlk I`r ^l ~bc ac`zcx~ gll~% bl{ g`z dx I`r gzli ~bcj`xc lg ~bc jsdendak3)>3)4= ~zd`akec jcel{

    ^zd`akec@JH dx ` >3)>3)4= ~zd`akec Dnca~dgt d~x }`z~x `an ~bcdzzce`~dlaxbd}x

    Da ~bdx x}chd`e ~zd`akec ~bc bt}l~casxc dx cps`e ~l ~bc ecak~b lg `eck ~dicx :

    @@J dx ~bc bt}l~casxc@H dx ` eck

    @J @H :

    0= @H :

    0=: @H

    ;=; @H

    0=>3 >3

    J

    H

  • 7/30/2019 TAKS Math Study Guide

    156/303

    Ljoch~dwc 7

    033

    Hlaxscel dx la ` jl`~ 8 idecx nsc xls~b lg ~bc }dcz Xbc {`a~x ~lkl ~l ` zcx~`sz`a~ ~b`~ dx nsc {cx~ lg ~bc }dcz% `x xbl{a jcel{Gdan ~bc `}}zlrdi`~c ndx~`ahc Hlaxscel isx~ ~z`wce ~l zc`hb ~bczcx~`sz`a~

    ^bc jl`~% zcx~`sz`a~% `an }dcz glzi ` zdkb~ ~zd`akec ^bc kdwca`akecx ic`xszc 8= `an 4= ^bc l~bcz `akec lg ~bc ~zd`akecic`xszcx 02= "4= 8=$ 7=

    Sxc ~bc }zl}cz~dcx lg 8=)7=)4= ~zd`akecx

    Tls accn ~l ffan ~bc ecak~b lg@Z% ~bc xckica~ hlaach~dak ~bc

    jl`~ ~l ~bc zcx~`sz`a~@Z dx ~bc bt}l~casxc lg ~bc ~zd`akec

    ^bc ndx~`ahc gzli ~bc jl`~ ~l ~bc }dcz dx kdwca@] 8 ^bdx dx~bc elakcz eck lg ~bc ~zd`akec

    ^bc ecak~b lg ~bc elakcz eck lg ` 8=)7=)4= ~zd`akec dx cps`e ~l~bc ecak~b lg ~bc xblz~cz eck ~dicx 8Ec~rcps`e ~bc ecak~b lg ~bc xblz~cz eck% Z] Xlewc glzr

    r 8 8

    r

    88 0;8

    Z] 0;8

    ^bc ecak~b lg ~bc bt}l~casxc%@Z% dx : ~dicx ~bc ecak~b lg ~bcxblz~cz eck Xsjx~d~s~c Z] 0;8

    @@Z :"0;8$

    @Z 8>7Hlaxscel isx~ ~z`wce `}}zlrdi`~cet 8>7 idecx ~l zc`hb ~bczcx~`sz`a~

    8=

    @

    ]Z ]dcz

    Zcx~`sz`a~

  • 7/30/2019 TAKS Math Study Guide

    157/303

  • 7/30/2019 TAKS Math Study Guide

    158/303

    Ljoch~dwc 7

    03;

    Bl{ Nl Tls Sxc ^z`axglzi`~dlax ~l Xlewc ]zljecix

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    t

    r

    3

    >

    7

    ;

    2

    4

    :

    8

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    Edac lgzcgech~dla

    t

    r

    3

    >

    7

    ;

    2

    4

    :

    8

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    Hca~cz lg zl~`~dla

  • 7/30/2019 TAKS Math Study Guide

    159/303

    Ljoch~dwc 7

    032

    [bca ffkszcx `zc~z`axglzicn% }zdical~`~dla dx lg~ca sxcn~l a`ic ~bc di`kc!^bc }lda~ ] dx ~bcdi`kc lg }lda~ ]!

    ^bc kz`}b lg ps`nzde`~cz`e IAE] dx xbl{a jcel{

    Gdan ~bc di`kc lg ps`nzde`~cz`e IAE] ~z`axe`~cn 8 sad~x zdkb~ `an

    : sad~x nl{a

    ]lda~ I b`x hllznda`~cx ":% :$ Sxc ~bc kz`}b ~l ffan ~bcelh`~dla lgI X~`z~ `~ I `an hlsa~ 8 sad~x ~l ~bc zdkb~ `an: sad~x nl{a ^bc hllznda`~cx lgI `zc "3% =$

    ]lda~ Ab`x hllznda`~cx "8% 8$ Sxc ~bc kz`}b ~l ffan ~bcelh`~dla lgA X~`z~ `~ A`an hlsa~ 8 sad~x ~l ~bc zdkb~ `an: sad~x nl{a ^bc hllznda`~cx lgA `zc "7% 0$

    ]lda~ E b`x hllznda`~cx "0% 8$ Sxc ~bc kz`}b ~l ffan ~bcelh`~dla lgE X~`z~ `~ E `an hlsa~ 8 sad~x ~l ~bc zdkb~ `an: sad~x nl{a ^bc hllznda`~cx lgE `zc ">% 0$

    ]lda~ ] b`x hllznda`~cx "=% :$ Sxc ~bc kz`}b ~l ffan ~bcelh`~dla lg] X~`z~ `~ ] `an hlsa~ 8 sad~x ~l ~bc zdkb~ `an: sad~x nl{a ^bc hllznda`~cx lg] `zc "8% =$

    ^bc kz`}b lg ps`nzde`~cz`e IAE] dx xbl{a jcel{

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8> 0 : 8 > 3 7

    ]

    E A I

    E

    I

    A

    ]

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8> 0 : 8 > 3 7

    E

    I

    A

    ]

  • 7/30/2019 TAKS Math Study Guide

    160/303

    Ljoch~dwc 7

    034

    ^bc kz`}b lg@JH dx xbl{a jcel{

    Gdan ~bc hllznda`~cx lg@JH% ~bc di`kc lg@JH zcch~cn`hzlxx ~bct)`rdx `an ~z`axe`~cn : sad~x s}

    Zcch~@ ">% 0$ `hzlxx ~bct)`rdx ^bcr)hllznda`~c lg@ dx ~bcack`~dwc lg ~bcr)hllznda`~c lg@ ^bcr)hllznda`~c lg@ dx >

    Dg ~bc }lda~ dx ~bca ~z`axe`~cn : sad~x s}% ~bct)hllznda`~c lg@

    {dee jc : ilzc ~b`a ~bct)hllznda`~c lg@ 0 : 8@ b`x hllznda`~cx ">% 8$

    Zcch~ J "3% >$ `hzlxx ~bct)`rdx ^bcr)hllznda`~c lgJ dx ~bcack`~dwc lg ~bcr)hllznda`~c lgJ ^bcr)hllznda`~c lgJ dx 3

    Dg ~bc }lda~ dx ~bca ~z`axe`~cn : sad~x s}% ~bct)hllznda`~c lgJ{dee jc : ilzc ~b`a ~bct)hllznda`~c lgJ > : 7

    J b`x hllznda`~cx "3% 7$

    Zcch~ H "2% 0$ `hzlxx ~bct)`rdx ^bcr)hllznda`~c lgH dx ~bcack`~dwc lg ~bcr)hllznda`~c lgH ^bcr)hllznda`~c lgH dx 2

    Dg ~bc }lda~ dx ~bca ~z`axe`~cn : sad~x s}% ~bct)hllznda`~c lgH{dee jc : ilzc ~b`a ~bct)hllznda`~c lgH 0 : 8

    H b`x hllznda`~cx "2% 8$

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    @ H

    J

  • 7/30/2019 TAKS Math Study Guide

    161/303

    Ljoch~dwc 7

    07=

    @JH dx xbl{a la ~bc kz`}b jcel{ Dg@JH dx zcch~cn `hzlxx ~bcedact r% {b`~ `zc ~bc hllznda`~cx lg@% J% `an H

    3

    7

    ;

    2

    4

    0=

    0 0:8>37;240= : 8 > 3 7 ; 2 4 0=

    ]

    ]

    t

    9r

  • 7/30/2019 TAKS Math Study Guide

    163/303

    ^bc kz`}b lgZX^dx xbl{a jcel{ Gdan ~bc hllznda`~cx lgX dgZX^dx zl~ ~cn 4= helhf{dxc `jls~ }lda~ ^

    DgZX^dx zl~ ~cn 4= helhf{dxc `jls~ }lda~ ^% X^ {dee jc}cz}candhse`z ~l X^

    ^bc xel}cx lg }cz}candhse`z edacx `zc ack`~dwc zchd}zlh`ex Dg ~bc

    xel}c lgX^ dx 3

    3

    % ~bca ~bc xel}c lgX^xblsen jc 3

    3

    Sxc ~bc xel}c lgX^% 33% ~l ffan }lda~ X X~`z~dak `~ }lda~ ^%

    hlsa~ 3 sad~x nl{a `an 3 sad~x ~l ~bc zdkb~

    ^bc }lda~ X {dee b`wc hllznda`~cx "2% 8$

    t

    r

    3

    >

    7

    ;

    2

    4

    0=

    00

    0:

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0=

    00

    0:

    0 0:8>37;240=000: : 8 > 3 7 ; 2 4 0= 00 0:

    ^

    Z

    X

    Xcc Ljoch~dwc 8%}`kc 74% glz ilzcdaglzi`~dla `jls~xel}c!

    Ljoch~dwc 7

    07:

  • 7/30/2019 TAKS Math Study Guide

    164/303

    Ljoch~dwc 7

    Al{ }z`h~dhc {b`~ tlswc ec`zacn!

    078

    ^zt D~^bc kz`}b jcel{ xbl{x ~bc edact r`an@J {d~b can}lda~x `~"3% :$ `an ">% ;$ [b`~ `zc ~bc hllznda`~cx lg ~bc can}lda~x lg

    @J `g~cz@J dx zcch~cn `hzlxxt r% ;$ dx zcch~cn `hzlxxt r%

    ~bdx kdwcx sx J \\\\\\\\

    [bca zcch~dak `hzlxxtr% ~bc lzncz lg ~bc hllznda`~cx glz `at }lda~ dx

    zcwczxcn! [bca@ "3% :$ dx zcch~cn `hzlxxtr% ~bdx kdwcx sx@ ":% 3$!

    [bca J ">% ;$ dx zcch~cn `hzlxxtr% ~bdx kdwcx sx J ";% >$!

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    @

    J

    t9r

  • 7/30/2019 TAKS Math Study Guide

    165/303

  • 7/30/2019 TAKS Math Study Guide

    166/303

    Ljoch~dwc 7

    073

    Pscx~dla 3;

    Ellf `~ ~bc xb`}c jcel{!

    [bdhb lg ~bcxc }`~~czax h`a jc i`nc sxdaklaet ~z`axe`~dlax% zl~`~dlax% lz ` hlijda`~dlalg ~z`axe`~dlax `an zl~`~dlax3 g~

    8=

    Nlelzcx

    2 g~

    >3

    @ax{cz Fct? }`kc :4=

    @ax{cz Fct? }`kc :4=@ax{cz Fct? }`kc :4=

  • 7/30/2019 TAKS Math Study Guide

    168/303

    Ljoch~dwc 7

    07;

    Pscx~dla 78

    [bdhb xc~ lg hllznda`~cx zc}zcxca~x ~bc wcz~dhcxlg ~bc di`kc lg ps`nzde`~cz`eIA]P `g~cz `~z`axe`~dla lg > sad~x ecg~ `an : sad~x s}% 3$% "2% 3$% ";% 3$

    Pscx~dla 7>

    [bdhb ~z`axglzi`~dla lg^ZX hzc`~cx ^ZXxbl{a jcel{ sad~x zdkb~ `an 8 sad~xnl{a

    H Zcch~ ^ZX `hzlxx ~bcr)`rdx `an ~bca~z`axe`~c d~ 7 sad~x nl{a

    N ^z`axe`~c^ZX 7 sad~x zdkb~ `an 8 sad~xnl{a

    @ax{cz Fct? }`kc :40@ax{cz Fct? }`kc :40

    t

    r

    3

    >

    7

    ;

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    0 0:8>37; : 8 > 3 7 ;

    A ]

    I P

    t

    r

    3

    >

    7

    ;

    2

    4

    8

    :

    0

    =

    0

    :

    8

    >

    3

    7

    ;

    2

    4

    0 0:8>37;24 : 8 > 3 7 ; 2 4

    Z X

    X Z

    ^

    ^

  • 7/30/2019 TAKS Math Study Guide

    169/303

  • 7/30/2019 TAKS Math Study Guide

    170/303

    [b`~ 8)ndicaxdla`e ffkszc nlcx ~bdx ac~ zc}zcxca~$"0% 3$

    ">% :$

    Ps`nz`a~ DPs`nz`a~ DD

    Ps`nz`a~ DWPs`nz`a~ DDD

    ack`~dwcr)hllznda`~cxack`~dwct)hllznda`~cx

    "% $

    }lxd~dwcr)hllznda`~cx}lxd~dwct)hllznda`~cx

    "&% &$

    }lxd~dwcr)hllznda`~cxack`~dwct)hllznda`~cx

    "&% $

    t

    r

    Lzdkda"=% =$

    "r%t$r)`rdx

    t)hllznda`~c

    t)`rdxr)hllznda`~c

    Lznczcn}`dz

    0;8

  • 7/30/2019 TAKS Math Study Guide

    175/303

    ^bc }lda~x kz`}bcn jcel{ `zc `x gleel{x? ] ":% 0$% Z ">% 3$%

    X "8% 8$% ^"8% 3$% S"0% :$% `an W"3% 0$ A`ic ~bc ffkszc

    glzicn jt nz`{dak ]Z% Z^% ^W% `an W]

    E`jce ~bcxc }lda~x? ] ":% 0$% Z ">% 3$% ^"8% 3$% `an W"3% 0$Nz`{ ~bc edac xckica~x ~b`~ hlaach~ ~bci

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    Ljoch~dwc ;

    0;>

    ^{l lznczcn }`dzx h`a jc sxcn ~l a`ic ~bc can}lda~x lg ` edacxckica~

    Glz cr`i}ec%@J b`x ~bc lznczcn }`dzx ":% 0$ `an "8% >$ `x d~xcan}lda~x

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    @

    J

  • 7/30/2019 TAKS Math Study Guide

    176/303

    Ljoch~dwc ;

    ^W`an ZZ] `zc hlakzsca~ `an }`z`eece ^Z `an W] `zc `exlhlakzsca~ `an }`z`eece @ ps`nzde`~cz`e da {bdhb jl~b }`dzx lgl}}lxd~c xdncx `zc hlakzsca~ `an }`z`eece dx ` }`z`eecelkz`i

    Gdkszc ]Z^Wdx ` }`z`eecelkz`i

    t

    r

    3

    >

    8

    :

    0

    0

    :

    8

    >

    3

    =0:8>3 0 : 8 > 3

    W ]

    S

    X

    ^ Z

    0;3

  • 7/30/2019 TAKS Math Study Guide

    177/303

    Ljoch~dwc ;

    0;7

    ^bc idn}lda~ lg ` edac xckica~ dx ~bc }lda~ ~b`~ edcx b`eg{`t jc~{cca~bc xckica~x can}lda~x `an ndwdncx ~bc xckica~ da~l ~{l hlakzsca~}`z~x ^bc hllznda`~cx lg ~bc idn}lda~ `zc ~bc `wcz`kc lg ~bchllznda`~cx lg ~bc can}lda~x

    Lac {`t ~l ffan ~bc idn}lda~ lg ` edac xckica~ dx ~l sxc ~bc gleel{dak

    glzise`

    Idn}lda~ Glzise`

    Glz `at ~{l }lda~x "r0%t0$ `an "r:% t:$% ~bc hllznda`~cx lg ~bcidn}lda~ lg ~bc edac xckica~ ~bct nc~czidac `zc kdwca jt ~bcglzise` jcel{