IIT JEE Super Course in Mathematics: Algebra I

365 Pages·2011·9.66 MB·English

by  Trishna Knowledge Systems

Super Course in Mathematics

ALGEBRA I

for ITT-JEE

Volume 1
Q@TUME, tate srenetoet ater neste samen oer mia

EVE rc te most succsesul lseroom-baeed enience examination fining
i ARORA ENC! insite in nd, For mote deta, vst wana timeteducaton com

Ve im f rs puis caplyinerin aben fons sures fave eid andrei his ot un
temp ender sy peel pfeil nce ur aly vee eed sah, YP uch ear hoa ae
to eotire the veruily and earercy of he formation pretend wir, never Ie pul ier nor its atlas bear an
rexpurlisfer ny daroge arg cw inadvertent eatin eigence ur Pracarece epograplial 9 atu Cat
sy ave oud Ce way nt ech

Gop ight 9s Kowal 9psteme,
Tierutes Peach Eduston SOU Aaa

Mo pute Boole uy be utd tepsduce in yan ahatceve chose pabLaber's pce wate conse

ThigeBock mayor meyncting ade 2 casts tharwoe part etthe peat sesog. The ot bles seers the ughe ts remove

a onaterl pase hs Boe ate

TEEN great easene
SEN UBaS2391 18D

Heal ome: Asa). Secos 3, Koevleds Bot end, h Recs, NOIDA 301 3, Indi
Tepsteed Dice 11 Local S9pping Cate, Pashahea Pati New Debi LIC, Tdi
re

Chopter |

Chapter?

Chapter

Chapter

Chapters

Contents

Prevents

omfg «Som MCU car CED, ond LE 8 Hater pn
dnd loniaion = tien = fogartiny = Yohrmade = Sadat = tmp

Istimrte vem Conmeaie ian = svtrminents = puri taal

amen,

voy = tess iguaion afm Yams ®

Quasi Fapationsand Fxpressions

Hacks of she Chexiate Ppuatan «Syms Sancsons + Sars of Pants
Af 8 Deime Dynaton w inombveon simian
Mont + Guetans Pippesions = Socieim nd

ression + Patna Pan 2 epee e

1igonometry

S hinducion + trigmamesrs tuexionsstale + Feribe Prapeny
Pancoonsiendtnagin efit nti» bomnats joie Fanti
Sees + Cnr Mow ns of Praesent Angles» Prt bombs * Cra

pe gf om ingle + inne Cher Mow ts = tipaeomesie

Prmpertier af riangles

S tmnducion + hans uf Sin for Sine Foranias, «tie of Cavin for Canine

Pmpertes of Iangles

S Sypowes = Sie +

vilontcSorssarSriecndty» CoamesrSers Sens

ExGah + Scdnotan Covi Soir» armen Seon Sensi

Femwnen ead & + Smonatin Sanbel 2 sSignar » Swoon wf Sins = Poni
Preface

Ube HT-ILE, tas most callegging amorgstwatinz. lve ngoceig etecacs exaust remzins on the ep at tbe
proce it of vvorl lab of soca very yee Uke 2c wai of hole arts naz and wots se dents sy Fa
tnt carUage posed yt 1-3 canoe tet othe bx a cn or othe Sede neque Urroo gt
ndsstrding ofthe fondemsutalesace,veseoring ls abby capes th esatedstisn ans excepto
roberts conse ma tp this ightydomnalingecternes cams

he ptr: of tue I-ILS hs oa ening nee tu yen, ee az epang den ques a te-bywop tic
plex rerun the fatcnaentals and to go edecuate pent the vue tapes etquestins tact ae aeted "aS
LULL: over teas sseel yrs lnespctie ots enack of engizaeing ody ts seen cies le ipo
to ha # soe soneepnl grown in atomic lye art Chemusey:&es ot pensar vodseteing of se
tyece nt the opacity of soem 45.09 concen peolane ery lever lo sence of winking? Rit
rote insets prone gunk sting.

"Use seces af bok crea ¢ sours of cmaing vt gove heya te ssbool evs tara of Clee XL ad Clee XL
ne is eater Scan the eksone othe prepstion sea spating sods, Ines backs Eve 20a deg 28 #e
‘siete of auiing ca eopirnt to lists gral 9 cowry dood step-by-step ppesact

1 Maser Ue Concepoaed ConceptSiradat

‘Testis cote al he coop in te bee ITP-TEE albus Bye ei theo aposite ait The trie
se enplined in dete end ace usted log slved exper dealing De sie p Seatons of he shoe
Teta FinSolvethe Rxemplee—Concept Conector
fttssandpthe theory contn. in sae 7 pond rambo ald Baar we provide 3° ay ae deed

ree aateneceegieane rack tinh a ecnaen tegen
eee Sa

thoraniled Ie yes oe legos erect pels stay
Noam

& cin tots of isa esha ks mas othe erferece hoa xn hs mek, ici ns an ened by an
idl. ie pottngether 3p 3-esm ct highly sie ety momen an, Phe ref om the
Fes tutes fa Shashi tegen aris experts Fa es parang acing he fn aad
their aptetin 2nd devaleg High aby sty rer tor Wl at LLMs (Leemplan: rece nf Mags
‘ont lsnestier bet 1 the rhe | ancl fate in Inds he eaten the combed owed af cho
‘eperonen tan isha irererted in ie solbpaparaery sores While theses tess honk hays heen seamed
espn frail Meese ceqsameste oe 11h, orosane tht yon end oes eat yoaeparaion

ie wish yan the wry hoe
CHAPTER | PREREQUISITES

mm CHAPTER OUTLINE

Pies
smo ATF ets

So's ue omens Saree 2-4)

ve can Stark 5 hme, omen
ererecnantco Dccrinans

a Sor Ino ean Gevmen
a Prerinani avn + coe Shara
cane san Loner
ides Goce Sore
Gomer Sr 418 Ingomar ursaneras
Lugsita 1 Coe Saree
const Sond 18 3 Fone Cain incl
Pepi oe coe Sree

cowl Stora
12 Prerguiites

SET OF REAL NUMBERS

(ne 38 Ps nn npn eaten oe ay th of
tealuchecsand sot donot hy Real manera
heh rte tations are enclaves

ational Numbers

A moonbae which ea base in he fon hae

cand arm inept eg int gual to O rine 38g 6
Sate enone at
‘eet ot stena noabsey i ceacted 29

ver egy 8 2, TF at ties. AUT ae

ots thr the shove,

Mase. fe ereiig Seema and sim he exproned

Representing vn

§decinalsin the ational oem

thes bs = hi

Thea 1206 x= PARAS.

and 195 —7.350895,

Snhomstngs ree,

Integers

A intgers ire “sional embers av we chasifid n.6
regaiee ingens, rennin ceive mages these fe
gen dencies hy

Pa

‘he set posi nega i thet [5 2.354.
call ona natn umborear de dered by
eee

nie tgs or tatu’ mare} cat be cai
Inve prin naribare nd ounposte umber,

Apres mare: nbc dray not hive & fator
ther tha adil elle pene rum 3.3,3,2,
WotR namphevl pine tino

1 punitive purer, whisk fey a pree abe.
called sumpesite ures 412,24, 102,
tsp amare

Teenie:

Irrational Numbers

ere ice ana nec erational mar
be

erage. 7
veranda Ue sircumierenar ice lie
disreerand ies 2-813. snd vcd heen
trend uke dt hes beeen 2nd 3 and fps
ty aa 212.7%

"hetmpwtant shrastet ania nal umber
{hat wil ave ry -erinaing ar ron energies
nal preven

Tsung a re er witha termnating
st reset deco a ratonal manber whew re
fata a erating nd mg dena

seme Frtonal numbers,

ets any We ral nurbers ene fe an Fae

vember of ae nunhes ell rat nal nurs

SURDS

A aud rata sor wha ee ent fa
lina wanda
Tete: puitve rata nes a

on 28 irrational ther ies

Af and #19 a eertonal nuns and ane sad

Bat 16%

€Q~ Ho i nutasint
thes eagles funda E+), ARS,

and ons

Th the above earepl, RHINE mpracnte

Doni sued we (J+ VSB) cece a in

sna aud

Equality of surds
Leaaealcbesa.onel munbersaiad dh aad i bestnle
esas wal i ate newton mune

Tat dh
Fores,

enaeu

ty Weelyrre do seca yes

6 Way

Rationalizing factor

Waal Lae rail marches suc) at amd fs

uous, Gs Wizomial and (fa Jb} se multigieaton

by tla vb) aves us (a= bp etic ie ston nate

CONCEPT STRANDS

(Concept Strand 1

| fn the vale

Concopi Strand 2
Ve hema omcliomg ‘ete

Preroqites 13

a dy esl sb ection af he

spate cach af (la eb eal soe oe
Combidse the fallowing cvmple:

1 ee 208) ene rena ten eT

ingots 20ettdia ayd—2 © Q

0 EE] a ae enstamg tat ot
oe Fl
ans I v2
= snl na

fy 8x2 fat! 5 the ationatiaing Sauer of

24 58), ance or onitisinson sod ng te

senting .— By == abs — a+ Ba ebm

25 860

pousueess (9°)

Solution
fe th onder

fh Sth vot th ede sd 2nd oe
‘When a pail fuga sarde ae uli her
ar ot hapa le hal Sit” the mel pind

sso a] -ivE5]
The fcr with the fh ender sand is (97 AB i

conjgate's {85-4457 ]s ho predece(Q5-<3]

‘whan th ase prin mtg Wy (8h

the praa’s fa]

‘Whenthe shove iarulisedy (8 —} the
sent i322", which eration

Hence [54S eration for
LA Prerequisites

Roots of surds

Syasencu af expeosion uf he uen fa 4 sb

ne Be VE VTL vb deal) wee, ese

se itch ad JB, dae ean ss obtaad

ews

seit be ofthe oem abe —3

ere zy ae

CONCEPT STRANDS

Concept Sian 3

ed goa

Soustion

posite lise that =

hevwine shea a

cannot rapa. =e

Concept Strand 4

Hed dascay

Solution

asthe shove suave nse GE gy Ve

ow saring at eet
Grbegpeate se aah dhe 2a, wee

Syauteg both cies, at
meant tzy—b
‘esa ele fran

Slay. Yard ll be oe Gnas toa yh

as vos sle= da wm be atthe nnn Yo eye =e ant

AR Wb oe Ua wit se 08 me too ve ie
wheezy 2 we esa
‘caer the above

sss by nee ange

ry 2 3G Nar atts aye Is
42-36. 59- Lye 15 ax 8
Shag bra wee gE DNF =S2—3
= ae 5

Concept Stand §

Pind th ere ros st
[ssipejire

Solution
Inns bemees that tb tea cepsison conte,
at therm and

1) coms otsstemssceectbeset 2, Beant VF

4s.(01 bP, wach sequiltoet 1») aabiar sbend

das the stows RES odes can be sect ts check
waster the aren cession cen 30 cee the
Peter esi bh

= (la be T vee

= [eel ef ie al

easscnbssostittas goa capseoa al vi
Preroqiites LS

H.C (OR G.C.D) AND L.C.M

TGP dans or hae sin ton G02 abide or
pein smn chon tn eGo aa er ea
tron

HOF

TG (er 8.0.1 te Tage elo uf a ot me ga
uber here, poate inked

Ter example,

4 TER af se mune 28.21 98187
(Gince’ ee ange ator al ie hee eer
6) MEP Ss
Thi shure, 2d 6 ara. be lvl prime ar
‘psn Tey lene sone tr er
ant

Lom

TOM ofomess mee susan Le etl abe wih
sadist oy each af ese assem dct Fang
Ter example,

11M ot hese. of wambar (18 24,21 38

[Etre fai sales bey fiche dvldey
fyd¥ end 21 was veniedes

LOMB e Hf ino C129 > 11 2820
[ilaeroe thatthe at af eamlers 9, 12 He
rave rine]

CONCEPT STRANDS
Concept Strand 6
There ste ees “umber wf ses i © fd the

sir ane arg" vony of #8 on 36 de
ible nu (Ube dio es ranged = moo #1,
feldspar Wf ou, Hind the nurmber of ldo
inane ld

Sotation

Surber wf dle >the Fok

(Bes hohe:

Results

(0 Bea aad b ace re aes pounce wget ab —
LoMotia.bh HCE of, >

1) HACE of two a nore peynoaual express w the
padfuowuad sayrerson of Righeet dege, whl,
Adee enc fem withoet sansa,

For cumple, ELLE af Bt ~3r~ 6 (2-30 -1h
eos ole?

i.) LOM of to ct owe po'ramielezpesnons the
papuosuad exes oF the leet dese WAR
chs bls by each oF hese wabostionwinda.
Foresunpls LEM of xix- 1hex— in +4043),
Fer br bbs saa)

ie) HLGE abo oe sare factions

Ihe mamersinsst_dhete Factions

~ TGR al as danninctorwal tse irene

For cxanpl, HOS of is gen by

Hacrer@neay og 7”
Lec ef (27) 18
(0) Licatet one sso tees
{GM of ss rreratone tess frstions

HLH nthe dennminnta of these astons

Sr soups. LOM of

Leste af i5.88521 1

Ter Reo

Wafer of itn he ld
Tae d mkace hive rset

eM aie

Frame lth =
Th drove quale salle he
Tis the are of vles the be

Concent Strand?

Find te hepgot two wu, hi vas $28 a4