For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations

Transcription

1 GCE Edecel GCE Mthemtcs Mthemtcl Fomule d Sttstcl Tles Fo use Edecel Advced Susd GCE d Advced GCE emtos Coe Mthemtcs C C4 Futhe Pue Mthemtcs FP FP Mechcs M M5 Sttstcs S S4 Fo use fom Ju 008 UA08598

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3 TABLE OF CONTENTS Pge 4 Coe Mthemtcs C 4 Mesuto 4 Athmetc sees 5 Coe Mthemtcs C 5 Cose ule 5 Boml sees 5 Logthms d epoetls 5 Geometc sees 5 Numecl tegto 6 Coe Mthemtcs C 6 Logthms d epoetls 6 Tgoometc dettes 6 Dffeetto 7 Coe Mthemtcs C4 7 Itegto 8 Futhe Pue Mthemtcs FP 8 Summtos 8 Numecl soluto of equtos 8 Coodte geomet 8 Cocs 8 Mt tsfomtos 9 Futhe Pue Mthemtcs FP 9 Ae of secto 9 Mclu s d Tlo s Sees 0 Tlo polomls Futhe Pue Mthemtcs FP Vectos Hpeolcs 4 Itegto 4 Ac legth 5 Sufce e of evoluto UA08598 Edecel AS/A level Mthemtcs Fomule Lst: C C4, FP FP Cotets Pge Issue Septeme 007

4 6 Mechcs M 6 Thee e o fomule gve fo M ddto to those cddtes e epected to kow. 6 Mechcs M 6 Cetes of mss 6 Mechcs M 6 Moto ccle 6 Cetes of mss 6 Uvesl lw of gvtto 7 Mechcs M4 7 Thee e o fomule gve fo M4 ddto to those cddtes e epected to kow. 7 Mechcs M5 7 Momets of et 7 Momets s vectos 8 Sttstcs S 8 Polt 8 Dscete dstutos 8 Cotuous dstutos 9 Coelto d egesso 0 The Noml dstuto fucto Pecetge pots of the Noml dstuto Sttstcs S Dscete dstutos Cotuous dstutos Boml cumultve dstuto fucto 8 Posso cumultve dstuto fucto 9 Sttstcs S 9 Epectto lge 9 Smplg dstutos 9 Coelto d egesso 9 No-pmetc tests 0 Pecetge pots of the dstuto Ctcl vlues fo coelto coeffcets Rdom umes Sttstcs S4 Smplg dstutos 4 Pecetge pots of Studet s t dstuto 5 Pecetge pots of the F dstuto Thee e o fomule povded fo Decso Mthemtcs uts D d D. UA08598 Edecel AS/A level Mthemtcs Fomule Lst: M M5, S S4 Cotets Pge Issue Septeme 007

5 The fomule ths ooklet hve ee ged ccodg to the ut whch the e fst toduced. Thus cddte sttg ut m e equed to use the fomule tht wee toduced pecedg ut e.g. cddtes sttg C mght e epected to use fomule fst toduced C o C. It m lso e the cse tht cddtes sttg Mechcs d Sttstcs uts eed to use fomule toduced ppopte Coe Mthemtcs uts, s outled the specfcto. UA08598 Edecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007

6 Coe Mthemtcs C Mesuto Sufce e of sphee = 4 Ae of cuved sufce of coe = slt heght Athmetc sees u = + d S = + l = [ + d] 4 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme 007

7 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme Coe Mthemtcs C Cddtes sttg C m lso eque those fomule lsted ude Coe Mthemtcs C. Cose ule = + c c cos A Boml sees N whee!!! C, R Logthms d epoetls log log log Geometc sees u = S = S = fo < Numecl tegto The tpezum ule: d h{ }, whee h

8 Coe Mthemtcs C Cddtes sttg C m lso eque those fomule lsted ude Coe Mthemtcs C d C. Logthms d epoetls e l Tgoometc dettes s A B s Acos B cos As B cos A B cos Acos B s As B t A t B t A B A B k t At B A B A B s A s B s cos A B A B s A s B cos s A B A B cos A cos B cos cos A B A B cos A cos B s s Dffeetto f t k sec cot cosec f g f k sec k sec t cosec cosec cot f g f g g 6 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme 007

9 Coe Mthemtcs C4 Cddtes sttg C4 m lso eque those fomule lsted ude Coe Mthemtcs C, C d C. Itegto + costt f f d sec k t k k t l sec cot l s cosec l cosec cot l t sec l sec t l t 4 dv du u d uv v d d d UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C4 Issue Septeme 007 7

10 Futhe Pue Mthemtcs FP Cddtes sttg FP m lso eque those fomule lsted ude Coe Mthemtcs C d C. Summtos 6 4 Numecl soluto of equtos The Newto-Rphso teto fo solvg f 0 : f f Coodte geomet The pepedcul dstce fom h, k to c 0 s The cute gle etwee les wth gdets m d m s ct h k c m m m m Cocs Pol Rectgul Hpeol Stdd Fom 4 = c Pmetc Fom t, t ct, c t Foc, 0 Not equed Dectces Not equed 8 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007

11 Mt tsfomtos Atclockwse otto though out O: cos s s cos Reflecto the le cos s t : s cos UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 9

12 Futhe Pue Mthemtcs FP Cddtes sttg FP m lso eque those fomule lsted ude Futhe Pue Mthemtcs FP d Coe Mthemtcs C C4. Ae of secto A = d pol coodtes Comple umes e cos s { cos s } cos s k e The oots of z e gve z, fo k 0,,,, Mclu s d Tlo s Sees f f0 f 0 f 0 f 0!! f f f! f f! f f f f f!! e ep!! l fo ll 5 s! 5!! 4 cos! 4!! 5 ct 5 Tlo polomls h f h f h f f eo! h f h f h f f! f f f! f f f! fo ll fo ll 0 h f eo f 0 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007

13 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 Futhe Pue Mthemtcs FP Cddtes sttg FP m lso eque those fomule lsted ude Futhe Pue Mthemtcs FP, d Coe Mthemtcs C C4. Vectos The esolved pt of the decto of s. The pot dvdg AB the to : s Vecto poduct: ˆ s k j c. c. c. c c c c..c c If A s the pot wth posto vecto k j d the decto vecto s gve k j, the the stght le though A wth decto vecto hs ctes equto z The ple though A wth oml vecto k j hs ctes equto. d d z 0 whee The ple though o-colle pots A, B d C hs vecto equto c c The ple though the pot wth posto vecto d pllel to d c hs equto c t s The pepedcul dstce of,, fom 0 d z s d.

14 Hpeolc fuctos cosh sh sh sh cosh cosh cosh sh cosh l{ } sh l{ } th l Cocs Ellpse Pol Hpeol Rectgul Hpeol Stdd Fom 4 c Pmetc Fom cos, s t, t sec, t cosh, sh ct, c t Eccetct e e e e e e = Foc e, 0, 0 e, 0 c, c Dectces e + = c e Asmptotes oe oe 0, 0 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007

15 Dffeetto f f cs ccos ct sh cosh cosh sh th sech sh cosh th Itegto + costt; 0 whee elevt f f d sh cosh cosh sh th l cosh cs ct cosh l{ } sh l l { } th l UA08598 Edecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007

16 4 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 Ac legth s d d d ctes coodtes t t t s d d d d d pmetc fom Sufce e of evoluto d d d d d d S s t t t

17 BLANK PAGE TURN OVER FOR MECHANICS & STATISTICS FORMULAE UA08598 Edecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007 5

18 Mechcs M Thee e o fomule gve fo M ddto to those cddtes e epected to kow. Cddtes sttg M m lso eque those fomule lsted ude Coe Mthemtcs C. Mechcs M Cddtes sttg M m lso eque those fomule lsted ude Coe Mthemtcs C, C d C. Cetes of mss Fo ufom odes: Tgul lm: log med fom vete s Ccul c, dus, gle t cete : fom cete s Secto of ccle, dus, gle t cete : fom cete Mechcs M Cddtes sttg M m lso eque those fomule lsted ude Mechcs M, d lso those fomule lsted ude Coe Mthemtcs C C4. Moto ccle Tsvese veloct: v Tsvese cceleto: v Rdl cceleto: Cetes of mss Fo ufom odes: v Sold hemsphee, dus : fom cete 8 Hemsphecl shell, dus : Sold coe o pmd of heght h: fom cete h ove the se o the le fom cete of se to vete 4 Cocl shell of heght h: h ove the se o the le fom cete of se to vete Uvesl lw of gvtto Gmm Foce d 6 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Mechcs M M Issue Septeme 007

19 Mechcs M4 Thee e o fomule gve fo M4 ddto to those cddtes e epected to kow. Cddtes sttg M4 m lso eque those fomule lsted ude Mechcs M d M, d lso those fomule lsted ude Coe Mthemtcs C C4 d Futhe Pue Mthemtcs FP. Mechcs M5 Cddtes sttg M5 m lso eque those fomule lsted ude Mechcs M d M, d lso those fomule lsted ude Coe Mthemtcs C C4 d Futhe Pue Mthemtcs FP. Momets of et Fo ufom odes of mss m: Th od, legth l, out pepedcul s though cete: ml Rectgul lm out s ple sectg edges of legth l: Th od, legth l, out pepedcul s though ed: 4 ml Rectgul lm out edge pepedcul to edges of legth l: Rectgul lm, sdes d, out pepedcul s though cete: m Hoop o cldcl shell of dus out s though cete: Hoop of dus out dmete: m Dsc o sold clde of dus out s though cete: Dsc of dus out dmete: m Sold sphee, dus, out dmete: 4 m Sphecl shell of dus out dmete: 5 m m m ml 4 ml Pllel es theoem: I A I Pepedcul es theoem: Momets s vectos G z mag The momet out O of F ctg t s I I I fo lm the - ple F UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Mechcs M4 M5 Issue Septeme 007 7

20 Sttstcs S Polt P A B P A P B P A B P A B P AP B A P B AP A P A B P B AP A P B AP A Dscete dstutos Fo dscete dom vle X tkg vlues wth poltes PX = Epectto me: EX = = PX = Vce: VX = = PX = = Fo fucto g X : EgX = g PX = PX = Cotuous dstutos Stdd cotuous dstuto: Dstuto of X P.D.F. Me Vce Noml N, e 8 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

21 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Coelto d egesso Fo set of ps of vlues, S S S The poduct momet coelto coeffcet s S S S } }{ { The egesso coeffcet of o s S S Lest sques egesso le of o s whee

22 THE NORMAL DISTRIBUTION FUNCTION The fucto tulted elow s z, defed s z = z t e dt. z z z z z z z z z z UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

23 PERCENTAGE POINTS OF THE NORMAL DISTRIBUTION The vlues z the tle e those whch dom vle Z N0, eceeds wth polt p; tht s, PZ > z = z = p. p z p z UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

24 Sttstcs S Cddtes sttg S m lso eque those fomule lsted ude Sttstcs S, d lso those lsted ude Coe Mthemtcs C d C. Dscete dstutos Stdd dscete dstutos: Dstuto of X P X Me Vce Boml B, p p p p p p Posso Po e! Cotuous dstutos Fo cotuous dom vle X hvg polt dest fucto f Epectto me: E X f d Vce: V X f d f d Fo fucto g X : Eg X g f d Cumultve dstuto fucto: Stdd cotuous dstuto: 0 F P X 0 0 f t dt Dstuto of X P.D.F. Me Vce Ufom Rectgul o [, ] UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

25 BINOMIAL CUMULATIVE DISTRIBUTION FUNCTION The tulted vlue s PX, whee X hs oml dstuto wth de d pmete p. p = = 5, = = 6, = = 7, = = 8, = = 9, = = 0, = UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

26 p = =, = = 5, = = 0, = UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

27 p = = 5, = = 0, = UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 5

28 p = = 40, = UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

29 p = = 50, = UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 7

30 POISSON CUMULATIVE DISTRIBUTION FUNCTION The tulted vlue s PX, whee X hs Posso dstuto wth pmete. = = = = UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

31 Sttstcs S Cddtes sttg S m lso eque those fomule lsted ude Sttstcs S d S. Epectto lge Fo depedet dom vles X d Y E XY E X E Y, V X Y V X V Y Smplg dstutos Fo dom smple X me d vce, X,, X of depedet osevtos fom dstuto hvg X s used estmto of, wth S s used estmto of, whee V X Fo dom smple of osevtos fom N, X ~ N0, / S X X Fo dom smple of osevtos fom N, d, depedetl, dom smple of osevtos fom N, X Y ~ N0, Coelto d egesso Spem s k coelto coeffcet s s 6d No-pmetc tests Goodess-of-ft test d cotgec tles: O E E ~ UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 9

32 PERCENTAGE POINTS OF THE DISTRIBUTION The vlues the tle e those whch dom vle wth the dstuto o degees of feedom eceeds wth the polt show UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

33 CRITICAL VALUES FOR CORRELATION COEFFICIENTS These tles coce tests of the hpothess tht populto coelto coeffcet s 0. The vlues the tles e the mmum vlues whch eed to e eched smple coelto coeffcet ode to e sgfct t the level show, o oe-tled test. Poduct Momet Coeffcet Spem s Coeffcet Level Smple Level Level UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

34 RANDOM NUMBERS UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

35 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S4 Issue Septeme 007 Sttstcs S4 Cddtes sttg S4 m lso eque those fomule lsted ude Sttstcs S, S d S. Smplg dstutos Fo dom smple of osevtos fom, N ~ S ~ / t S X lso vld mtched-ps stutos Fo dom smple of osevtos fom, N d, depedetl, dom smple of osevtos fom, N, ~ / / F S S If ukow the ~ p t S Y X whee p S S S

36 PERCENTAGE POINTS OF STUDENT S t DISTRIBUTION The vlues the tle e those whch dom vle wth Studet s t dstuto o degees of feedom eceeds wth the polt show UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S4 Issue Septeme 007

37 PERCENTAGE POINTS OF THE F DISTRIBUTION The vlues the tle e those whch dom vle wth the F dstuto o d degees of feedom eceeds wth polt 0.05 o 0.0. Polt / If uppe pecetge pot of the F dstuto o d degees of feedom s f, the the coespodg lowe pecetge pot of the F dstuto o d degees of feedom s / f. UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S4 Issue Septeme 007 5

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