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Cambridge Pre-U Revised Syllabus.

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Cambridge Pre-U Revised Syllabus

MINISTRY OF EDUCATION, SINGAPORE
in collaboration with
UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE
General Certificate of Education Advanced Level



List MF26



LIST OF FORMULAE
AND

STATISTICAL TABLES


for Mathematics and Further Mathematics




For use from 2017 in all papers for the H1, H2 and H3 Mathematics and
H2 Further Mathematics syllabuses.


CST310



This document consists of11printed pages and1blank page.

© UCLES & MOE 2015

PURE MATHEMATICS

Algebraic series

Binomial expansion:
nnnnnnbbanbanbanaba++




+




+




+=+33221321)(, wherenis a positive integer and
)!(!
!


rnr
n
r
n
=






Maclaurin expansion:
+++++=)0(f!)0(f!2)0(f)0f()f()(
2nn
n
xxxx
++++++=+rnxr
rnnnxnnnxx!
)1()1(
!2
)1(1)1(2()1<x
++++++=!!3!21e
32
r
xxxx
rx(allx)
++
++=
+
)!12(
)1(
!5!3sin
1253
r
xxxxx
rr
(allx)
+++=)!2(
)1(
!4!21cos
242
r
xxxx
rr
(allx)
+++=+
+
r
xxxxx
rr132)1(
32)1ln((11<x)


Partial fractions decomposition

Non-repeated linear factors:
)()())((dcx
B
bax
A
dcxbax
qpx
+++=++
+
Repeated linear factors:
22
2
)()()())((dcx
C
dcx
B
bax
A
dcxbax
rqxpx
+++++=++
++
Non-repeated quadratic factor:
)()())((2222
2
cx
CBx
bax
A
cxbax
rqxpx
+
+++=++
++



2

Trigonometry
BABABAsincoscossin)sin(±±
BABABAsinsincoscos)cos(±
BA
BABAtantan1
tantan)tan(
±±
AAAcossin22sin
AAAAA2222sin211cos2sincos2cos
A
AA2tan1
tan22tan
)(cos)(sin2sinsin2
1
2
1QPQPQP++
)(sin)(cos2sinsin2
1
2
1QPQPQP+
)(cos)(cos2coscos2
1
2
1QPQPQP++
)(sin)(sin2coscos2
1
2
1QPQPQP+

Principal values:
π2
1sin1xπ2
1(x1)
0cos1xπ(x1)
ππ2
11
2
1tan<<x

Derivatives
)f(x)(fx
x1sin21
1
x

x1cos21
1
x

x1tan21
1
x+
cosecxcosecxcotx
xsecxxtansec


3

Integrals
(Arbitrary constants are omitted;adenotes a positive constant.)
)f(xxxd)f(

22
1
ax+


a
x
a
1tan1

22
1
xa



a
x1sin()ax<

22
1
ax


+

ax
ax
aln2
1(ax>)

22
1
xa



+
xa
xa
aln2
1(ax<)
xtan)ln(secx(π2
1<x)
xcot)ln(sinx(π<<x0)
xcosec)cotln(cosecxx+(π<<x0)
xsec)tanln(secxx+(π2
1<x)

Vectors
The point dividingABin the ratioμλ:has position vectorμλ
λμ
+
+ba
Vector product:










=






×






=×
1221
3113
2332
3
2
1
3
2
1
baba
baba
baba
b
b
b
a
a
a
ba

4
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