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.
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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(
