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
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
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 007 5 Eeel GCE Mthemts Gettg Stte
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 007 4 Eeel GCE Mthemts Gettg Stte
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 007 7 Eeel GCE Mthemts Gettg Stte 5
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 007 6 Eeel GCE Mthemts Gettg Stte
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 007 9 Eeel GCE Mthemts Gettg Stte 7
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 007 8 Eeel GCE Mthemts Gettg Stte
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.
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 007 0 Eeel GCE Mthemts Gettg Stte
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
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
Fomule Booklet BLANK PAGE TURN OVER FOR MECHANICS & STATISTICS FORMULAE UA08598 Eeel AS/A level Mthemts Fomule Lst Issue Septeme 007 5 Eeel GCE Mthemts Gettg Stte
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 007 4 Eeel GCE Mthemts Gettg Stte
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 007 7 Eeel GCE Mthemts Gettg Stte 5
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 007 6 Eeel GCE Mthemts Gettg Stte
Eeel GCE Mthemts Gettg Stte 7 Eeel GCE Mthemts Fomule Booklet UA08598 Eeel AS/A level Mthemts Fomule Lst: Sttsts S Issue Septeme 007 9 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