Ask a question from expert

Ask now

Cambridge Pre-U Revised Syllabus: List of Formulas and Statistical Tables

12 Pages3210 Words245 Views
   

Added on  2021-10-01

About This Document

Get the list of formulas and statistical tables for Mathematics and Further Mathematics for Cambridge Pre-U Revised Syllabus. This document consists of 11 printed pages and 1 blank page. Use it in all papers for the H1, H2 and H3 Mathematics and H2 Further Mathematics syllabuses.

Cambridge Pre-U Revised Syllabus: List of Formulas and Statistical Tables

   Added on 2021-10-01

BookmarkShareRelated Documents
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 of 11 printed pages and 1 blank page.

© UCLES & MOE 2015
Cambridge Pre-U Revised Syllabus: List of Formulas and Statistical Tables_1

PURE MATHEMATICS

Algebraic series

Binomial expansion:
nnnnnn bbanbanbanaba ++




+




+




+=+ 33221 3 2 1)( , where n is a positive integer and
)!(!
!


rnr
n
r
n
=






Maclaurin expansion:
+++++= )0(f!)0(f!2)0(f)0f()f( )(
2 nn
n
xxxx
++++++=+ rn xr
rnnnxnnnxx !
)1()1(
!2
)1(1)1( 2 ( )1 <x
++++++= !!3!21e
32
r
xxxx
rx (all x)
++
++=
+
)!12(
)1(
!5!3sin
1253
r
xxxxx
rr
(all x)
+++= )!2(
)1(
!4!21cos
242
r
xxxx
rr
(all x)
+++=+
+
r
xxxxx
rr 132 )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
Cambridge Pre-U Revised Syllabus: List of Formulas and Statistical Tables_2

Trigonometry
BABABA sincoscossin)sin( ±±
BABABA sinsincoscos)cos( ±
BA
BABA tantan1
tantan)tan(
±±
AAA cossin22sin
AAAAA 2222 sin211cos2sincos2cos
A
AA 2tan1
tan22tan
)(cos)(sin2sinsin 2
1
2
1 QPQPQP ++
)(sin)(cos2sinsin 2
1
2
1 QPQPQP +
)(cos)(cos2coscos 2
1
2
1 QPQPQP ++
)(sin)(sin2coscos 2
1
2
1 QPQPQP +

Principal values:
π2
1 sin1x π2
1 ( x 1)
0 cos1x π ( x 1)
ππ 2
11
2
1 tan << x

Derivatives
)f(x )(fx
x1sin 21
1
x

x1cos 21
1
x

x1tan 21
1
x+
cosec x cosec x cot x
xsec xxtansec


3
Cambridge Pre-U Revised Syllabus: List of Formulas and Statistical Tables_3

Integrals
(Arbitrary constants are omitted; a denotes a positive constant.)
)f(x xx d )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(sec x ( π2
1<x )
xcot )ln(sin x ( π<< x0 )
xcosec )cotln(cosec xx+ ( π<< x0 )
xsec )tanln(sec xx+ ( π2
1<x )

Vectors
The point dividing AB in the ratio μλ: has position vector μλ
λμ
+
+ ba
Vector product:










=






×






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

4
Cambridge Pre-U Revised Syllabus: List of Formulas and Statistical Tables_4

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
Proving Green's Theorem
|9
|1785
|79

10 Statistical Calculations and Solutions for Practice - A Comprehensive Guide for Students
|8
|781
|359

Advanced Mathematics Assignment
|12
|606
|243

Approximate Derivatives and Differential Equations Solutions
|8
|1368
|198

Solution of the Diffusion Equation
|9
|1710
|387

Calculation Project
|9
|721
|220