Algebra Made Easy for Middle School and High School by K P Basu Kalipada Basu Calcutta

738 Pages·2019·51.2 MB·English

by  K P Basu Kalipada Basu

ALGEBRA MADE EASY

.)
{A$pioved by iJie Govei nment ofBengal
Vide Gakutia Gazette, 9(h Kovember, 1933)
AIGEBRA MADE BAST
MTRICULATION ALGEBRA
(
roB
JIATRICTJUTION STUDENTS OF THE INDIAN
UNIVERSITIES
BY
KALIPADA BASU, M.A.
LAM PBOFESSOR OF.AUTSaUTlCS, DACCA COLTJCGK rELLOiy
*.
AKD EXAMIXER, CM.CUXTA EXIVERSITY
Wd
ATJTHOR OR “MATRICDriATIOX GEOAICTRY”/'lXTERi[EDIATEADGEBRA"
‘iXTERVEDIATE SOETD GEOKETRY*’ ETC TTC.
FORTIETH EDITION
THE K. P. BASU LIBRARY,
11, jrOHENDRA GOSSAIN LANE,
OALOUTTA
1933
[Copff right Hegisiered]
Revised by
3S’E1PENDEA NATH SEN, D Sc, PES
POST GRADUATE LECTUBEP. IN MiVTUEMATICS, 04.Ij0DTTA UNIVEBSITY
SECRETARY) CAECDTTA IfATHEJIATlCAL SOCIETY HEMBEBt
BOARD 01 3IATHE3IATICS, CALCUTTA UNIVERSITY
EXAMINERINTHEUNIVERSITIESORCALCUTTA,
DACCA, BENARFS, ALLAHABAD, ETC ETC
,
PnhMudblJ K BASU BA & T Basd, BA
.1
Tut K. P. Basu Library,
11, Mobendra Gossain lAine, Calcutta
PiniHby Tridibl'iII Basu, ba
ThlK P Bvsl PBiNfiNG Work*,
11, IMobeiidra Gossaui Lane, Calcutta
Drawings by Manuja Guha, Artist.
PREFACE
The present work is intended as a text-book in AJprebra
for all classes of students in our schools It differs,
m
however, several respects from the existing text-books on
the subject at present in use
Algebra like every other branch of j^Iathematics should
be studied more as a subject for mental discipline than for
anything else An intelligent grasp of principles there-
fore is to be chiefly aimed at and not the mere learning
by rote of a certain number of rules with some readiness
in their application. This is the ideal I have ever kept in
m
view the preparation of this work
The elementary principles of the subject have been
dwelt upon at considerable length in the earlier chapters
of the book The full import of negative quantities has
been explained it is beheved, with some degree of clear-
ness, almost at the very outset, and rules for their addition
and subtraction have subsequently been deduced there-
from by a very simple mode of reasoning
The proposition of each article after being clearly de-
monstrated has been copiously illustrated by a number of
select examples, a much larger number of other examples,
arranged progressively, has then been added as an exercise
for the student The last article of each chapter consists
of a number of miscellaneous examples fully worked out
as interesting illustrations of special artifices these again
,
are followed by similar others for exercise.
The chapters on Formulse and Factors wiU, it is hoped,
be particularly acceptable to the young learner The sub-
ject of factorisation has been treated exhaustively as far
as the hmits of this work would allow The last chapter,
on Elimmation and Miscellaneous Artifices, will I hope,
be of considerable use to the more advanced student.
PREFACE
Tl
Entrance Examination Papers of the Calcutta Univer-
sity from 1858 to 1890 will he found at the very end Th&
more important and difficult problems from these papers-
are fully worked out in the body of the work in illustra-
tion of the principles upon which their solutions depend^
whilst others, comparatively simpler, have been suitably
introduced among the exermses just to give the student
an opportunity of reassuring himself, when successful in
working them out with unaided exertion, that his know-
ledge has to some extent at least, come up to the Univer-
sity standard With the examination papers are also-
given references to the pages where these problems are to
he found in the body of the work.
Instead of ending the hook with a collection of mis-
cellaneous examples promiscuously arranged, Ihave added
a number of miscellaneous examples in the form of separate
examination papers, any one of which may he regarded
as a good exercise for the student at a setting of about
two hours and a half.
The entire book contains nearly 8000 examples in all,,
of which over 400 are fuUy worked out Many of these
examples have been specially devised for this workwhilst,
for the rest I am indebted to several of the standard works
of English authors as also to many of the examination
papers of the Indian and English Universities
I have attempted to make the work useful to the school
student as a means of acquinng algebraical skill along with
a sound knowledge of principles, and I have spared no pauis
for it Itis nowfor all experienced teachers of mathematics
to judge as to howfarI have been successful in my endeav-
our. To gentlemen interested in the cause of education I
shall he much obliged if they willkindly communicate to me
any corrections or suggestions that they may consider
necessary for the improvement of the work.
K
Dacca * March, 1690. P. BASU
PREFACE YU
PREFACE TO THE SECOND EDITION
A FEW words of explanation seem to be necessary in
connection intii the publication of this edition The fiist
edition having been pubhshed rather unseasonably last year,
I did not at all anticipate that a second edition would be in
demand so soon Accordingly the work of re-pubhcationwas
not taken at hand earher than January last. But the book
beginmng to be received with increased favour in different
educational circles \nth the commencement of the new aca-
demic session, the first edition, consisting of 2250 copies, was
found to be exhausted before the end of the last month
Hence, in the interests of the students of all those schools in
which the book has been adopted as atext-book, mypublisher
had no other alternative than to hasten the work by all
possible means In consequence of thiS; I am sorry, I have
not been able to give the book as thorough a revision as I
intended, nor to effect such improvements as have been
kindly suggested by some fnends.
K
Dacca Maich 1891 P. BASH
:
PREFACE TO THE FIFTH EDITION
In this edition the bulk of the work has increased by
about 60 pages The additions that have been made aie as
follows • (1) an increase in the number of examples of exer-
m
cises the earlier chapters of the book (2) the insertion of
;
examples unth Fiactional Indices in the chapters on Multiph-
iron and Division (3) the introduction of three sets of
,
"Miscellaneous Exercises in suitable places in the body of the
work (4) an article on the Method of finding the Cnie Root
,
of a Compound Algebraical Expression and a chapter on
(5)
,
Qmdiatic Egiiaiions For several of these improvements I
am indebted to the land and repeated suggestions of friends
who
are practical workers in the field of education It is
therefore hoped that the present edition will be found consi-
derably more useful than its predecessors
Dacca Janmiy,189d. K P BASH
7m PREFACE
PREFACE TO THE SIXTH EDITION
In this edition the book has been thoroughly revised and
answers to the examples in aU the exercises have been care-
fully vended. Some additions and alterations have been occa-
sionally made, but they do not deserve any special mention
I am indebted to several friends for their kindness inpointing
out errors and mispnnts My special thanks are due to
Babu Bepinbihan (ianguly, B A Teacher, Jubilee School,
,
D B
Dacca, and to Moulvie Abdullah Khan, Teacher, School,
Dipalpur (Montgomery)
Dacca Apiim5 K P BASU
PREFACE TO THE THIRTY-SEVENTH EDITION
In this edition which has been revised by me, certain new
matters have been added in accordance with the recent Sylla-
buses of Studies prescribed by the Education Department
of the Bengal Government The order of the subjeot-matteis
has also been altered to some extent so as to make the book
more useful and interesting to the student in general.
The subject of Graphs has been treated more fully owing
to its growing importance and has been introduced in an
earlier portion of the book to familiarise the student with the
prmciples of the Graphic method from the beginning.
No pains have been spared to make the book most exhaus-
tive by necessary additions and alterations, and Prof K P
Basu’s charaoteristio mode of treatment which has led to the
great excellence and success of the present treatise as a text
m
book has been followed all such changes
It IS therefore hoped that in its present form the book will
be found to be more useful to the teacher as well as to the
pupil
My best thanks are due to my esteemed fnend Prof
M
Monoranjan Das-Gupta, A of the City College, Calcutta,
and Babu Tridibesh Basu, youngest son ofProf K P Basu,
for their invaluable assistances in the preparation of the
present edition
Calcutta, Apnl, 1930 N N SEN
CONTENTS
Page
INTRODUCTION 1
CHAPTER
I
8YMOLS SIGNS SUBSTITUTIONS
• •
5
Symbols •••
5
Signs ff*
8
Substitutions ••
n
CHAPTER
POSITIVE AND NEGATIVE QUANTITIES
Positive and Negative Quantities •*• 17
Crraphical Illustrations ••• 18
CHAPTER in
y
iroUR SBIPLE RULES
Addition 20
Subtraction 29
Removal andInsertion of Brackets «• 33
Multiplication ••• 36
Division 48
••
Miscellaneous Exercises I ••• > $ • 63
CHAPTER IV
SBIPLE FOELIULiE AND THEIR APPLICATION
Simple Formulas and their Application
CHAPTER V ' '
SlilPLE EQUATIONS
Simple Equations 73
•t