The formulae in this booklet have been arranged according to the unit in which they are first

Transcription

1 Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge ccog to the ut whch the e fst touce. Thus cte sttg ut m e eque to use the fomule tht wee touce peceg ut e.g. ctes sttg C mght e epecte to use fomule fst touce C o C. It m lso e the cse tht ctes sttg Mechcs Sttstcs uts ee to use fomule touce ppopte Coe Mthemtcs uts, s outle the specfcto. Eecel GCE Mthemtcs Gettg Stte

2 Fomule Booklet Coe Mthemtcs C Mesuto Sufce e of sphee 4π Ae of cuve sufce of coe π slt heght Athmetc sees u S l [ ] 4 UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme 007 Eecel GCE Mthemtcs Gettg Stte

3 Fomule Booklet Coe Mthemtcs C Ctes sttg C m lso eque those fomule lste ue Coe Mthemtcs C. Cose ule c c cos A Boml sees! whee C!! <, Logthms epoetls log log log Geometc sees u S S fo < Numecl tegto The tpezum ule: h{ 0... }, whee h UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme Eecel GCE Mthemtcs Gettg Stte

4 Fomule Booklet Coe Mthemtcs C Ctes sttg C m lso eque those fomule lste ue Coe Mthemtcs C C. Logthms epoetls e l Tgoometc ettes 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 π 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 Eecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme Eecel GCE Mthemtcs Gettg Stte

5 Fomule Booklet Coe Mthemtcs C4 Ctes sttg C4 m lso eque those fomule lste ue Coe Mthemtcs C, C C. Itegto costt f f sec k t cot t k k l sec l s cosec l cosec cot l t sec l sec t l t 4 π v u u uv v UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C4 Issue Septeme Eecel GCE Mthemtcs Gettg Stte 5

6 Fomule Booklet Futhe Pue Mthemtcs FP Ctes sttg FP m lso eque those fomule lste ue Coe Mthemtcs C C. Summtos 6 4 Numecl soluto of equtos The Newto-Rphso teto fo solvg f 0 : f f Coote geomet The pepecul stce fom h, k to c 0 s h k c m m The cute gle etwee les wth gets m m s ct m m Cocs Pol Rectgul Hpeol St Fom 4 c Pmetc Fom t, t ct, c t Foc, 0 Not eque Dectces Not eque 8 UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme Eecel GCE Mthemtcs Gettg Stte

7 Fomule Booklet Mt tsfomtos cosθ Atclockwse otto though θ out O: sθ sθ cosθ Reflecto the le cos θ s θ tθ : s θ cos θ UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme Eecel GCE Mthemtcs Gettg Stte 7

8 Fomule Booklet Futhe Pue Mthemtcs FP Ctes sttg FP m lso eque those fomule lste ue Futhe Pue Mthemtcs FP Coe Mthemtcs C C4. Ae of secto A θ pol cootes Comple umes θ e cosθ sθ { cosθ sθ } cosθ s θ k e π The oots of z e gve z, fo k 0,,,, Mclu s Tlo s Sees f f0 f 0 f 0 f 0!! f f f f f!! f f f f f!! e ep fo ll!! l < 5 s fo ll! 5!! 4 cos fo ll! 4!! 5 ct 5 Tlo polomls h f h f h f f eo! h f h f h f f ξ 0 < ξ < h! f f f f eo! f f f f ξ < ξ <! 0 UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme Eecel GCE Mthemtcs Gettg Stte

9 Eecel GCE Mthemtcs Gettg Stte 9 Eecel GCE Mthemtcs Fomule Booklet UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 Futhe Pue Mthemtcs FP Ctes sttg FP m lso eque those fomule lste ue Futhe Pue Mthemtcs FP, Coe Mthemtcs C C4. Vectos The esolve pt of the ecto of s. The pot vg AB the to μ λ : s μ λ λ μ Vecto pouct: ˆ s k j θ c. c. c. c c c c..c c If A s the pot wth posto vecto k j the ecto vecto s gve k j, the the stght le though A wth ecto vecto hs ctes equto λ z The ple though A wth oml vecto k j hs ctes equto. z whee 0 The ple though o-colle pots A, B C hs vecto equto c c μ λ μ λ μ λ The ple though the pot wth posto vecto pllel to c hs equto c t s The pepecul stce of,, γ β α fom 0 z s γ β α.

10 Fomule Booklet Hpeolc fuctos cosh sh sh sh cosh cosh cosh sh cosh l{ } sh l{ } th l < Cocs Ellpse Pol Hpeol Rectgul Hpeol St Fom 4 c Pmetc Fom cosθ, sθ t, t sec θ, t θ ± cosh θ, sh θ 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 Eecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme Eecel GCE Mthemtcs Gettg Stte

11 Fomule Booklet Dffeetto f f cs ccos ct sh cosh cosh sh th sh cosh sech th Itegto costt; > 0 whee elevt f f sh cosh th cosh sh l cosh cs ct < cosh l{ } sh l l l { } th > < UA08598 Eecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007 Eecel GCE Mthemtcs Gettg Stte

12 Eecel GCE Mthemtcs Gettg Stte Eecel GCE Mthemtcs Fomule Booklet 4 UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 Ac legth s ctes cootes t t t s pmetc fom Sufce e of evoluto S s t t t π π

13 Fomule Booklet BLANK PAGE TURN OVER FOR MECHANICS & STATISTICS FORMULAE UA08598 Eecel AS/A level Mthemtcs Fomule Lst Issue Septeme Eecel GCE Mthemtcs Gettg Stte

14 Fomule Booklet Mechcs M Thee e o fomule gve fo M to to those ctes e epecte to kow. Ctes sttg M m lso eque those fomule lste ue Coe Mthemtcs C. Mechcs M Ctes sttg M m lso eque those fomule lste ue Coe Mthemtcs C, C C. Cetes of mss Fo ufom oes: Tgul lm: log me fom vete sα Ccul c, us, gle t cete α : fom cete α sα Secto of ccle, us, gle t cete α : fom cete α Mechcs M Ctes sttg M m lso eque those fomule lste ue Mechcs M, lso those fomule lste ue Coe Mthemtcs C C4. Moto ccle Tsvese veloct: v θ Tsvese cceleto: v θ v Rl cceleto: θ Cetes of mss Fo ufom oes: Sol hemsphee, us : Hemsphecl shell, us : Sol coe o pm of heght h: Cocl shell of heght h: Uvesl lw of gvtto Gm m Foce fom cete 8 fom cete h ove the se o the le fom cete of se to vete 4 h ove the se o the le fom cete of se to vete 6 UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Mechcs M M Issue Septeme Eecel GCE Mthemtcs Gettg Stte

15 Fomule Booklet Mechcs M4 Thee e o fomule gve fo M4 to to those ctes e epecte to kow. Ctes sttg M4 m lso eque those fomule lste ue Mechcs M M, lso those fomule lste ue Coe Mthemtcs C C4 Futhe Pue Mthemtcs FP. Mechcs M5 Ctes sttg M5 m lso eque those fomule lste ue Mechcs M M, lso those fomule lste ue Coe Mthemtcs C C4 Futhe Pue Mthemtcs FP. Momets of et Fo ufom oes of mss m: Th o, legth l, out pepecul s though cete: ml Rectgul lm out s ple sectg eges of legth l: ml Th o, legth l, out pepecul s though e: 4 ml Rectgul lm out ege pepecul to eges of legth l: Rectgul lm, ses, out pepecul s though cete: m Hoop o clcl shell of us out s though cete: m Hoop of us out mete: m Dsc o sol cle of us out s though cete: Dsc of us out mete: m Sol sphee, us, out mete: 4 m Sphecl shell of us out mete: 5 m m 4 ml Pllel es theoem: I A I G mag Pepecul es theoem: I I I fo lm the - ple Momets s vectos The momet out O of F ctg t s z F UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Mechcs M4 M5 Issue Septeme Eecel GCE Mthemtcs Gettg Stte 5

16 Fomule Booklet Sttstcs S Polt P A B P A P B P A B P A B P A P B A P B A P A P A B P B A P A P B A P A Dscete stutos Fo scete om vle X tkg vlues wth poltes PX Epectto me: EX μ PX Vce: VX σ μ PX PX μ Fo fucto gx : EgX g PX Cotuous stutos St cotuous stuto: Dstuto of X P.D.F. Me Vce Noml N μ, σ μ σ e σ π μ σ 8 UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte

17 Eecel GCE Mthemtcs Gettg Stte 7 Eecel GCE Mthemtcs Fomule Booklet UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Coelto egesso Fo set of ps of vlues, S S S The pouct momet coelto coeffcet s S S S } }{ { The egesso coeffcet of o s S S Lest sques egesso le of o s whee

18 Fomule Booklet THE NORMAL DISTRIBUTION FUNCTION The fucto tulte elow s Φz, efe s Φz z t π e t. z Φz z Φz z Φz z Φz z Φz UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte

19 Fomule Booklet PERCENTAGE POINTS OF THE NORMAL DISTRIBUTION The vlues z the tle e those whch om vle Z N0, ecees wth polt p; tht s, PZ > z Φz p. p z p z UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 Eecel GCE Mthemtcs Gettg Stte 9

20 Fomule Booklet Sttstcs S Ctes sttg S m lso eque those fomule lste ue Sttstcs S, lso those lste ue Coe Mthemtcs C C. Dscete stutos St scete stutos: Dstuto of X P X Me Vce Boml B, p p p p p p Posso Poλ λ λ e λ λ! Cotuous stutos Fo cotuous om vle X hvg polt est fucto f Epectto me: E X μ f σ Vce: V X f f Fo fucto gx : μ Eg X g f Cumultve stuto fucto: F P X 0 St cotuous stuto: μ 0 f t 0 Dstuto of X P.D.F. Me Vce t Ufom Rectgul o [, ] UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte

21 Fomule Booklet BINOMIAL CUMULATIVE DISTRIBUTION FUNCTION The tulte vlue s PX, whee X hs oml stuto wth e pmete p. p , , , , , , UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 Eecel GCE Mthemtcs Gettg Stte

22 Fomule Booklet p , , , UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 Eecel GCE Mthemtcs Gettg Stte

23 Fomule Booklet p , , UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte

24 Fomule Booklet p , UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte

25 Fomule Booklet p , UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte 5

26 Fomule Booklet POISSON CUMULATIVE DISTRIBUTION FUNCTION The tulte vlue s PX, whee X hs Posso stuto wth pmete λ. λ λ UA08598 Eecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme Eecel GCE Mthemtcs Gettg Stte