WELSH JOINT EDUCATION COMMITTEE CYD-BWYLLGOR ADDYSG CYMRU MATHEMATICS. FORMULA BOOKLET (New Specification)

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1 WELSH JOINT EDUCATION COMMITTEE CYD-BWYLLGOR ADDYSG CYMRU Gl Ciic o Eucio Avc Lvl/Avc Susii Tssgi Asg Giol So Uwch/Uwch Gol MATHEMATICS FORMULA BOOKLET Nw Spciicio Issu 004

2 Msuio Suc o sph 4π A o cuv suc o co Aihmic Sis u S l [ ] Gomic Sis u S S o < Summios 6 4 Biomil Sis wh C!!! Pu Mhmics π sl high N <, R.. Logihms poils l Compl Nums { cosθ isiθ } cos θ isi θ θ i cosθ isiθ Th oos o z k i π giv z, o k 0,,,,

3 Mclui s Tlo s Sis 0! 0! 0 0!!!! o ll!! p l < o ll!!! si o ll! 4!! cos 4 o ll!!! sih o ll! 4!! cosh 4 h < < Hpolic Fucios sih cosh cosh sih sih sih cosh cosh l cosh } { l{ } sih l h <

4 Cooi Gom Coics Ellips Pol Hpol S 4 Fom Pmic cosθ, siθ, Fom scθ, θ ± coshθ, sihθ Rcgul Hpol c c c, Eccici < > Foci ±, 0, 0 ±, 0 ± c, ± c Dicics ± ± ± c Asmpos o o 0, 0 ± Tigoomic Iiis si A ± B si Acos B ± cos Asi B cos A ± B cos Acos B si Asi B A ± B A ± B A ± B k A B Fo Vcos A : si A, A B A B si A si B si cos A B A B si A si B cos si A B A B cos A cos B cos cos A B A B cos A cos B si si cos A Th solu o i h icio o is Th poi iviig AB i h io Mi somios. λ : μ is π μ λ λ μ cosθ Aiclockwis oio hough θ ou O: siθ Rlcio i h li θ : cosθ si θ si θ cosθ siθ cosθ 4

5 Diiio Fucio g sc sc sc co cosc cosc cosc co si cos sih Diviv g g g cosh cosh sih h sch sih cosh h

6 Igio cos; > 0 wh lv Fucio Igl l sc co l si cosc l cosc co l sc l sc l 4 π sc sih cosh cosh sih h l cosh si < cosh l{ } sih l l h { } l v u u uv v > < 6

7 A o sco θ A pol coois Ac lgh s csi coois s pmic om Suc o voluio s S π π s S π π Numicl Mhmics Numicl igio Th pzium ul: } { 0 h, wh h Simpso s Rul: h } 4 { 4 0, wh h is v Numicl Soluio o Equios Th Nwo-Rphso iio o solvig 0 : Mchics Moio i cicl Tsvs vloci: v θ ω Ril cclio: v θ ω Cs o Mss o Uiom Bois Tigul lmi: log mi om v 7

8 Poili 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 Bs Thom: Disc isiuios P A j Poili & Sisics P A j P B A j B Σ P A P B A Fo isc om vil X kig vlus Epcio m: Vic: V X Fo ucio gx : E X μ Σ i p i i i i σ Σ i μ pi Σ i pi Eg X Σ g i p i wih poiliis μ pi S isc isiuios: Disiuio o X P X M Vic Biomil B, p Poisso Poλ p p p p p λ λ λ λ! Coiuous isiuios Fo coiuous om vil X hvig poili si ucio Epcio m: E X μ Vic: V X σ μ Fo ucio gx : Cumuliv isiuio ucio: S coiuous isiuios: Eg X g F P X μ Disiuio o X P.D.F. M Vic Uiom Rcgul o [, ] U[,] Noml N μ, σ μ μ σ σ σ π 8

9 Epcio lg Fo ip om vils X Y E XY E X E Y, V X ± Y V X V Y Smplig isiuios Fo om smpl X, X,, m μ vic σ X X is uis simo o μ, wih S is uis simo o σ, wh o ip osvios om isiuio hvig σ V X Fo om smpl o osvios om N μ, σ X μ ~ N0, σ / X μ ~ S / S Σ X i X I X is h osv um o succsss i ip Boulli ils i ch o which h X poili o succss is p, Y, h E Y p V Y p p Fo om smpl o osvios om N μ, σ, ipl, om smpl o osvios om N μ, σ X Y μ μ ~ N0, σ σ 9

10 Mho o Ls Squs I α β, i,,...,, i i i h h ls squs sims o β α spcivl, wh S / S,, S i i i i i i / S i i i / I,.,..., ip ch is isiu s N0, σ, h i i is osvio om N α, σ, S ii is osvio om N β, σ S iii, 0 0 h ls squs sim o α β, 0 0 is osvio om N 0, σ 0 S RJC/JD/W Fu, 009 0