Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
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1 Peso Edecel Level Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics (9MA0) Advced Subsidiy GCE i Futhe Mthemtics (8FM0) Fo fist cetifictio fom Jue 09 fo: Advced GCE i Futhe Mthemtics (9FM0) This copy is the popety of Peso. It is ot to be emoved fom the emitio oom o mked i y wy.
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3 Cotets Itoductio AS Level i Mthemtics Pue Mthemtics Sttistics Mechics A Level i Mthemtics 4 Pue Mthemtics 4 Sttistics 6 Mechics 7 4 AS Level i Futhe Mthemtics 8 Pue Mthemtics 8 Sttistics Mechics 4 5 A Level i Futhe Mthemtics 5 Pue Mthemtics 5 Sttistics Mechics 5 6 Sttisticl Tbles 6 Biomil Cumultive Distibutio Fuctio 6 Pecetge Poits Of The Noml Distibutio Poisso Cumultive Distibutio Fuctio Pecetge Poits of the Distibutio Citicl Vlues fo Coeltio Coefficiets 4 Rdom Numbes 5 Pecetge Poits of Studet s t Distibutio 6 Pecetge Poits of the F Distibutio 7
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5 Itoductio The fomule i this booklet hve bee ged by qulifictio. Studets sittig AS o A Level Futhe Mthemtics ppes my be equied to use the fomule tht wee itoduced i AS o A Level Mthemtics ppes. It my lso be the cse tht studets sittig Mechics d Sttistics ppes will eed to use fomule itoduced i the ppopite Pue Mthemtics ppes fo the qulifictio they e sittig. Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
6 AS Level i Mthemtics Pue Mthemtics Mesutio Sufce e of sphee = 4 Ae of cuved sufce of coe = slt height Biomil seies ( b) b b b b ( N) whee! C! ( )! Logithms d epoetils logb log log l e b Diffeetitio Fist Piciples f ( h) f ( ) f ( ) =lim h0 h Sttistics Pobbility P(A) = P(A) Stdd devitio Stdd devitio = (Vice) Itequtile ge = IQR = Q Q Fo set of vlues,,...,... ( i ) S ( i ) i i Stdd devitio = S o Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
7 Sttisticl tbles The followig sttisticl tbles e equied fo A Level Mthemtics: Biomil Cumultive Distibutio Fuctio (see pge 5) Rdom Numbes (see pge 4) Mechics Kiemtics Fo motio i stight lie with costt cceletio: v = u + t s = ut + ½ t s = vt - ½ t v = u + s s = ½ (u + v)t Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
8 A Level i Mthemtics Pue Mthemtics Mesutio Sufce e of sphee = 4 Ae of cuved sufce of coe = slt height Aithmetic seies S = ( + l) = [ + ( )d] Biomil seies ( b ) b b b b ( N) whee! C! ( )! ( ) ( ) ( ) ( ) (, ) Logithms d epoetils logb log log l e b Geometic seies S = ( ) S = fo < Numeicl itegtio The tpezium ule: b y d h{(y 0 + y ) + (y + y y )}, whee b h 4 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
9 Tigoometic idetities si ( A B) siacos B cosa sib cos( AB) cosa cosb sia sib ta tb t ( A B) ( A B ( k ) ) tatb A B A B siasib si cos A B A B siasib cos si A B A B cosacosb cos cos A B A B cosa cosb si si Diffeetitio Fist Piciples f ( h) f ( ) f ( ) =lim h0 h f() t k seck cotk cosec k f( ) g( ) f () k sec k kseck tk kcosec k kcosec k cot k f ( ) g( ) f( ) g ( ) (g( )) Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 5 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
10 Itegtio (+ costt) f() f( ) d sec k t k k tk cot k coseck seck l seck k l si k k l cosec k cot k, l t( k) k k l sec k t k, l t( k 4 ) k k dv du u d uv v d d d Numeicl solutio of equtios The Newto-Rphso itetio fo solvig f( ) 0 : f( ) f ( ) Sttistics Pobbility P(A) = P(A) P( A B) P( A) P( B) P( A B) P( AB) P( A)P( B A) P( B A)P( A) P( A B) P( B A)P( A) P( B A)P( A) Fo idepedet evets A d B, P(BA) = P(B), P(AB) = P(A), P(A B) = P(A) P(B) 6 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
11 Stdd devitio Stdd devitio = (Vice) Itequtile ge = IQR = Q Q Fo set of vlues,,...,... i S ( ) i ( ) i i Stdd devitio = S o Discete distibutios Distibutio of X P(X = ) Me Vice Biomil B(, p) p ( p ) p p( p) Smplig distibutios Fo dom smple of obsevtios fom N(, ) X ~ N(0, ) / Sttisticl tbles The followig sttisticl tbles e equied fo A Level Mthemtics: Biomil Cumultive Distibutio Fuctio (see pge 5) Pecetge Poits Of The Noml Distibutio (0) Citicl Vlues fo Coeltio Coefficiets: Poduct Momet Coefficiet (see pge ) Rdom Numbes (see pge 4) Mechics Kiemtics Fo motio i stight lie with costt cceletio: v = u + t s = ut + ½ t s = vt - ½ t v = u + s s = ½ (u + v)t Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 7 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
12 4 AS Level i Futhe Mthemtics Studets sittig AS Level Futhe Mthemtics ppe my lso equie those fomule listed fo A Level Mthemtics i Sectio. Pue Mthemtics Summtios 6 ( )( ) 4 ( ) Mti tsfomtios Aticlockwise ottio though bout O: cos si si cos Reflectio i the lie cos si y (t ) : si cos Ae of secto (pol coodites) A = d Comple umbes { (cos isi )} (cos isi ) The oots of z e give by k i z e, fo k 0,,,, 8 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
13 Mclui s d Tylo s Seies ( ) f( ) f(0) f (0) f (0) f (0)!! e ep( )!! fo ll l ( ) ( ) ( ) si! 5 5! ( ) ( )! fo ll cos! 4 4! ( ) ()! fo ll 5 ct ( ) ( ) 5 Vectos Vecto poduct: b b si ˆ i b b j k b b b b b b b. ( bc) b b b b. ( c) c. ( b) c c If A is the poit with positio vecto b bi b jbk b y b c i j k d the diectio vecto b is give by, the the stight lie though A with diectio vecto b hs ctesi equtio z b ( ) The ple though A with oml vecto y z d 0 whee d. i j k hs ctesi equtio The ple though o-collie poits A, B d C hs vecto equtio ( b ) ( c ) ( ) b c The ple though the poit with positio vecto d pllel to b d c hs equtio sb tc The pepedicul distce of,, ) ( fom y z d 0 is d Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 9 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
14 Hypebolic fuctios cosh sih sih sih cosh cosh cosh sih cosh l{ } ( ) sih l{ } th l ( ) Diffeetitio f() csi f() ccos ct sih cosh cosh sih th sech sih cosh th 0 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
15 Itegtio (+ costt; 0 whee elevt) f() f( ) d sih cosh cosh sih th l cosh csi ( ) ct cosh, l{ } ( ) sih, l { } l th ( ) l Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
16 Sttistics Discete distibutios Fo discete dom vible X tkig vlues Epecttio (me): E(X) = = i P(X = i ) Vice: V(X) = = ( i ) P(X = i ) = i with pobbilities P(X = i) P(X = i ) i Discete distibutios Stdd discete distibutios: Distibutio of X P(X = ) Me Vice p Biomil B(, p) p p p( p) Poisso Po ( ) e! Cotiuous distibutios Fo cotiuous dom vible X hvig pobbility desity fuctio f Epecttio (me): E( X ) f( ) d X Vice: V( ) ( ) f( )d f( )d Fo fuctio ) g( X : E(g( X )) g( ) f( ) d Cumultive distibutio fuctio: F( ) P( X ) f ( t) dt Stdd cotiuous distibutio: Distibutio of X P.D.F. Me Vice Noml N(, ) e Uifom (Rectgul) o [, b] b ( b) ( b ) Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
17 Coeltio d egessio Fo set of pis of vlues, y ) ( i ) S ( i ) i ( yi ) S yy ( yi y) yi ( i i ( i)( yi) S y ( i )( yi y) i yi The poduct momet coeltio coefficiet is: ( i)( yi) S y ( )( ) i i y i yi y S S yy { ( i ) }{ ( yi y) } ( i) ( yi) i yi The egessio coefficiet of y o is S ( )( y y) b S ( ) y i i i Lest sques egessio lie of y o is y b whee y b Residul Sum of Sques (RSS) = Sy Syy Syy S Spem s k coeltio coefficiet is s 6d ( ) No-pmetic tests Goodess-of-fit test d cotigecy tbles: ( O i Ei E ) i ~ Sttisticl tbles The followig sttisticl tbles e equied fo AS Level Futhe Mthemtics: Biomil Cumultive Distibutio Fuctio (see pge 5) Poisso Cumultive Distibutio Fuctio (see pge ) Pecetge Poits of the Distibutio (see pge ) Citicl Vlues fo Coeltio Coefficiets: Poduct Momet Coefficiet d Spem s Coefficiet (see pge ) Rdom Numbes (see pge 4) Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
18 Mechics Cetes of mss Fo uifom bodies: Tigul lmi: log medi fom vete Cicul c, dius, gle t cete : si fom cete Secto of cicle, dius, gle t cete si : fom cete 4 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
19 5 A Level i Futhe Mthemtics Studets sittig A Level Futhe Mthemtics ppe my lso equie those fomule listed fo A Level Mthemtics i Sectio. Pue Mthemtics Summtios 6 ( )( ) 4 ( ) Mti tsfomtios Aticlockwise ottio though bout O: cos si si cos Reflectio i the lie cos si y (t ) : si cos Ae of secto (pol coodites) A = d Comple umbes { (cos isi )} (cos isi ) The oots of z e give by k i z e, fo k 0,,,, Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 5 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
20 Mclui s d Tylo s Seies ( ) f( ) f(0) f (0) f (0) f (0)!! e ep( )!! fo ll l ( ) ( ) ( ) si! 5 5! ( ) ( )! fo ll cos! 4 4! ( ) ()! fo ll 5 ct ( ) ( ) 5 Vectos Vecto poduct: b b si ˆ i b b j k b b b b b b b. ( bc) b b b b. ( c) c. ( b) c c If A is the poit with positio vecto b bi b jbk y z b b b c i j k d the diectio vecto b is give by, the the stight lie though A with diectio vecto b hs ctesi equtio ( ) The ple though A with oml vecto y z d 0 whee d. i j k hs ctesi equtio The ple though o-collie poits A, B d C hs vecto equtio ( b ) ( c ) ( ) b c The ple though the poit with positio vecto d pllel to b d c hs equtio sb tc The pepedicul distce of (,, ) fom y z d 0 is d 6 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
21 Hypebolic fuctios cosh sih sih sih cosh cosh cosh sih cosh l{ } ( ) sih l{ } th l ( ) Coics Ellipse Pbol Hypebol Rectgul Hypebol Stdd Fom b y y y 4 b y c Pmetic Fom ( cos, bsi ) ( t, t) ( sec, b t ) ( cosh, b sih ) ct, c t Ecceticity e b ( e ) e e b ( e ) e = Foci ( e, 0) (, 0) ( e, 0) ( c, c ) Diectices e + y = c e Asymptotes oe oe y 0, y 0 b Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 7 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
22 Diffeetitio f() csi f() ccos ct sih cosh cosh sih th sech sih cosh th 8 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
23 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 9 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07 Itegtio (+ costt; 0 whee elevt) f() d ) f( sih cosh cosh sih th l cosh ) ( csi ct ) ( l, cosh } { { } l, sih ) ( th l l Ac legth y s d d d (ctesi coodites) t t y t s d d d d d (pmetic fom) d d d s (pol fom)
24 Sufce e of evolutio S = dy y d d (ctesi coodites) S = d dy y dt dt dt (pmetic fom) S = d si d d (pol fom) 0 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
25 Sttistics Discete distibutios Fo discete dom vible X tkig vlues Epecttio (me): E(X) = = i P(X = i) i with pobbilities P(X = i) Vice: V(X) = = ( i ) P(X = i) = P(X = i) Fo fuctio g( X ) : E(g(X)) = g( i) P(X = i) The pobbility geetig fuctio of X is G ( t ) E t X X i d E( X) G () d V( X) G () G () G () X X X X Fo Z = X + Y, whee X d Y e idepedet: G ( t) G ( t) G ( t) Z X Y Discete distibutios Stdd discete distibutios: Distibutio of X P(X = ) Me Vice P.G.F. p Biomil B(, p) p p p( p) p pt Poisso Po ( ) e e t! Geometic Geo(p) p o,, p p p p pt ( pt ) Negtive biomil o, +, p ( p) p ( p) p pt ( pt ) Cotiuous distibutios Fo cotiuous dom vible X hvig pobbility desity fuctio f Epecttio (me): E( X ) f( ) d X Vice: V( ) ( ) f( )d f( )d Fo fuctio ) g( X : E(g( X )) g( ) f( ) d Cumultive distibutio fuctio: F( ) P( X ) f ( t) dt Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
26 Stdd cotiuous distibutio: Distibutio of X P.D.F. Me Vice Noml N(, ) e Uifom (Rectgul) o [, b] b ( b) ( b ) Coeltio d egessio Fo set of pis of vlues, y ) ( i ) S ( i ) i ( yi ) S yy ( yi y) yi ( i i ( i)( yi) S y ( i )( yi y) i yi The poduct momet coeltio coefficiet is ( i)( yi) S y ( )( ) i i y i yi y S S yy { ( i ) }{ ( yi y) } ( i) ( yi) i yi The egessio coefficiet of y o is S ( )( y y) b S ( ) y i i i Lest sques egessio lie of y o is y b whee y b Residul Sum of Sques (RSS) = Sy Syy Syy S Spem s k coeltio coefficiet is s 6d ( ) Epecttio lgeb Fo idepedet dom vibles X d Y E( XY ) E( X ) E( Y), V( X by ) V( X ) b V( Y) Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
27 Smplig distibutios (i) Tests fo me whe is kow Fo dom smple me d vice X, X,, X of idepedet obsevtios fom distibutio hvig : X is ubised estimto of, with V( X ) S is ubised estimto of, whee S ( X X ) i Fo dom smple of obsevtios fom X N(, ), ~ N(0, ) / Fo dom smple of obsevtios fom N(, ) d, idepedetly, dom smple of obsevtios fom N(, ( X Y ) ( ) ) y y y, y ~ N(0,) y y (ii) Tests fo vice d me whe is ot kow Fo dom smple of obsevtios fom N(, ) : ( ) S ~ X ~ S / t (lso vlid i mtched-pis situtios) Fo dom smple of obsevtios fom N(, ) d, idepedetly, dom smple of obsevtios fom N(, ) y y y S S y / / y ~ F, y If y (ukow) the ( X Y) ( y) ~ t S p y y whee y y ( ) S ( ) S S p y Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
28 No-pmetic tests Goodess-of-fit test d cotigecy tbles: ( O i Ei E ) i ~ Sttisticl tbles The followig sttisticl tbles e equied fo A Level Futhe Mthemtics: Biomil Cumultive Distibutio Fuctio (see pge 5) Pecetge Poits Of The Noml Distibutio (see pge 0) Poisso Cumultive Distibutio Fuctio (see pge ) Pecetge Poits of the Distibutio (see pge ) Citicl Vlues fo Coeltio Coefficiets: Poduct Momet Coefficiet d Spem s Coefficiet (see pge ) Rdom Numbes (see pge 4) Pecetge Poits of Studet s t Distibutio (see pge 5) Pecetge Poits of the F Distibutio (see pge 6 4 Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
29 Mechics Cetes of mss Fo uifom bodies: Tigul lmi: log medi fom vete Cicul c, dius, gle t cete : si fom cete Secto of cicle, dius, gle t cete si : fom cete Solid hemisphee, dius : 8 fom cete Hemispheicl shell, dius : fom cete Solid coe o pymid of height h: h 4 bove the bse o the lie fom cete of bse to vete Coicl shell of height h: h bove the bse o the lie fom cete of bse to vete Motio i cicle Tsvese velocity: v Tsvese cceletio: v Rdil cceletio: v Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 5 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
30 6 Sttisticl Tbles Biomil Cumultive Distibutio Fuctio The tbulted vlue is P(X ), whee X hs biomil distibutio with ide d pmete p. p = = 5, = = 6, = = 7, = = 8, = = 9, = = 0, = Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
31 p = =, = = 5, = = 0, = Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 7 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
32 p = = 5, = = 0, = Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
33 p = = 40, = Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 9 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
34 p = = 50, = Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
35 Pecetge Poits Of The Noml Distibutio The vlues z i the tble e those which dom vible Z N(0, ) eceeds with pobbility p; tht is, P(Z > z) = (z) = p. p z p z Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
36 Poisso Cumultive Distibutio Fuctio The tbulted vlue is P(X ), whee X hs Poisso distibutio with pmete. = = = = Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
37 Pecetge Poits of the Distibutio The vlues i the tble e those which dom vible with the distibutio o degees of feedom eceeds with the pobbility show Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
38 Citicl Vlues fo Coeltio Coefficiets These tbles coce tests of the hypothesis tht popultio coeltio coefficiet is 0. The vlues i the tbles e the miimum vlues which eed to be eched by smple coeltio coefficiet i ode to be sigifict t the level show, o oe-tiled test. Poduct Momet Coefficiet Smple Level Spem s Coefficiet Level Level Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
39 Rdom Numbes Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 5 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
40 Pecetge Poits of Studet s t Distibutio The vlues i the tble e those which dom vible with Studet s t distibutio o degees of feedom eceeds with the pobbility show Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
41 Pecetge Poits of the F Distibutio The vlues i the tble e those which dom vible with the F distibutio o d degees of feedom eceeds with pobbility 0.05 o 0.0. Pobbility If uppe pecetge poit of the F distibutio o d degees of feedom is f, the the coespodig lowe pecetge poit of the F distibutio o d degees of feedom is / f. Peso Edecel Level Advced Subsidiy d Advced GCE i Mthemtics d Futhe Mthemtics 7 Mthemticl Fomule d Sttisticl Tbles Vesio.0 Accedited pe-publictio Mch 07 Peso Eductio Limited 07
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
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