Appedices Of the vrious ottios i use, the IB hs chose to dopt system of ottio bsed o the recommedtios of the Itertiol Orgiztio for Stdrdiztio (ISO). This ottio is used i the emitio ppers for this course without epltio. If forms of ottio other th those listed i this guide re used o prticulr emitio pper, they re defied withi the questio i which they pper. Becuse studets re required to recogize, though ot ecessrily use, IB ottio i emitios, it is recommeded tht techers itroduce studets to this ottio t the erliest opportuity. Studets re ot llowed ccess to iformtio bout this ottio i the emitios. Studets must lwys use correct mthemticl ottio, ot clcultor ottio. the set of positive itegers d zero, {0,1,, 3,...} the set of itegers, {0, 1,, 3,...} the set of positive itegers, {1,, 3,...} the set of rtiol umbers the set of positive rtiol umbers, {, 0} the set of rel umbers the set of positive rel umbers, {, 0} { 1, } the set with elemets 1, ( A ) { } U the umber of elemets i the fiite set A the set of ll such tht is elemet of is ot elemet of the empty (ull) set the uiversl set Uio 5 Mthemtics SL guide
A b Itersectio is proper subset of is subset of the complemet of the set A divides b 1/, to the power of 1, th root of (if 0 the 0 ) modulus or bsolute vlue of, tht is is pproimtely equl to is greter th is greter th or equl to is less th is less th or equl to is ot greter th is ot less th for 0, for 0, u the th term of sequece or series d r the commo differece of rithmetic sequece the commo rtio of geometric sequece S the sum of the first terms of sequece, u1 u... u S the sum to ifiity of sequece, u1 u... ui u1 u... u i1 r the r th biomil coefficiet, r = 0, 1,,, i the epsio of ( b f : A B f is fuctio uder which ech elemet of set A hs imge i set B ) f : y f is fuctio uder which is mpped to y Mthemtics SL guide 53
f ( ) 1 f the imge of uder the fuctio f the iverse fuctio of the fuctio f f g the composite fuctio of f d g lim f ( ) dy d the limit of f ( ) s teds to the derivtive of y with respect to f ( ) the derivtive of f ( ) with respect to d y d the secod derivtive of y with respect to f ( ) the secod derivtive of f ( ) with respect to d y d the th derivtive of y with respect to ( f ) ( ) the th derivtive of f ( ) with respect to y d the idefiite itegrl of y with respect to b y d the defiite itegrl of y with respect to betwee the limits d b e log epoetil fuctio (bse e) of logrithm to the bse of l the turl logrithm of, loge si, cos, t A(, y ) [AB] AB (AB) Â ˆ CAB the circulr fuctios the poit A i the ple with Crtesi coordites d y the lie segmet with ed poits A d B the legth of [AB] the lie cotiig poits A d B the gle t A the gle betwee [CA] d [AB] 54 Mthemtics SL guide
ABC the trigle whose vertices re A, B d C v AB the vector v the vector represeted i mgitude d directio by the directed lie segmet from A to B the positio vector OA i, j, k uit vectors i the directios of the Crtesi coordite es AB v w P( A ) the mgitude of the mgitude of AB the sclr product of v d w probbility of evet A P( A ) probbility of the evet ot A P( A B ) probbility of the evet A give the evet B 1, Observtios f1, f frequecies with which the observtios 1, occur r B(, p ) umber of wys of selectig r items from items biomil distributio with prmeters d p N(, ) orml distributio with me d vrice X ~ B(, p ) the rdom vrible X hs biomil distributio with prmeters d p X ~ N(, ) the rdom vrible X hs orml distributio with me d vrice popultio me popultio vrice popultio stdrd devitio me of set of dt, 1,, 3,... Mthemtics SL guide 55
z r stdrdized orml rdom vrible, z cumultive distributio fuctio of the stdrdized orml vrible with distributio N(0, 1) Perso s product momet correltio coefficiet 56 Mthemtics SL guide