Pearson Edexcel International Advanced Subsidiary/Advanced .

Pearson Edexcel InternationalAdvanced Subsidiary/AdvancedLevel in Mathematics,Further Mathematicsand Pure MathematicsMathematical Formulae and Statistical TablesFor use in Pearson Edexcel International Advanced Subsidiaryand Advanced Level examinationsPure Mathematics P1 – P4Further Pure Mathematics FP1 – FP3Mechanics M1 – M3Statistics S1 – S3First examination from January 2019Issue 2This copy is the property of Pearson. It is not to be removed from theexamination room or marked in any way.P59773RA 2021 Pearson Education Ltd.1/1/1/1/1/1/1/1/1/1/1/1/

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Summary of Pearson Edexcel International AdvancedSubsidiary/Advanced Level in Mathematics, FurtherMathematics and Pure Mathematics MathematicalFormulae and Statistical Tables BookletIssue 2 changesSummary of changes made between previous issue and this current issuePagenumberThe following sentence has been removed as it only applies to reflections, not rotationsand it is confusing to have it in this section:In FP1, θ will be a multiple of 45 .6Under heading Conics, the following formula for the ellipse in the standard form:x2y2 1a2a2has been corrected as follows:x2y2 1a2b29Formulae on lines 6–8 in the list of Integration have been corrected from:10to show formulae on lines 6–9 as follows:1x2 a2 x arcosh ,   ln{x a x 2 a 2 }   (x a)1a x2 x arsinh ,   ln{x a x2 a2 }21a2 x21a x1 x ln artanh    ( x a) a 2a a xa1x2 a21x aln2a x aUnder heading Mechanics M1, the statement ‘Candidates sitting M1 may also requirethose formulae listed under Pure Mathematics P1’ has been expanded to read‘Candidates sitting M1 may also require those formulae listed under Pure MathematicsP1 and P2.’13

Summary of changes made between previous issue and this current issuePagenumberUnder heading Statistics S1, the following statement has been added: ‘Candidates sittingS1 may also require those formulae listed under Pure Mathematics P1 and P2.’14Under heading Correlation and regression, the following formula:15r SxySxxS yy ( xi )( yi )n2( yi ) 2 ( xi ) 22 yi xi n n ( xi x )( yi y ) { ( xi x ) 2 }{ ( yi y ) 2 }( xi )( yi )n2( yi ) 2 ( xi ) 22 xy iin n ( xi x )( yi y ){ ( xi x ) 2 }{ ( yi y ) 2 } xi yi has been corrected as follows:r SxySxxS yy xi yi Under heading Statistics S3, the statement ‘Candidates sitting S3 may also require thoseformulae listed under Statistics S1 and S2’ has been expanded to read ‘Candidatessitting S3 may also require those formulae listed under Statistics S1 and S2, and PureMathematics P1, P2, P3 and P4.’25Under heading Sampling distributions, the following formula:25has been corrected as follows:( X Y ) ( μx μ y )σ x2 σ y2 nxny N(0, 1)In the table Random Numbers, spacing between numbers shown has been adjusted tomake them easier to read.28If you need further information on these changes or what they mean, contact us via our website s.html

ContentsIntroduction1Pure Mathematics P13Mensuration3Cosine rule3Pure Mathematics P23Arithmetic series3Geometric series3Logarithms and exponentials3Binomial series3Numerical integration3Pure Mathematics P34Logarithms and exponentials4Trigonometric identities4Differentiation4Integration5Pure Mathematics P45Binomial series5Integration5Further Pure Mathematics FP16Summations6Numerical solution of equations6Conics6Matrix transformations6Further Pure Mathematics FP27Area of a sector7Complex numbers7Maclaurin’s and Taylor’s Series7Further Pure Mathematics FP38Vectors8Hyperbolic functions9Conics9

Differentiation10Integration10Arc length11Surface area of revolution11Mechanics M113There are no formulae given for M1 in addition to those candidates are expected to know. 13Mechanics M213Centres of mass13Mechanics M313Motion in a circle13Centres of mass13Universal law of gravitation13Statistics S114Probability14Discrete distributions14Continuous distributions14Correlation and regression15The Normal Distribution Function16Percentage Points Of The Normal Distribution17Statistics S218Discrete distributions18Continuous distributions18Binomial Cumulative Distribution Function19Poisson Cumulative Distribution Function24Statistics S325Expectation algebra25Sampling distributions25Correlation and regression25Non-parametric tests25Percentage Points Of The χ 2 Distribution Function26Critical Values For Correlation Coefficients27Random Numbers28

IntroductionThe formulae in this booklet have been arranged by unit. A candidate sitting a unit may be required to useformulae that were introduced in a preceding unit (e.g. candidates sitting units P3 and P4 might be expectedto use formulae first introduced in units P1 and P2).It may also be the case that candidates sitting Mechanics and Statistics units need to use formulae introducedin appropriate Pure Mathematics units, as outlined in the specification.No formulae are required for the unit Decision Mathematics D1.Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 20211

2Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 2021

Pure Mathematics P1MensurationSurface area of sphere 4 πr 2Area of curved surface of cone πr slant heightCosine rulea2 b2 c2 2bc cos APure Mathematics P2Arithmetic seriesun a (n 1)dSn 11n(a l) n[2a (n 1)d ]22Geometric seriesun ar n 1a (1 r n )1 raS for r 11 rSn Logarithms and exponentialsloga x log b xlog b aBinomial series n n n (a b) n a n a n 1b a n 2b 2 a n rb r b n   (n ) 1 2 r n n!where n Cr r r !(n r )!(1 x) n 1 nx n(n 1) 2n(n 1) (n r 1) rx x    ( x 1, n )1 21 2 rNumerical integrationThe trapezium rule: bay dx 1b ah{(y0 yn ) 2( y1 y2 . yn 1)}, where h 2nPearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 20213

Pure Mathematics P3Candidates sitting Pure Mathematics P3 may also require those formulae listed underPure Mathematics P1 and P2.Logarithms and exponentialse x ln a a xTrigonometric identitiessin (A B) sin A cos B cos A sin Btan(A B) cos (A B) cos A cos Bsin A sin Btan A tan B A B1 tan A tan B sin A sin B 2 sinA BA Bcos22sin A sin B 2 cosA BA Bsin22cos A cos B 2 cos1 k 2 A BA Bcos22cos A cos B 2 sinA BA Bsin22Differentiationf (x)f ′(x)tan kxk sec2 kxsec xsec x tan xcot x cosec2 xcosec x cosec x cot xf ( x)g( x)f ' ( x) g ( x) f ( x) g' ( x)(g ( x)) 24Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 2021

Integration ( constant)f (x) f (x)sec2 kx1tan kxktan xln sec x cot xln sin x dxPure Mathematics P4Candidates sitting Pure Mathematics P4 may also require those formulae listed underPure Mathematics P1, P2 and P3.Binomial series(1 x) n 1 nx n(n 1) 2n(n 1) (n r 1) rx x    ( x 1, n )1 2 r1 2Integration ( constant)f (x)cosec xsec xdv u dx dx uv f (x)  dx 1 ln cosec x cot x ,   ln tan x 2 1 1ln sec x tan x ,   ln tan x 4 2duvdxdx Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 20215

Further Pure Mathematics FP1Candidates sitting Further Pure Mathematics FP1 may also require those formulae listed underPure Mathematics P1 and P2.Summationsn r2 1n(n 1)(2n 1)63 1 2n (n 1)24r 1n rr 1Numerical solution of equationsThe Newton-Raphson iteration for solving f ( x ) 0 : xn 1 xn f ( xn )f ' ( xn )ConicsParabolaRectangularHyperbolaStandardFormy2 4axxy c2ParametricForm(at 2, 2at) c ct , tFoci(a, 0)Not requiredDirectricesx aNot requiredMatrix transformations cos θAnticlockwise rotation through θ about O: sin θ cos 2θReflection in the line y (tan θ)x: sin 2θ6 sin θ cos θ sin 2θ cos 2θ Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 2021

Further Pure Mathematics FP2Candidates sitting Further Pure Mathematics FP2 may also require those formulae listed underFurther Pure Mathematics FP1, and Pure Mathematics P1, P2, P3 and P4.Area of a sectorA 1 2r dθ      (polar coordinates)2Complex numberseiθ cos θ i sin θ{r(cos θ i sin θ)}n r n (cos n θ i sin n θ)The roots of z 1 are given by z en2 πk in, for k 0, 1, 2, , n 1Maclaurin’s and Taylor’s Seriesf (x) f (0) x f ′(0) x2x r (r)f ″(0) f (0) r!2!f (x) f (a) (x a) f ′(a) f (a x) f (a) x f ′(a) ex exp (x) 1 x ln(1 x) x ( x a)2( x a ) r (r)f ″(a) f (a) r!2!x2x r (r)f ″(a) f (a) r!2!x2xr    for all xr!2!x2x3xr ( 1)r 1    ( 1 x 1)r23sin x x x3x5x 2 r 1 ( 1)r    for all x3!5!(2r 1)!cos x 1 x2x4x2r ( 1)r    for all x2!4!(2r )!arctan x x x3x5x 2 r 1 ( 1)r    ( 1 x 1)352r 1Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and PureMathematics – Mathematical Formulae and Statistical Tables – Issue 2 – January 2021 Pearson Education Limited 20217