For use in Edexcel Advanced Subsidiary GCE and Advanced ...· Edexcel GCE in Mathematics ... For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations = Core Mathematics

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  • GCE

    Edexcel GCE in Mathematics Mathematical Formulae and Statistical Tables

    For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations =Core Mathematics C1 C4 Further Pure Mathematics FP1 FP3 Mechanics M1 M5 Statistics S1 S4

    For use from June 2009

    This copy is the property of Edexcel. It is not to be removed from the examination room or marked in any way.

    =

  • Edexcel AS/A level Mathematics Formulae List: C1 C4, FP1 FP3 Contents Page Issue 1 September 2009 1

    TABLE OF CONTENTS

    Page

    4 Core Mathematics C1

    4 Mensuration 4 Arithmetic series 5 Core Mathematics C2

    5 Cosine rule 5 Binomial series 5 Logarithms and exponentials 5 Geometric series 5 Numerical integration 6 Core Mathematics C3

    6 Logarithms and exponentials 6 Trigonometric identities 6 Differentiation 7 Core Mathematics C4

    7 Integration 8 Further Pure Mathematics FP1

    8 Summations 8 Numerical solution of equations 8 Conics 8 Matrix transformations 9 Further Pure Mathematics FP2

    9 Area of sector 9 Maclaurins and Taylors Series 10 Further Pure Mathematics FP3

    10 Vectors 11 Hyperbolics 12 Differentiation 12 Integration 13 Arc length 13 Surface area of revolution

  • 2 Edexcel AS/A level Mathematics Formulae List: M1M5, S1S4 Contents Page Issue 1 September 2009

    14 Mechanics M1

    14 There are no formulae given for M1 in addition to those candidates are expected to know. 14 Mechanics M2

    14 Centres of mass 14 Mechanics M3

    14 Motion in a circle 14 Centres of mass 14 Universal law of gravitation 15 Mechanics M4

    15 There are no formulae given for M4 in addition to those candidates are expected to know. 15 Mechanics M5

    15 Moments of inertia 15 Moments as vectors 16 Statistics S1

    16 Probability 16 Discrete distributions 16 Continuous distributions 17 Correlation and regression 18 The Normal distribution function 19 Percentage points of the Normal distribution 20 Statistics S2

    20 Discrete distributions 20 Continuous distributions 21 Binomial cumulative distribution function 26 Poisson cumulative distribution function 27 Statistics S3

    27 Expectation algebra 27 Sampling distributions 27 Correlation and regression 27 Non-parametric tests 28 Percentage points of the 2 distribution 29 Critical values for correlation coefficients 30 Random numbers 31 Statistics S4

    31 Sampling distributions 32 Percentage points of Students t distribution 33 Percentage points of the F distribution There are no formulae provided for Decision Mathematics units D1 and D2.

  • Edexcel AS/A level Mathematics Formulae List Issue 1- September 2009 3

    The formulae in this booklet have been arranged according to the unit in which they are first introduced. Thus a candidate sitting a unit may be required to use the formulae that were introduced in a preceding unit (e.g. candidates sitting C3 might be expected to use formulae first introduced in C1 or C2). It may also be the case that candidates sitting Mechanics and Statistics units need to use formulae introduced in appropriate Core Mathematics units, as outlined in the specification.

  • 4 Edexcel AS/A level Mathematics Formulae List: Core Mathematics C1 Issue 1 September 2009

    Core Mathematics C1

    Mensuration

    Surface area of sphere = 4 r 2

    Area of curved surface of cone = r slant height

    Arithmetic series

    un = a + (n 1)d

    Sn = 21 n(a + l) =

    21 n[2a + (n 1)d]

  • Edexcel AS/A level Mathematics Formulae List: Core Mathematics C2 Issue 1 September 2009 5

    Core Mathematics C2 Candidates sitting C2 may also require those formulae listed under Core Mathematics C1.

    Cosine rule

    a2 = b2 + c2 2bc cos A

    Binomial series

    2

    1

    )( 221 nrrnnnnn bbarn

    ban

    ban

    aba ++

    ++

    +

    +=+ KK (n )

    where )!(!

    !C rnr

    nrn

    rn

    ==

  • 6 Edexcel AS/A level Mathematics Formulae List: Core Mathematics C3 Issue 1 September 2009

    Core Mathematics C3 Candidates sitting C3 may also require those formulae listed under Core Mathematics C1 and C2.

    Logarithms and exponentials

    xax a=lne

    Trigonometric identities

    BABABA sincoscossin)(sin = BABABA sinsincoscos)(cos m=

    ))(( tantan1tantan)(tan 21 +

    = kBABABABA

    m

    2cos

    2sin2sinsin BABABA +=+

    2sin

    2cos2sinsin BABABA +=

    2cos

    2cos2coscos BABABA +=+

    2sin

    2sin2coscos BABABA +=

    Differentiation

    f(x) f (x)

    tan kx k sec2 kx

    sec x sec x tan x

    cot x cosec2 x

    cosec x cosec x cot x

    )g()f(

    xx

    ))(g(

    )(g)f( )g()(f2x

    xxxx

  • Edexcel AS/A level Mathematics Formulae List: Core Mathematics C4 Issue 1 September 2009 7

    Core Mathematics C4 Candidates sitting C4 may also require those formulae listed under Core Mathematics C1, C2 and C3.

    Integration (+ constant)

    f(x) xx d)f(

    sec2 kx k1 tan kx

    xtan xsecln

    xcot xsinln

    xcosec )tan(ln,cotcosecln 21 xxx +

    xsec )tan(ln,tansecln 4121 ++ xxx

    = xxuvuvx

    xvu d

    ddd

    dd

  • 8 Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP1 Issue 1 September 2009

    Further Pure Mathematics FP1 Candidates sitting FP1 may also require those formulae listed under Core Mathematics C1 and C2.

    Summations

    )12)(1(61

    1

    2 ++==

    nnnrn

    r

    2241

    1

    3 )1( +==

    nnrn

    r

    Numerical solution of equations

    The Newton-Raphson iteration for solving 0)f( =x : )(f)f(

    1n

    nnn x

    xxx

    =+

    Conics

    Parabola Rectangular Hyperbola

    Standard Form axy 4

    2 = xy = c2

    Parametric Form (at

    2, 2at)

    tcct,

    Foci )0 ,(a Not required

    Directrices ax = Not required

    Matrix transformations

    Anticlockwise rotation through about O:

    cos sinsincos

    Reflection in the line xy )(tan= :

    2cos2sin2sin 2cos

    In FP1, will be a multiple of 45.

  • Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP2 Issue 1 September 2009 9

    Further Pure Mathematics FP2 Candidates sitting FP2 may also require those formulae listed under Further Pure Mathematics FP1 and Core Mathematics C1C4. Area of a sector

    A = d

    21 2r (polar coordinates)

    Complex numbers

    sinicosei += )sini(cos)}sini(cos{ nnrr nn +=+

    The roots of 1=nz are given by nk

    zi2

    e

    = , for 1 , ,2 ,1 ,0 = nk K

    Maclaurins and Taylors Series

    KK )0(f!

    )0(f!2

    )0(f)0f()f( )(2

    +++++= rr

    rxxxx

    KK )(f!

    )( )(f!2

    )()(f)()f()f( )(2

    +

    ++

    ++= araxaaxaaxax r

    r

    KK )(f!

    )(f!2

    )(f)f()f( )(2

    +++++=+ arxaxaxaxa r

    r

    xrxxxx

    rx allfor

    !

    !21)exp(e

    2

    KK +++++==

    )11( )1( 32

    )1(ln 132

  • 10 Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP3 Issue 1 September 2009

    Further Pure Mathematics FP3 Candidates sitting FP3 may also require those formulae listed under Further Pure Mathematics FP1, and Core Mathematics C1C4.

    Vectors

    The resolved part of a in the direction of b is b

    a.b

    The point dividing AB in the ratio : is

    ++ ba

    Vector product:

    ===

    1221

    3113

    2332

    321

    321 sinbabababababa

    bbbaaakji

    nbaba

    )()()(

    321

    321

    321

    bac.acb.cba. ===cccbbbaaa

    If A is the point with position vector kjia 321 aaa ++= and the direction vector b is given by

    kjib 321 bbb ++= , then the straight line through A with direction vector b has cartesian equation

    )( 3

    3

    2

    2

    1

    1 =

    =

    =

    baz

    bay

    bax

    The plane through A with normal vector kjin 321 nnn ++= has cartesian equation

    a.n==+++ ddznynxn where0321

    The plane through non-collinear points A, B and C has vector equation

    cbaacabar ++=++= )1()()( The plane through the point with position vector a and parallel to b and c has equation

    cbar ts ++=

    The perpendicular distance of ) , ,( from 0321 =+++ dznynxn is 23

    22

    21

    321

    nnn

    dnnn

    ++

    +++ .

  • Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP3 Issue 1September 2009 11

    Hyperbolic functions 1sinhcosh 22 = xx

    xxx coshsinh22sinh = xxx 22 sinhcosh2cosh +=

    )1( 1lnarcosh }{ 2 += xxxx }{ 1lnarsinh 2 ++= xxx

    )1( 11lnartanh 21

  • 12 Edexcel AS/A level Mathematics Formulae List: Further Pure Mathematics FP3 Issue 1September 2009

    Differentiation

    f(x) f (x)

    xarcsin 21

    1

    x

    xarccos 21

    1

    x

    xarctan 211x+

    xsinh xcosh xcosh xsinh xtanh x2sech

    xarsinh 21

    1

    x+

    xarcosh 1

    12 x

    artanh x 211x

    Integration (+ constant; 0>a where relevant)

    f(x) xx d)f(

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