GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd.

Transcription

1 GCE AS d A Level MATHEMATICS FORMULA BOOKLET Fom Septeme 07 Issued 07

2 Pue Mthemtcs Mesuto Suce e o sphee = 4 Ae o cuved suce o coe = heght slt Athmetc Sees S = + l = [ + d] Geometc Sees S = S = o < Summtos 6 4 Boml Sees N whee!!! C,.. R Logthms d epoetls l e Comple Numes s cos } s cos { The oots o z e gve y k z e, o,,,, 0 k

3 Mclu s d Tylo s Sees 0! 0! 0 0!!!! ll o!! ep e l ll o!!! s ll o! 4!! cos 4 t ll o!!! sh ll o! 4!! cosh 4 th Hypeolc Fuctos sh cosh cosh sh sh sh cosh cosh l cosh } { l{ } sh l th

4 Tgoometc Idettes s A B s AcosB cos As B cos A B cos AcosB s As B ta tb t A B A B k tatb Fo t t A: t s A, t 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 cosb cos cos A B A B cos A cosb s s t cos A t Vectos The esolute o the decto o s The pot dvdg AB the to. : s The equto o ple Ctes om s y z k. The pepedcul dstce etwee two skew les s D, whee d e posto vectos o pots o ech le d s mutul pepedcul to oth les. y c The pepedcul dstce etwee pot d le s D, whee the coodtes o the pot e, y d the equto o the le s gve y y c. k The pepedcul dstce etwee pot d ple s D, whee,, e the coodtes o the pot d y z k s the equto o the ple. 4

5 Mt tsomtos -D cos s Atclockwse otto though out O: s cos Relecto the le y t : cos s s cos Mt tsomtos -D Atclockwse otto though out: -s y-s z-s 0 0 cos 0 s cos s 0 0 cos s 0 0 s cos 0 0 s cos s 0 cos 0 0 whee tclockwse o postve otto out O o -s s the sese j k, tclockwse o postve otto out Oy o y-s s the sese k, tclockwse o postve otto out Oz o z-s s the sese j.

6 Deetto Fucto g t sec sec sec t cot cosec cosec cosec cot s cos t sh cosh cosh th Devtve g g g sh sech sh cosh th 6

7 Itegto + costt; 0 whee elevt Fucto t cot Itegl l sec l s cosec l cosec cot l t sec l sec t l t 4 sec t sh cosh cosh th s sh l cosh t cosh l{ } sh l l th { } l dv u d uv d du v d d Ae o secto A d pol coodtes 7

8 Numecl Mthemtcs Numecl tegto d 0 y The tpezum ule: y h{ y y y y }, whee h Numecl Soluto o Equtos The Newto-Rphso teto o solvg 0 : Mechcs Moto ccle Tsvese velocty: v Rdl cceleto: v Cetes o Mss o Uom Bodes Tgul lm: log med om vete Sem ccle: 4 om stght edge log s o symmety Qute ccle: 4 4 y om vete 8

9 Polty P A B P A P B P A B P A B P AP B A P B A P A P A B P B AP A P B A P A Byes Theoem: Dscete dstutos P A j Polty & Sttstcs P Aj P B Aj B P A P B A Fo dscete dom vle X tkg vlues wth poltes Epectto me: Vce: V X E X p Fo ucto g X : Eg X g p p p p Stdd dscete dstutos: Dstuto o X P X Me Vce Boml B, p Posso Po p e p p p p! Cotuous dstutos Fo cotuous dom vle X hvg polty desty ucto Epectto me: E X d Vce: V X d d Fo ucto g X : Eg X g d Cumultve dstuto ucto: Stdd cotuous dstutos: F P X t dt Dstuto o X P.D.F. Me Vce Uom Rectgul o [, ] U[,] Noml N, e Epoetl Ep e 9

10 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 me d vce X, X,, X o depedet osevtos om dstuto hvg X s used estmto o, wth S s used estmto o, whee V X Fo dom smple o osevtos om N, X ~ N0, / X ~ t S / S X X I X s the oseved ume o successes depedet Beoull tls ech o whch the X polty o success s p, d Y, the E Y p d V Y p p Fo dom smple o osevtos om N, d, depedetly, dom smple o osevtos om N, y y y X Y y ~ N0, y y 0

11 Coelto d Regesso Fo smple o ps o osevtos, y S y S yy y y y y S y y y y A mesue o le ssocto etwee two vles X d Y s gve y the Peso poduct - momet coelto coecet. Sy Fo the smple,y,,y,...,,y, t s gve y. S S Gve dt, the pmetes d o the le egesso model my e estmted usg the pcple o lest sques. The lest sques estmte ˆ o the pmete s gve y ˆ Sy. S The lest sques estmte ˆ o the pmete s gve y The lest sques egesso le s gve y y ˆ ˆ. yy ˆ y ˆ. Spem's k coelto coecet s gve y s 6 d. SS/LG/W447E