Rectangle Square Triangle Parallelogram Trapezoid Circle P = 2l + 2w P = 4s P = a + b + c P = 2a + 2b P = a + b + c + d C = 2pr = pd

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Sharleen Washington
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1 Geoet eiete d Ae = eiete, A = Ae, C = Cicufeece, V = Volue ectgle Sque Tigle llelog Tpezoid Cicle = l + w = 4s = + + c = + = + + c + d C = p = pd A = lw A = s A= A = A= ( + c) A = p c w s c d d l Volue ectgul Solid ectgul id igt Cicul Coe igt Cicul Clide Spee V = lw V lw = 3 V = p V = p V = 4 p w l l w Agles Clssified Mesue Acute igt Otuse Stigt 0 < A< 90 A= < A< 80 A= 80 A A A A Tigles Clssified Sides Sclee Isosceles Equiltel No two sides e equl. At lest two sides e equl. All tee sides e equl. C Z A B X Y Tigles Clssified Agles Acute igt Otuse All tee gles e cute. Oe gle is igt gle. Oe gle is otuse. C Z A B X Y

2 US Custo Sste of Mesueet Metic Sste of Mesueet Legt ices (i.) = foot (ft) 3 feet = d (d) Legt illiete () = 0.00 ete cetiete (c) = 0.0 ete = 000 = 00 c 36 ices = d 580 feet = ile (i) deciete (d) ete () = 0. ete =.0 ete = 0 d Cpcit dekete (d) = 0 etes cup (c) = 8 fluid ouces (fl oz) ectoete () = 00 etes pits = qut (qt) cups = pit (pt) = 6 fluid ouces kiloete (k) = 000 etes 4 quts = gllo (gl) Cpcit (Liquid Volue) Weigt 6 ouces (oz) = poud (l) 000 pouds = to (T) Tie 60 secods (sec) = iute (i) 60 iutes = ou () 4 ous = d 7 ds = week illilite (L) lite (L) ectolite (L) kilolite (kl) Weigt illig (g) cetig (cg) decig (dg) = 0.00 lite =.0 lite = 00 lites = 000 lites = 0.00 g = 0.0 g = 0. g L = 000 L kl = 0 L g = 000 g Tepetue Celsius (C) to Feeit (F) 9 F = C+ 3 5 Feeit (F) to Celsius (C) 5 F - 3 C = 9 g (g) =.0 g dekg (dg) = 0 gs ectog (g) = 00 gs kilog (kg) = 000 gs g = 0.00 kg etic to (t) = 000 kilogs kg = 0.00 t t = 000 kg =,000,000 g =,000,000,000 g US Custo d Metic Equivlets Legt Volue i.. 54 c ect = ft 305 d 94 i. 6 k Ae i c ft 093 d 836 c 394 i ft. 09 d k 6 i c 055. i ft. 96 d ce ces i c 3 3 ft c 06 i ft 3 3 qt 946 L L. 06 qt gl L L 64 gl Mss oz 835. g g 035 oz l kg kg 05. l

3 Nottio d Teiolog Epoets... = fctos Fctios epoet se ueto deoito Lest Coo Multiple (LCM) Give set of wole ues, te sllest ue tt is ultiple of ec of tese wole ues. tios o : o to A copiso of two qutities divisio. opotios c = A stteet tt two tios e equl. d Getest Coo Fcto (GCF) Give set of iteges, te lgest itege tt is fcto (o diviso) of ll of te iteges. Tpes of Nues Equlit d Iequlit Sols = is equl to is ot equl to < is less t > is gete t Sets is less t o equl to is gete t o equl to Te ept set o ull set (solized o { }): A set wit o eleets. Te uio of two (o oe) sets (solized ): Te set of ll eleets tt elog to eite oe set o te ote set o to ot sets. Te itesectio of two (o oe) sets (solized ): Te set of ll eleets tt elog to ot sets. Te wod o is used to idicte uio d te wod d is used to idicte itesectio. Algeic d Itevl Nottio fo Itevls Tpe of Itevl Algeic Nottio Itevl Nottio Ope Itevl < < (, ) Gp Closed Itevl, Ntul Nues (Coutig Nues): N = {,, 3, 4, 5, 6,... } Hlf-ope Itevl < <, ) (, Wole Nues: W = { 0,,, 3, 4, 5, 6,... } Iteges: Z = {..., 4, 3,,, 0,,, 3, 4,... } tiol Nues: A ue tt c e witte i te fo wee d e iteges d 0. Itiol Nues: A ue tt c e witte s ifiite oepetig decil. el Nues: All tiol d itiol ues. Cople Nues: All el ues d te eve oots of egtive ues. Te stdd fo of cople ue is + i, wee d e el ues, is clled te el pt d is clled te igi pt. Asolute Vlue Te distce el ue is fo 0. > Ope Itevl < Hlf-ope Itevl (, ) -,, ) (-, dicls Te sol is clled dicl sig. Te ue ude te dicl sig is clled te dicd. Te coplete epessio, suc s 64, is clled dicl o dicl epessio. I cue oot epessio 3, te ue 3 is clled te ide. I sque oot epessio suc s, te ide is udestood to e d is ot witte. Te Igi Nue i i = - d i = ( -) =-

4 Fouls d Teoes ecet A = (te pecet popotio), 00 B wee = pecet (witte s te tio 00 ) B = se (ue we e fidig te pecet of) A = out ( pt of te se) B = A (te sic pecet equtio), wee = te o pecet (s decil o fctio) B = se (ue we e fidig te pecet of) A = out ( pt of te se) ofit ofit: Te diffeece etwee sellig pice d cost. ecet of ofit: pofit = sellig pice - cost. ecet of pofit sed o cost: pofit cost. ecet of pofit sed o sellig pice: Iteest Siple Iteest: I = t Copoud Iteest: A= + Cotiuousl Copouded Iteest: A= wee I = iteest (eed o pid) A = out ccuulted t pofit sellig pice e t = picipl (te out ivested o oowed) = ul iteest te i decil o fctio fo t = tie (oe e o fctio of e) = te ue of ties pe e iteest is copouded e = Te tgoe Teoe I igt tigle, te sque of te legt of te poteuse is equl to te su of te sques of te legts of te two legs: c = + oilit of Evet poilit of evet ue of outcoes i evet = ue of outcoes i sple spce Distce-te-Tie d = t Te distce tveled d equls te poduct of te te of speed d te tie t. Specil oducts. - = ( + ) ( - ): Diffeece of two sques. + + = = - : Sque of ioil su : Sque of ioil diffeece = ( + ) ( - + ): Su of two cues = ( - ) ( + + ): Diffeece of two cues Cge-of-Bse Foul fo Logits Fo,,, > 0 d,, log log = log Distce Betwee Two oits Te distce d etwee poits, ( ) + ( - ) is d = - Midpoit Foul Te idpoit etwee poits, is + +,.. c. 90 ( ) d (, ) ( ) d (, )

5 iciples d opeties opeties of Additio d Multiplictio opet Additio Multiplictio Couttive opet Associtive opet + = + ( + )+ c = + + c = c = ( c ) Idetit + 0 = 0 + = = = Ivese + (-)= 0 = 0 Zeo-Fcto Lw: 0 = 0 = 0 Distiutive opet: ( + c)= + c Additio (o Sutctio) iciple of Equlit A = B, A + C = B + C, d A - C = B - C ve te se solutios (wee A, B, d C e lgeic epessios). Multiplictio (o Divisio) iciple of Equlit A = B, AC = BC, d A B = ve te se solutios C C (wee A d B e lgeic epessios d C is ozeo costt, C 0). opeties of Epoets Fo ozeo el ues d d iteges d : Te epoet = Te epoet 0 0 = Te poduct ule = Te quotiet ule Negtive epoets + - = - = owe ule = owe of poduct = owe of quotiet Zeo-Fcto opet = If d e el ues, d = 0, te = 0 o = 0 o ot. opeties of tiol Nues (o Fctios) If is tiol epessio d,,, d K e poloils wee,, S 0, te Te Fudetl iciple Multiplictio Divisio Additio Sutctio opeties of dicls K = K = S S S = S + + = - If d e positive el ues, is positive itege, is itege, d. =. = 3. = opeties of Logits is el ue te = = 4. o, i dicl ottio, = = Fo > 0,,, > 0, d el ue,. log = 0 3. = log. log = 4. log = 5. log = log + log Te poduct ule 6. log = log - log Te quotiet ule 7. log = log Te powe ule opeties of Equtios wit Epoets d Logits Fo > 0,,. If =, te =.. If =, te =. 3. If log = log, te = ( > 0 d > 0). 4. If =, te log = log ( > 0 d > 0).

6 Equtios d Iequlities Lie Equtio i (Fist-Degee Equtio i ) + = c, wee,, d c e el ues d 0. Tpes of Equtios d tei Solutios Coditiol: Fiite Nue of Solutios Idetit: Ifiite Nue of Solutios Cotdictio: No Solutio Lie Iequlities Lie Iequlities ve te followig fos wee,, d c e el ues d 0: + < c d + c + > c d + c Copoud Iequlities Te iequlities c < + < d d c + d e clled copoud lie iequlities. (Tis icludes c< + d d c + < d s well.) Asolute Vlue Equtios Fo stteets d, c > 0:. If = c, te = c o = c.. If + = c, te + = c o + = c. 3. If =, te eite = o =. Asolute Vlue Iequlities Fo c > 0:. If < c, te - c< < c.. If + < c, te - c< + < c. 3. If > c, te < - c o > c. 4. If + > c, te + < - c o + > c. (Tese stteets old tue fo d s well.) udtic Equtio A equtio tt c e witte i te fo + + c = 0, wee,, d c e el ues d 0. udtic Foul Te solutios of te geel qudtic equtio c + + c = 0, wee 0, e = - ± - 4. Te Disciit Te epessio 4c, te pt of te qudtic foul tt lies ude te dicl sig, is clled te disciit. If 4c > 0, tee e two el solutios. If 4c = 0, tee is oe el solutio, If 4c < 0, tee e two oel solutios. =-. 4. If + = c+ d, te eite + = c + d o + = -( c+ d). Sstes of Lie Equtios Sstes of Lie Equtios (Two Viles) Te sste is... cosistet, d te equtios e idepedet. (Oe solutio) icosistet, d te equtios e idepedet. (No solutio) cosistet, d te equtios e depedet. (Ifiite ue of solutios)

7 Fuctios Fuctio, eltio, Doi, d ge A eltio is set of odeed pis of el ues. Te doi D of eltio is te set of ll fist coodites i te eltio. Algeic Opetios wit Fuctios f f. ( f + g)= f + g 4. g ( )= g. ( f - g)= f - g 5. f g f g = Te ge of eltio is te set of ll secod coodites i te eltio. 3. ( f g)= f g A fuctio is eltio i wic ec doi eleet s ectl oe coespodig ge eleet. Oe-to-Oe Fuctios A fuctio is oe-to-oe fuctio if fo ec vlue of i te ge tee is ol oe coespodig vlue of i te doi. Ivese Fuctios If f is oe-to-oe fuctio wit odeed pis of te fo (, ), te its ivese fuctio, deoted s f -, is lso oe-to-oe fuctio wit odeed pis of te fo,. If f d g e oe-to-oe fuctios d f ( g )= fo ll i Dg d g( f )= fo ll i Df, te f d g e ivese fuctios. Gps of Fuctios Te Ctesi Coodite Sste udt II ( egtive, positive) (-, +) udt III ( egtive, egtive) (-, -) -is Lie Fuctios (Lies) udt I ( positive, positive) (+, +) (0, 0) Oigi -is udt IV ( positive, egtive) (+, -) Stdd fo: A + B = C Wee A d B do ot ot equl 0 Slope of lie: - = Wee - Slope-itecept fo: = + Wit slope d -itecept (0, ) oit-slope fo: - = - Wit slope d poit, lie ( ) o te Hoizotl lie, slope 0: = Veticl lie, udefied slope: llel lies ve te se slope. = epedicul lies ve slopes tt e egtive ecipocls of ec ote. udtic Fuctios (ols) ols of te fo = + + c:. Vete: - - f,.. Lie of Set: ols of te fo : = - + k. Vete: ( k, ). Lie of Set: = =- 3. Te gp is oizotl sift of uits d veticl sift of k uits of te gp of =. I ot cses:. If > 0, te pol opes upwd. Lie of Set Vete. If < 0, te pol opes dowwd.

8 Coic Sectios Equtios of Hoizotl ol Equtio of Cicle = + + c + o = -k wee 0. Te pol opes left if < 0 d igt if > 0. Te vete is t ( k, ). Te equtio of cicle wit dius d cete k, + ( - ) =. - k is (, k) (, ) Te lie = k is te lie of set. Equtio of Ellipse Te stdd fo fo te equtio of ellipse wit its cete t te oigi is d (- ) Te poits,0,0 e te -itecepts (clled vetices). d ( 0, - ) Te poits 0, e te -itecepts (clled vetices). We > : + =. Te seget of legt joiig te -itecepts is clled te jo is. Te seget of legt joiig te -itecepts is clled te io is. We > : k + Te seget of legt joiig te -itecepts is clled te jo is. Te seget of legt joiig te -itecepts is clled te io is. Te stdd fo fo te equtio of ellipse wit its ( - ) ( - k) cete t (, k) is + =. k k - - (, k) + Equtio of Hpeol I geel, tee e two stdd fos fo equtios of peols wit tei cetes t te oigi... -itecepts (vetices) t,0 -,0 No -itecepts d Asptotes: = d =- Te cuves ope left d igt. -itecepts (vetices) t 0, 0, - No -itecepts d Asptotes: = d =- Te cuves ope up d dow. = (, 0) is Te equtio of peol wit its cete t k, ( - ) ( - k) ( - k) ( - ) o (0, ) (0, ) = (, 0) = =

Properties of Addition and Multiplication. For Addition Name of Property For Multiplication

Properties of Addition and Multiplication. For Addition Name of Property For Multiplication Nottio d Sols Tpes of Nues Ntul Nues (Coutig Nues): N = {,, 3, 4, 5, 6,...} Wole Nues: W = { 0,,, 3, 4, 5, 6,...} Iteges: Z = {..., 4, 3,,, 0,,, 3, 4,...} Rtiol Nues: tiol ue is ue tt e witte i te fo of