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Pearson Edexcel A Level GCE in Mathematics Formulae Book

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics andFurther MathematicsMathematical Formulae and statistical tables First certification from 2018 Advanced Subsidiary GCE in Mathematics (8MA0)Advanced GCE in Mathematics (9MA0)Advanced Subsidiary GCE in Further Mathematics (8FM0)First certification from 2019 Advanced GCE in Further Mathematics (9FM0)This copy is the property of Pearson . It is not to be removed from the examination room or marked in any 2017 Pearson Education , BTEC and LCCI qualificationsEdexcel, BTEC and LCCI qualifications are awarded by Pearson , the UK s largest awarding body offering academic and vocational qualifications that are globally recognised and benchmarked. For further information, please visit our qualification website at Alternatively, you can get in touch with us using the details on our contact us page at PearsonPearson is the world s leading learning company, with 35,000 employees in more than 70 countries working to help people of all ages to make measurable progress in their lives through learning.

A Level Further Mathematics papers may be required to use the formulae that were introduced in AS or A Level Mathematics papers. It may also be the case that students sitting Mechanics and Statistics papers will need to use formulae introduced in the appropriate Pure Mathematics papers for the qualification they are sitting.

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Transcription of Pearson Edexcel A Level GCE in Mathematics Formulae Book

1 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics andFurther MathematicsMathematical Formulae and statistical tables First certification from 2018 Advanced Subsidiary GCE in Mathematics (8MA0)Advanced GCE in Mathematics (9MA0)Advanced Subsidiary GCE in Further Mathematics (8FM0)First certification from 2019 Advanced GCE in Further Mathematics (9FM0)This copy is the property of Pearson . It is not to be removed from the examination room or marked in any 2017 Pearson Education , BTEC and LCCI qualificationsEdexcel, BTEC and LCCI qualifications are awarded by Pearson , the UK s largest awarding body offering academic and vocational qualifications that are globally recognised and benchmarked. For further information, please visit our qualification website at Alternatively, you can get in touch with us using the details on our contact us page at PearsonPearson is the world s leading learning company, with 35,000 employees in more than 70 countries working to help people of all ages to make measurable progress in their lives through learning.

2 We put the learner at the centre of everything we do, because wherever learning flourishes, so do people. Find out more about how we can help you and your learners at to third party material made in this sample assessment materials are made in good faith. Pearson does not endorse, approve or accept responsibility for the content of materals, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)All information in this document is correct at time of 978 1 4469 4857 6 Pearson Education Limited 2017 ContentsIntroduction 11 AS Mathematics 3 Pure Mathematics 3 Statistics 3 Mechanics 42 A Level Mathematics 5 Pure Mathematics 5 Statistics 7 Mechanics

3 83 AS Further Mathematics 9 Pure Mathematics 9 Statistics 13 Mechanics 154 A Level Further Mathematics 17 Pure Mathematics 17 Statistics 23 Mechanics 275 Statistical Tables 29 Binomial Cumulative Distribution Function 29 Percentage Points of The Normal Distribution 34 Poisson Cumulative Distribution Function 35 Percentage Points of the 2 Distribution 36 Critical Values for Correlation Coefficients 37 Random Numbers 38 Percentage Points of Student s t Distribution 39 Percentage Points of the F Distribution 401 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 2017 IntroductionThe Formulae in this booklet have been arranged by qualification.

4 Students sitting AS or A Level Further Mathematics papers may be required to use the Formulae that were introduced in AS or A Level Mathematics may also be the case that students sitting Mechanics and Statistics papers will need to use Formulae introduced in the appropriate Pure Mathematics papers for the qualification they are Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 20173 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 20171 AS MathematicsPure MathematicsMensurationSurface area of sphere = 4 r2 Area of curved surface of cone = r slant heightBinomial series(a + b)n = an + n1 an 1b + n2 an 2b2 +.

5 + nr an rbr + .. + bn (n )where nr = nCr = nrn r!!()! Logarithms and exponentialsloga x = loglogbbxaex lna = axDifferentiationFirst Principles =+ fff()lim()()xxhxhh0 StatisticsProbabilityPP()() = AA1 Standard deviationStandard deviation = (Variance)Interquartile range = IQR = Q3 Q1 For a set of n values x1, x2, .. xi, .. xnSxx = (xi x)2 = xi2 2( )ixn14 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 2017 Standard deviation = Sxxn or xnx22 Statistical tablesThe following statistical tables are required for A Level Mathematics :Binomial Cumulative Distribution Function (see page 29)Random Numbers (see page 38)MechanicsKinematicsFor motion in a straight line with constant acceleration.

6 V = u + ats = ut + 12at 2s = vt 12at 2v2 = u2 + 2ass = 12(u + v)t5 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 20172 A Level MathematicsPure MathematicsMensurationSurface area of sphere = 4 r2 Area of curved surface of cone = r slant heightArithmetic seriesSn = 12n(a + l) = 12n[2a + (n 1)d]Binomial series(a + b)n = an + n1 an 1b + n2 an 2b2 + .. + nr an rbr + .. + bn (n )where nr = nCr = nrn r!!()! (1 + x)n = 1 + nx + nn() 112x2 + .. + nnnrr()..().. + 1112xr + .. ( x < 1, n )Logarithms and exponentialsloga x = loglogbbxaex lna = axGeometric seriesSn = arrn()11 S = ar1 for r < 126 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 2017 Trigonometric identitiessin (A B) = sinA cosB cosA sinBcos (A B) = cosA cosB sinA sinBtan (A B) = tantantantanABAB 1 (A B (k + 12) )

7 SinA + sinB = 2 sinABAB+ 22cossinA sinB = 2 cosAB AB+ 22sincosA + cosB = 2 cosABAB+ 22coscosA cosB = 2 sinAB AB+ 22sinSmall angle approximationssin cos 1 22 tan where is measured in radiansDifferentiationFirst Principles =+ fff()lim()()xxhxhh0f(x) f (x)tankx ksec2 kxseckx kseckx tankxcotkx kcosec2 kxcoseckx kcoseckx cotkxfg()()xx fgfg(g() ()() ()())xxxxx27 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 2017 Integration (+ constant)f(x) f(x) dxsec2 kx 1k tankxtankx 1kln seckx cotkx 1kln sinkx coseckx 1kln coseckx + cotkx , 1kln tan (12kx) seckx 1kln seckx + tankx , 1kln tan (12kx + 14 ) uddvxdx = uv vdduxdxNumerical MethodsThe trapezium rule: yab dx 12h{(y0 + yn) + 2(y1 + y2 +.)}

8 + yn 1)}, where h = ban The Newton-Raphson iteration for solving f(x) = 0 : xn+1 = xn ff()()xxnn StatisticsProbabilityPP()() = AA1P(A B) = P(A) + P(B) P(A B)P(A B) = P(A)P(B A)P(A B) = PPPPPP()()()()()()BAABAABAA|||+ For independent events A and B,P(B A) = P(B) P(A B) = P(A) P(A B) = P(A) P(B) 28 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 2017 Standard deviationStandard deviation = (Variance)Interquartile range = IQR = Q3 Q1 For a set of n values x1, x2, .. xi, .. xnSxx = (xi x)2 = xi2 2( )ixnStandard deviation = Sxxn or xnx22 Discrete distributionsDistribution of XP(X = x)MeanVarianceBinomial B(n, p)nx px(1 p)n xnpnp(1 p)Sampling distributionsFor a random sample of n observations from N( , 2)/X n ~ N(0, 1)Statistical tablesThe following statistical tables are required for A Level Mathematics :Binomial Cumulative Distribution Function (see page 29)Percentage Points of The Normal Distribution (see page 34)Critical Values for Correlation Coefficients: Product Moment Coefficient (see page 37)Random Numbers (see page 38)MechanicsKinematicsFor motion in a straight line with constant acceleration.

9 V = u + ats = ut + 12at 2s = vt 12at 2v2 = u2 + 2ass = 12(u + v)t9 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 20173 AS Further MathematicsStudents sitting an AS Level Further Mathematics paper may also require those Formulae listed forA Level Mathematics in Section MathematicsSummationsrrn21= = 16n(n + 1)(2n + 1)rrn31= = 14n2(n + 1)2 Matrix transformationsAnticlockwise rotation through about O: cossinsincos Reflection in the line y = (tan )x: cos2sin2sin2cos2 Area of a sectorA = 12 r2 d (polar coordinates)Complex numbers{r(cos + i sin )}n = rn (cosn + i sinn )The roots of zn = 1 are given by z = e2i kn, for k = 0, 1, 2.

10 , n 1310 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics Mathematical Formulae and Statistical Tables Issue 1 July 2017 Pearson Education Limited 2017 Maclaurin s and Taylor s Seriesf(x) = f (0) + x f (0) + x22!f (0) + .. + xrr!f(r)(0) + ..ex = exp(x) = 1 + x + x22! + .. + xrr! + .. for all xln (1 + x) = x x22 + x33 .. + ( 1)r+1 xrr + .. ( 1 < x 1)sinx = x x33! + x55! .. + ( 1)r xrr2121++()! + .. for all xcosx = 1 x22! + x44! .. + ( 1)r xrr22()! + .. for all xarctanx = x x33 + x55 .. + ( 1)r xrr2121++ + .. ( 1 x 1)VectorsVector product: a b = a b sin n = ijkaaabbbabababababab123123233231131221= a.


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