GCE Edexcel GCE in Mathematics Mathematical Formulae and Statistical Tables

GCE Edecel GCE Mthemtcs Mthemtcl Fomule d Sttstcl Tles Fo use Edecel Advced Susd GCE d Advced GCE emtos Coe Mthemtcs C C4 Futhe Pue Mthemtcs FP FP Mechcs M M5 Sttstcs S S4 Fo use fom Ju 009 UA08598

TABLE OF CONTENTS Pge 4 Coe Mthemtcs C 4 Mesuto 4 Athmetc sees 5 Coe Mthemtcs C 5 Cose ule 5 Boml sees 5 Logthms d epoetls 5 Geometc sees 5 Numecl tegto 6 Coe Mthemtcs C 6 Logthms d epoetls 6 Tgoometc dettes 6 Dffeetto 7 Coe Mthemtcs C4 7 Itegto 8 Futhe Pue Mthemtcs FP 8 Summtos 8 Numecl soluto of equtos 8 Coodte geomet 8 Cocs 9 Mt tsfomtos 0 Futhe Pue Mthemtcs FP 0 Ae of secto 0 Mclu s d Tlo s Sees 0 Tlo polomls Futhe Pue Mthemtcs FP Vectos Hpeolcs Cocs Dffeetto Itegto 4 Ac legth 4 Sufce e of evoluto UA08598 Edecel AS/A level Mthemtcs Fomule Lst: C C4, FP FP Cotets Pge Issue Septeme 007

6 Mechcs M 6 Thee e o fomule gve fo M ddto to those cddtes e epected to kow. 6 Mechcs M 6 Cetes of mss 6 Mechcs M 6 Moto ccle 6 Cetes of mss 6 Uvesl lw of gvtto 7 Mechcs M4 7 Thee e o fomule gve fo M4 ddto to those cddtes e epected to kow. 7 Mechcs M5 7 Momets of et 7 Momets s vectos 8 Sttstcs S 8 Polt 8 Dscete dstutos 8 Cotuous dstutos 9 Coelto d egesso 0 The Noml dstuto fucto Pecetge pots of the Noml dstuto Sttstcs S Dscete dstutos Cotuous dstutos Boml cumultve dstuto fucto 8 Posso cumultve dstuto fucto 9 Sttstcs S 9 Epectto lge 9 Smplg dstutos 9 Coelto d egesso 9 No-pmetc tests 0 Pecetge pots of the χ dstuto Ctcl vlues fo coelto coeffcets Rdom umes Sttstcs S4 Smplg dstutos 4 Pecetge pots of Studet s t dstuto 5 Pecetge pots of the F dstuto Thee e o fomule povded fo Decso Mthemtcs uts D d D. UA08598 Edecel AS/A level Mthemtcs Fomule Lst: M M5, S S4 Cotets Pge Issue Septeme 007

The fomule ths ooklet hve ee ged ccodg to the ut whch the e fst toduced. Thus cddte sttg ut m e equed to use the fomule tht wee toduced pecedg ut e.g. cddtes sttg C mght e epected to use fomule fst toduced C o C. It m lso e the cse tht cddtes sttg Mechcs d Sttstcs uts eed to use fomule toduced ppopte Coe Mthemtcs uts, s outled the specfcto. UA08598 Edecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007

Coe Mthemtcs C Mesuto Sufce e of sphee 4π Ae of cuved sufce of coe π slt heght Athmetc sees u d S l [ d] 4 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme 007

UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme 007 5 Coe Mthemtcs C Cddtes sttg C m lso eque those fomule lsted ude Coe Mthemtcs C. Cose ule c c cos A Boml sees N whee!!! C <, R Logthms d epoetls log log log Geometc sees u S S fo < Numecl tegto The tpezum ule: d h{ 0... }, whee h

Coe Mthemtcs C Cddtes sttg C m lso eque those fomule lsted ude Coe Mthemtcs C d C. Logthms d epoetls e l Tgoometc dettes 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 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C Issue Septeme 007

Coe Mthemtcs C4 Cddtes sttg C4 m lso eque those fomule lsted ude Coe Mthemtcs C, C d C. Itegto costt f f d sec k t k k t l sec cot l s cosec l cosec cot l t sec l sec t l t 4 π dv du u d uv v d d d UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Coe Mthemtcs C4 Issue Septeme 007 7

Futhe Pue Mthemtcs FP Cddtes sttg FP m lso eque those fomule lsted ude Coe Mthemtcs C d C. Summtos 6 4 Numecl soluto of equtos The Newto-Rphso teto fo solvg f 0 : f f Coodte geomet The pepedcul dstce fom h, k to c 0 s The cute gle etwee les wth gdets m d m s ct h k c m m m m Cocs Pol Rectgul Hpeol Stdd Fom 4 c Pmetc Fom t, t ct, c t Foc, 0 Not equed Dectces Not equed 8 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007

Mt tsfomtos Atclockwse otto though θ out O: cosθ sθ sθ cosθ Reflecto the le cos θ s θ tθ : s θ cos θ UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 9

Futhe Pue Mthemtcs FP Cddtes sttg FP m lso eque those fomule lsted ude Futhe Pue Mthemtcs FP d Coe Mthemtcs C C4. Ae of secto A dθ pol coodtes 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 d Tlo s Sees f f0 f 0 f 0 f 0!! f f f f f!! f f f f f!! e ep!! l fo ll 5 s! 5!! 4 cos! 4!! 5 ct 5 Tlo polomls h f h f h f f eo! < fo ll fo ll h f h f h f f ξ 0 < ξ < h! f f f f eo! f f f f ξ < ξ <! 0 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007

UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 Futhe Pue Mthemtcs FP Cddtes sttg FP m lso eque those fomule lsted ude Futhe Pue Mthemtcs FP, d Coe Mthemtcs C C4. Vectos The esolved pt of the decto of s. The pot dvdg AB the to μ λ : s μ λ λ μ Vecto poduct: ˆ s k j θ c. c. c. c c c c..c c If A s the pot wth posto vecto k j d the decto vecto s gve k j, the the stght le though A wth decto vecto hs ctes equto λ z The ple though A wth oml vecto k j hs ctes equto. d d z 0 whee The ple though o-colle pots A, B d C hs vecto equto c c μ λ μ λ μ λ The ple though the pot wth posto vecto d pllel to d c hs equto c t s The pepedcul dstce of,, γ β α fom 0 d z s d γ β α.

Hpeolc fuctos cosh sh sh sh cosh cosh cosh sh cosh l{ } sh l{ } th l < Cocs Ellpse Pol Hpeol Rectgul Hpeol Stdd 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 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007

Dffeetto f f cs ccos ct sh cosh cosh sh th sech sh cosh th Itegto costt; > 0 whee elevt f f d sh cosh cosh sh th l cosh cs ct < cosh l{ } sh l l th l { } > < UA08598 Edecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007

4 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Futhe Pue Mthemtcs FP Issue Septeme 007 Ac legth s d d d ctes coodtes t t t s d d d d d pmetc fom Sufce e of evoluto d d d d d d S s t t t π π

BLANK PAGE TURN OVER FOR MECHANICS & STATISTICS FORMULAE UA08598 Edecel AS/A level Mthemtcs Fomule Lst Issue Septeme 007 5

Mechcs M Thee e o fomule gve fo M ddto to those cddtes e epected to kow. Cddtes sttg M m lso eque those fomule lsted ude Coe Mthemtcs C. Mechcs M Cddtes sttg M m lso eque those fomule lsted ude Coe Mthemtcs C, C d C. Cetes of mss Fo ufom odes: Tgul lm: log med fom vete sα Ccul c, dus, gle t cete α : fom cete α sα Secto of ccle, dus, gle t cete α : fom cete α Mechcs M Cddtes sttg M m lso eque those fomule lsted ude Mechcs M, d lso those fomule lsted ude Coe Mthemtcs C C4. Moto ccle Tsvese veloct: v θ Tsvese cceleto: v θ v Rdl cceleto: θ Cetes of mss Fo ufom odes: Sold hemsphee, dus : fom cete 8 Hemsphecl shell, dus : fom cete Sold coe o pmd of heght h: h ove the se o the le fom cete of se to vete 4 Cocl shell of heght h: h ove the se o the le fom cete of se to vete Uvesl lw of gvtto Gmm Foce d 6 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Mechcs M M Issue Septeme 007

Mechcs M4 Thee e o fomule gve fo M4 ddto to those cddtes e epected to kow. Cddtes sttg M4 m lso eque those fomule lsted ude Mechcs M d M, d lso those fomule lsted ude Coe Mthemtcs C C4 d Futhe Pue Mthemtcs FP. Mechcs M5 Cddtes sttg M5 m lso eque those fomule lsted ude Mechcs M d M, d lso those fomule lsted ude Coe Mthemtcs C C4 d Futhe Pue Mthemtcs FP. Momets of et Fo ufom odes of mss m: Th od, legth l, out pepedcul s though cete: ml Rectgul lm out s ple sectg edges of legth l: Th od, legth l, out pepedcul s though ed: 4 ml Rectgul lm out edge pepedcul to edges of legth l: Rectgul lm, sdes d, out pepedcul s though cete: m Hoop o cldcl shell of dus out s though cete: Hoop of dus out dmete: m Dsc o sold clde of dus out s though cete: Dsc of dus out dmete: m Sold sphee, dus, out dmete: 4 m Sphecl shell of dus out dmete: 5 m m m ml 4 ml Pllel es theoem: I I Pepedcul es theoem: Momets s vectos A G z mag The momet out O of F ctg t s I I I fo lm the - ple F UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Mechcs M4 M5 Issue Septeme 007 7

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 dstutos Fo dscete dom vle X tkg vlues wth poltes PX Epectto me: EX μ Σ PX Vce: VX σ Σ μ PX Σ PX μ Fo fucto gx : EgX Σg PX Cotuous dstutos Stdd cotuous dstuto: Dstuto of X P.D.F. Me Vce Noml N μ, σ μ σ e σ π μ σ 8 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 9 Coelto d egesso Fo set of ps of vlues, S Σ Σ Σ S Σ Σ Σ S Σ Σ Σ Σ The poduct momet coelto coeffcet s Σ Σ Σ Σ Σ Σ Σ Σ Σ Σ S S S } }{ { The egesso coeffcet of o s S S Σ Σ Lest sques egesso le of o s whee

THE NORMAL DISTRIBUTION FUNCTION The fucto tulted elow s Φz, defed s Φz z t π e dt. z Φz z Φz z Φz z Φz z Φz 0.00 0.5000 0.50 0.695.00 0.84.50 0.9.00 0.977 0.0 0.5040 0.5 0.6950.0 0.848.5 0.945.0 0.978 0.0 0.5080 0.5 0.6985.0 0.846.5 0.957.04 0.979 0.0 0.50 0.5 0.709.0 0.8485.5 0.970.06 0.980 0.04 0.560 0.54 0.7054.04 0.8508.54 0.98.08 0.98 0.05 0.599 0.55 0.7088.05 0.85.55 0.994.0 0.98 0.06 0.59 0.56 0.7.06 0.8554.56 0.9406. 0.980 0.07 0.579 0.57 0.757.07 0.8577.57 0.948.4 0.988 0.08 0.59 0.58 0.790.08 0.8599.58 0.949.6 0.9846 0.09 0.559 0.59 0.74.09 0.86.59 0.944.8 0.9854 0.0 0.598 0.60 0.757.0 0.864.60 0.945.0 0.986 0. 0.548 0.6 0.79. 0.8665.6 0.946. 0.9868 0. 0.5478 0.6 0.74. 0.8686.6 0.9474.4 0.9875 0. 0.557 0.6 0.757. 0.8708.6 0.9484.6 0.988 0.4 0.5557 0.64 0.789.4 0.879.64 0.9495.8 0.9887 0.5 0.5596 0.65 0.74.5 0.8749.65 0.9505.0 0.989 0.6 0.566 0.66 0.7454.6 0.8770.66 0.955. 0.9898 0.7 0.5675 0.67 0.7486.7 0.8790.67 0.955.4 0.9904 0.8 0.574 0.68 0.757.8 0.880.68 0.955.6 0.9909 0.9 0.575 0.69 0.7549.9 0.880.69 0.9545.8 0.99 0.0 0.579 0.70 0.7580.0 0.8849.70 0.9554.40 0.998 0. 0.58 0.7 0.76. 0.8869.7 0.9564.4 0.99 0. 0.587 0.7 0.764. 0.8888.7 0.957.44 0.997 0. 0.590 0.7 0.767. 0.8907.7 0.958.46 0.99 0.4 0.5948 0.74 0.7704.4 0.895.74 0.959.48 0.994 0.5 0.5987 0.75 0.774.5 0.8944.75 0.9599.50 0.998 0.6 0.606 0.76 0.7764.6 0.896.76 0.9608.55 0.9946 0.7 0.6064 0.77 0.7794.7 0.8980.77 0.966.60 0.995 0.8 0.60 0.78 0.78.8 0.8997.78 0.965.65 0.9960 0.9 0.64 0.79 0.785.9 0.905.79 0.96.70 0.9965 0.0 0.679 0.80 0.788.0 0.90.80 0.964.75 0.9970 0. 0.67 0.8 0.790. 0.9049.8 0.9649.80 0.9974 0. 0.655 0.8 0.799. 0.9066.8 0.9656.85 0.9978 0. 0.69 0.8 0.7967. 0.908.8 0.9664.90 0.998 0.4 0.6 0.84 0.7995.4 0.9099.84 0.967.95 0.9984 0.5 0.668 0.85 0.80.5 0.95.85 0.9678.00 0.9987 0.6 0.6406 0.86 0.805.6 0.9.86 0.9686.05 0.9989 0.7 0.644 0.87 0.8078.7 0.947.87 0.969.0 0.9990 0.8 0.6480 0.88 0.806.8 0.96.88 0.9699.5 0.999 0.9 0.657 0.89 0.8.9 0.977.89 0.9706.0 0.999 0.40 0.6554 0.90 0.859.40 0.99.90 0.97.5 0.9994 0.4 0.659 0.9 0.886.4 0.907.9 0.979.0 0.9995 0.4 0.668 0.9 0.8.4 0.9.9 0.976.5 0.9996 0.4 0.6664 0.9 0.88.4 0.96.9 0.97.40 0.9997 0.44 0.6700 0.94 0.864.44 0.95.94 0.978.50 0.9998 0.45 0.676 0.95 0.889.45 0.965.95 0.9744.60 0.9998 0.46 0.677 0.96 0.85.46 0.979.96 0.9750.70 0.9999 0.47 0.6808 0.97 0.840.47 0.99.97 0.9756.80 0.9999 0.48 0.6844 0.98 0.865.48 0.906.98 0.976.90.0000 0.49 0.6879 0.99 0.889.49 0.99.99 0.9767 4.00.0000 0.50 0.695.00 0.84.50 0.9.00 0.977 0 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

PERCENTAGE POINTS OF THE NORMAL DISTRIBUTION The vlues z the tle e those whch dom vle Z N0, eceeds wth polt p; tht s, PZ > z Φz p. p z p z 0.5000 0.0000 0.0500.6449 0.4000 0.5 0.050.9600 0.000 0.544 0.000.6 0.000 0.846 0.0050.5758 0.500.064 0.000.090 0.000.86 0.0005.905 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

Sttstcs S Cddtes sttg S m lso eque those fomule lsted ude Sttstcs S, d lso those lsted ude Coe Mthemtcs C d C. Dscete dstutos Stdd dscete dstutos: Dstuto of X P X Me Vce Boml B, p p p p p p Posso Poλ λ λ e λ λ! Cotuous dstutos Fo cotuous dom vle X hvg polt dest fucto f Epectto me: E X μ f d Vce: V X f d f d σ Fo fucto gx : Cumultve dstuto fucto: Stdd cotuous dstuto: μ Eg X g f d μ 0 F P X 0 0 f t dt Dstuto of X P.D.F. Me Vce Ufom Rectgul o [, ] UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

BINOMIAL CUMULATIVE DISTRIBUTION FUNCTION The tulted vlue s PX, whee X hs oml dstuto wth de d pmete p. p 0.05 0.0 0.5 0.0 0.5 0.0 0.5 0.40 0.45 0.50 5, 0 0.778 0.5905 0.447 0.77 0.7 0.68 0.60 0.0778 0.050 0.0 0.9774 0.985 0.85 0.77 0.68 0.58 0.484 0.70 0.56 0.875 0.9988 0.994 0.974 0.94 0.8965 0.869 0.7648 0.686 0.59 0.5000.0000 0.9995 0.9978 0.99 0.9844 0.969 0.9460 0.90 0.8688 0.85 4.0000.0000 0.9999 0.9997 0.9990 0.9976 0.9947 0.9898 0.985 0.9688 6, 0 0.75 0.54 0.77 0.6 0.780 0.76 0.0754 0.0467 0.077 0.056 0.967 0.8857 0.7765 0.6554 0.59 0.40 0.9 0. 0.66 0.094 0.9978 0.984 0.957 0.90 0.806 0.744 0.647 0.544 0.445 0.48 0.9999 0.9987 0.994 0.980 0.964 0.995 0.886 0.808 0.7447 0.656 4.0000 0.9999 0.9996 0.9984 0.9954 0.989 0.9777 0.9590 0.908 0.8906 5.0000.0000.0000 0.9999 0.9998 0.999 0.998 0.9959 0.997 0.9844 7, 0 0.698 0.478 0.06 0.097 0.5 0.084 0.0490 0.080 0.05 0.0078 0.9556 0.850 0.766 0.5767 0.4449 0.94 0.8 0.586 0.04 0.065 0.996 0.974 0.96 0.850 0.7564 0.647 0.5 0.499 0.64 0.66 0.9998 0.997 0.9879 0.9667 0.994 0.8740 0.800 0.70 0.608 0.5000 4.0000 0.9998 0.9988 0.995 0.987 0.97 0.9444 0.907 0.847 0.774 5.0000.0000 0.9999 0.9996 0.9987 0.996 0.990 0.98 0.964 0.975 6.0000.0000.0000.0000 0.9999 0.9998 0.9994 0.9984 0.996 0.99 8, 0 0.664 0.405 0.75 0.678 0.00 0.0576 0.09 0.068 0.0084 0.009 0.948 0.8 0.657 0.50 0.67 0.55 0.69 0.064 0.06 0.05 0.994 0.969 0.8948 0.7969 0.6785 0.558 0.478 0.54 0.0 0.445 0.9996 0.9950 0.9786 0.947 0.886 0.8059 0.7064 0.594 0.4770 0.6 4.0000 0.9996 0.997 0.9896 0.977 0.940 0.899 0.86 0.796 0.667 5.0000.0000 0.9998 0.9988 0.9958 0.9887 0.9747 0.950 0.95 0.8555 6.0000.0000.0000 0.9999 0.9996 0.9987 0.9964 0.995 0.989 0.9648 7.0000.0000.0000.0000.0000 0.9999 0.9998 0.999 0.998 0.996 9, 0 0.60 0.874 0.6 0.4 0.075 0.0404 0.007 0.00 0.0046 0.000 0.988 0.7748 0.5995 0.46 0.00 0.960 0. 0.0705 0.085 0.095 0.996 0.9470 0.859 0.78 0.6007 0.468 0.7 0.8 0.495 0.0898 0.9994 0.997 0.966 0.944 0.84 0.797 0.6089 0.486 0.64 0.59 4.0000 0.999 0.9944 0.9804 0.95 0.90 0.88 0.74 0.64 0.5000 5.0000 0.9999 0.9994 0.9969 0.9900 0.9747 0.9464 0.9006 0.84 0.746 6.0000.0000.0000 0.9997 0.9987 0.9957 0.9888 0.9750 0.950 0.90 7.0000.0000.0000.0000 0.9999 0.9996 0.9986 0.996 0.9909 0.9805 8.0000.0000.0000.0000.0000.0000 0.9999 0.9997 0.999 0.9980 0, 0 0.5987 0.487 0.969 0.074 0.056 0.08 0.05 0.0060 0.005 0.000 0.99 0.76 0.544 0.758 0.440 0.49 0.0860 0.0464 0.0 0.007 0.9885 0.998 0.80 0.6778 0.556 0.88 0.66 0.67 0.0996 0.0547 0.9990 0.987 0.9500 0.879 0.7759 0.6496 0.58 0.8 0.660 0.79 4 0.9999 0.9984 0.990 0.967 0.99 0.8497 0.755 0.6 0.5044 0.770 5.0000 0.9999 0.9986 0.996 0.980 0.957 0.905 0.88 0.784 0.60 6.0000.0000 0.9999 0.999 0.9965 0.9894 0.9740 0.945 0.8980 0.88 7.0000.0000.0000 0.9999 0.9996 0.9984 0.995 0.9877 0.976 0.945 8.0000.0000.0000.0000.0000 0.9999 0.9995 0.998 0.9955 0.989 9.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9997 0.9990 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

p 0.05 0.0 0.5 0.0 0.5 0.0 0.5 0.40 0.45 0.50, 0 0.5404 0.84 0.4 0.0687 0.07 0.08 0.0057 0.00 0.0008 0.000 0.886 0.6590 0.445 0.749 0.584 0.0850 0.044 0.096 0.008 0.00 0.9804 0.889 0.758 0.558 0.907 0.58 0.5 0.084 0.04 0.09 0.9978 0.9744 0.9078 0.7946 0.6488 0.495 0.467 0.5 0.45 0.070 4 0.9998 0.9957 0.976 0.974 0.844 0.77 0.58 0.48 0.044 0.98 5.0000 0.9995 0.9954 0.9806 0.9456 0.88 0.787 0.665 0.569 0.87 6.0000 0.9999 0.999 0.996 0.9857 0.964 0.954 0.848 0.79 0.68 7.0000.0000 0.9999 0.9994 0.997 0.9905 0.9745 0.947 0.888 0.806 8.0000.0000.0000 0.9999 0.9996 0.998 0.9944 0.9847 0.9644 0.970 9.0000.0000.0000.0000.0000 0.9998 0.999 0.997 0.99 0.9807 0.0000.0000.0000.0000.0000.0000 0.9999 0.9997 0.9989 0.9968.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9998 5, 0 0.46 0.059 0.0874 0.05 0.04 0.0047 0.006 0.0005 0.000 0.0000 0.890 0.5490 0.86 0.67 0.080 0.05 0.04 0.005 0.007 0.0005 0.968 0.859 0.604 0.980 0.6 0.68 0.067 0.07 0.007 0.007 0.9945 0.9444 0.87 0.648 0.46 0.969 0.77 0.0905 0.044 0.076 4 0.9994 0.987 0.98 0.858 0.6865 0.555 0.59 0.7 0.04 0.059 5 0.9999 0.9978 0.98 0.989 0.856 0.76 0.564 0.40 0.608 0.509 6.0000 0.9997 0.9964 0.989 0.944 0.8689 0.7548 0.6098 0.45 0.06 7.0000.0000 0.9994 0.9958 0.987 0.9500 0.8868 0.7869 0.655 0.5000 8.0000.0000 0.9999 0.999 0.9958 0.9848 0.9578 0.9050 0.88 0.6964 9.0000.0000.0000 0.9999 0.999 0.996 0.9876 0.966 0.9 0.849 0.0000.0000.0000.0000 0.9999 0.999 0.997 0.9907 0.9745 0.9408.0000.0000.0000.0000.0000 0.9999 0.9995 0.998 0.997 0.984.0000.0000.0000.0000.0000.0000 0.9999 0.9997 0.9989 0.996.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9995 4.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 0, 0 0.585 0.6 0.088 0.05 0.00 0.0008 0.000 0.0000 0.0000 0.0000 0.758 0.97 0.756 0.069 0.04 0.0076 0.00 0.0005 0.000 0.0000 0.945 0.6769 0.4049 0.06 0.09 0.055 0.0 0.006 0.0009 0.000 0.984 0.8670 0.6477 0.44 0.5 0.07 0.0444 0.060 0.0049 0.00 4 0.9974 0.9568 0.898 0.696 0.448 0.75 0.8 0.050 0.089 0.0059 5 0.9997 0.9887 0.97 0.804 0.67 0.464 0.454 0.56 0.055 0.007 6.0000 0.9976 0.978 0.9 0.7858 0.6080 0.466 0.500 0.99 0.0577 7.0000 0.9996 0.994 0.9679 0.898 0.77 0.600 0.459 0.50 0.6 8.0000 0.9999 0.9987 0.9900 0.959 0.8867 0.764 0.5956 0.44 0.57 9.0000.0000 0.9998 0.9974 0.986 0.950 0.878 0.755 0.594 0.49 0.0000.0000.0000 0.9994 0.996 0.989 0.9468 0.875 0.7507 0.588.0000.0000.0000 0.9999 0.999 0.9949 0.9804 0.945 0.869 0.748.0000.0000.0000.0000 0.9998 0.9987 0.9940 0.9790 0.940 0.8684.0000.0000.0000.0000.0000 0.9997 0.9985 0.995 0.9786 0.94 4.0000.0000.0000.0000.0000.0000 0.9997 0.9984 0.996 0.979 5.0000.0000.0000.0000.0000.0000.0000 0.9997 0.9985 0.994 6.0000.0000.0000.0000.0000.0000.0000.0000 0.9997 0.9987 7.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9998 8.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 4 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

p 0.05 0.0 0.5 0.0 0.5 0.0 0.5 0.40 0.45 0.50 5, 0 0.774 0.078 0.07 0.008 0.0008 0.000 0.0000 0.0000 0.0000 0.0000 0.644 0.7 0.09 0.074 0.0070 0.006 0.000 0.000 0.0000 0.0000 0.879 0.57 0.57 0.098 0.0 0.0090 0.00 0.0004 0.000 0.0000 0.9659 0.766 0.47 0.40 0.096 0.0 0.0097 0.004 0.0005 0.000 4 0.998 0.900 0.68 0.407 0.7 0.0905 0.00 0.0095 0.00 0.0005 5 0.9988 0.9666 0.885 0.667 0.78 0.95 0.086 0.094 0.0086 0.000 6 0.9998 0.9905 0.905 0.7800 0.56 0.407 0.74 0.076 0.058 0.007 7.0000 0.9977 0.9745 0.8909 0.765 0.58 0.06 0.56 0.069 0.06 8.0000 0.9995 0.990 0.95 0.8506 0.6769 0.4668 0.75 0.40 0.059 9.0000 0.9999 0.9979 0.987 0.987 0.806 0.60 0.446 0.44 0.48 0.0000.0000 0.9995 0.9944 0.970 0.90 0.77 0.5858 0.84 0..0000.0000 0.9999 0.9985 0.989 0.9558 0.8746 0.7 0.546 0.450.0000.0000.0000 0.9996 0.9966 0.985 0.996 0.846 0.697 0.5000.0000.0000.0000 0.9999 0.999 0.9940 0.9745 0.9 0.87 0.6550 4.0000.0000.0000.0000 0.9998 0.998 0.9907 0.9656 0.9040 0.7878 5.0000.0000.0000.0000.0000 0.9995 0.997 0.9868 0.9560 0.885 6.0000.0000.0000.0000.0000 0.9999 0.999 0.9957 0.986 0.946 7.0000.0000.0000.0000.0000.0000 0.9998 0.9988 0.994 0.9784 8.0000.0000.0000.0000.0000.0000.0000 0.9997 0.9984 0.997 9.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9996 0.9980 0.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9995.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9999.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 0, 0 0.46 0.044 0.0076 0.00 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.555 0.87 0.0480 0.005 0.000 0.000 0.0000 0.0000 0.0000 0.0000 0.8 0.44 0.54 0.044 0.006 0.00 0.000 0.0000 0.0000 0.0000 0.99 0.6474 0.7 0.7 0.074 0.009 0.009 0.000 0.0000 0.0000 4 0.9844 0.845 0.545 0.55 0.0979 0.00 0.0075 0.005 0.000 0.0000 5 0.9967 0.968 0.706 0.475 0.06 0.0766 0.0 0.0057 0.00 0.000 6 0.9994 0.974 0.8474 0.6070 0.48 0.595 0.0586 0.07 0.0040 0.0007 7 0.9999 0.99 0.90 0.7608 0.54 0.84 0.8 0.045 0.0 0.006 8.0000 0.9980 0.97 0.87 0.676 0.45 0.47 0.0940 0.0 0.008 9.0000 0.9995 0.990 0.989 0.804 0.5888 0.575 0.76 0.0694 0.04 0.0000 0.9999 0.997 0.9744 0.894 0.704 0.5078 0.95 0.50 0.0494.0000.0000 0.999 0.9905 0.949 0.8407 0.6548 0.4 0.7 0.00.0000.0000 0.9998 0.9969 0.9784 0.955 0.780 0.5785 0.59 0.808.0000.0000.0000 0.999 0.998 0.9599 0.877 0.745 0.505 0.9 4.0000.0000.0000 0.9998 0.997 0.98 0.948 0.846 0.6448 0.478 5.0000.0000.0000 0.9999 0.999 0.996 0.9699 0.909 0.769 0.57 6.0000.0000.0000.0000 0.9998 0.9979 0.9876 0.959 0.8644 0.7077 7.0000.0000.0000.0000 0.9999 0.9994 0.9955 0.9788 0.986 0.89 8.0000.0000.0000.0000.0000 0.9998 0.9986 0.997 0.9666 0.8998 9.0000.0000.0000.0000.0000.0000 0.9996 0.997 0.986 0.9506 0.0000.0000.0000.0000.0000.0000 0.9999 0.999 0.9950 0.9786.0000.0000.0000.0000.0000.0000.0000 0.9998 0.9984 0.999.0000.0000.0000.0000.0000.0000.0000.0000 0.9996 0.9974.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.999 4.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9998 5.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 5

p 0.05 0.0 0.5 0.0 0.5 0.0 0.5 0.40 0.45 0.50 40, 0 0.85 0.048 0.005 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.99 0.0805 0.0 0.005 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6767 0.8 0.0486 0.0079 0.000 0.000 0.0000 0.0000 0.0000 0.0000 0.869 0.4 0.0 0.085 0.0047 0.0006 0.000 0.0000 0.0000 0.0000 4 0.950 0.690 0.6 0.0759 0.060 0.006 0.000 0.0000 0.0000 0.0000 5 0.986 0.797 0.45 0.6 0.04 0.0086 0.00 0.000 0.0000 0.0000 6 0.9966 0.9005 0.6067 0.859 0.096 0.08 0.0044 0.0006 0.000 0.0000 7 0.999 0.958 0.7559 0.47 0.80 0.055 0.04 0.00 0.000 0.0000 8 0.9999 0.9845 0.8646 0.59 0.998 0.0 0.00 0.006 0.0009 0.000 9.0000 0.9949 0.98 0.78 0.495 0.959 0.0644 0.056 0.007 0.000 0.0000 0.9985 0.970 0.89 0.589 0.087 0.5 0.05 0.0074 0.00.0000 0.9996 0.9880 0.95 0.75 0.4406 0.05 0.0709 0.079 0.00.0000 0.9999 0.9957 0.9568 0.809 0.577 0.4 0.85 0.086 0.008.0000.0000 0.9986 0.9806 0.8968 0.70 0.4408 0. 0.075 0.09 4.0000.0000 0.9996 0.99 0.9456 0.8074 0.57 0.74 0.6 0.040 5.0000.0000 0.9999 0.997 0.978 0.8849 0.6946 0.440 0.4 0.0769 6.0000.0000.0000 0.9990 0.9884 0.967 0.7978 0.568 0.85 0.4 7.0000.0000.0000 0.9997 0.995 0.9680 0.876 0.6885 0.49 0.48 8.0000.0000.0000 0.9999 0.998 0.985 0.90 0.79 0.565 0.79 9.0000.0000.0000.0000 0.9994 0.997 0.967 0.870 0.6844 0.47 0.0000.0000.0000.0000 0.9998 0.9976 0.987 0.956 0.7870 0.567.0000.0000.0000.0000.0000 0.999 0.995 0.9608 0.8669 0.68.0000.0000.0000.0000.0000 0.9997 0.9970 0.98 0.9 0.785.0000.0000.0000.0000.0000 0.9999 0.9989 0.997 0.9595 0.8659 4.0000.0000.0000.0000.0000.0000 0.9996 0.9966 0.9804 0.9 5.0000.0000.0000.0000.0000.0000 0.9999 0.9988 0.994 0.9597 6.0000.0000.0000.0000.0000.0000.0000 0.9996 0.9966 0.9808 7.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9988 0.997 8.0000.0000.0000.0000.0000.0000.0000.0000 0.9996 0.9968 9.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9989 0.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9997.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9999.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 6 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

p 0.05 0.0 0.5 0.0 0.5 0.0 0.5 0.40 0.45 0.50 50, 0 0.0769 0.005 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.794 0.08 0.009 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5405 0.7 0.04 0.00 0.000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7604 0.50 0.0460 0.0057 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 4 0.8964 0.4 0. 0.085 0.00 0.000 0.0000 0.0000 0.0000 0.0000 5 0.96 0.66 0.94 0.0480 0.0070 0.0007 0.000 0.0000 0.0000 0.0000 6 0.988 0.770 0.6 0.04 0.094 0.005 0.000 0.0000 0.0000 0.0000 7 0.9968 0.8779 0.588 0.904 0.045 0.007 0.0008 0.000 0.0000 0.0000 8 0.999 0.94 0.668 0.07 0.096 0.08 0.005 0.000 0.0000 0.0000 9 0.9998 0.9755 0.79 0.447 0.67 0.040 0.0067 0.0008 0.000 0.0000 0.0000 0.9906 0.880 0.586 0.6 0.0789 0.060 0.00 0.000 0.0000.0000 0.9968 0.97 0.707 0.86 0.90 0.04 0.0057 0.0006 0.0000.0000 0.9990 0.9699 0.89 0.50 0.9 0.066 0.0 0.008 0.000.0000 0.9997 0.9868 0.8894 0.670 0.79 0.6 0.080 0.0045 0.0005 4.0000 0.9999 0.9947 0.99 0.748 0.4468 0.878 0.0540 0.004 0.00 5.0000.0000 0.998 0.969 0.869 0.569 0.80 0.0955 0.00 0.00 6.0000.0000 0.999 0.9856 0.907 0.689 0.889 0.56 0.047 0.0077 7.0000.0000 0.9998 0.997 0.9449 0.78 0.5060 0.69 0.0765 0.064 8.0000.0000 0.9999 0.9975 0.97 0.8594 0.66 0.56 0.7 0.05 9.0000.0000.0000 0.999 0.986 0.95 0.764 0.4465 0.974 0.0595 0.0000.0000.0000 0.9997 0.997 0.95 0.89 0.560 0.86 0.0.0000.0000.0000 0.9999 0.9974 0.9749 0.88 0.670 0.900 0.6.0000.0000.0000.0000 0.9990 0.9877 0.990 0.7660 0.509 0.99.0000.0000.0000.0000 0.9996 0.9944 0.9604 0.848 0.64 0.59 4.0000.0000.0000.0000 0.9999 0.9976 0.979 0.90 0.760 0.449 5.0000.0000.0000.0000.0000 0.999 0.9900 0.947 0.804 0.556 6.0000.0000.0000.0000.0000 0.9997 0.9955 0.9686 0.87 0.664 7.0000.0000.0000.0000.0000 0.9999 0.998 0.9840 0.90 0.760 8.0000.0000.0000.0000.0000.0000 0.999 0.994 0.9556 0.889 9.0000.0000.0000.0000.0000.0000 0.9997 0.9966 0.9765 0.8987 0.0000.0000.0000.0000.0000.0000 0.9999 0.9986 0.9884 0.9405.0000.0000.0000.0000.0000.0000.0000 0.9995 0.9947 0.9675.0000.0000.0000.0000.0000.0000.0000 0.9998 0.9978 0.986.0000.0000.0000.0000.0000.0000.0000 0.9999 0.999 0.99 4.0000.0000.0000.0000.0000.0000.0000.0000 0.9997 0.9967 5.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9987 6.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9995 7.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9998 8.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 7

POISSON CUMULATIVE DISTRIBUTION FUNCTION The tulted vlue s PX, whee X hs Posso dstuto wth pmete λ. λ 0.5.0.5.0.5.0.5 4.0 4.5 5.0 0 0.6065 0.679 0. 0.5 0.08 0.0498 0.00 0.08 0.0 0.0067 0.9098 0.758 0.5578 0.4060 0.87 0.99 0.59 0.096 0.06 0.0404 0.9856 0.997 0.8088 0.6767 0.548 0.4 0.08 0.8 0.76 0.47 0.998 0.980 0.944 0.857 0.7576 0.647 0.566 0.45 0.4 0.650 4 0.9998 0.996 0.984 0.947 0.89 0.85 0.754 0.688 0.5 0.4405 5.0000 0.9994 0.9955 0.984 0.9580 0.96 0.8576 0.785 0.709 0.660 6.0000 0.9999 0.999 0.9955 0.9858 0.9665 0.947 0.889 0.8 0.76 7.0000.0000 0.9998 0.9989 0.9958 0.988 0.97 0.9489 0.94 0.8666 8.0000.0000.0000 0.9998 0.9989 0.996 0.990 0.9786 0.9597 0.99 9.0000.0000.0000.0000 0.9997 0.9989 0.9967 0.999 0.989 0.968 0.0000.0000.0000.0000 0.9999 0.9997 0.9990 0.997 0.99 0.986.0000.0000.0000.0000.0000 0.9999 0.9997 0.999 0.9976 0.9945.0000.0000.0000.0000.0000.0000 0.9999 0.9997 0.999 0.9980.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9997 0.999 4.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9998 5.0000.0000.0000.0000.0000.0000.0000.0000.0000 0.9999 6.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 7.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 8.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 9.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 λ 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 0.0 0 0.004 0.005 0.005 0.0009 0.0006 0.000 0.000 0.000 0.000 0.0000 0.066 0.074 0.0 0.007 0.0047 0.000 0.009 0.00 0.0008 0.0005 0.0884 0.060 0.040 0.096 0.00 0.08 0.009 0.006 0.004 0.008 0.07 0.5 0.8 0.088 0.059 0.044 0.00 0.0 0.049 0.00 4 0.575 0.85 0.7 0.70 0. 0.0996 0.0744 0.0550 0.040 0.09 5 0.589 0.4457 0.690 0.007 0.44 0.9 0.496 0.57 0.0885 0.067 6 0.6860 0.606 0.565 0.4497 0.78 0.4 0.56 0.068 0.649 0.0 7 0.8095 0.7440 0.678 0.5987 0.546 0.450 0.856 0.9 0.687 0.0 8 0.8944 0.847 0.796 0.79 0.660 0.595 0.5 0.4557 0.98 0.8 9 0.946 0.96 0.8774 0.805 0.7764 0.766 0.650 0.5874 0.58 0.4579 0 0.9747 0.9574 0.9 0.905 0.86 0.859 0.764 0.7060 0.645 0.580 0.9890 0.9799 0.966 0.9467 0.908 0.888 0.8487 0.800 0.750 0.6968 0.9955 0.99 0.9840 0.970 0.957 0.96 0.909 0.8758 0.864 0.796 0.998 0.9964 0.999 0.987 0.9784 0.9658 0.9486 0.96 0.898 0.8645 4 0.9994 0.9986 0.9970 0.994 0.9897 0.987 0.976 0.9585 0.9400 0.965 5 0.9998 0.9995 0.9988 0.9976 0.9954 0.998 0.986 0.9780 0.9665 0.95 6 0.9999 0.9998 0.9996 0.9990 0.9980 0.996 0.994 0.9889 0.98 0.970 7.0000 0.9999 0.9998 0.9996 0.999 0.9984 0.9970 0.9947 0.99 0.9857 8.0000.0000 0.9999 0.9999 0.9997 0.999 0.9987 0.9976 0.9957 0.998 9.0000.0000.0000.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9965 0.0000.0000.0000.0000.0000 0.9999 0.9998 0.9996 0.999 0.9984.0000.0000.0000.0000.0000.0000 0.9999 0.9998 0.9996 0.999.0000.0000.0000.0000.0000.0000.0000 0.9999 0.9999 0.9997 8 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

Sttstcs S Cddtes sttg S m lso eque those fomule lsted ude Sttstcs S d S. 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 X me μ d vce σ, X,, X of depedet osevtos fom dstuto hvg X s used estmto of μ, wth S s used estmto of σ, whee σ V X Fo dom smple of osevtos fom N μ, σ X μ ~ N0, σ / S Σ X X Fo dom smple of osevtos fom N μ, d, depedetl, dom smple of osevtos fom N μ, X Y μ μ ~ N0, σ σ σ σ Coelto d egesso Spem s k coelto coeffcet s s 6Σd No-pmetc tests Goodess-of-ft test d cotgec tles: O E E ~ χ ν UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007 9

PERCENTAGE POINTS OF THE χ DISTRIBUTION The vlues the tle e those whch dom vle wth the χ dstuto o ν degees of feedom eceeds wth the polt show. ν 0.995 0.990 0.975 0.950 0.900 0.00 0.050 0.05 0.00 0.005 0.000 0.000 0.00 0.004 0.06.705.84 5.04 6.65 7.879 0.00 0.00 0.05 0.0 0. 4.605 5.99 7.78 9.0 0.597 0.07 0.5 0.6 0.5 0.584 6.5 7.85 9.48.45.88 4 0.07 0.97 0.484 0.7.064 7.779 9.488.4.77 4.860 5 0.4 0.554 0.8.45.60 9.6.070.8 5.086 6.750 6 0.676 0.87.7.65.04 0.645.59 4.449 6.8 8.548 7 0.989.9.690.67.8.07 4.067 6.0 8.475 0.78 8.44.646.80.7.490.6 5.507 7.55 0.090.955 9.75.088.700.5 4.68 4.684 6.99 9.0.666.589 0.56.558.47.940 4.865 5.987 8.07 0.48.09 5.88.60.05.86 4.575 5.580 7.75 9.675.90 4.75 6.757.074.57 4.404 5.6 6.04 8.549.06.7 6.7 8.00.565 4.07 5.009 5.89 7.04 9.8.6 4.76 7.688 9.89 4 4.075 4.660 5.69 6.57 7.790.064.685 6.9 9.4.9 5 4.60 5.9 6.6 7.6 8.547.07 4.996 7.488 0.578.80 6 5.4 5.8 6.908 7.96 9..54 6.96 8.845.000 4.67 7 5.697 6.408 7.564 8.67 0.085 4.769 7.587 0.9.409 5.78 8 6.65 7.05 8. 9.90 0.865 5.989 8.869.56 4.805 7.56 9 6.844 7.6 8.907 0.7.65 7.04 0.44.85 6.9 8.58 0 7.44 8.60 9.59 0.85.44 8.4.40 4.70 7.566 9.997 8.04 8.897 0.8.59.40 9.65.67 5.479 8.9 4.40 8.64 9.54 0.98.8 4.04 0.8.94 6.78 40.89 4.796 9.60 0.96.689.09 4.848.007 5.7 8.076 4.68 44.8 4 9.886 0.856.40.848 5.659.96 6.45 9.64 4.980 45.558 5 0.50.54.0 4.6 6.47 4.8 7.65 40.646 44.4 46.98 6.60.98.844 5.79 7.9 5.56 8.885 4.9 45.64 48.90 7.808.879 4.57 6.5 8.4 6.74 40. 4.94 46.96 49.645 8.46.565 5.08 6.98 8.99 7.96 4.7 44.46 48.78 50.99 9. 4.56 6.047 7.708 9.768 9.088 4.557 45.7 49.588 5.6 0.787 4.95 6.79 8.49 0.599 40.56 4.77 46.979 50.89 5.67 0 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

CRITICAL VALUES FOR CORRELATION COEFFICIENTS These tles coce tests of the hpothess tht populto coelto coeffcet ρ s 0. The vlues the tles e the mmum vlues whch eed to e eched smple coelto coeffcet ode to e sgfct t the level show, o oe-tled test. Poduct Momet Coeffcet Spem s Coeffcet Level Smple Level 0.0 0.05 0.05 0.0 0.005 Level 0.05 0.05 0.0 0.8000 0.9000 0.9500 0.9800 0.9900 4.0000 - - 0.6870 0.8054 0.878 0.94 0.9587 5 0.9000.0000.0000 0.6084 0.79 0.84 0.88 0.97 6 0.886 0.8857 0.949 0.5509 0.6694 0.7545 0.89 0.8745 7 0.74 0.7857 0.899 0.5067 0.65 0.7067 0.7887 0.84 8 0.649 0.78 0.8 0.476 0.58 0.6664 0.7498 0.7977 9 0.6000 0.7000 0.78 0.448 0.5494 0.69 0.755 0.7646 0 0.566 0.6485 0.7455 0.487 0.54 0.60 0.685 0.748 0.564 0.68 0.709 0.98 0.497 0.5760 0.658 0.7079 0.505 0.5874 0.678 0.80 0.476 0.559 0.69 0.685 0.485 0.5604 0.6484 0.646 0.4575 0.54 0.60 0.664 4 0.467 0.585 0.664 0.507 0.4409 0.540 0.59 0.64 5 0.4464 0.54 0.606 0.8 0.459 0.497 0.574 0.66 6 0.494 0.509 0.584 0.7 0.44 0.48 0.5577 0.6055 7 0.44 0.4877 0.566 0.70 0.4000 0.468 0.545 0.5897 8 0.404 0.476 0.550 0.077 0.887 0.4555 0.585 0.575 9 0.9 0.4596 0.55 0.99 0.78 0.448 0.555 0.564 0 0.805 0.4466 0.58 0.94 0.687 0.49 0.504 0.5487 0.70 0.464 0.509 0.84 0.598 0.47 0.49 0.568 0.608 0.45 0.4975 0.774 0.55 0.4 0.485 0.556 0.58 0.460 0.486 0.7 0.48 0.4044 0.476 0.55 4 0.44 0.4070 0.4757 0.65 0.65 0.96 0.46 0.505 5 0.69 0.977 0.466 0.598 0.97 0.88 0.454 0.4958 6 0.06 0.90 0.457 0.546 0. 0.809 0.445 0.4869 7 0.4 0.88 0.4487 0.497 0.7 0.79 0.47 0.4785 8 0.80 0.755 0.440 0.45 0.5 0.67 0.497 0.4705 9 0.8 0.685 0.45 0.407 0.06 0.60 0.46 0.469 0 0.06 0.64 0.45 0.070 0.68 0.0 0.665 0.406 40 0.640 0.8 0.68 0.84 0.5 0.787 0.8 0.60 50 0.5 0.79 0.9 0.678 0.44 0.54 0.997 0.0 60 0.44 0.545 0.005 0.550 0.98 0.5 0.776 0.060 70 0.98 0.54 0.78 0.448 0.85 0.99 0.597 0.864 80 0.85 0.0 0.60 0.64 0.745 0.07 0.449 0.70 90 0.745 0.074 0.45 0.9 0.654 0.966 0.4 0.565 00 0.654 0.967 0.7 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

RANDOM NUMBERS 86 84 0 07 0 9 05 97 96 88 07 7 6 04 89 48 9 0 60 78 48 99 47 09 46 9 7 0 94 79 00 08 50 40 6 78 48 06 7 8 6 0 06 64 65 94 4 7 6 74 66 6 9 4 97 80 56 90 79 66 94 8 40 97 79 9 0 4 5 5 04 0 7 76 04 99 09 9 5 66 70 56 0 5 5 7 87 55 0 68 98 56 7 9 65 97 6 56 6 79 95 7 57 6 5 58 96 6 66 0 49 9 97 44 99 5 56 86 80 57 78 40 58 40 86 4 77 5 94 05 9 56 4 7 60 46 05 7 9 0 8 98 79 7 4 4 76 54 77 66 9 84 09 88 56 75 86 4 67 04 4 50 97 9 5 0 0 57 0 87 7 7 70 8 40 4 0 66 6 90 5 94 50 48 88 95 09 4 09 0 7 5 56 40 76 0 59 99 5 4 4 7 88 9 4 65 00 84 06 79 74 97 96 4 46 67 48 06 99 4 4 8 78 7 65 7 9 47 06 84 55 4 7 06 74 59 4 9 0 4 45 75 6 05 4 96 08 64 89 0 5 5 7 5 04 56 67 0 74 07 6 49 86 87 6 4 5 76 49 79 78 80 9 89 09 57 07 4 40 74 94 44 97 77 04 5 0 76 60 9 9 40 8 06 85 85 7 84 6 5 55 4 66 47 99 90 0 90 8 4 6 0 9 69 78 87 6 8 98 5 8 57 5 4 9 9 6 5 89 86 00 47 6 0 70 0 8 94 7 67 6 54 5 90 4 79 0 95 5 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S Issue Septeme 007

Sttstcs S4 Cddtes sttg S4 m lso eque those fomule lsted ude Sttstcs S, S d S. Smplg dstutos Fo dom smple of osevtos fom N μ, σ S σ X μ ~ S / ~ χ t lso vld mtched-ps stutos Fo dom smple of osevtos fom N μ, d, depedetl, dom smple of osevtos fom N μ, σ S S / σ / σ ~ F, σ If σ σ σ ukow the X Y μ μ S p ~ t whee S p S S UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S4 Issue Septeme 007

PERCENTAGE POINTS OF STUDENT S t DISTRIBUTION The vlues the tle e those whch dom vle wth Studet s t dstuto o ν degees of feedom eceeds wth the polt show. ν 0.0 0.05 0.05 0.0 0.005.078 6.4.706.8 6.657.886.90 4.0 6.965 9.95.68.5.8 4.54 5.84 4.5..776.747 4.604 5.476.05.57.65 4.0 6.440.94.447.4.707 7.45.895.65.998.499 8.97.860.06.896.55 9.8.8.6.8.50 0.7.8.8.764.69.6.796.0.78.06.56.78.79.68.055.50.77.60.650.0 4.45.76.45.64.977 5.4.75..60.947 6.7.746.0.58.9 7..740.0.567.898 8.0.74.0.55.878 9.8.79.09.59.86 0.5.75.086.58.845..7.080.58.8..77.074.508.89.9.74.069.500.807 4.8.7.064.49.797 5.6.708.060.485.787 6.5.706.056.479.779 7.4.70.05.47.77 8..70.048.467.76 9..699.045.46.756 0.0.697.04.457.750.09.694.07.449.78 4.07.69.0.44.78 6.06.688.08.45.79 8.04.686.04.49.7 40.0.684.0.4.704 45.0.679.04.4.690 50.99.676.009.40.678 55.97.67.004.96.668 60.96.67.000.90.660 70.94.667.994.8.648 80.9.664.990.74.69 90.9.66.987.69.6 00.90.660.984.64.66 0.89.659.98.6.6 0.89.658.980.58.67 4 UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S4 Issue Septeme 007

PERCENTAGE POINTS OF THE F DISTRIBUTION The vlues the tle e those whch dom vle wth the F dstuto o ν d ν degees of feedom eceeds wth polt 0.05 o 0.0. Polt ν /ν 4 5 6 8 0 4 6.4 99.5 5.7 4.6 0. 4.0 8.9 4.9 4.9 49. 54. 8.5 9.00 9.6 9.5 9.0 9. 9.7 9.40 9.4 9.46 9.50 0. 9.55 9.8 9. 9.0 8.94 8.85 8.79 8.74 8.64 8.5 4 7.7 6.94 6.59 6.9 6.6 6.6 6.04 5.96 5.9 5.77 5.6 5 6.6 5.79 5.4 5.9 5.05 4.95 4.8 4.74 4.68 4.5 4.7 6 5.99 5.4 4.76 4.5 4.9 4.8 4.5 4.06 4.00.84.67 7 5.59 4.74 4.5 4..97.87.7.64.57.4. 8 5. 4.46 4.07.84.69.58.44.5.8..9 9 5. 4.6.86.6.48.7..4.07.90.7 0 4.96 4.0.7.48...07.98.9.74.54 0.05 0.0 4.84.98.59.6.0.09.95.85.79.6.40 4.75.89.49.6..00.85.75.69.5.0 4 4.60.74.4..96.85.70.60.5.5. 6 4.49.6.4.0.85.74.59.49.4.4.0 8 4.4.55.6.9.77.66.5.4.4.5.9 0 4.5.49.0.87.7.60.45.5.8.08.84 5 4.4.9.99.76.60.49.4.4.6.96.7 0 4.7..9.69.5.4.7.6.09.89.6 40 4.08..84.6.45.4.8.08.00.79.5 60 4.00.5.76.5.7.5.0.99.9.70.9 0.9.07.68.45.9.8.0.9.8.6.5.84.00.60.7..0.94.8.75.5.00 405. 5000. 540. 565. 5764. 5859. 598. 6056. 606. 65. 666. 98.50 99.00 99.7 99.5 99.0 99. 99.7 99.40 99.4 99.46 99.50 4. 0.8 9.46 8.7 8.4 7.9 7.49 7. 7.05 6.60 6. 4.0 8.00 6.69 5.98 5.5 5. 4.80 4.55 4.7.9.45 5 6.6.7.06.9 0.97 0.67 0.9 0.05 9.89 9.47 9.0 6.70 0.90 9.78 9.5 8.75 8.47 8.0 7.87 7.7 7. 6.88 7.0 9.55 8.45 7.85 7.46 7.9 6.84 6.6 6.47 6.07 5.65 8.0 8.65 7.59 7.0 6.6 6.7 6.0 5.8 5.67 5.8 4.86 9 0.60 8.0 6.99 6.4 6.06 5.80 5.47 5.6 5. 4.7 4. 0 0.00 7.56 6.55 5.99 5.64 5.9 5.06 4.85 4.7 4..9 9.65 7. 6. 5.67 5. 5.07 4.74 4.54 4.40 4.0.60 9. 6.9 5.95 5.4 5.06 4.8 4.50 4.0 4.6.78.6 4 8.86 6.5 5.56 5.04 4.70 4.46 4.4.94.80.4.00 6 8.5 6. 5.9 4.77 4.44 4.0.89.69.55.8.75 8 8.9 6.0 5.09 4.58 4.5 4.0.7.5.7.00.57 0 8.0 5.85 4.94 4.4 4.0.87.56.7..86.4 5 7.77 5.57 4.68 4.8.86.6...99.6.7 0 7.56 5.9 4.5 4.0.70.47.7.98.84.47.0 40 7. 5.8 4..8.5.9.99.80.66.9.80 60 7.08 4.98 4..65.4..8.6.50..60 0 6.85 4.79.95.48.7.96.66.47.4.95.8 6.6 4.6.78..0.80.5..8.79.00 If uppe pecetge pot of the F dstuto o ν d ν degees of feedom s f, the the coespodg lowe pecetge pot of the F dstuto o ν d ν degees of feedom s / f. UA08598 Edecel AS/A level Mthemtcs Fomule Lst: Sttstcs S4 Issue Septeme 007 5

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