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H. Mulholland
Butterworths
PURE MATHEMATICS
FOR ADVANCED LEVEL
Iaterworths Pubinaions on Kelated Subjects
APPLIED MATHEMATICS FOR ADVANCED LEVEL, 1560
H, MULHOLLAND AND J. TLC, PHILLIPS,
FUNDAMENTALS OF STATISTICS, 958
H.MULIOLLAND AND G. 8. JONES
PURE MATHEMATICS
FOR ADVANCED LEVEL
2, D. BUNDAY, B.Sc. (Hows.), Pap.
Baadfird Caierity
H. MULHOLLAND, M.Sc. KLM.A.
Lsverpoal Repional College of Teohnologe
LONDON
BUTTERWORTHS
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Narr a sei Fry Raft
PREFACE
‘Tas isa test book of Pure Miuthematies yrittn to meet che need
ofthe student stndying forthe General Ceiliate of Eavcation at
‘Adviaced level, he took assumes 4 koowledge of mpataematies
‘yp lo Ordiey Tove wal ve all he Pore Males neneny
foe the Advanaad Jeet etannation in Mathewson (426), of the
[Northern LniversitieToint Marenlation Board together ith the
arent majority ofthe work requzed forthe Adstaoed Lovet exam
{hetiona of tie Souhora Universities Joint Board, the Welsh Joi
(Conmuttee and London Univers.
The taehing method adopted i for the most part thse suggerted
by the sarinie mports of the Mathenitod Assoctm. Ihe
‘phe Drovehout iy been oa feck flog ie have Lied
Teinicte where paul reall nerd vote vues
{han is given in Oy book, Tr his aye Dope dat all stodents can
Prognot quickly Im the ‘uedeestanding and applcation of these
CGohmiques without the hindrance of having to justly everyting
fey da. Talat tp comes ata later age hoi eather
‘deetopert.
Tr convesicuce the book hoa been prepared in the ever Alacbeas
(Cuptors 1-5), ‘Tegonomstry (Chapters 6 #), Calbtlos (Chupters
5-16), and Co-ordiate Geometrs (Chapters 17-2, bot this not
te ieply that Poe cuter should he read In is order. For the
$udeft at school Us ile aided Hy te teacher; Zor the student
trorkiig shine We weal rscommend an advance on u broed oat
‘ough Chapeers | 4,6 9, £0, 12 he at rwo secon), 13 37,18,
‘This ays the foundatioas for all tae aaa tops son! this bev
savance can ten be maintained, We sould nogget Ihatetch
Chapre 7, U1, 14, 15, 160d 20 be ref a Jest Foo ages. NOt
‘only wil tha make for easier digetiou of thy many lacus aud
techniques dfvuned in thew cuson, tut wl also provide for
‘ooetatt revision and extension ofthis maria
"The book facdee over 250 Kked exarapler and about 1860
cxamples forthe rudeht to else. ‘The worked exumples indiczte
the man applications of Ihe ideas and techniques cicned ‘The
‘rons se atthe ead of he serous wan dhe alert
‘Eemone puta saiorward, All ovr etdcs seald ate
thaws creas, Tic emus atthe enya tho ap tet
Sted Bag Sra asf routine pe tes aro et
amy et hor past papers sot by tha ari sxamining Boor
Finally thee are sont nda oi an arth) nti ae f
fnnce diel ntare. The ser sould vot be too mayed i he
ir ona eve ll of the
For sononiecr te rls and formulae obsind have bees
anbaledy he fast nowhere Tnbe ently the Chae
Shics Ce cel detved. Thon Zola LD? he sea sat
Sbtiked i Chapter Ib, Tenor ppt Uhl ese Pormla be
ron
Weshouid ks to capress var hark co she Joine Masrculation
osrd GB.) the Southern Universise Toho Board (SUI).
the Saleh Join Commitee 4-1) and Tandon airs (LUS
{ir granting vs permission to eae questions fran fhe sxaminations
inthis Book Toe abbreviations above have been tues to lndicte
Ue sows cl sich questo
‘Hal oe sheuid se to thauk ovr publishers for the care and
rele they have takes over te general presentation af The ox
RDB.
HM.
CONTENTS
PREFACE
1, OPERATIONS WITH REAL NUMBEIS.
mn
12
3
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ts,
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1
19,
“Tu nue. sous
guages evvaLI89 On CRHONOHN
SIMCULTARFOUE FEEATIONE
rseqeatrrns
unvarion
agra. raxcn08S
sas
Locantunes
BoUATIONS NE WHUCH ME UNAM AN TE
2, FINITE SEQUENCES AND SLRILS
24
22
23.
2a,
Srquenens ano Sr
Thue amnieuic seqUENCE 3D sts
ree ONT CMREEREE SHQUENCY ANT SRIFE
“Ti mee cawnteNC SOEs
2. THE BINOMIAL THEOREM
3
32
Fey
3a
ag eMOMTAT TURK FOR A fOSITIR TeTECMAY
Phone oP TE SINOMAL LHLOREM WHER EE A,
"Tu usornat, mOR 1 NO POET
Muarapesrioar moceno
5
»
4. COMME. SUSUR
43,
42
43
44,
45.
Terence
Tine guuee FOR THE MaKELAMTONe AF crane
Ime cienaineAL RuMUSGAON oF coNRLE
TT GrOWTTRY OF CONES NOMI
“Tue exe RonTs oF rary
$ Tk QUADRATIC FUNCTION AND THE
QUADRATIC LQUATION
mn
52
‘Tom ames QUATRATIC RIEATION
Thee quasaanc FuNerIon
Tua xauarian nervaun Tae nore OF » quAnnaTIS
{QCAMGN 4% Tub COTIEUNTE
5, PROPERTIES OF THE TRIGONOMETRIC
TUNCTIONS
63,
9.
“Thu wassunenene uF anus
‘ia atGOsoMLIINE RATIO 9OR 8 ACTS ANCA
‘Tee TQOROMETRIC RATIOS TOR Ie ANGLE
“Tae anari o# THE TRIGONGMETEE FORCHONE
‘Tus avpition vonage
Mvnawce AND suureuLsiua antiLe romain AF
‘Tee recto Femara
“Tae risicrin acim sin
‘Tue nevenan ratconedeTRIs FENG
6, SMALL anvines
VRIGONOMETRIC EQUATIONS
1.
“Tr otuaL meeRASHON FOR ANCHE WITH 8 AN
Tricannwrme EQUATIONS LyYOLMNG EAFERRTT
135
18
1
cowrines
“TrigesoETAGe KUAMONS DOOLUNG MELEE
‘Ta savaenon aos 4 bsi0 d=
‘THE SOLUTION OF TRIANGLES
Bu
pes
83
Be
us sr Foawoua
Fc HRA
Tir AREA OF A TALOLE
Misersannous apvisexn¥o%s
‘THE FUNDAMENTAL, IDEAS OF “ILE
DIFHERENTIAR CATCOLUS,
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92.
93,
ou
9s.
surerexe
GRAPITCA REPRENINEATION OF & FUNCTION
“Tir RATE UW CHANGE OP 4 FENCTION
Lows sn anu None
Tre CALOLLAUON OF TE BERALIVE FOR SOME
SOME TUCANTQIES OF DILFERENTIATION
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toa.
1s.
108.
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ins.
op.
roe.
su,
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ermpnceroN
DrmENTATios OF A CONSTANT
Derrrenstistion, OF THR 34 OF DILRENCR OF
Dirreusiuanion oF 2 PRODUCE
Davencererion a 6 Quon
LDarerevramos of tae TRIeCreRER FUNCTIONS
‘SecoNo AND HMGLER DERTEAmHNES
TiersgpeTiamon OF 4 FENUROR OF A FUNCTION
Tier DURIATI Cf 4* WHERE WIS UHCRTIVE OR A
[DunutRSTIATION a ubsuAge FONCTIONS
DOTERATUATON eu AARETRIE EQUATIONS
LST oF sTasann FoI,
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16
18
