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

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Ginger Lane
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1 Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule fst toue C o C. It m lso e the se tht tes sttg Mehs Sttsts uts ee to use fomule toue ppopte Coe Mthemts uts, s outle the spefto. Eeel GCE Mthemts Gettg Stte

2 Fomule Booklet Coe Mthemts C Mesuto Sufe e of sphee 4π Ae of uve sufe of oe π slt heght Athmet sees u S l [ ] 4 UA08598 Eeel AS/A level Mthemts Fomule Lst: Coe Mthemts C Issue Septeme 007 Eeel GCE Mthemts Gettg Stte

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

4 Fomule Booklet Coe Mthemts C Ctes sttg C m lso eque those fomule lste ue Coe Mthemts C C. Logthms epoetls e l Tgoomet ettes s A ± B s Aos B ± os As B os A ± B os Aos 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 os A B A B s A s B os s A B A B os A os B os os A B A B os A os B s s π Dffeetto f t k se ot ose f g f k se k se t ose ose ot f g f g g 6 UA08598 Eeel AS/A level Mthemts Fomule Lst: Coe Mthemts C Issue Septeme Eeel GCE Mthemts Gettg Stte

5 Fomule Booklet Coe Mthemts C4 Ctes sttg C4 m lso eque those fomule lste ue Coe Mthemts C, C C. Itegto ostt f f se k t ot t k k l se l s ose l ose ot l t se l se t l t 4 π v u u uv v UA08598 Eeel AS/A level Mthemts Fomule Lst: Coe Mthemts C4 Issue Septeme Eeel GCE Mthemts Gettg Stte 5

6 Fomule Booklet Futhe Pue Mthemts FP Ctes sttg FP m lso eque those fomule lste ue Coe Mthemts C C. Summtos 6 4 Numel soluto of equtos The Newto-Rphso teto fo solvg f 0 : f f Coote geomet The pepeul ste fom h, k to 0 s h k m m The ute gle etwee les wth gets m m s t m m Cos Pol Retgul Hpeol St Fom 4 Pmet Fom t, t t, t Fo, 0 Not eque Detes Not eque 8 UA08598 Eeel AS/A level Mthemts Fomule Lst: Futhe Pue Mthemts FP Issue Septeme Eeel GCE Mthemts Gettg Stte

7 Fomule Booklet Mt tsfomtos osθ Atlokwse otto though θ out O: sθ sθ osθ Refleto the le os θ s θ tθ : s θ os θ UA08598 Eeel AS/A level Mthemts Fomule Lst: Futhe Pue Mthemts FP Issue Septeme Eeel GCE Mthemts Gettg Stte 7

8 Fomule Booklet Futhe Pue Mthemts FP Ctes sttg FP m lso eque those fomule lste ue Futhe Pue Mthemts FP Coe Mthemts C C4. Ae of seto A θ pol ootes Comple umes θ e osθ sθ { osθ sθ } osθ s θ k e π The oots of z e gve z, fo k 0,,,, Mlu 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 os fo ll! 4!! 5 t 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 Eeel AS/A level Mthemts Fomule Lst: Futhe Pue Mthemts FP Issue Septeme Eeel GCE Mthemts Gettg Stte

9 Eeel GCE Mthemts Gettg Stte 9 Eeel GCE Mthemts Fomule Booklet UA08598 Eeel AS/A level Mthemts Fomule Lst: Futhe Pue Mthemts FP Issue Septeme 007 Futhe Pue Mthemts FP Ctes sttg FP m lso eque those fomule lste ue Futhe Pue Mthemts FP, Coe Mthemts C C4. Vetos The esolve pt of the eto of s. The pot vg AB the to μ λ : s μ λ λ μ Veto pout: ˆ s k j θ..... If A s the pot wth posto veto k j the eto veto s gve k j, the the stght le though A wth eto veto hs tes equto λ z The ple though A wth oml veto k j hs tes equto. z whee 0 The ple though o-olle pots A, B C hs veto equto μ λ μ λ μ λ The ple though the pot wth posto veto pllel to hs equto t s The pepeul ste of,, γ β α fom 0 z s γ β α.

10 Fomule Booklet Hpeol futos osh sh sh sh osh osh osh sh osh l{ } sh l{ } th l < Cos Ellpse Pol Hpeol Retgul Hpeol St Fom 4 Pmet Fom osθ, sθ t, t se θ, t θ ± osh θ, sh θ t, t Eett e < e e e > e e Fo ± e, 0, 0 ± e, 0 ±, ± Detes ± e ± ± e Asmptotes oe oe ± 0, 0 UA08598 Eeel AS/A level Mthemts Fomule Lst: Futhe Pue Mthemts FP Issue Septeme Eeel GCE Mthemts Gettg Stte

11 Fomule Booklet Dffeetto f f s os t sh osh osh sh th sh osh seh th Itegto ostt; > 0 whee elevt f f sh osh th osh sh l osh s t < osh l{ } sh l l l { } th > < UA08598 Eeel AS/A level Mthemts Fomule Lst Issue Septeme 007 Eeel GCE Mthemts Gettg Stte

12 Eeel GCE Mthemts Gettg Stte Eeel GCE Mthemts Fomule Booklet 4 UA08598 Eeel AS/A level Mthemts Fomule Lst: Futhe Pue Mthemts FP Issue Septeme 007 A legth s tes ootes t t t s pmet fom Sufe e of evoluto S s t t t π π

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

14 Fomule Booklet Mehs M Thee e o fomule gve fo M to to those tes e epete to kow. Ctes sttg M m lso eque those fomule lste ue Coe Mthemts C. Mehs M Ctes sttg M m lso eque those fomule lste ue Coe Mthemts C, C C. Cetes of mss Fo ufom oes: Tgul lm: log me fom vete sα Cul, us, gle t ete α : fom ete α sα Seto of le, us, gle t ete α : fom ete α Mehs M Ctes sttg M m lso eque those fomule lste ue Mehs M, lso those fomule lste ue Coe Mthemts C C4. Moto le Tsvese velot: v θ Tsvese eleto: v θ v Rl eleto: θ Cetes of mss Fo ufom oes: Sol hemsphee, us : Hemsphel shell, us : Sol oe o pm of heght h: Col shell of heght h: Uvesl lw of gvtto Gm m Foe fom ete 8 fom ete h ove the se o the le fom ete of se to vete 4 h ove the se o the le fom ete of se to vete 6 UA08598 Eeel AS/A level Mthemts Fomule Lst: Mehs M M Issue Septeme Eeel GCE Mthemts Gettg Stte

15 Fomule Booklet Mehs M4 Thee e o fomule gve fo M4 to to those tes e epete to kow. Ctes sttg M4 m lso eque those fomule lste ue Mehs M M, lso those fomule lste ue Coe Mthemts C C4 Futhe Pue Mthemts FP. Mehs M5 Ctes sttg M5 m lso eque those fomule lste ue Mehs M M, lso those fomule lste ue Coe Mthemts C C4 Futhe Pue Mthemts FP. Momets of et Fo ufom oes of mss m: Th o, legth l, out pepeul s though ete: ml Retgul lm out s ple setg eges of legth l: ml Th o, legth l, out pepeul s though e: 4 ml Retgul lm out ege pepeul to eges of legth l: Retgul lm, ses, out pepeul s though ete: m Hoop o ll shell of us out s though ete: m Hoop of us out mete: m Ds o sol le of us out s though ete: Ds of us out mete: m Sol sphee, us, out mete: 4 m Sphel shell of us out mete: 5 m m 4 ml Pllel es theoem: I A I G mag Pepeul es theoem: I I I fo lm the - ple Momets s vetos The momet out O of F tg t s z F UA08598 Eeel AS/A level Mthemts Fomule Lst: Mehs M4 M5 Issue Septeme Eeel GCE Mthemts Gettg Stte 5

16 Fomule Booklet Sttsts 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 Dsete stutos Fo sete om vle X tkg vlues wth poltes PX Epetto me: EX μ PX Ve: VX σ μ PX PX μ Fo futo gx : EgX g PX Cotuous stutos St otuous stuto: Dstuto of X P.D.F. Me Ve Noml N μ, σ μ σ e σ π μ σ 8 UA08598 Eeel AS/A level Mthemts Fomule Lst: Sttsts S Issue Septeme Eeel GCE Mthemts Gettg Stte

17 Eeel GCE Mthemts Gettg Stte 7 Eeel GCE Mthemts Fomule Booklet UA08598 Eeel AS/A level Mthemts Fomule Lst: Sttsts S Issue Septeme Coelto egesso Fo set of ps of vlues, S S S The pout momet oelto oeffet s S S S } }{ { The egesso oeffet of o s S S Lest sques egesso le of o s whee

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

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