Sl No Topic Notes NCERT QA Video 1 Rational Numbers 8 32

Sl No Topic Notes NCERT QA Video 1 Rational Numbers 8 32 38 2 Linear Equations in one Variables 9 42 47 59 67 74 85 3 Understanding Quadrilaterals 10 89 4 Practical Geometry 12 5 Data Handling 13 6 Squares and Square Roots 15 7 Cubes and cube root 16 8 Comparing quantities 17 9 Algebraic Expressions and Identities 18 10 Visualising Solid Shapes 20 11 Mensuration 22 12 Exponents and powers 24 13 Direct and Inverse Propotions 25 14 Factorisation 26 15 Introduction to Graphs 28 16 Playing with numbers 30

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CBSEClass-VIII

MATHEMATICS

Thedevelopmentoftheupperprimarysyllabushasattemptedtoemphasizethe

developmentofmathematicalunderstandingandthinkinginthechild.Itemphasizesthe

needtolookattheupperprimarystageasthestageoftransitiontowardsgreater

abstraction,wherethechildwillmovefromusingconcretematerialsandexperiencestodeal

withabstractnotions.Ithasbeenrecognizedasthestagewhereinthechildwilllearntouse

andunderstandmathematicallanguageincludingsymbols.Thesyllabusaimstohelpthe

learnerrealizethatmathematicsasadisciplinerelatestoourexperiencesandisusedin

dailylife,andalsohasanabstractbasis.Allconcretedevicesthatareusedintheclassroom

arescaffoldsandpropswhichareanintermediatestageoflearning.Thereisanemphasisin

takingthechildthroughtheprocessoflearningtogeneralize,andalsocheckingthe

generalization.Helpingthechildtodevelopabetterunderstandingoflogicandappreciating

thenotionofproofisalsostressed.

Thesyllabusemphasizestheneedtogofromconcretetoabstract,consolidatingand

expandingtheexperiencesofthechild,helpinghergeneralizeandlearntoidentifypatterns.

Itwouldalsomakeanefforttogivethechildmanyproblemstosolve,puzzlesandsmall

challengesthatwouldhelpherengagewithunderlyingconceptsandideas.Theemphasisin

thesyllabusisnotonteachinghowtouseknownappropriatealgorithms,butonhelpingthe

childdevelopanunderstandingofmathematicsandappreciatetheneedforanddevelop

differentstrategiesforsolvingandposingproblems.Thisisinadditiontogivingthechild

ampleexposuretothestandardprocedureswhichareefficient.Childrenwouldalsobe

expectedtoformulateproblemsandsolvethemwiththeirowngroupandwouldtrytomake

anefforttomakemathematicsapartoftheoutsideclassroomactivityofthechildren.The

effortistotakemathematicshomeasahobbyaswell.

Thesyllabusbelievesthatlanguageisaveryimportantpartofdevelopingmathematical

understanding.Itisexpectedthattherewouldbeanopportunityforthechildtounderstand

thelanguageofmathematicsandthestructureoflogicunderlyingaproblemora

description.Itisnotsufficientfortheideastobeexplainedtothechild,buttheeffortshould

betohelpherevolveherownunderstandingthroughengagementwiththeconcepts.

http://mycbseguide.com/


Childrenareexpectedtoevolvetheirowndefinitionsandmeasurethemagainstnewerdata

andinformation.Thisdoesnotmeanthatnodefinitionsorclearideaswillbepresentedto

them,butitistosuggestthatsufficientscopefortheirownthinkingwouldbeprovided.

Thus,thecoursewouldde-emphasizealgorithmsandrememberingoffacts,andwould

emphasizetheabilitytofollowlogicalsteps,developandunderstandargumentsaswell.

Also,anoverloadofconceptsandideasisbeingavoided.Wewanttoemphasizeatthisstage

fractions,negativenumbers,spatialunderstanding,datahandlingandvariablesas

importantcornerstonesthatwouldformulatetheabilityofthechildtounderstandabstract

mathematics.Thereisalsoanemphasisondevelopinganunderstandingofspatialconcepts.

Thisportionwouldincludesymmetryaswellasrepresentationsof3-Din2-D.Thesyllabus

bringsindatahandlingalso,asanimportantcomponentofmathematicallearning.Italso

includesrepresentationsofdataanditssimpleanalysisalongwiththeideaofchanceand

probability.

Theunderlyingphilosophyofthecourseistodevelopthechildasbeingconfidentand

competentindoingmathematics,havingthefoundationstolearnmoreanddevelopingan

interestindoingMathematics.Thefocusisnotongivingcomplicatedarithmeticand

numericalcalculations,buttodevelopasenseofestimationandanunderstandingof

mathematicalideas.

GeneralPointsinDesigningTextbookforUpperPrimaryStageMathematics

1.Theemphasisinthedesigningofthematerialshouldbeonusingalanguagethatthechild

canandwouldbeexpectedtounderstandherselfandwouldberequiredtoworkuponina

group.Theteachertoonlyprovidesupportandfacilitation.

2.Theentirematerialwouldhavetobeimmersedinandemergefromcontextsofchildren.

Therewouldbeexpectationthatthechildrenwouldverbalizetheirunderstanding,their

generalizations,andtheirformulationsofconceptsandproposeandimprovetheir

definitions.

3.Thereneedstobespaceforchildrentoreasonandprovidelogicalargumentsfordifferent

ideas.Theyarealsoexpectedtofollowlogicalargumentsandidentifyincorrectand

unacceptablegeneralizationsandlogicalformulations.

4.Childrenwouldbeexpectedtoobservepatternsandmakegeneralizations.Identify

exceptionstogeneralizationsandextendthepatternstonewsituationsandchecktheir

validity.



5.Needtobeawareofthefactthattherearenotonlymanywaystosolveaproblemand

theremaybemanyalternativealgorithmsbuttheremaybemanyalternativestrategiesthat

maybeused.Someproblemsneedtobeincludedthathavethescopeformanydifferent

correctsolutions.

6.Thereshouldbeaconsciousnessaboutthedifferencebetweenverificationandproof.

Shouldbeexposedtosomesimpleproofssothattheycanbecomeawareofwhatproof

means.

7.Thebookshouldnotappeartobedryandshouldinvariouswaysbeattractivetochildren.

Thepointsthatmayinfluencethisinclude;thelanguage,thenatureofdescriptionsand

examples,inclusionorlackofillustrations,inclusionofcomicstripsorcartoonstoillustrate

apoint,inclusionofstoriesandotherinterestingtextsforchildren.

8.Mathematicsshouldemergeasasubjectofexplorationandcreationratherthanfinding

knownoldanswerstoold,complicatedandoftenconvolutedproblemsrequiringblind

applicationofun-understoodalgorithms.

9.Thepurposeisnotthatthechildrenwouldlearnknowndefinitionsandthereforenever

shouldwebeginbydefinitionsandexplanations.Conceptsandideasgenerallyshouldbe

arrivedatfromobservingpatterns,exploringthemandthentryingtodefinethemintheir

ownwords.Definitionsshouldevolveattheendofthediscussion,asstudentsdevelopthe

clearunderstandingoftheconcept.

10.Childrenshouldbeexpectedtoformulateandcreateproblemsfortheirfriendsand

colleaguesaswellasforthemselves.

11.Thetextbookalsomustexpectthattheteacherswouldformulatemanycontextualand

contextuallyneededproblemsmatchingtheexperienceandneedsofthechildrenofher

class.

12.Thereshouldbecontinuityofthepresentationwithinachapterandacrossthechapters.

Opportunitiesshouldbetakentogivestudentsthefeelforneedofatopic,whichmayfollow

later.

CourseStructureforClass-VIII

NumberSystem(50hrs)

RationalNumbers:

Propertiesofrationalnumbers.(includingidentities).Usinggeneralformof

expressiontodescribeproperties



Consolidationofoperationsonrationalnumbers.

RepresentationofrationalnumbersonthenumberlineBetweenanytworational

numbersthereliesanotherrationalnumber(Makingchildrenseethatifwetaketwo

rationalnumbersthenunlikeforwholenumbers,inthiscaseyoucankeepfinding

moreandmorenumbersthatliebetweenthem.)

Wordproblem(higherlogic,twooperations,includingideaslikearea)

(ii)Powers

Integersasexponents.

Lawsofexponentswithintegralpowers

(iii)Squares,Squareroots,Cubes,Cuberoots.

SquareandSquareroots

Squarerootsusingfactormethodanddivisionmethodfornumberscontaining(a)no

morethantotal4digitsand(b)nomorethan2decimalplaces

Cubesandcubesroots(onlyfactormethodfornumberscontainingatmost3digits)

Estimatingsquarerootsandcuberoots.Learningtheprocessofmovingnearertothe

requirednumber.

(iv)Playingwithnumbers

Writingandunderstandinga2and3digitnumberingeneralizedform(100a+10b+c

,wherea,b,ccanbeonlydigit0-9)andengagingwithvariouspuzzlesconcerning

this.(Likefindingthemissingnumeralsrepresentedbyalphabetsinsumsinvolving

anyofthefouroperations.)Childrentosolveandcreateproblemsandpuzzles.

Numberpuzzlesandgames

Deducingthedivisibilitytestrulesof2,3,5,9,10foratwoorthree-digitnumber

expressedinthegeneralformAlgebra(20hrs)(i)AlgebraicExpressions

Multiplicationanddivisionofalgebraicexp.(Coefficientshouldbeintegers)

Somecommonerrors(e.g.2+x≠2x,7x+y≠7xy)

Identities(a±b)2=a2±2ab+b2,a2–b2=(a–b)(a+b)

Factorisation(simplecasesonly)asexamplesthefollowingtypesa(x+y),(x±y)2,a2

–b2,

(x+a).(x+b)



Solvinglinearequationsinonevariableincontextualproblemsinvolving

multiplicationanddivision(wordproblems)(avoidcomplexcoefficientinthe

equations)

RatioandProportion(25hrs)

Slightlyadvancedproblemsinvolvingapplicationsonpercentages,profit&loss,

overheadexpenses,Discount,tax.

Differencebetweensimpleandcompoundinterest(compoundedyearlyupto3years

orhalf-yearlyupto3stepsonly),Arrivingattheformulaforcompoundinterest

throughpatternsandusingitforsimpleproblems.

Directvariation–Simpleanddirectwordproblems

Inversevariation–Simpleanddirectwordproblems

Time&workproblems–SimpleanddirectwordproblemsGeometry(40hrs)

(i)Understandingshapes:

-Propertiesofquadrilaterals–Sumofanglesofaquadrilateralisequalto3600(By

verification)

-Propertiesofparallelogram(Byverification)

1. Oppositesidesofaparallelogramareequal,

2. (Oppositeanglesofaparallelogramareequal,

3. Diagonalsofaparallelogrambisecteachother.[Why(iv),(v)and(vi)followfrom(ii)]

4. Diagonalsofarectangleareequalandbisecteachother.

5. Diagonalsofarhombusbisecteachotheratrightangles.

6. Diagonalsofasquareareequalandbisecteachotheratrightangles.

(iii)Representing3-Din2-D

IdentifyandMatchpictureswithobjects[morecomplicatede.g.nested,joint2-Dand

3-Dshapes(notmorethan2)].

Drawing2-Drepresentationof3-Dobjects(Continuedandextended)

Countingvertices,edges&faces&verifyingEuler’srelationfor3-Dfigureswithflat

faces(cubes,cuboids,tetrahedrons,prismsandpyramids)

1. Construction:ConstructionofQuadrilaterals:



Givenfoursidesandonediagonal

Threesidesandtwodiagonals

Threesidesandtwoincludedangles

Twoadjacentsidesandthreeangles

Mensuration(15hrs)

1. Areaofatrapeziumandapolygon.

2. Conceptofvolume,measurementofvolumeusingabasicunit,volumeofacube,cuboid

andcylinder

3. Volumeandcapacity(measurementofcapacity)

4. Surfaceareaofacube,cuboid,cylinder.

Datahandling(15hrs)

1. Readingbar-graphs,ungroupeddata,arrangingitintogroups,representationofgrouped

datathroughbar-graphs,constructingandinterpretingbar-graphs.

2. SimplePiechartswithreasonabledatanumbers

3. Consolidatingandgeneralizingthenotionofchanceineventsliketossingcoins,diceetc.

Relatingittochanceinlifeevents.Visualrepresentationoffrequencyoutcomesof

repeatedthrowsofthesamekindofcoinsordice.Throwingalargenumberofidentical

dice/coinstogetherandaggregatingtheresultofthethrowstogetlargenumberof

individualevents.Observingtheaggregatingnumbersoveralargenumberofrepeated

events.Comparingwiththedataforacoin.Observingstringsofthrows,notionof

randomness

Introductiontographs(15hrs)PRELIMINARIES:

1. Axes(Sameunits),CartesianPlane

2. Plottingpointsfordifferentkindofsituations(perimetervslengthforsquares,areaasa

functionofsideofasquare,plottingofmultiplesofdifferentnumbers,simpleinterestvs

numberofyearsetc.)

Readingofffromthegraphs

Readingoflineargraphs

Readingofdistancevstimegraph



CBSEClass8Mathematics

RevisionNotes

Chapter–01

RationalNumbers

Rationalnumbersareclosedundertheoperationsofaddition,subtractionand

multiplication.

Theoperationsadditionandmultiplicationare

(i)commutativeforrationalnumbers.

(ii)associativeforrationalnumbers.

Therationalnumber0istheadditiveidentityforrationalnumbers.

Therationalnumber1isthemultiplicativeidentityforrationalnumbers.

Theadditiveinverseoftherationalnumber is andvice-versa.

Thereciprocalormultiplicativeinverseoftherationalnumber is if x =1

Distributivityofrationalnumbers:Forallrationalnumbersa,bandc,

a(b+c)=ab+acanda(b–c)=ab–ac

Rationalnumberscanberepresentedonanumberline.

Betweenanytwogivenrationalnumberstherearecountlessrationalnumbers.The

ideaofmeanhelpsustofindrationalnumbersbetweentworationalnumbers.

PositiveRationals:NumeratorandDenominatorbothareeitherpositiveornegative.

Example:

NegativeRationals:NumeratorandDenominatorbothareofoppositesigns.

Example:

AdditiveInverse:Additiveinverse(negative) + = + =0, istheadditive

inverseof istheadditiveinverseof .

MulitiplicativeInverse(reciprocal): x =1= x where isthereciprocalof .

Zerohasnoreciprocal.Thereciprocalof1is1andof-1is-1.




RevisionNotes

Chapter–02

LinearEquationsinOneVariable

Astatementofequalityoftwoalgebraicexpressionsinvolvingoneormorevariables.

Example:x+2=3

Linear Equation in One variable: The expressions which form the equation that

containsinglevariableandthehighestpowerofthevariableintheequationisone.

Analgebraicequationisanequalityinvolvingvariables.Itsaysthatthevalueofthe

expressionononesideoftheequalitysignisequaltothevalueoftheexpressionon

theotherside.

TheequationswestudyinClassesVI,VIIandVIIIarelinearequationsinonevariable.

In such equations, the expressions which form the equation contain only one

variable. Further, the equations are linear, i.e., the highest power of the variable

appearingintheequationis1.

Alinearequationmayhaveforitssolutionanyrationalnumber.

Anequationmayhavelinearexpressionsonbothsides.Equationsthatwestudiedin

ClassesVIandVIIhadjustanumberononesideoftheequation.

Justasnumbers,variablescan,also,be transposedfromonesideof theequationto

theother.

Occasionally,theexpressionsformingequationshavetobesimplifiedbeforewecan

solvethembyusualmethods.Someequationsmaynotevenbelineartobeginwith,

buttheycanbebroughttoalinearformbymultiplyingbothsidesoftheequationby

asuitableexpression.

Theutilityof linearequations is intheirdiverseapplications;differentproblemson

numbers,ages,perimeters, combinationof currencynotes,andsooncanbe solved

usinglinearequations.




RevisionNotes

Chapter–3

UnderstandingQuadrilaterals

Parallelogram:Aquadrilateralwitheachpairofoppositesidesparallel.

(1)Oppositesidesareequal.

(2)Oppositeanglesareequal.

(3)Diagonalsbisectoneanother.

Rhombus:Aparallelogramwithsidesofequallength.

(1)Allthepropertiesofaparallelogram.

(2)Diagonalsareperpendiculartoeachother.

Rectangle:Aparallelogramwitharightangle.

(1)Allthepropertiesofaparallelogram.

(2)Eachoftheanglesisarightangle.

(3)Diagonalsareequal.

Square:Arectanglewithsidesofequallength.

(1)Allthepropertiesofaparallelogram,rhombusandarectangle.



Kite:Aquadrilateralwithexactlytwopairsofequalconsecutivesides

(1)Thediagonalsareperpendiculartooneanother

(2)Oneofthediagonalsbisectstheother.

(3)Inthefigure but .

Trapezium:Aquadrilateralhavingexactlyonepairofparallelsides.

Diagonal:Asimpleclosedcurvemadeupofonlylinesegments.Alinesegment

connectingtwonon-consecutiveverticesofapolygoniscalleddiagonal.

Convex:Themeasureofeachangleislessthan .

Concave:Themeasureofatleastoneangleismorethan

Quadrilateral:Polygonhavingfoursides.

Elementofquadrilateral:

(i)Sides:Linesegmentsjoiningthepoints.

(ii)Vertices:Pointofintersectionoftwoconsecutivesides.

(iii)Oppositesides:Twosidesofaquadrilateralhavingnocommonendpoint.

(iv)OppositeAngles:Twoanglesofaquadrilateralnothavingacommonarm.

(v)Diagonals:Linesegmentobtainedbyjoiningtheoppositevertices.

(vi)AdjacentAngles:Twoanglesofaquadrilateralhavingacommonarm.

(vii)AdjacentSides:Twosidesofaquadrilateralhavingacommonendpoint.




RevisionNotes

Chapter–4

PracticalGeometry

Aquadrilateralhas10parts-4sides,4anglesand2diagonals.Fivemeasurements

candetermineaquadrilateraluniquely.

Fivemeasurementscandetermineaquadrilateraluniquely.

Aquadrilateralcanbeconstructeduniquelyifthelengthsofitsfoursidesanda

diagonalisgiven.

Aquadrilateralcanbeconstructeduniquelyifitstwodiagonalsandthreesidesare

known.

Aquadrilateralcanbeconstructeduniquelyifitstwoadjacentsidesandthreeangles

areknown.

Aquadrilateralcanbeconstructeduniquelyifitsthreesidesandtwoincludedangles

aregiven.




RevisionNotes

Chapter–6SquaresandSquareRoots

Square:Numberobtainedwhenanumberismultipliedbyitself.Itisthenumber

raisedtothepower2.22=2x2=4(squareof2is4).

Ifanaturalnumbermcanbeexpressedasn2,wherenisalsoanaturalnumber,then

misasquarenumber.

Allsquarenumbersendwith0,1,4,5,6or9atunit’splace.

Squarenumberscanonlyhaveevennumberofzerosattheend.

Squarerootistheinverseoperationofsquare.

Therearetwointegralsquarerootsofaperfectsquarenumber.

Positivesquarerootofanumberisdenotedbythesymbol Forexample,32=9gives

PerfectSquareorSquarenumber:Itisthesquareofsomenaturalnumber.If

m=n2,thenmisaperfectsquarenumberwheremandnarenaturalnumbers.

Example:1=1x1=12,4=2x2=22.

PropertiesofSquarenumber:

(i)Anumberendingin2,3,7or8isneveraperfectsquare.Example:152,1028,6593

etc.

(ii)Anumberendingin0,1,4,5,6or9maynotnecessarilybeasquarenumber.

Example:20,31,24,etc.

(iii)Squareofevennumbersareeven.Example:22=4,42=16etc.

(iv)Squareofoddnumbersareodd.Example:52=25,92=81,etc.

(v)Anumberendinginanoddnumberofzeroescannotbeaperferctsquare.

Example:10,1000,900000,etc.

(vi)Thedifferenceofsquaresoftwoconsecutivenaturalnumberisequaltotheir

sum.(n+1)2-n2=n+1+n.Example:42-32=4+3=7.122-112=12+11=23,etc.

(vii)Atriplet(m,n,p)ofthreenaturalnumbersm,nandpiscalledPythagorean

triplet,ifm2+n2=p2:32+42=25=52




RevisionNotes

Chapter–7

CubesandCubeRoot

Cubenumber:Numberobtainedwhenanumberismultipliedbyitself threetimes.

23=2x2x2=8,33=3x3x3=27,etc.

Numbers like 1729, 4104, 13832, are knownasHardy – RamanujanNumbers. They

canbeexpressedassumoftwocubesintwodifferentways.

Numbersobtainedwhenanumber ismultipliedby itself three timesareknownas

cubenumbers.Forexample1,8,27,...etc.

Ifintheprimefactorisationofanynumbereachfactorappearsthreetimes,thenthe

numberisaperfectcube.

Thesymbol denotescuberoot.Forexample

PerfectCube:Anaturalnumberissaidtobeaperfectcubeifitisthecubeofsome

naturalnumber.Example:8isperfectcube,becausethereisanaturalnumber2such

that8=23,but18 isnotaperfect cube,because there isnonaturalnumberwhose

cubeis18.

Thecubeofanegativenumberisalwaysnegative.

PropertiesofCubeofNumber:

(i)Cubesofevennumberareeven.

(ii)Cubesofoddnumbersareodd.

(iii)The sumof the cubesof firstnnaturalnumbers is equal to the squareof their

sum.

(iv)Cubesofthenumbersendingwiththedigits0,1,4,5,6and9endwithdigits0,1,

4,5,6and9respectively.

(v)Cubeofthenumberendingin2endsin8andcubeofthenumberendingin8ends

in2.

(vi)Cubeof thenumberending in3ends in7andcubeof thenumberending in7

endsin3.




RevisionNotes

Chapter–8

ComparingQuantities

Ratio:Comparingbydivisioniscalledratio.Quantitieswritteninratiohavethesame

unit.Ratiohasnounit.Equalityoftworatiosiscalledproportion.

Productofextremes=Productofmeans

Percentage:Percentagemeansforeveryhundred.Theresultofanydivisioninwhich

thedivisoris100isapercentage.Thedivisorisdenotedbyaspecialsymbol%,read

aspercent.

ProfitandLoss:

(i)CostPrice(CP):Theamountforwhichanarticleisbought.

(ii)SellingPrice(SP):Theamountforwhichanarticleissold.

Additionalexpensesmadeafterbuyinganarticleareincludedinthecostpriceand

areknownasoverheadexpenses.Thesemayincludeexpenseslikeamountspenton

repairs,labourcharges,transportation,etc.

Discountisareductiongivenonmarkedprice.Discount=MarkedPrice–SalePrice.

Discountcanbecalculatedwhendiscountpercentageisgiven.Discount=Discount%

ofMarkedPrice

Additionalexpensesmadeafterbuyinganarticleareincludedinthecostpriceand

areknownasoverheadexpenses.CP=Buyingprice+Overheadexpenses

SalestaxischargedonthesaleofanitembythegovernmentandisaddedtotheBill

Amount.Salestax=Tax%ofBillAmount

SimpleInterest:Iftheprincipalremainsthesamefortheentireloanperiod,thenthe

interestpaidiscalledsimpleinterest.

Compoundinterestistheinterestcalculatedonthepreviousyear’samount(A=P+I)

(i)Amountwheninterestiscompoundedannually Pisprincipal,Ris

rateofinterest,nistimeperiod

(ii)Amountwheninterestiscompoundedhalfyearly




RevisionNotes

Chapter–9

AlgebraicExpressionsandIdentities

Expressionsareformedfromvariablesandconstants.

Constant:Asymbolhavingafixednumericalvalue.Example:2, ,2.1,etc.

Variable:Asymbolwhichtakesvariousnumericalvalues.Example:x,y,z,etc.

AlgebricExpression:Acombinationofconstantsandvariablesconnectedbythesign

+,-, and iscalledalgebraicexpression.

Termsareadded to formexpressions. Terms themselves are formedasproduct of

factors.

Expressions that contain exactly one, two and three terms are called monomials,

binomialsandtrinomialsrespectively.Ingeneral,anyexpressioncontainingoneor

more terms with non-zero coefficients (and with variables having non- negative

exponents)iscalledapolynomial.

Liketermsareformedfromthesamevariablesandthepowersofthesevariablesare

thesame,too.Coefficientsofliketermsneednotbethesame.

While adding (or subtracting) polynomials, first look for like terms and add (or

subtract)them;thenhandletheunliketerms.

Therearenumberofsituations inwhichweneedtomultiplyalgebraicexpressions:

for example, in finding area of a rectangle, the sides of which are given as

expressions.

Monomial:Anexpressioncontainingonlyoneterm.Example:-3,4x,3xy,etc.

Binomial:Anexpressioncontainingtwoterms.Example:2x-3,4x+3y,xy-4,etc.

Trinomial: An expression containing three terms. Example: ,

3x+2y+5z,etc.

Polynomial:Ingeneral,anyexpressioncontainingoneormoretermswithnon-zero

coefficients (andwithvariableshavingnon-negative exponents).Apolynomialmay

containanynumberofterms,oneormorethanone.

Amonomialmultipliedbyamonomialalwaysgivesamonomial.

While multiplying a polynomial by a monomial, we multiply every term in the



polynomialbythemonomial.

In carrying out themultiplication of a polynomial by a binomial (or trinomial),we

multiplytermbyterm,i.e.,everytermofthepolynomialismultipliedbyeveryterm

inthebinomial(ortrinomial).Notethatinsuchmultiplication,wemaygettermsin

theproductwhicharelikeandhavetobecombined.

Anidentityisanequality,whichistrueforallvaluesofthevariablesintheequality.

On the other hand, an equation is true only for certain values of its variables. An

equationisnotanidentity.

Thefollowingarethestandardidentities:

(a+b)2=a2+2ab+b2(I)

(a–b)2=a2–2ab+b2(II)

(a+b)(a–b)=a2–b2(III)

Anotherusefulidentityis(x+a)(x+b)=x2+(a+b)x+ab(IV)

Theabovefouridentitiesareusefulincarryingoutsquaresandproductsofalgebraic

expressions. They also allow easy alternative methods to calculate products of

numbersandsoon.

Coefficients:Inthetermofanexpressionanyofthefactorswiththesignoftheterm

iscalledthecoefficientoftheproductoftheotherfactors.

Terms:Variouspartsofanalgebraicexpressionwhichareseparatedby+and–signs.

Example:Theexpression4x+5hastwoterms4xand5.

(i)ConstantTerm:Atermofexpressionhavingnolateralfactor.

(ii) Liketerm: The termhaving the same literal factors.Example2xyand -4xyare

liketerms.

(iii) Unliketerm: The termshavingdifferent literal factors.Example: and 3xy

areunliketerms.

Factors:Eachterminanalgebraicexpressionisaproductofoneormorenumber(s)

and/or literals. These number (s) and/or literal (s) are known as the factor of that

term.Aconstantfactoriscallednumericalfactor,whileavariablefactorisknownas

aliteralfactor.Theterm4xistheproductofitsfactors4andx.




RevisionNotes

Chapter–10

Visualisingsolidshapes

Therearethreetypesofshapes:

(i)Onedimensionalshapes:Shapeshavinglengthonly.Example:aline.

(ii)TwodimensionalShapes:Planeshapeshavingtwomeasurementslikelengthand

breadth.Example:apolygon,atriangle,arectangle,etc.generally,twodimensional

figuresareknownas2-Dfigures.

(iii)ThreedimensionalShapes:Solidobjectsandshapeshavinglength,breadthand

heightordepth.Example:Cubes,cylinders,cone,cuboid,spheres,etc.

(iv)Face:Aflatsurfaceofathreedimensionalfigure.

(v)Edge:Linesegmentwheretwofacesofsolidmeet.

Polyhedron:Athree-dimensionalfigurewhosefacesareallpolygons.

Prism:Apolyhedronwhosebottomandtopfaces(knownasbases)arecongruent

polygonsandfacesknownaslateralfacesareparallelograms.Whenthesidefacesare

rectangles,theshapeisknownasrightprism.

Pyramid:Apolyhedronwhosebaseisapolygonandlateralfacesaretriangles.

Vertex:Apointwherethreeofmoreedgesmeet.



Base:Thefacethatisusedtonameapolyhedron.

Euler’sformulaforanypolyhedronisF+V–E=2,whereFstandsfornumberof

faces,VfornumberofverticesandEfornumberofedges.

Recognising2Dand3Dobjects.

Recognisingdifferentshapesinnestedobjects.

3Dobjectshavedifferentviewsfromdifferentpositions.

Mapping:Amapdepictsthelocationofaparticularobject/placeinrelationtoother

objects/places.

Amapisdifferentfromapicture.

Symbolsareusedtodepictthedifferentobjects/places.

Thereisnoreferenceorperspectiveinamap.

Mapsinvolveascalewhichisfixedforaparticularmap.

Convex:Thelinesegmentjoininganytwopointsonthesurfaceofapolyhedron

entirelyliesinsideoronthepolyhedron.Example:Cube,cuboid,tetrahedron,

pyramid,prism,etc.




RevisionNotes

Chapter–11

Mensuration

Perimeter:Lengthofboundaryofasimpleclosedfigure.

Perimeterof:

Rectangle=2(l+b)

Square=4a

Parallelogram=2(sumoftwoadjacentsides)

Area:Themeasureofregionenclosedinasimpleclosedfigure.

Areaofatrapezium=halfofthesumofthelengthsofparallelsides×perpendicular

distancebetweenthem.

Areaofarhombus=halftheproductofitsdiagonals.

Triangle= xbasexheight

Diagonalof:

Rectangle=

Square=

Surfaceareaofasolidisthesumoftheareasofitsfaces.

Surfaceareaof:

acuboid=2(lb+bh+hl)

acube=6l2



acylinder= (r+h)

Amountofregionoccupiedbyasolidiscalleditsvolume.

Volumeof

acuboid=lxbxh

acube=l3

acylinder= r2h

(i)1cm3=1ml

(ii)1L=1000cm3

(iii)1m3=1000000cm3=1000L




RevisionNotes

Chapter–12

ExponentsandPowers

Numberswithexponentsobeythefollowinglawsofexponents.

(a)

(b)

(c)

(d)

(e)

(f)

Verysmallnumberscanbeexpressedinstandardformusingnegativeexponents.

UseofExponentstoExpressSmallNumberinStandardform:

(i)Verylargeandverysmallnumberscanbeexpressedinstandardform.

(ii)Standardformisalsocalledscientificnotationform.

(iii) A number written as is said to be in standard form if m is a decimal

numbersuchthat andniseitherapositiveoranegativeinteger.

Examples:150,000,000,000=1.5x1011.

Exponentialnotationisapowerfulwaytoexpressrepeatedmultiplicationofthesame

number.Foranynon-zerorationalnumber‘a’andanaturalnumbern,theproducta

xaxax...........xa(ntimes)=an.

It is known as the nth power of ‘a’ and is read as ‘a’ raised to the power n’. The

rationalnumberaiscalledthebaseandniscalledexponent.




RevisionNotes

Chapter–13

DirectandInverseProportions

Variations:Ifthevaluesoftwoquantitiesdependoneachotherinsuchawaythata

changeinonecausescorrespondingchangeintheother,thenthetwoquantitiesare

saidtobeinvariation.

DirectVariationorDirectProportion:

Twoquantitiesxandyaresaidtobeindirectproportioniftheyincrease(decrease)

togetherinsuchamannerthattheratiooftheircorrespondingvaluesremains

constant.Thatisif =k[kisapositivenumber,thenxandyaresaidtovarydirectly.

Insuchacaseify1,y2arethevaluesofycorrespondingtothevaluesx1,xofx

respectivelythen = .

Ifthenumberofarticlespurchasedincreases,thetotalcostalsoincreases.

Morethanmoneydepositedinabank,moreistheinterestearned.

Quantitiesincreasingordecreasingtogetherneednotalwaysbeindirectproportion,

sameinthecaseofinverseproportion.

Whentwoquantitiesxandyareindirectproportion(orvarydirectly),theyare

writtenas .Symbol standsfor‘isproportionto’.

InverseProportion:Twoquantitiesxandyaresaidtobeininverseproportionif

anincreaseinxcausesaproportionaldecreaseiny(andvice-versa)insucha

mannerthattheproductoftheircorrespondingvaluesremainsconstant.Thatis,ifxy

=k,thenxandyaresaidtovaryinversely.Inthiscaseify1,y2arethevaluesofy

correspondingtothevaluesx1,x2ofxrespectivelythenx1,Y1=x2,y2or =

Whentwoquantitiesxandyareininverseproportion(orvaryinversely),theyare

writtenasx .Example:Ifthenumberofworkersincreases,timetakentofinish

thejobdecreases.OrIfthespeedwillincreasethetimerequiredtocoveragiven

distancewilldecrease.




RevisionNotes

Chapter–14

Factorisation

Factorisation:Representationofanalgebraicexpressionastheproductoftwoor

moreexpressionsiscalledfactorization.Eachsuchexpressioniscalledafactorofthe

givenalgebraicexpression.

Whenwefactoriseanexpression,wewriteitasaproductoffactors.Thesefactors

maybenumbers,algebraicvariablesoralgebraicexpressions.

Anirreduciblefactorisafactorwhichcannotbeexpressedfurtherasaproductof

factors.

Asystematicwayoffactorisinganexpressionisthecommonfactormethod.It

consistsofthreesteps:

(i)Writeeachtermoftheexpressionasaproductofirreduciblefactors

(ii)Lookforandseparatethecommonfactorsand

(iii)Combinetheremainingfactorsineachterminaccordancewiththedistributive

law.

Sometimes,allthetermsinagivenexpressiondonothaveacommonfactor;butthe

termscanbegroupedinsuchawaythatallthetermsineachgrouphaveacommon

factor.Whenwedothis,thereemergesacommonfactoracrossallthegroupsleading

totherequiredfactorisationoftheexpression.Thisisthemethodofregrouping.

Infactorisationbyregrouping,weshouldrememberthatanyregrouping(i.e.,

rearrangement)ofthetermsinthegivenexpressionmaynotleadtofactorisation.We

mustobservetheexpressionandcomeoutwiththedesiredregroupingbytrialand

error.

Anumberofexpressionstobefactorisedareoftheformorcanbeputintotheform:

a2+2ab+b2,a2–2ab+b2,a2–b2andx2+(a+b)x+ab.Theseexpressionscanbe

easilyfactorisedusingIdentitiesI,II,IIIandIV

a2+2ab+b2=(a+b)2

a2-2ab+b2=(a-b)2

a2–b2=(a+b)(a-b)



x2+(a+b)x+ab=(x+a)(x+b)

Inexpressionswhichhavefactorsofthetype(x+a)(x+b),rememberthenumerical

termgivesab.Itsfactors,aandb,shouldbesochosenthattheirsum,withsigns

takencareof,isthecoefficientofx.

Weknowthatinthecaseofnumbers,divisionistheinverseofmultiplication.This

ideaisapplicablealsotothedivisionofalgebraicexpressions.

Inthecaseofdivisionofapolynomialbyamonomial,wemaycarryoutthedivision

eitherbydividingeachtermofthepolynomialbythemonomialorbythecommon

factormethod.

Inthecaseofdivisionofapolynomialbyapolynomial,wecannotproceedby

dividingeachterminthedividendpolynomialbythedivisorpolynomial.Instead,we

factoriseboththepolynomialsandcanceltheircommonfactors.

Inthecaseofdivisionsofalgebraicexpressionsthatwestudiedinthischapter,we

have

Dividend=Divisor×Quotient.

Ingeneral,however,therelationis

Dividend=Divisor×Quotient+Remainder

Thus,wehaveconsideredinthepresentchapteronlythosedivisionsinwhichthe

remainderiszero.

Therearemanyerrorsstudentscommonlymakewhensolvingalgebraexercises.You

shouldavoidmakingsucherrors.




RevisionNotes

Chapter–15

IntroductiontoGraphs

Graphicalpresentationofdataiseasiertounderstand.

(i)Abargraphisusedtoshowcomparisonamongcategories.

(ii)Apiegraphisusedtocomparepartsofawhole.

(iii)AHistogramisabargraphthatshowsdatainintervals.

Alinegraphdisplaysdatathatchangescontinuouslyoverperiodsoftime.

Alinegraphwhichisawholeunbrokenlineiscalledalineargraph.

Forfixingapointonthegraphsheetweneed,x-coordinateandy-coordinate.

The relation between dependent variable and independent variable is shown

throughagraph.

A Bar Graph: A pictorial representation of numerical data in the form of bars

(rectangles)ofuniformwidthwithequalspacing.Thelength(orheight)ofeachbar

representsthegivennumber.

A Pie Graph: A pie graph is used to compare parts of a whole. The various

observationsorcomponentsarerepresentedbythesectorsofthecircle.



AHistogram:Histogramisatypeofbardiagram,wheretheclassintervalsareshown

onthehorizontalaxisandtheheightsofthebars(rectangles)showthefrequencyof

theclassinterval,butthereisnogapbetweenthebarsasthereisnogapbetweenthe

classintervals.

LinearGraph:Alinegraphinwhichallthelinesegmentsformapartofasingleline.

Coordinates: A point in Cartesian plane is represented by an ordered pair of

numbers.

OrderedPair:Apairofnumberswritteninspecifiedorder.




RevisionNotes

Chapter–16

PlayingwithNumbers

Numberingeneralform:Anumberissaidtobeinageneralformifitisexpressed

asthesumoftheproductsofitsdigitswiththeirrespectiveplacevalues.

Numberscanbewritteningeneralform.Thus,atwodigitnumberabwillbewritten

asab=10a+b.

Thegeneralformofnumbersarehelpfulinsolvingpuzzlesornumbergames.

Thereasonsforthedivisibilityofnumbersby10,5,2,9or3canbegivenwhen

numbersarewritteningeneralform.

TestsofDivisiblity:

(i)Divisibilityby2:Anumberisdivisibleby2whenitsone’sdigitis0,2,4,6or

8.Explanation:Givennumberabc=100a+10b+c.100aand10baredivisibleby2

because100and10aredivisibleby2.Thusgivennumberisdivisibleby2onlywhen

a=0,2,4,6or8.

(ii)Divisibilityby3:Anumberisdivisibleby3whenthesumofitsdigitsisdivisible

by3.Example:givennumber=61785.Sumofdigits=6+1+7+8+5=27whichis

divisibleby3.Therefore,61785isdivisibley3.

(iii)Divisibilityby4:Anumberisdivisibleby4whenthenumberformedbyitslast

twodigitsisdivisibleby4.

Example:6216,548,etc.

(iv)Divisibilityby5:Anumberisdivisibleby5whenitsonesdigitis0or5.

Example:645,540etc.

(v)Divisibilityby6:Anumberisdivisibleby6whenitisdivisiblebyboth2and3.

Example:246,7230,etc.

(vi)Divisibilityby9:Anumberisdivisibleby9whenthesumofitsdigitsisdivisible

by9.

Example:consideranumber215847.Sumofdigits=2+1+5+8+4+7=27whichis

divisibleby9.Therefore,215847isdivisibleby9.

(vii)Divisibilityby10:Anumberisdivisibleby10whenitsonesdigitis0.Example:



540,890,etc.

(viii)Divisibilityby11:Anumberisdivisibleby11whenthedifferenceofthesumof

itsdigitsinoddplacesandthesumofitsdigitsinevenplacesiseitherooramultiple

of11.

Example:consideranumber462.

Sumofdigitsinoddplaces=4+2=6

Sumofdigitsinevenplaces=6

Difference=6-6=0,whichiszero.So,thenumberisdivisibleby11.



CBSEClass–VIIIMathematics

NCERTSolutions

CHAPTER-1

RationalNumbers(Ex.1.1)

Questions

1.Usingappropriatepropertiestofind:

(i)

(ii)

Ans.(i)

= [UsingAssociativeproperty]

= [Usingdistributiveproperty]

=

=

=

= = =2

(ii)



= [UsingAssociativeproperty]

= [Usingdistributiveproperty]

=

= =

= =

2.Writetheadditiveinverseofeachofthefollowing:

(i) (ii) (iii) (iv) (v)

Ans.Weknowthatadditiveinverseofarationalnumber is suchthat

(i)Additiveinverseof is (ii)Additiveinverseof is

(iii)Additiveinverseof is (iv)Additiveinverseof is

(v)Additiveinverseof is

3.Verifythat for:

(i) (ii)



Ans.(i)Putting in

L.H.S.=R.H.S.

Hence,verified.

(ii)Putting in

L.H.S.=R.H.S.

Hence,verified.

4.Findthemultiplicativeinverseofthefollowing:

(i) (ii) (iii)

(iv) (v) (vi)

Ans.Weknowthatmultiplicativeinverseofarationalnumber is suchthat

(i)Multiplicativeinverseof is

(ii)Multiplicativeinverseof is



(iii)Multiplicativeinverseof is

(iv)Multiplicativeinverseof is

(v)Multiplicativeinverseof is

(vi)Multiplicativeinverseof is =-1

5.Namethepropertyundermultiplicationusedineachofthefollowing:

(i)

(ii)

(iii)

Ans.(i)1isthemultiplicativeidentity.

(ii)commutativityproperty.

(iii)MultiplicativeInverseproperty.

6.Multiply bythereciprocalof

Ans.Thereciprocalof is

Accordingtothequestion,

=



7.Tellwhatpropertyallowsyoutocompute

as

Ans.Byusingassociativepropertyofmultiplication,

wewillcomputeas .

8.Is themultiplicativeinverseof Whyorwhynot?

Ans.Sincemultiplicativeinverseofarationalnumber is if

Therefore, = =

Butitsproductmustbepositive1.

Therefore, isnotthemultiplicativeinverseof

9.Is0.3themultiplicativeinverseof Whyorwhynot?

Ans.Sincemultiplicativeinverseofarationalnumber is if

Therefore, = =1

Therefore,Yes0.3isthemultiplicativeinverseof

10.Write:

(i)Therationalnumberthatdoesnothaveareciprocal.



(ii)Therationalnumbersthatareequaltotheirreciprocals.

(iii)Therationalnumberthatisequaltoitsnegative.

Ans.(i)0

(ii)1and

(iii)0

11.Fillintheblanks:

(i)Zerohas____________reciprocal.

(ii)Thenumbers___________and__________aretheirownreciprocals.

(iii)Thereciprocalof is_____________.

(iv)Reciprocalof where is_____________.

(v)Theproductoftworationalnumbersisalwaysa____________.

(vi)Thereciprocalofapositiverationalnumberis_______________

Ans.(i)No

(ii)1,

(iii)

(iv)

(v)RationalNumber

(vi)Positive




NCERTSolutions

CHAPTER-1

RationalNumbers(Ex.1.2)

1.Representthesenumbersonthenumberline:

(i)

(ii)

Ans.(i)

Here,P

(ii)

Here,M=



2.Represent onthenumberline.

Ans.Here,B= C= andD=

3.Writefiverationalnumberswhicharesmallerthan2.

Ans. andsoon.

4.Findtenrationalnumbersbetween and

Ans. and

Here,L.C.M.of5and2is10.

and

Again, and

Tenrationalnumberbetween and are

.

5.Findfiverationalnumbersbetween:



(i) and

(ii) and

(iii) and

Ans.(i) and

L.C.M.of3and5is15.

and

Again and

Fiverationalnumbersbetween and are .

(ii) and

L.C.M.of2and3is6.

and

Fiverationalnumbersbetween and are .

(iii) and

L.C.M.of4and2is4.



and

Again and

Fiverationalnumbersbetween and are

6.Write5rationalnumbersgreaterthan

Ans.Fiverationalnumbersgreaterthan are:

[Otherrationalnumbersmayalsobepossible]


Ans. and

L.C.M.of5and4is20.

and

Again and

Tenrationalnumbersbetween and are:




NCERTSolutions

CHAPTER-2

LinearEquationsinOneVariable(Ex.2.1)

Solvethefollowingquestions.

1.

Ans.

=7+2[Adding2tobothsides]

=9

2.

Ans.

=10–3[Subtracting3frombothsides]

=7

3.

Ans.

[Subtracting2frombothsides]

4.



Ans.

[Subtracting frombothsides]

5.

Ans.

[Dividingbothsidesby6]

6.

Ans.

= [Multiplyingbothsidesby5]

=50

7.



Ans.

[Multiplyingbothsidesby3]


8.

Ans.

[Multiplyingbothsidesby1.5]

9.

Ans.

[Adding9tobothsides]




10.

Ans.

[Adding8tobothsides]


11.

Ans.



12.

Ans.








NCERTSolutions

CHAPTER-2


1.Ifyousubtract fromanumberandmultiplytheresultby youget Whatis

thenumber?

Ans.Letthenumberbe



[Adding tobothsides]

Hence,therequirednumberis

2.Theperimeterofarectangularswimmingpoolis154m.Itslengthis2mmorethan

twiceitsbreadth.Whatarethelengthandbreadth?



Ans.Letthebreadthofthepoolbe m.

Then,thelengthofthepool= m

Perimeter=

154=




m

Hence,lengthofthepool=

=50+2=52m

And,breadthofthepool=25m.

3.Thebaseofanisoscelestriangleis cm.Theperimeterofthetriangleis cm.

Whatisthelengthofeitheroftheremainingequalsides?

Ans.Leteachofequalsidesofanisoscelestrianglebe cm.

Perimeterofatriangle=Sumofallthreesides



[Subtracting fromboththesides]


cm

Hence,eachequalsideofanisoscelestriangleis cm.

4.Sumoftwonumbersis95.Ifoneexceedstheotherby15,findthenumbers.

Ans.Sumoftwonumber=95

Letthefirstnumberbe

thenanothernumberbe .






Hence,thefirstnumber=40

Andanothernumber=40+15=55.

5.Twonumbersareintheratio5:3.Iftheydifferby18,whatarethenumbers?

Ans.Letthetwonumbersbe and

Accordingtoquestion,


Hence,firstnumber= =45andsecondnumber= =27.

6.Threeconsecutiveintegersaddupto51.Whataretheseintegers?

Ans.Letthethreeconsecutiveintegersbe and






Hence,firstinteger=16,

secondinteger=16+1=17and

thirdinteger=16+2=18.

7.Thesumofthreeconsecutivemultiplesof8is888.Findthemultiples.

Ans.Letthethreeconsecutivemultiplesof8be and




Hence,firstmultipleof8=288,

secondmultipleof8=288+8=296and

thirdmultipleof8=288+16=304.



8.Threeconsecutiveintegersaresuchthatwhentheyaretakeninincreasingorderand

multipliedby2,3and4respectively,theyaddupto74.Findthesenumbers.

Ans.Letthethreeconsecutiveintegersbe and




Hencefirstinteger=7,secondinteger

=7+1=8andthirdinteger=7+2=9.

9.TheagesofRahulandHaroonareintheratio5:7.Fouryearslaterthesumoftheir

ageswillbe56years.Whataretheirpresentages?

Ans.LetthepresentagesofRahulandHaroonbe yearsand yearsrespectively.

Accordingtocondition,





Hence,presentageofRahul= =20yearsand

presentageofHaroon= =28years.

10.Thenumberofboysandgirlsinaclassareintheratio7:5.Thenumberofboysis8

morethanthenumberofgirls.Whatisthetotalclassstrength?

Ans.Letthenumberofgirlsbe

Then,thenumberofboys=


[Transposing toL.H.S.and40toR.H.S.]

[Dividingbothsidesby ]

Hencethenumberofgirls=20andnumberofboys=20+8=28.

11.Baichung’sfatheris26yearsyoungerthanBaichung’sgrandfatherand29years

olderthanBaichung.Thesumoftheagesofallthethreeis135years.Whatistheageof

eachoneofthem?



Ans.LetBaichung’sagebe years,

thenBaichung’sfather’sage= years

andBaichung’sgrandfather’sage= years.

Accordingtocondition,



years

Hence,Baichung’sage=17years,

Baichung’sfather’sage=17+29=46years

AndBaichung’sgrandfather’sage=17+29+26=72years.

12.FifteenyearsfromnowRavi’sagewillbefourtimeshispresentage.WhatisRavi’s

presentage?

Ans.LetRavi’spresentagebe years.

Afterfifteenyears,Ravi’sage= years.

Fifteenyearsfromnow,Ravi’sage= years.




[Transposing toL.H.S.]


years

Hence,Ravi’spresentagebe5years.

13.Arationalnumberissuchthatwhenyoumultiplyitby andadd totheproduct,

youget Whatisthenumber?

Ans.Lettherationalnumberbe


[Subtracting frombothsides]




Hence,therationalnumberis

14.Lakshmiisacashierinabank.ShehascurrencynotesofdenominationsRs.100,Rs.

50andRs.10respectively.Theratioofthenumberofthesenotesis2:3:5.Thetotal

cashwithLakshmiisRs.4,00,000.Howmanynotesofeachdenominationdoesshe

have?

Ans.Letnumberofnotesbe and



Hence,numberofdenominationsofRs.100notes= =2,000

NumberofdenominationsofRs.50notes= =3,000

NumberofdenominationsofRs.10notes= =5000

Therefore,requireddenominationsofnotesofRs.100,Rs.50andRs.10are2000,3000and

5000respectively.

15.IhaveatotalofRs.300incoinsofdenominationRe.1,Rs.2andRs.5.Thenumberof

Rs.2coinsis3timesthenumberofRs.5coins.Thetotalnumberofcoinsis160.How

manycoinsofeachdenominationarewithme?



Ans.Totalsumofmoney=Rs.300

LetthenumberofRs.5coinsbe

numberofRs.2coinsbe and

numberofRe.1coinsbe




Hence,thenumberofcoinsofRs.5denomination=20

NumberofcoinsofRs.2denomination= =60

NumberofcoinsofRs.1denomination= =160–80=80

16.Theorganizersofanessaycompetitiondecidethatawinnerinthecompetitiongets

aprizeofRs.100andaparticipantwhodoesnotwin,getsaprizeofRs.25.Thetotal

prizemoneydistributedisRs.3,000.Findthenumberofwinners,ifthetotalnumberof

participantsis63.

Ans.Totalsumofmoney=Rs.3000

LetthenumberofwinnersofRs.100be



Andthosewhoarenotwinners=


75x+1575-1575=3000-1575[Subtracting1575frombothsides]

75x=1425


Hence,thenumberofwinneris19.




NCERTSolutions

CHAPTER-2


Solvethefollowingequationsandcheckyourresults.

1.

Ans.

Tocheck:

54=54

L.H.S.=R.H.S.

Hence,itiscorrect.

2.

Ans.



Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.

3.

Ans.

Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.

4.



Ans.

Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.

5.

Ans.

Tocheck:



10–1=9

9=9

L.H.S.=R.H.S.

Hence,itiscorrect.

6.

Ans.

Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.



7.

Ans.

Tocheck:

40=40

L.H.S.=R.H.S.

Hence,itiscorrect.

8.

Ans.



Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.

9.

Ans.



Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.

10.

Ans.



Tocheck:

L.H.S.=R.H.S.

Hence,itiscorrect.




NCERTSolutions

CHAPTER-2


1.Aminathinksofanumberandsubtracts fromit.Shemultipliestheresultby8.The

resultnowobtainedis3timesthesamenumbershethoughtof.Whatisthenumber?

Ans.LetAminathinksofanumber


Hence,thenumberis4.

2.Apositivenumberis5timesanothernumber.If21isaddedtoboththenumbers,

thenoneofthenewnumbersbecomestwicetheothernewnumber.Whatarethe

numbers?

Ans.Letanothernumberbe

Thenpositivenumber=




Hence,anothernumber=7

andpositivenumber= =35

3.Sumofthedigitsofatwo-digitnumberis9.Whenweinterchangethedigits,itis

foundthattheresultingnewnumberisgreaterthantheoriginalnumberby27.Whatis

thetwo-digitnumber?

Ans.Lettheunitplacedigitofatwo-digitnumberbe

Therefore,thetensplacedigit=

2-digitnumber=10xtensplacedigit+unitplacedigit

Originalnumber=

Accordingtothequestion,Newnumber

=Originalnumber+27

10x+9-x=90-10x+x+27

Hence,the2-digitnumber=

=10(9–6)+6



=

=30+6=36

4.Oneofthetwodigitsofatwo-digitnumberisthreetimestheotherdigit.Ifyou

interchangethedigitsofthistwo-digitnumberandaddtheresultingnumbertothe

originalnumber,youget88.Whatistheoriginalnumber?

Ans.Lettheunitplacedigitofatwo-digitnumberbe

Therefore,thetensplacedigit=

2-digitnumber=10xtensplacedigit+unitplacedigit

Originalnumber= =

Accordingtothequestion,Newnumber+Originalnumber=88

Hence,the2-digitnumber=

5.Shobo’smother’spresentageissixtimesShobo’spresentage.Shobo’sagefiveyears

fromnowwillbeonethirdofhismother’spresentage.Whataretheirpresentages?

Ans.LetShobo’spresentagebe years.

AndShobo’smother’spresentage= years




years.

Hence,Shobo’spresentage=5years

AndShobo’smother’spresentage= =30years.

6.Thereisanarrowrectangularplot,reservedforaschool,inMahulivillage.The

lengthandbreadthoftheplotareintheratio11:4.AttherateRs.100permeteritwill

costthevillagepanchayatRs.75,000tofencetheplot.Whatarethedimensionsofthe

plot?

Ans.Letthelengthandbreadthoftherectangularplotbe and respectively.

Perimeteroftheplot= = =750m

WeknowthatPerimeterofrectangle=2(length+breadth)

Therefore,accordingtothequestion,

Hence,lengthofrectangularplot= =275m

Andbreadthofrectangularplot= =100m

7.Hasanbuystwokindsofclothmaterialsforschooluniforms,shirtmaterialthatcosts

himRs.50permetreandtrousermaterialthatcostshimRs.90permetre.Forevery2

metresofthetrousermaterialhebuys3metresofshirtmaterial.Hesellsthematerials

at12%and10%profitrespectively.HistotalsaleisRs.36,660.Howmuchtrouser

materialdidhebuy?



Ans.Letratiobetweenshirtmaterialandtrousermaterialbe

Thecostofshirtmaterial=

Thesellingpriceat12%gain=

=

= =

Thecostoftrousermaterial=

Thesellingpriceat10%gain=

=

= =


=100meters

Now,trousermaterial= =

=200metres

Hence,Hasanbought200metresofthetrousermaterial.

8.Halfofaherdofdeeraregrazinginthefieldandthreefourthsoftheremainingare

playingnearby.Therest9aredrinkingwaterfromthepond.Findthenumberofdeer



intheherd.

Ans.Letthetotalnumberofdeerintheherdbe


Hence,thetotalnumberofdeerintheherdis72.

9.Agrandfatheristentimesolderthanhisgranddaughter.Heisalso54yearsolder

thanher.Findtheirpresentages.

Ans.Letpresentageofgranddaughterbe years.

Therefore,Grandfather’sage= years


years



Hence,granddaughter’sage=6yearsandgrandfather’sage= =60years.

10.Aman’sageisthreetimeshisson’sage.Tenyearsagohewasfivetimeshisson’s

age.Findtheirpresentages.

Ans.LetthepresentageofAman’ssonbe years.

Therefore,Aman’sage= years


=20years

Hence,Aman’sson’spresentage=20years

AndAman’spresentage= =60years




NCERTSolutions

CHAPTER-2


Solvethefollowinglinearequations.

1.

Ans.

=

Tocheck:



L.H.S.=R.H.S.

Therefore,itiscorrect.

2.

Ans.

Tocheck:

21=21

L.H.S.=R.H.S.




3.

Ans.

Tocheck:



L.H.S.=R.H.S.


4.

Ans.

Tocheck:

1=1

L.H.S.=R.H.S.




5.

Ans.

Tocheck:



L.H.S.=R.H.S.


6.

Ans.



Tocheck:

L.H.S.=R.H.S.


Simplifyandsolvethefollowinglinearequation.

7.

Ans.



Tocheck:

L.H.S.=R.H.S.


8.

Ans.



Tocheck:

0=0

L.H.S.=R.H.S.


9.

Ans.



Tocheck:

L.H.S.=R.H.S.


10.

Ans.



Tocheck:

L.H.S.=R.H.S.





NCERTSolutions

CHAPTER-2


Solvethefollowingequations.

1.

Ans.

2.

Ans.



3.

Ans.

4.

Ans.

5.



Ans.

6.TheagesofHariandHarryareintheratio5:7.Fouryearsfromnowtheratioof

theirageswillbe3:4.Findtheirpresentages.

Ans.LettheAgesofHariandHarrybe yearsand years.


Hence,theageofHari= =

=20years

AndtheageofHarry= =

=28years.



7.Thedenominatorofarationalnumberisgreaterthanitsnumeratorby8.Ifthe

numeratorisincreasedby17andthedenominatorisdecreasedby1,thenumber

obtainedis Findtherationalnumber.

Ans.Letthenumeratorofarationalnumberbe thenthedenominatoris

Therefore,Rationalnumber=


Hence,therequiredrationalnumber

=




NCERTSolutions

CHAPTER-3

UnderstandingQuadrilaterals(Ex.3.1)

1.Givenherearesomefigures:

Classifyeachofthemonthebasisofthefollowing:

(a)Simplecurve

(b)Simpleclosedcurve

(c)Polygon

(d)Convexpolygon

(e)Concavepolygon

Ans.(a)Simplecurve

(b)Simpleclosedcurve



(c)Polygons

(d)Convexpolygons

(e)Concavepolygon

2.Howmanydiagonalsdoeseachofthefollowinghave?

(a)Aconvexquadrilateral

(b)Aregularhexagon

(c)Atriangle

Ans.(a)Aconvexquadrilateralhastwodiagonals.

Here,ACandBDaretwodiagonals.



(b)Aregularhexagonhas9diagonals.

Here,diagonalsareAD,AE,BD,BE,FC,FB,AC,ECandFD.

(c)Atrianglehasnodiagonal.

3.Whatisthesumofthemeasuresoftheanglesofaconvexquadrilateral?Willthis

propertyholdifthequadrilateralisnotconvex?(Makeanon-convexquadrilateraland

try)

Ans.LetABCDisaconvexquadrilateral,thenwedrawadiagonalACwhichdividesthe

quadrilateralintwotriangles.

A+B+ C+ D

= 1+ 6+ 5+ 4+ 3+ 2

=( 1+ 2+ 3)+( 4+ 5+ 6)

=



[ByAnglesumpropertyoftriangle]

=

Hence,thesumofmeasuresofthetrianglesofaconvexquadrilateralis

Yes,ifquadrilateralisnotconvexthen,thispropertywillalsobeapplied.

LetABCDisanon-convexquadrilateralandjoinBD,whichalsodividesthequadrilateralin

twotriangles.

Usinganglesumpropertyoftriangle,

In ABD, 1+ 2+ 3= ……….(i)

In BDC, 4+ 5+ 6= ……….(i)

Addingeq.(i)and(ii),

1+ 2+ 3+ 4+ 5+ 6=

1+ 2+( 3+ 4)+ 5+ 6

=

A+ B+ C+ D=

Henceproved.

4.Examinethetable.(Eachfigureisdividedintotrianglesandthesumoftheangles

deducedfromthat.)



Figure

Side 3 4 5 6

Anglesum

Whatcanyousayabouttheanglesumofaconvexpolygonwithnumberofsides?

Ans.(a)When =7,then

Anglesumofapolygon=

(b)When =8,then

Anglesumofapolygon=

(c)When =10,then

Anglesumofapolygon=

(d)When = then

Anglesumofapolygon=

5.Whatisaregularpolygon?Statethenameofaregularpolygonof:

(a)3sides

(b)4sides



(c)6sides

Ans.Aregularpolygon:Apolygonhavingallsidesofequallengthandtheinterioranglesof

equalsizeisknownasregularpolygon.

(i)3sides

Polygonhavingthreesidesiscalledatriangle.

(ii)4sides

Polygonhavingfoursidesiscalledaquadrilateral.

(iii)6sides

Polygonhavingsixsidesiscalledahexagon.

6.Findtheanglemeasures inthefollowingfigures:

Ans.(a)Usinganglesumpropertyofaquadrilateral,



(b)Usinganglesumpropertyofaquadrilateral,

(a)Firstbaseinteriorangle

=

Secondbaseinteriorangle

=

Thereare5sides, =5



Anglesumofapolygon=

= =

(b)Anglesumofapolygon=

= =

Henceeachinteriorangleis

7.(a)Find



(b)Find

Ans.(a)Sincesumoflinearpairanglesis

And

Also

[Exteriorangleproperty]



(b)Usinganglesumpropertyofaquadrilateral,

Sincesumoflinearpairanglesis

……….(i)

……….(ii)

……….(iii)

……….(iv)

Addingeq.(i),(ii),(iii)and(iv),






NCERTSolutions

CHAPTER-3


1.Find inthefollowingfigures:

Ans.(a)Here,

[Linearpair]

And

[Linearpair]

Exteriorangle =Sumofoppositeinteriorangles



(b)Sumoftheanglesofapentagon

=

=

=

Bylinearpairsofangles,

……….(i)

……….(ii)

……….(iii)

……….(iv)

……….(v)

Addingeq.(i),(ii),(iii),(iv)and(v),



2.Findthemeasureofeachexteriorangleofaregularpolygonof:

(a)9sides

(b)15sides

Ans.(i)Sumofanglesofaregularpolygon=

=

Eachinteriorangle=

Eachexteriorangle=

(ii)Sumofexterioranglesofaregularpolygon=

Eachexteriorangle=

=24degrees

3.Howmanysidesdoesaregularpolygonhave,ifthemeasureofanexteriorangleis

Ans.Letnumberofsidesbe

Sumofexterioranglesofaregularpolygon=

Numberofsides=

Hence,theregularpolygonhas15sides.

4.Howmanysidesdoesaregularpolygonhaveifeachofitsinterioranglesis

Ans.Letnumberofsidesbe

Exteriorangle=



Sumofexterioranglesofaregularpolygon=

Numberofsides=

Hence,theregularpolygonhas24sides.

5.(a)Isitpossibletohavearegularpolygonwithofeachexteriorangleas

(b)Canitbeaninteriorangleofaregularpolygon?Why?

Ans.(a)No.(Since22isnotadivisorof )

(b)No,(Becauseeachexteriorangleis whichisnotadivisorof )

6.(a)Whatistheminimuminterioranglepossibleforaregularpolygon?Why?

(b)Whatisthemaximumexterioranglepossibleforaregularpolygon?

Ans.(a)Theequilateraltrianglebeingaregularpolygonof3sideshastheleastmeasureof

an

interiorangleof

Sumofalltheanglesofatriangle

=

(b)By(a),wecanobservethatthegreatestexteriorangleis

.




NCERTSolutions

CHAPTER-3


1.GivenaparallelogramABCD.Completeeachstatementalongwiththedefinitionor

propertyused.

(i)AD=_______________

(ii) DCB=______________

(iii)OC=_____________

(iv) DAB+ CDA=________

Ans.(i)AD=BC

[Sinceoppositesidesofaparallelogramareequal]

(ii) DCB= DAB

[Sinceoppositeanglesofaparallelogramareequal]

(iii)OC=OA

[Sincediagonalsofaparallelogrambisecteachother]

(iv) DAB+ CDA=

[Adjacentanglesinaparallelogramaresupplementary]

2.Considerthefollowingparallelograms.Findthevaluesoftheunknowns



Note:Forgettingcorrectanswer,read infigure(iii)

Ans.(i) B+ C=



[Adjacentanglesinaparallelogramaresupplementary]

And


Also


(ii)

[Adjacentanglesina gmaresupplementary]

[Correspondingangles]

y=x=130degrees


(iii)

[Verticallyoppositeangles]



[Anglesumpropertyofatriangle]

[Alternateangles]

(iv)


[Adjacentanglesina gmaresupplementary]

And

[Oppositeanglesareequalina gm]



(v)

[Oppositeanglesareequalina gm]


And

[Alternateangles]

3.CanaquadrilateralABCDbeaparallelogram,if:

(i) D+ B=

(ii)AB=DC=8cm,AD=4cmandBC=4.4cm?

(iii) A= and C=

Ans.(i) D+ B=

Itcanbe,buthere,itneedstobeasquareorarectangle.

(ii)No,inthiscase,becauseonepairofoppositesidesareequalandanotherpairofopposite

sidesareunequal.So,itisnotaparallelogram.



(iii)No. A C.

Sinceoppositeanglesareequalinparallelogramandhereoppositeanglesarenotequalin

quadrilateralABCD.Thereforeitisnotaparallelogram.

4.Drawaroughfigureofaquadrilateralthatisnotaparallelogrambuthasexactlytwo

oppositeanglesofequalmeasures.

Ans.ABCDisaquadrilateralinwhichangles A= C=

Therefore,itcouldbeakite.

5.Themeasureoftwoadjacentanglesofaparallelogramareintheratio3:2.Findthe

measureofeachoftheanglesoftheparallelogram.

Ans.Lettwoadjacentanglesbe and

Sincetheadjacentanglesinaparallelogramaresupplementary.



Oneangle=

AndAnotherangle=

6.Twoadjacentanglesofaparallelogramhaveequalmeasure.Findthemeasureofthe

anglesoftheparallelogram.

Ans.Leteachadjacentanglebe

Sincetheadjacentanglesinaparallelogramaresupplementary.

Hence,eachadjacentangleis

7.TheadjacentfigureHOPWisaparallelogram.Findtheanglemeasures and

Statethepropertiesyouusetofindthem.

HOP+

Ans.Here HOP=

[Anglesoflinearpair]

And E= HOP



[Oppositeanglesofa gmareequal]

PHE= HPO

[Alternateangles]

Now EHO= O=


Hence, and

8.ThefollowingfiguresGUNSandRUNSareparallelograms.Find and (Lengthsare

incm)

Ans.(i)InparallelogramGUNS,

GS=UN

[Oppositesidesofparallelogramareequal]



cm

AlsoGU=SN

[Oppositesidesofparallelogramareequal]

cm

Hence, =6cmand =9cm.

(ii)InparallelogramRUNS,

[Diagonalsof gmbisectseachother]

cm

And

cm

Hence, cmand cm.

9.Inthefigure,bothRISKandCLUEareparallelograms.Findthevalueof



Ans.InparallelogramRISK,

RIS= K=

[Oppositeanglesofa gmareequal]

[Linearpair]

And ECI= L=



=

Also

[Verticallyoppositeangles]

10.Explainhowthisfigureisatrapezium.Whichofitstwosidesareparallel?



Ans.Here, M+ L=

[Sumofinterioroppositeanglesis ]

NMandKLareparallel.

Hence,KLMNisatrapezium.

11.Find Cinfigure,if

Ans.Here, B+ C=

[ ]

12.Findthemeasureof Pand Sif ingivenfigure.

(Ifyoufind Ristheremorethanonemethodtofind P)

Ans.Here, P+ Q=

[Sumofco-interioranglesis ]

P+



P=

P=

R= [Given]

S+

S=

S=

Yes,onemoremethodistheretofind P.

S+ R+ Q+ P=

[Anglesumpropertyofquadrilateral]

P=

P=




NCERTSolutions

CHAPTER-3


1.Statewhethertrueorfalse:

(a)Allrectanglesaresquares.

(b)Allrhombusesareparallelograms.

(c)Allsquaresarerhombusesandalsorectangles.

(d)Allsquaresarenotparallelograms.

(e)Allkitesarerhombuses.

(f)Allrhombusesarekites.

(g)Allparallelogramsaretrapeziums.

(h)Allsquaresaretrapeziums.

Ans.(a)False.Since,squareshaveallsidesareequal.

(b)True.Since,inrhombus,oppositeanglesareequalanddiagonalsintersectatmid-point.

(c)True.Since,squareshavethesamepropertyofrhombusbutnotarectangle.

(d)False.Since,allsquareshavethesamepropertyofparallelogram.

(e)False.Since,allkitesdonothaveequalsides.

(f)True.Since,allrhombuseshaveequalsidesanddiagonalsbisecteachother.

(g)True.Since,trapeziumhasonlytwoparallelsides.

(h)True.Since,allsquareshavealsotwoparallellines.



2.Identifyallthequadrilateralsthathave:

(a)foursidesofequallengths.

(b)fourrightangles.

Ans.(a)Rhombusandsquarehavesidesofequallength.

(b)Squareandrectanglehavefourrightangles.

3.Explainhowasquareis:

(a)aquadrilateral

(b)aparallelogram

(c)arhombus

(d)arectangle

Ans.(i)Asquareisaquadrilateral,sinceithasfourequallengthsofsides.

(ii)Asquareisaparallelogram,sinceitcontainsbothpairsofoppositesidesequal.

(iii)Asquareisalreadyarhombus.Since,ithasfourequalsidesanddiagonalsbisectat

toeachother.

(iv)Asquareisaparallelogram,sincehavingeachadjacentanglearightangleandopposite

sidesareequal.

4.Namethequadrilateralwhosediagonals:

(i)bisecteachother.

(ii)areperpendicularbisectorsofeachother.

(iii)areequal.

Ans.(i)Ifdiagonalsofaquadrilateralbisecteachotherthenitisarhombus,parallelogram,



rectangleorsquare.

(ii)Ifdiagonalsofaquadrilateralareperpendicularbisectorofeachother,thenitisa

rhombusorsquare.

(iii)Ifdiagonalsareequal,thenitisasquareorrectangle.

5.Explainwhyarectangleisaconvexquadrilateral.

Ans.Arectangleisaconvexquadrilateralsinceitsvertexareraisedandbothofitsdiagonals

lieinitsinterior.

6.ABCisaright-angledtriangleandOisthemid-pointofthesideoppositetotheright

angle.ExplainwhyOisequidistantfromA,BandC.(Thedottedlinesaredrawn

additionallytohelpyou.)

Ans.Since,tworighttrianglesmakearectanglewhereOisequidistantpointfromA,B,Cand

DbecauseOisthemid-pointofthetwodiagonalsofarectangle.

SinceACandBDareequaldiagonalsandintersectatmid-point.

So,OistheequidistantfromA,B,CandD.




NCERTSolutions

CHAPTER-4

PracticalGeometry(Ex.4.1)

1.Constructthefollowingquadrilaterals:

(i)QuadrilateralABCD

AB=4.5cm,BC=5.5cm,CD=4cm,AD=6cm,AC=7cm

(ii)QuadrilateralJUMP

JU=3.5cm,UM=4cm,MP=5cm,PJ=4.5cm,PU=6.5cm

(iii)ParallelogramMORE

OR=6cm,RE=4.5cm,EO=7.5cm

(iv)RhombusBEST

BE=4.5cm,ET=6cm

Ans.(i)Given:AB=4.5cm,BC=5.5cm,CD=4cm,AD=6cm,AC=7cm

Toconstruct:AquadrilateralABCD

Stepsofconstruction:

(a)DrawAB=4.5cm.

(b)Drawanarctakingradius5.5cmfrompointB.

(c)Takingradius7cm,drawananotherarcfrompointAwhichintersectsthefirstarcat

pointC.

(d)JoinBCandAC.

(e)Drawanarcofradius6cmfrompointAanddrawanotherarcofradius4cmfrompoint

CwhichintersectsatD.

(f)JoinADandCD.

ItisrequiredquadrilateralABCD.



(ii)Given:JU=3.5cm,UM=4cm,MP=5cm,PJ=4.5cm,PU=6.5cm

Toconstruct:AquadrilateralJUMP


(a)DrawJU=3.5cm.

(b)Drawanarcofradius4.5cmtakingcentreJandthendrawanotherarcofradius6.5cm

takingUascentre.BotharcsintersectatP.

(c)JoinPJandPU.

(d)Drawarcofradius5cmand4cmtakingPandUascentresrespectively,whichintersect

atM.

(e)JoinMPandMU.

ItisrequiredquadrilateralJUMP.

(iii)Given:OR=6cm,RE=4.5cm,EO=7.5cm

Toconstruct:AparallelogramMORE


(a)DrawOR=6cm.

(b)Drawarcsofradius7.5cmandradius4.5cmtakingOandRascentresrespectively,

whichintersectatE.

(c)JoinOEandRE.

(d)Drawanarcof6cmradiustakingEascentre.

(e)Drawanotherarcof4.5cmradiustakingOascentre,whichintersectsatM.



(f)JoinOMandEM.

ItisrequiredparallelogramMORE.

(iv)Given:BE=4.5cm,ET=6cm

Toconstruct:ArhombusBEST


(a)DrawTE=6cmandbisectitintotwoequalparts.

(b)DrawupanddownperpendicularstoTE.

(c)Drawtwoarcsof4.5cmtakingEandTascentres,whichintersectatS.

(d)Againdrawtwoarcsof4.5cmtakingEandTascentres,whichintersectsatB.

(e)JoinTS,ES,BTandEB.

ItistherequiredrhombusBEST.




NCERTSolutions

CHAPTER-4



(i)QuadrilateralLIFT

LI=4cm,IF=3cm,TL=2.5cm,LF=4.5cm,IT=4cm

(ii)QuadrilateralGOLD

OL=7.5cm,GL=6cm,GD=6cm,LD=5cm,OD=10cm

(iii)RhombusBEND

BN=5.6cm,DE=6.5cm

Ans.(i)Given:LI=4cm,IF=3cm,TL=2.5cm,LF=4.5cm,IT=4cm

Toconstruct:AquadrilateralLIFT


(a)DrawalinesegmentLI=4cm.

(b)Takingradius4.5cm,drawanarctakingLascentre.

(c)Drawanarcof3cmtakingIascentrewhichintersectsthefirstarcatF.

(d)JoinFIandFL.

(e)Drawanotherarcofradius2.5cmtakingLascentreand4cmtakingIascentrewhich

intersectatT.

(f)JoinTF,TlandTI.

ItistherequiredquadrilateralLIFT.



(ii)Given:OL=7.5cm,GL=6cm,GD=6cm,LD=5cm,OD=10cm

Toconstruct:AquadrilateralGOLD


(a)DrawalinesegmentOL=7.5cm.

(b)Drawanarcofradius5cmtakingLascentreandanotherarcofradius10cmtakingOas

centrewhichintersectthefirstarcatpointD.

(c)JoinLDandOD.

(d)Drawanarcofradius6cmfromDanddrawanotherarcofradius6cmtakingLas

centre,whichintersectsatG.

(e)JoinGDandGO.

ItistherequiredquadrilateralGOLD.

(iii)Given:BN=5.6cm,DE=6.5cm



Toconstruct:ArhombusBEND


(a)DrawDE=6.5cm.

(b)DrawperpendicularbisectoroflinesegmentDE.

(c)Drawtwoarcsofradius2.8cmfromintersectionpointO,whichintersectsthe

perpendicularbisectoratBandN.

(d)JoinBE,BDaswellasNDandNE.

ItistherequiredrhombusBEND.




NCERTSolutions

CHAPTER-4



(i)QuadrilateralMORE

MO=6cm,OR=4.5cm,∠M=60°,∠O=105°,∠R=105°

(ii)QuadrilateralPLAN

PL=4cm,LA=6.5cm,∠P=90°,∠A=110°,∠N=85°

(iii)ParallelogramHEAR

HE=5cm,EA=6cm,∠R=85°

(iv)RectangleOKAY

OK=7cm,KA=5cm

Ans.(i)Given:MO=6cm,OR=4.5cm,

∠M=60°,∠O=105°,∠R=105°

Toconstruct:AquadrilateralMORE


(a)DrawalinesegmentMO=6cm.

(b)Construct∠R=105°andtakingradius4.5cm,drawanarctakingOascentre,which

intersectsatR.

(c)Alsoconstructanangle105°atRandproducethesideRE.

(d)Constructanotherangleof60°atpointMandproducethesideME.BothsidesMEandRE



intersectatE.

ItistherequiredquadrilateralMORE.

(ii)Given:PL=4cm,LA=6.5cm,

∠P=90°,∠A=110°,∠N=85°

Toconstruct:AquadrilateralPLAN

Tofind:∠L=360°-(90°+85°+110°)=360°-285°=75°


(a)DrawalinesegmentPL=4cm.

(b)Constructangleof90°atPandproducethesidePN.

(c)Constructangleof75°atLandwithLascentre,drawanarcofradius6cm,which

intersectsatA.

|(d)Construct∠A=110°atAandproducethesideANwhichintersectsPNatN.

ItistherequiredquadrilateralPLAN.

(iii)Given:HE=5cm,EA=6cm,∠R=85°

Toconstruct:AparallelogramHEAR

Tofind:∠H=180°-85°=95°

[ Sumofadjacentangleof||gmis180°]




(a)DrawalinesegmentHE=5cm.

(b)Construct∠H=95°anddrawanarcofradius6cmwithcentreH.ItintersectsARatR.

(c)JoinRH.

(d)Draw∠R=∠E=85°anddrawanarcofradius6cmwithEasacentrewhichintersects

RAatA.

(e)JoinRA.

ItistherequiredparallelogramHEAR.

(iv)Given:OK=7cm,KA=5cm

Toconstruct:ArectangleOKAY


(a)DrawalinesegmentOK=7cm.

(b)Constructangle90°atbothpointsOandKandproducethesesides.

(c)Drawtwoarcsofradius5cmfrompointsOandKrespectively.ThesearcsintersectatY

andA.

(d)JoinYA.

ItistherequiredrectangleOKAY.




NCERTSolutions

CHAPTER-4



(i)QuadrilateralDEAR

DE=4cm,EA=5cm,AR=4.5cm,∠E=60°,∠A=90°

(ii)QuadrilateralTRUE

TR=3.5cm,RU=3cm,UE=4cm,∠R=75°,∠U=120°

Ans:(i)Given:DE=4cm,EA=5cm,AR=4.5cm,∠E=60°,∠A=90°

Toconstruct:AquadrilateralDEAR


(a)DrawalinesegmentDE=4cm.

(b)AtpointE,constructanangleof60°.

(c)Takingradius5cm,drawanarcfrompointEwhichintersectsatA.

(d)Construct∠A=90°,drawanarcofradius4.5cmwithcentreAwhichintersectatR.

(e)JoinRD.

ItistherequiredquadrilateralDEAR.

(ii)Given:TR=3.5cm,RU=3cm,UE=4cm,∠R=75°,∠U=120°



Toconstruct:AquadrilateralTRUE


(a)DrawalinesegmentTR=3.5cm.

(b)Constructanangle75°atRanddrawanarcofradius3cmwithRascentre,which

intersectsatU.

(c)Constructanangleof120°atUandproducethesideUE.

(d)Drawanarcofradius4cmwithUascentre.

(e)JoinUEandTE.

ItistherequiredquadrilateralTRUE.




NCERTSolutions

CHAPTER-4


Drawthefollowing:

1.ThesquareREADwithRE=5.1cm.

Solution:Given:RE=5.1cm

Toconstruct:thesquareREAD.


(i)DrawalinesegmentRE=5.1cm.

(ii)AtpointE,constructanangleof90oanddrawanarcofradius5.1cm,markthe

intesectionoflineandarcaspointA.

(iii)FrompointR,drawanarcofradius5.1cmandfrompointA,drawanotherarcofradius

5.1cm,marktheintersectionofthetwoarcsaspointD.

(iv)JoinADandRD.

ItistherequiredsquareREAD.

2.Arhombuswhosediagonalsare5.2cmand6.4cm.

Solution:Given:Diagonalsofarhombus

AC=5.2cmandBD=6.4cm.



Toconstruct:ArhombusABCD.


(i)DrawAC=5.2cmanddrawaperpendicularbisectoronAC.

(ii)FromthemidpointO,drawtwoarcsofradius3.2cmcuttingtheperpendicularbisector

onbothsides.

(iii)MarkthepointsofintersectionofarcsandperpendicularbisectorasBandD.

(iv)JoinAB,BC,CDandDA.

ItisrequiredrhombusABCD.

3.Arectanglewithadjacentsidesoflength5cmand4cm.

Solution:Given:MN=5cmandMP=4cm.

Toconstruct:ArectangleMNOP


(a)DrawasegmentMN=5cm.

(b)AtpointsMandN,drawperpendicularsoflengths4cmandproducethem.

(c)TakingcentresMandN,drawtwoarcsof4cmeach,whichintersectPandQ



respectively.

(d)JoinsidePO.

ItisrequiredrectangleMNOP.

4.AparallelogramOKAYwhereOK=5.5cmandKA=4.2cm.

Solution:

Given:OK=5.5cmandKA=4.2cm.

Toconstruct:AparallelogramOKAY.


(a)DrawalinesegmentOK=5.5cm.

(b)Drawanangleof90oatKanddrawanarcofradiusKA=4.2cm,whichintersectsat

pointA.

(c)DrawanotherarcofradiusAY=5.5cmandatpointO,drawanotherarcofradius4.2cm

whichintersectatY.

(d)JoinAYandOY.

ItistherequiredparallelogramOKAY.




NCERTSolutions

CHAPTER-5

DataHandling(Ex.5.1)

1.Forwhichofthesewouldyouuseahistogramtoshowthedata:

(a)Thenumberoflettersfordifferentareasinapostman’sbag.

(b)Theheightofcompetitorsinanathleticsmeet.

(c)Thenumbercassettesproducedby5companies.

(d)Thenumberofpassengersboardingtrainsfrom7.00a.m.to7.00p.m.atastation.

Givereasonforeach.

Ans.Since,Histogramisagraphicalrepresentationofdata,ifdatarepresentedinmannerof

class-interval.

Therefore,forcase(b)and(d),wewoulduseahistogramtoshowthedata,becauseinthese

cases,datacanbedividedintoclass-intervals.

Incase(b),agroupofcompetitiorshavingdifferentheightsinanathleticsmeet.

Incase(d),thenumberofpassengersboardingtrainsinanintervalofonehouratastation.

2.Theshopperswhocometoadepartmentalstorearemarkedas:man(M),woman

(W),boy(B)orgirl(G).Thefollowinglistgivestheshopperswhocameduringthefirst

hourinthemorning.

WWWGBWWMGGMMWWWWGBMWBGGMWWMMWWWMWBWGM

WWWWGWMMWMWGWMGWMMBGGW

Makeafrequencydistributiontableusingtallymarks.

Drawabargraphtoillustrateit.

Ans.Thefrequencydistributiontableisasfollows:



Theillustrationofdatabybar-graphisasfollows:

3.Theweeklywages(in`)of30workersinafactoryare:

830,835,890,810,835,836,869,845,898,890,820,860,832,833,855,845,804,808,812,840,

885,835,835,836,878,840,868,890,806,840

Usingtallymarks,makeafrequencytablewithintervalsas800–810,810–820andso

on.

Ans.Therepresentationofdatabyfrequencydistributiontableusingtallymarksisas

follows:

4.DrawahistogramforthefrequencytablemadeforthedatainQuestion3andanswer

thefollowingquestions.



(i)Howmanyworkersearn`850andmore?

(ii)Howmanyworkersearnlessthan`850?

Ans.830–840grouphasthemaximumnumberofworkers.

(i)10workerscanearnmorethan`850.

(ii)20workersearnlessthan`850.

5.Thenumberofhoursforwhichstudentsofaparticularclasswatchedtelevision

duringholidaysisshownthroughthegivengraph.



Answerthefollowing:

(i)ForhowmanyhoursdidthemaximumnumberofstudentswatchT.V.?

(ii)HowmanystudentswatchedTVforlessthan4hours?

(iii)Howmanystudentsspentmorethan5hoursinwatchingTV?

Ans.

(i)ThemaximumnumberofstudentswatchedT.V.for4–5hours.

(ii)34studentswatchedT.V.forlessthan4hours.

(iii)14studentsspentmorethan5hoursinwatchingT.V.




NCERTSolutions

CHAPTER-5


1.Asurveywasmadetofindthetypeofmusicthatacertaingroupofyoungpeople

likedinacity.Adjoiningpiechartshowsthefindingsofthissurvey.

Fromthispiechart,answerthefollowing:

(i)If20peoplelikedclassicalmusic,howmanyyoungpeopleweresurveyed?

(ii)Whichtypeofmusicislikedbythemaximumnumberofpeople?

(iii)Ifacassettecompanyweretomake1000CD’s,howmanyofeachtypewouldthey

make?

Ans.(i)10%represents20people.

Therefore100%represents=

=200people

Hence,200peopleweresurveyed.

(ii)Lightmusicislikedbythemaximumnumberofpeople.

(iii)CD’sofclassicalmusic=



=100

CD’sofsemi-classicalmusic= =200

CD’soflightmusic= =400

CD’soffolkmusic= =300

2.Agroupof360peoplewereaskedtovotefortheirfavouriteseasonfromthethree

seasonsrainy,winterandsummer.

(i)Whichseasongotthemostvotes?

(ii)Findthecentralangleofeachsector.

(iii)Drawapiecharttoshowthisinformation.

Ans.(i)Winterseasongotthemostvotes.

(ii)Centralangleofsummerseason=

Centralangleofrainyseason=

Centralangleofwinterseason=



(iii)

3.Drawapiechartshowingthefollowinginformation.Thetableshowsthecolours

preferredbyagroupofpeople.

Ans.Here,centralangle=360°andtotalnumberofpeople=36



4.Theadjoiningpiechartgivesthemarksscoredinanexaminationbyastudentin

Hindi,English,Mathematics,SocialScienceandScience.Ifthetotalmarksobtainedby

thestudentswere540,answerthefollowingquestions:

(i)Inwhichsubjectdidthestudentscore105marks?

(Hint:for540marks,thecentralangle=360°.So,for105marks,whatisthecentral



angle?)

(ii)HowmanymoremarkswereobtainedbythestudentinMathematicsthaninHindi?

(iii)ExaminewhetherthesumofthemarksobtainedinSocialScienceandMathematics

ismorethanthatinScienceandHindi.

(Hint:Juststudythecentralangles)

Ans.

(i)Thestudentscored105marksinHindi.

(ii)MarksobtainedinMathematics=135

MarksobtainedinHindi=105

Difference=135–105=30

Thus,30moremarkswereobtainedbythestudentinMathematicsthaninHindi.

(iii)ThesumofmarksinSocialScienceandMathematics=97.5+135=232.5

ThesumofmarksinScienceandHindi=120+105=225

Yes,thesumofthemarksinSocialScienceandMathematicsismorethanthatinScienceand

Hindi.

5.Thenumberofstudentsinahostel,speakingdifferentlanguagesisgivenbelow.



Displaythedatainapiechart.

Ans.

Piechartatabovegivendataisasfollows.




NCERTSolutions

CHAPTER-5


1.Listtheoutcomesyoucanseeintheseexperiments.

(a)Spinningawheel

(b)Tossingtwocoinstogether

Ans.(a)TherearefourlettersA,B,CandDinaspinningwheel.Sothereare4outcomes.

(b)Whentwocoinsaretossedtogether.TherearefourpossibleoutcomesHH,HT,TH,TT.

(HereHTmeansheadonfirstcoinandtailonsecondcoinandsoon.)

2.Whenadieisthrown,listtheoutcomesofaneventofgetting:

(i)(a)aprimenumber

(b)notaprimenumber

(ii)(a)anumbergreaterthan5

(b)anumbernotgreaterthan5

Ans.(i)(a)Outcomesofeventofgettingaprimenumberare2,3and5.

(b)Outcomesofeventofnotgettingaprimenumberare1,4and6.



(ii)(a)Outcomesofeventofgettinganumbergreaterthan5is6.

(b)Outcomesofeventofnotgettinganumbergreaterthan5are1,2,3,4and5.

3.Findthe:

(a)ProbabilityofthepointerstoppingonDin(Question1(a)).

(b)Probabilityofgettinganacefromawellshuffleddeckof52playingcards.

(c)Probabilityofgettingaredapple.(Seefigurebelow)

Ans.(a)Inaspinningwheel,therearefivepointersA,A,B,C,D.Sothere

arefiveoutcomes.PointerstopsatDwhichisoneoutcome.

SotheprobabilityofthepointerstoppingonD=

(b)Thereare4acesinadeckof52playingcards.So,therearefoureventsofgettinganace.

So,probabilityofgettinganace=

(c)Totalnumberofapples=7

Numberofredapples=4



Probabilityofgettingredapple=

4.Numbers1to10arewrittenontenseparateslips(onenumberononeslip),keptina

boxandmixedwell.Oneslipischosenfromtheboxwithoutlookingintoit.Whatisthe

probabilityof:

(i)gettinganumber6.

(ii)gettinganumberlessthan6.

(iii)gettinganumbergreaterthan6.

(iv)gettinga1-digitnumber.

Ans.(i)Outcomeofgettinganumber6fromtenseparateslipsisone.

Therefore,probabilityofgettinganumber6=

(ii)Numberslessthan6are1,2,3,4and5whicharefive.Sothereare5outcomes.

Therefore,probabilityofgettinganumberlessthan6=

(iii)Numbergreaterthan6outoftenthatare7,8,9,10.Sothereare4possibleoutcomes.

Therefore,probabilityofgettinganumbergreaterthan6=

(iv)Onedigitnumbersare1,2,3,4,5,6,7,8,9outoften.

Therefore,probabilityofgettinga1-digitnumber=

5.Ifyouhaveaspinningwheelwith3greensectors,1bluesectorand1redsector,what

istheprobabilityofgettingagreensector?Whatistheprobabilityofgettinganone-

bluesector?

Ans.Therearefivesectors.Threesectorsaregreenoutoffivesectors.

Therefore,probabilityofgettingagreensector=

Thereisonebluesectoroutoffivesectors.



Non-bluesectors=5–1=4sectors

Therefore,probabilityofgettinganon-bluesector=

6.FindtheprobabilityoftheeventsgiveninQuestion2.

Ans.Whenadieisthrown,therearetotalsixoutcomes,i.e.,1,2,3,4,5and6.

(i)(a)2,3,5areprimenumbers.Sothereare3outcomesoutof6.

Therefore,probabilityofgettingaprimenumber=

(b)1,4,6arenottheprimenumbers.Sothereare3outcomesoutof6.

Therefore,probabilityofgettingaprimenumber=

(ii)(a)Only6isgreaterthan5.Sothereisoneoutcomeoutof6.

Therefore,probabilityofgettinganumbergreaterthan5=

(b)Numbersnotgreaterthan5are1,2,3,4and5.Sothereare5outcomesoutof6.

Therefore,probabilityofnotgettinganumbergreaterthan5=




NCERTSolutions

CHAPTER-6

SquaresandSquareRoots(Ex.6.1)

1.Whatwillbetheunitdigitofthesquaresofthefollowingnumbers:

(i)81(ii)272(iii)799(iv)3853(v)1234

(vi)26387(vii)52698(viii)99880(ix)12796(x)55555

Ans.(i)Thenumber81containsitsunit’splacedigit1.So,squareof1is1.

Hence,unit’sdigitofsquareof81is1.

(ii)Thenumber272containsitsunit’splacedigit2.So,squareof2is4.


(iii)Thenumber799containsitsunit’splacedigit9.So,squareof9is81.


(iv)Thenumber3853containsitsunit’splacedigit3.So,squareof3is9.


(v)Thenumber1234containsitsunit’splacedigit4.So,squareof4is16.


(vi)Thenumber26387containsitsunit’splacedigit7.So,squareof7is49.


(vii)Thenumber52698containsitsunit’splacedigit8.So,squareof8is64.


(viii)Thenumber99880containsitsunit’splacedigit0.So,squareof0is0.




(ix)Thenumber12796containsitsunit’splacedigit6.So,squareof6is36.


(x)Thenumber55555containsitsunit’splacedigit5.So,squareof5is25.


2.Thefollowingnumbersareobviouslynotperfectsquares.Givereasons.

(i)1057(ii)23453(iii)7928(iv)222222

(v)64000(vi)89722(vii)222000(viii)505050

Ans.(i)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore

1057isnotaperfectsquarebecauseitsunit’splacedigitis7.

(ii)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore


(iii)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore


(iv)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore


(v)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore

64000isnotaperfectsquarebecauseitsunit’splacedigitissingle0.

(vi)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore


(vii)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore

222000isnotaperfectsquarebecauseitsunit’splacedigitistriple0.

(viii)Since,perfectsquarenumberscontaintheirunit’splacedigit0,1,4,5,6,9.Therefore




3.Thesquaresofwhichofthefollowingwouldbeoddnumber:

(i)431(ii)2826(iii)7779(iv)82004

Ans.(i)431–Unit’sdigitofgivennumberis1andsquareof1is1.Therefore,squareof431

wouldbeanoddnumber.

(ii)2826–Unit’sdigitofgivennumberis6andsquareof6is36.Therefore,squareof2826

wouldnotbeanoddnumber.

(iii)7779–Unit’sdigitofgivennumberis9andsquareof9is81.Therefore,squareof7779

wouldbeanoddnumber.

(iv)82004–Unit’sdigitofgivennumberis4andsquareof4is16.Therefore,squareof82004

wouldnotbeanoddnumber.

4.Observethefollowingpatternandfindthemissingdigits:

=121

=10201

=1002001

=1…….2…….1

=1……………………

Ans. =121

=10201

=1002001

=10000200001

=100000020000001

5.Observethefollowingpatternandsupplythemissingnumbers:



=121

=10201

=102030201

=………………………

=10203040504030201

Ans. =121

=10201

=102030201

=1020304030201

=10203040504030201

6.Usingthegivenpattern,findthemissingnumbers:

Ans.



7.Withoutadding,findthesum:

(i)1+3+5+7+9

(ii)1+3+5+7+9+11+13+15+17+19

(iii)1+3+5+7+9+11+13+15+17+19+21+23

Ans.(i)Here,therearefiveoddnumbers.Thereforesquareof5is25.

1+3+5+7+9= =25

(ii)Here,therearetenoddnumbers.Thereforesquareof10is100.

1+3+5+7+9+11+13+15+17+19= =100

(iii)Here,therearetwelveoddnumbers.Thereforesquareof12is144.

1+3+5+7+9+11+13+15+17+19+21+23= =144

8.(i)Express49asthesumof7oddnumbers.

(ii)Express121asthesumof11oddnumbers.

Ans.(i)49isthesquareof7.Thereforeitisthesumof7oddnumbers.

49=1+3+5+7+9+11+13

(ii)121isthesquareof11.Thereforeitisthesumof11oddnumbers

121=1+3+5+7+9+11+13+15+17+19+21

9.Howmanynumbersliebetweensquaresofthefollowingnumbers:



(i)12and13

(ii)25and26

(iii)99and100

Ans.(i)Since,non-perfectsquarenumbersbetween and are

Here, =12

Therefore,non-perfectsquarenumbersbetween12and13= = =24

(i.e - -1=169-144-1=25-1=24)

(ii)Since,non-perfectsquarenumbersbetween and are

Here, =25


(i.e - -1=676-625-1=51-1=50)

(iii)Since,non-perfectsquarenumbersbetween and are

Here, =99


(i.e - -1=10000-9801-1=199-1=198)




NCERTSolutions

CHAPTER-6


1.Findthesquaresofthefollowingnumbers:

(i)32(ii)35(iii)86

(iv)93(v)71(vi)46

Ans.(i)

=900+120+4=1024

(ii)

=900+300+25=1225

(iii)

=6400+960+36=7396

(iv)

=8100+540+9=8649



(v)

=4900+140+1=5041

(vi)

=1600+480+36=2116

2.WriteaPythagorastripletwhoseonememberis:

(i)6(ii)14(iii)16(iv)18

Ans.(i)Therearethreenumbers and inaPythagoreanTriplet.

Here,

Therefore,Secondnumber

Thirdnumber

Hence,Pythagoreantripletis(6,8,10).

(ii)Therearethreenumbers

and inaPythagoreanTriplet.

Here,




Thirdnumber


(iii)Therearethreenumbers and inaPythagoreanTriplet.

Here,


Thirdnumber


(iv)Therearethreenumbers and inaPythagoreanTriplet.

Here,


Thirdnumber





NCERTSolutions

CHAPTER-6


1.Whatcouldbethepossible‘one’s’digitsofthesquarerootofeachofthefollowing

numbers:

(i)9801(ii)99856(iii)998001(iv)657666025

Ans.Since,Unit’sdigitsofsquareofnumbersare0,1,4,5,6and9.Therefore,thepossible

unit’sdigitsofthegivennumbersare:

(i)1(ii)6(iii)1(iv)5

2.Withoutdoinganycalculation,findthenumberswhicharesurelynotperfect

squares:

(i)153(ii)257(iii)408(iv)441

Ans.Since,allperfectsquarenumberscontaintheirunit’splacedigits0,1,4,5,6and9.

(i)Butgivennumber153hasitsunitdigit3.Soitisnotaperfectsquarenumber.

(ii)Givennumber257hasitsunitdigit7.Soitisnotaperfectsquarenumber.

(iii)Givennumber408hasitsunitdigit8.Soitisnotaperfectsquarenumber.

(iv)Givennumber441hasitsunitdigit1.Soitwouldbeaperfectsquarenumber

3.Findthesquarerootsof100and169bythemethodofrepeatedsubtraction.

Ans.Bysuccessivesubtractingoddnaturalnumbersfrom100,

100–1=99

99–3=96



96–5=91

91–7=84

84–9=75

75–11=64

64–13=51

51–15=36

36–17=19

19–19=0

Thissuccessivesubtractioniscompletedin10steps.

Therefore

Bysuccessivesubtractingoddnaturalnumbersfrom169,

169–1=168

168–3=165

165–5=160

160–7=153

153–9=144

144–11=133

133–13=120

120–15=105

105–17=88

88–19=69



69–21=48

48–23=25

25–25=0

Thissuccessivesubtractioniscompletedin13steps.

Therefore

4.FindthesquarerootsofthefollowingnumbersbythePrimeFactorizationmethod:

(i)729(ii)400(iii)1764(iv)4096(v)7744

(vi)9604(vii)5929(viii)9216(ix)529(x)8100

Ans.(i)729

= =27

(ii)400



= =20

(iii)1764

= =42

(iv)4096

= =64

(v)7744



= =88

(vi)9604

= =98

(vii)5929

= =77

(viii)9216



= =96

(ix)529

=23

(x)8100



= =90

5.Foreachofthefollowingnumbers,findthesmallestwholenumberbywhichit

shouldbemultipliedsoastogetaperfectsquarenumber.Also,findthesquarerootof

thesquarenumbersoobtained:

(i)252(ii)180(iii)1008

(iv)2028(v)1458(vi)768

Ans.(i)

252=

Here,primefactor7hasnopair.Therefore252mustbemultipliedby7tomakeitaperfect

square.

=1764

= =42

(ii)

180=




square.

180x5=900

= =30

(iii)

1008=


square.

=7056

And = =84

(iv)

2028=


square.



=6084

And = =78

(v)

1458=


square.

=2916

And = =54

(vi)

768=




square.

=2304

And = =48

6.Foreachofthefollowingnumbers,findthesmallestwholenumberbywhichit

shouldbedividedsoastogetaperfectsquare.Also,findthesquarerootofthesquare

numbersoobtained:

(i)252(ii)2925(iii)396

(iv)2645(v)2800(vi)1620

Ans.(i)

252=

Here,primefactor7hasnopair.Therefore252mustbedividedby7tomakeitaperfect

square.

252 7=36

And = =6

(ii)



2925=


square.

2925 13=225

And = =15

(iii)

396=


square.

396 11=36

And = =6

(iv)



2645=


square.

2645 5=529

And = =23

(v)

2800=


square.

2800 7=400

And = =20

(vi)

1620=




square.

1620 5=324

And = =18

7.ThestudentsofClassVIIIofaschooldonatedRs.2401inall,forPrimeMinister’s

NationalReliefFund.Eachstudentdonatedasmanyrupeesasthenumberofstudents

intheclass.Findthenumberofstudentsintheclass.

Ans.Here,Donatedmoney=Rs2401

Letthenumberofstudentsbe

Thereforedonatedmoney=


=2401

=

= =49

Hence,thenumberofstudentsis49.

8.2025plantsaretobeplantedinagardeninsuchawaythateachrowcontainsas

manyplantsasthenumberofrows.Findthenumberofrowsandthenumberofplants

ineachrow.

Ans.Here,Numberofplants=2025



Letthenumberofrowsofplantedplantsbe

Andeachrowcontainsnumberofplants=


=2025

= =45

Hence,eachrowcontains45plants.

9.Findthesmallestsquarenumberthatisdivisiblebyeachofthenumbers4,9and10.

Ans.L.C.M.of4,9and10is180.

Primefactorsof180=


square.

=900



Hence,thesmallestsquarenumberwhichisdivisibleby4,9and10is900.

10.Findthesmallestsquarenumberthatisdivisiblebyeachofthenumbers8,15and

20.

Ans.L.C.M.of8,15and20is120.

Primefactorsof120=

Here,primefactor2,3and5hasnopair.Therefore120mustbemultipliedby

tomakeitaperfectsquare.

120 2 3 5=3600

Hence,thesmallestsquarenumberwhichisdivisibleby8,15and20is3600.




NCERTSolutions

CHAPTER-6


1.FindthesquarerootsofeachofthefollowingnumbersbyDivisionmethod:

(i)2304(ii)4489(iii)3481(iv)529(v)3249(vi)1369

(vii)5776(viii)7921(ix)576(x)1024(xi)3136(xii)900

Ans.(i)2304

Hence,thesquarerootof2304is48.

(ii)4489


(iii)3481




(iv)529


(v)3249


(vi)1369




(vii)5776


(viii)7921


(ix)576




(x)1024


(xi)3136


(xii)900




2.Findthenumberofdigitsinthesquarerootofeachofthefollowingnumbers

(withoutanycalculation):

(i)64(ii)144(iii)4489(iv)27225(v)390625

Ans.(i)Here,64containstwodigitswhichiseven.

Therefore,numberofdigitsinsquareroot= (thatis8,whichissingledigit

number)

(ii)Here,144containsthreedigitswhichisodd.

Therefore,numberofdigitsinsquareroot= (thatis12,whichisa2-

digitnumber)

(iii)Here,4489containsfourdigitswhichiseven.

Therefore,numberofdigitsinsquareroot= (thatis67,whichisa2-digit

number)

(iv)Here,27225containsfivedigitswhichisodd.

Therefore,numberofdigitsinsquareroot= (thatis165,whichisa3-digit

number)



(v)Here,390625containssixdigitswhichiseven.

Therefore,thenumberofdigitsinsquareroot= (thatis625,whichisa3-digit

number)

3.Findthesquarerootofthefollowingdecimalnumbers:

(i)2.56(ii)7.29(iii)51.84(iv)42.25(v)31.36

Ans.(i)2.56

Hence,thesquarerootof2.56is1.6.

(ii)7.29


(iii)51.84




(iv)42.25


(v)31.36


4.Findtheleastnumberwhichmustbesubtractedfromeachofthefollowingnumbers

soastogetaperfectsquare.Also,findthesquarerootoftheperfectsquareso

obtained:



(i)402

(ii)1989

(iii)3250

(iv)825

(v)4000

Ans.(i)402

Weknowthat,ifwesubtracttheremainderfromthenumber,wegetaperfectsquare.

Here,wegetremainder2.Therefore2mustbesubtractedfrom402togetaperfectsquare.

402–2=400


(ii)1989




Here,wegetremainder53.Therefore53mustbesubtractedfrom1989togetaperfect

square.

1989–53=1936


(iii)3250



3250–1=3249




(iv)825



825–41=784


(v)4000




Here,wegetremainder31.Therefore31mustbesubtractedfrom4000togetaperfect

square.

4000–31=3969


5.Findtheleastnumberwhichmustbeaddedtoeachofthefollowingnumberssoasto

getaperfectsquare.Also,findthesquarerootoftheperfectsquaresoobtained:

(i)525(ii)1750(iii)252(iv)1825(v)6412

Ans.(i)525



Sincetheremainderis41.

Therefore

Nextperfectsquarenumber =529

Hence,numbertobeadded

=529–525=4

525+4=529


(ii)1750


Therefore



=1764–1750=14

1750+14=1764


(iii)252




Therefore



=256–252=4

252+4=256


(iv)1825


Therefore


Hence,numbertobeadded=1849–1825=24

1825+24=1849




(v)6412


Therefore



=6561–6412=149

6412+149=6561


6.Findthelengthofthesideofasquarewhoseareais ?

Ans.Letthelengthofthesideofasquarebe meter.

Areaofsquare


=441



=

=

=21m

Hence,thelengthofthesideofasquareis21m.

7.InarighttriangleABC, B=

(i)IfAB=6cm,BC=8cm,findAC.

(ii)IfAC=13cm,BC=5cm,findAB.

Ans.(i)UsingPythagorastheorem,

=36+84=100

AC=

AC=10cm

(ii)UsingPythagorastheorem,



=169–25

=144

AB=

AB=12cm

8.Agardenerhas1000plants.Hewantstoplanttheseinsuchawaythatthenumberof

rowsandnumberofcolumnsremainsame.Findtheminimumnumberofplantshe

needsmoreforthis.

Ans.Here,plants=1000

Sinceremainderis39.



Therefore



=1024–1000=24

1000+24=1024

Hence,thegardenerrequires24moreplants.

9.Thereare500childreninaschool.ForaP.T.drill,theyhavetostandinsucha

mannerthatthenumberofrowsisequaltothenumberofcolumns.Howmany

childrenwouldbeleftoutinthisarrangement?

Ans.Here,Numberofchildren=500

Bygettingthesquarerootofthisnumber,weget,

Ineachrow,thenumberofchildrenis22.

Andleftoutchildrenare16.




NCERTSolutions

CHAPTER-7

CubesandCubeRoots(Ex.7.1)

1.Whichofthefollowingnumbersarenotperfectcubes:

(i)216(ii)128(iii)1000(iv)100(v)46656

Ans.(i)216

Primefactorsof216=

Hereallfactorsareingroupsof3’s(intriplets)

Therefore,216isaperfectcubenumber.

(ii)128

Primefactorsof128=

Hereonefactor2doesnotappearina3’sgroup.



Therefore,128isnotaperfectcube.

(iii)1000

Primefactorsof1000=2X2X2X5X5X5

Hereallfactorsappearin3’sgroup.

Therefore,1000isaperfectcube.

(iv)100

Primefactorsof100=2x2x5x5

Hereallfactorsdonotappearin3’sgroup.

Therefore,100isnotaperfectcube.

(v)46656



Primefactorsof46656=

Hereallfactorsappearin3’sgroup.

Therefore,46656isaperfectcube.

2.Findthesmallestnumberbywhicheachofthefollowingnumbersmustbe

multipliedtoobtainaperfectcube:

(i)243(ii)256(iii)72(iv)675(v)100

Ans.(i)243

Primefactorsof243=

Here3doesnotappearin3’sgroup.

Therefore,243mustbemultipliedby3tomakeitaperfectcube.



(ii)256

Primefactorsof256=

Hereonefactor2isrequiredtomakea3’sgroup.


(iii)72

Primefactorsof72=

Here3doesnotappearin3’sgroup.


(iv)675



Primefactorsof675=

Herefactor5doesnotappearin3’sgroup.

Therefore675mustbemultipliedby5tomakeitaperfectcube.

(v)100

Primefactorsof100=

Herefactor2and5bothdonotappearin3’sgroup.

Therefore100mustbemultipliedby =10tomakeitaperfectcube.

3.Findthesmallestnumberbywhicheachofthefollowingnumbersmustbedividedto

obtainaperfectcube:

(i)81(ii)128(iii)135(iv)192(v)704

Ans.(i)81

Primefactorsof81=

Hereonefactor3isnotgroupedintriplets.

Therefore81mustbedividedby3tomakeitaperfectcube.

(ii)128



Primefactorsof128= X2

Hereonefactor2doesnotappearina3’sgroup.

Therefore,128mustbedividedby2tomakeitaperfectcube.

(iii)135

Primefactorsof135=

Hereonefactor5doesnotappearinatriplet.


(iv)192



Primefactorsof192=2X2X2X2X2X2X3



(v)704

Primefactorsof704=2X2X2X2X2X2X11



4.Parikshitmakesacuboidofplasticineofsides5cm,2cm,5cm.Howmanysuch

cuboidswillheneedtoformacube?

Ans.Givennumbers=

Since,Factorsof5and2botharenotingroupofthree.

Therefore,thenumbermustbemultipliedby =20tomakeitaperfectcube.

Henceheneeds20cuboids.




NCERTSolutions

CHAPTER-7

CubesandCubeRoots(Ex.7.2)

1.Findthecuberootofeachofthefollowingnumbersbyprimefactorizationmethod:

(i)64

(ii)512

(iii)10648

(iv)27000

(v)15625

(vi)13824

(vii)110592

(viii)46656

(ix)175616

(x)91125

Ans.(i)64

= =4

(ii)512



= =8

(iii)10648

= =22

(iv)27000

= =30

(v)15625



= =25

(vi)13824

= =24

(vii)110592



= =48

(viii)46656

= =36

(ix)175616



= =56

(x)91125

= =45

2.Statetrueorfalse:

(i)Cubeofanyoddnumberiseven.

(ii)Aperfectcubedoesnotendwithtwozeroes.

(iii)Ifsquareofanumberendswith5,thenitscubeendswith25.

(iv)Thereisnoperfectcubewhichendswith8.

(v)Thecubeofatwodigitnumbermaybeathreedigitnumber.



(vi)Thecubeofatwodigitnumbermayhavesevenormoredigits.

(vii)Thecubeofasingledigitnumbermaybeasingledigitnumber.

Ans.(i)False

Since, areallodd.

(ii)True

Since,aperfectcubeendswiththreezeroes.

e.g. soon

(iii)False

Since,

(Didnotendwith25)

(iv)False

Since =1728

[Endswith8]

And =10648

[Endswith8]

(v)FalseSince =1000

[Fourdigitnumber]

And =1331

[Fourdigitnumber]

(vi)FalseSince =970299

[Sixdigitnumber]

(vii)True

=1

[Singledigitnumber]

=8

[Singledigitnumber]

3.Youaretoldthat1,331isaperfectcube.Canyouguesswithoutfactorizationwhatis



itscuberoot?Similarlyguessthecuberootsof4913,12167,32768.

Ans.Weknowthat =1000andPossiblecubeof =1331

Since,cubeofunit’sdigit =1

Therefore,cuberootof1331is11.

4913

Weknowthat =343

Nextnumbercomeswith7asunitplace =4913

Hence,cuberootof4913is17.

12167

Weknowthat =27

Hereincube,onesdigitis7

Nownextnumberwith3asonesdigit

=2197

Andnextnumberwith3asonesdigit

=12167

Hencecuberootof12167is23.

32768

Weknowthat =8

Hereincube,onesdigitis8

Nownextnumberwith2asonesdigit

=1728


=10648


=32768

Hencecuberootof32768is32.




NCERTSolutions

CHAPTER-8

ComparingQuantities(Ex.8.1)

1.Findtheratioofthefollowing:

(a)Speedofacycle15kmperhourtothespeedofscooter30kmperhour.

(b)5mto10km

(c)50paisetoRs.5

Ans.(a)Speedofcycle=15km/hr

Speedofscooter=30km/hr

Henceratioofspeedofcycletothatofscooter=15:30= =1:2

(b) 1km=1000m

10km= =10000m

Ratio= = =1:2000

(c) Rs1=100paise

Rs5= =500paise

HenceRatio= = =1:10

2.Convertthefollowingratiostopercentages:

(a)3:4(b)2:3



Ans.(a)Percentageof3:4= =75%

(b)Percentageof2:3= =

3.72%of25studentsaregoodinmathematics.Howmanyarenotgoodinmathematics?

Ans.Totalnumberofstudents=25

Numberofgoodstudentsinmathematics=72%of25= =18

Numberofstudentsnotgoodinmathematics=25–18=7

Hencepercentageofstudentsnotgoodinmathematics= =28%

4.Afootballteamwon10matchesoutofthetotalnumberofmatchestheyplayed.If

theirwinpercentagewas40,thenhowmanymatchesdidtheyplayinall?

Ans.Lettotalnumberofmatchesbe


40%oftotalmatches=10

40%of =10

=25

Hencetotalnumberofmatchesare25.

5.IfChamelihadRs.600leftafterspending75%ofhermoney,howmuchmoneydid



shehaveinthebeginning?

Ans.Totalpercentageofmoneyshedidn'tspent=100%-75%=25%


25%=600

1%=600/25

100%=

HencethemoneyinthebeginningwasRs2,400.

6.If60%peopleinacitylikecricket,30%likefootballandtheremaininglikeother

games,thenwhatpercentofthepeoplelikeothergames?Ifthetotalnumberofpeople

are50lakh,findtheexactnumberwholikeeachtypeofgame.

Ans.Numberofpeoplewholikecricket=60%

Numberofpeoplewholikefootball=30%

Numberofpeoplewholikeothergames=100%–(60%+30%)=10%

NowNumberofpeoplewholikecricket=60%of50,00,000

= =30,00,000

AndNumberofpeoplewholikefootball

=30%of50,00,000

= =15,00,000

Numberofpeoplewholikeothergames=10%of50,00,000

= =5,00,000

Hence,numberofpeoplewholikeothergamesare5lakh.




NCERTSolutions

CHAPTER-8


1.Amangot10%increaseinhissalary.IfhisnewsalaryisRs.1,54,000,findhisoriginal

salary.

Ans.LetoriginalsalarybeRs.100.

ThereforeNewsalaryi.e.,10%increase

=100+10=Rs.110

NewsalaryisRs.110,whenoriginalsalary=Rs.100

NewsalaryisRs.1,whenoriginalsalary=

NewsalaryisRs.1,54,000,whenoriginalsalary= =Rs.1,40,000

HenceoriginalsalaryisRs.1,40,000.

2.OnSunday845peoplewenttotheZoo.OnMondayonly169peoplewent.Whatisthe

percentdecreaseinthepeoplevisitingtheZooonMonday?

Ans.OnSunday,peoplewenttotheZoo=845

OnMonday,peoplewenttotheZoo=169

Numberofdecreaseinthepeople=845–169=676

Decreasepercent= =80%

HencedecreaseinthepeoplevisitingtheZoois80%.



3.Ashopkeeperbuys80articlesforRs.2,400andsellsthemforaprofitof16%.Findthe

sellingpriceofonearticle.

Ans.No.ofarticles=80

CostPriceofarticles=Rs.2,400

AndProfit=16%

CostpriceofarticlesisRs.100,thensellingprice=100+16=Rs.116

CostpriceofarticlesisRs.1,thensellingprice=

CostpriceofarticlesisRs.2400,thensellingprice= =Rs.2784

Hence,SellingPriceof80articles=Rs.2784

ThereforeSellingPriceof1article

= =Rs.34.80

4.ThecostofanarticlewasRs.15,500,Rs.450werespentonitsrepairs.Ifitsoldfora

profitof15%,findthesellingpriceofthearticle.

Ans.Here,C.P.=Rs.15,500andRepaircost=Rs.450

ThereforeTotalCostPrice=15500+450=Rs.15,950

LetC.P.beRs.100,thenS.P.=100+15=Rs.115

WhenC.P.isRs.100,thenS.P.=Rs.115

WhenC.P.isRs.1,thenS.P.=

WhenC.P.isRs.15950,thenS.P.



= =Rs.18,342.50

5.AVCRandTVwereboughtforRs.8,000each.Theshopkeepermadealossof4%on

theVCRandaprofitof8%ontheTV.Findthegainorlosspercentonthewhole

transaction.

Ans.CostpriceofVCR=Rs.8000andCostpriceofTV=Rs.8000

TotalCostPriceofbotharticles

=Rs.8000+Rs.8000=Rs.16,000

NowVCRissoldat4%loss.

LetC.P.ofeacharticlebeRs.100,thenS.P.ofVCR=100–4=Rs.96




= =Rs.7,680

AndTVissoldat8%profit,thenS.P.ofTV=100+8=Rs.108




= =Rs.8,640

Then,TotalS.P.



=Rs.7,680+Rs.8,640=Rs.16,320

SinceS.P.>C.P.,

ThereforeProfit=S.P.–C.P.

=16320–16000=Rs.320

AndProfit%=

= =2%

Therefore,theshopkeeperhadagainof2%onthewholetransaction.

6.Duringasale,ashopofferedadiscountof10%onthemarkedpricesofalltheitems.

WhatwouldacustomerhavetopayforapairofjeansmarkedatRs.1450andtwoshirts

markedatRs.850each?

Ans.Rateofdiscountonallitems=10%

MarkedPriceofapairofjeans=Rs.1450andMarkedPriceofashirt=Rs.850

Discountonapairofjeans

= =Rs.145

S.P.ofapairofjeans=Rs.1450–Rs.145=Rs.1305

MarkedPriceoftwoshirts= =Rs.1700

Discountontwoshirts= =Rs.170

S.P.oftwoshirts=Rs.1700–Rs.170=Rs.1530

Thereforethecustomerhadtopay=1305+1530



=Discountonapairofjeans

=

=Rs.145

S.P.ofapairofjeans

=Rs.1450–Rs.145=Rs.2,835

Thus,thecustomerwillhavetopayRs.2,835

7.AmilkmansoldtwoofhisbuffaloesforRs.20,000each.Ononehemadeagainof5%

andontheotheralossof10%.Findhisoverallgainorloss.(Hint:FindCPofeach)

Ans.S.P.ofeachbuffalo=Rs.20,000

S.P.oftwobuffaloes= =Rs.40,000

Onebuffaloissoldat5%gain.

LetC.P.beRs.100,thenS.P.=100+5=Rs.105

WhenS.P.isRs.105,thenC.P.=Rs.100

WhenS.P.isRs.1,thenC.P.=

WhenS.P.isRs.20,000,thenC.P.

= =Rs.19,047.62

Anotherbuffaloissoldat10%loss.

LetC.P.beRs.100,thenS.P.=100–10=Rs.90

WhenS.P.isRs.90,thenC.P.=Rs.100



WhenS.P.isRs.1,thenC.P.=

WhenS.P.isRs.20,000,thenC.P.

= =Rs.22,222.22

TotalC.P.=Rs.19,047.62+Rs.22,222.22

=Rs.41,269.84

SinceC.P.>S.P.

Thereforehereitisloss.

Loss=C.P.–S.P.

=Rs.41,269.84–Rs.40,000.00=Rs.1,269.84

TheoveralllossofmilkmanwasRs.1269.84

8.ThepriceofaTVisRs.13,000.Thesalestaxchargedonitisattherateof12%.Find

theamountthatVinodwillhavetopayifhebuysit.

Ans.C.P.=Rs.13,000andS.T.rate=12%

LetC.P.beRs.100,thenS.P.forpurchaser

=100+12=Rs.112



WhenC.P.isRs.13,000,thenS.P.

= =Rs.14,560



HewillhavetopayRs.14,560

9.Arunboughtapairofskatesatasalewherethediscountgivenwas20%.Ifthe

amounthepaysisRs.1,600,findthemarkedprice.

Ans.S.P.=Rs.1,600andRateofdiscount=20%

LetM.P.beRs.100,thenS.P.forcustomer=100–20=Rs.80

WhenS.P.isRs.80,thenM.P.=Rs.100

WhenS.P.isRs.1,thenM.P.=

WhenS.P.isRs.1600,thenM.P.

= =Rs.2,000

Thus,themarkedpricewasRs.2,000

10.Ipurchasedahair-dryerforRs.5,400including8%VAT.FindthepricebeforeVAT

wasadded.

Ans.C.P.=Rs.5,400andRateofVAT=8%

LetC.P.withoutVATisRs.100,thenpriceincludingVAT=100+8=Rs.108

WhenpriceincludingVATisRs.108,thenoriginalprice=Rs.100

WhenpriceincludingVATisRs.1,thenoriginalprice=

WhenpriceincludingVATisRs.5400,thenoriginalprice= =Rs.5000

Thus,thepriceofHairDryerbeforetheadditionofVATwasRs5000




NCERTSolutions

CHAPTER-8


1.Calculatetheamountandcompoundintereston:

(a)Rs.10,800for3yearsat perannumcompoundedannually.

(b)Rs.18,000for yearsat10%perannumcompoundedannually.

(c)Rs.62,500for yearsat8%perannumcompoundedannually.

(d)Rs.8,000for yearsat9%perannumcompoundedhalfyearly.(Youcouldtheyear

byyearcalculationusingS.I.formulatoverify).

(e)Rs.10,000for yearsat8%perannumcompoundedhalfyearly.

Ans.(a)Here,Principal(P)=Rs.10800,Time(n)=3years,

Rateofinterest(R)=

Amount(A)=

= =

= =

=

=Rs.15,377.34(approx.)



CompoundInterest(C.I.)=A–P

=Rs.10800–Rs.15377.34=Rs.4,577.34

(b)Here,Principal(P)=Rs.18,000,Time(n)= years,Rateofinterest(R)

=10%p.a.

Amount(A)=

= =

= =

=Rs.21,780

Interestfor yearsonRs.21,780atrateof10%= =Rs.1,089

Totalamountfor years

=Rs.21,780+Rs.1089=Rs.22,869


=Rs.22869–Rs.18000=Rs.4,869

(c)Here,Principal(P)=Rs.62500,Time(n)= = years=3years(compoundedhalf

yearly)

Rateofinterest(R)=8%=4%(compoundedhalfyearly)



Amount(A)=

=

=

=

=

=Rs.70,304


=Rs.70304–Rs.62500=Rs.7,804

(d)Here,Principal(P)=Rs.8000,Time(n)=1years=2years(compoundedhalfyearly)

Rateofinterest(R)=9%= (compoundedhalfyearly)

Amount(A)=

=

=



=

=

=Rs.8,736.20


=Rs.8736.20–Rs.8000

=Rs.736.20

(e)Here,Principal(P)=Rs.10,000,Time(n)=1years=2years(compoundedhalfyearly)


Amount(A)=

=

=

=

=

=Rs.10,816


=Rs.10,816–Rs.10,000=Rs.816



2.KamalaborrowedRs.26,400fromaBanktobuyascooteratarateof15%p.a.

compoundedyearly.Whatamountwillshepayattheendof2yearsand4monthsto

cleartheloan?

(Hint:FindAfor2yearswithinterestiscompoundedyearlyandthenfindSIonthe2nd

yearamountfor years).

Ans.Here,Principal(P)=Rs.26,400,Time(n)=2years4months,Rateofinterest(R)=15%

p.a.

Amountfor2years(A)=

= =

= =

=Rs.34,914

Interestfor4months= yearsattherateof15%=

=Rs.1745.70

Totalamount=Rs.34,914+Rs.1,745.70

=Rs.36,659.70

3.FabinaborrowsRs.12,500perannumfor3yearsatsimpleinterestandRadha

borrowsthesameamountforthesametimeperiodat10%perannum,compounded

annually.Whopaysmoreinterestandbyhowmuch?

Ans.Here,Principal(P)=Rs.12,500,Time(T)=3years,Rateofinterest(R)



=12%p.a.

SimpleInterestforFabina=

= =Rs.4,500

AmountforRadha,P=Rs.12,500,R=10%and =3years

Amount(A)=

= =

= =

=Rs.16,637.50

C.I.forRadha=A–P

=Rs.16,637.50–Rs.12,500=Rs.4,137.50

Thus,Fabinapaysmoreinterest

=Rs.4,500–Rs.4,137.50=Rs.362.50

4.IborrowsRs.12,000fromJamshedat6%perannumsimpleinterestfor2years.HadI

borrowedthissumat6%perannumcompoundinterest,whatextraamountwouldI

havetopay?

Ans.Here,Principal(P)=Rs.12,000,Time(T)=2years,Rateofinterest(R)=6%p.a.

SimpleInterest=



= =Rs.1,440

Hadheborrowedthissumat6%p.a.,then

CompoundInterest=

=

=

=

=

=Rs.13,483.20–Rs.12,000

=Rs.1,483.20

Differenceinbothinterests

=Rs.1,483.20–Rs.1,440.00=Rs.43.20

Thus,theextraamounttobepaidisRs.43.20

5.VasudevaninvestedRs.60,000ataninterestrateof12%perannumcompoundedhalf

yearly.Whatamountwouldheget:

(i)after6months?

(ii)after1year?

Ans.(i)Here,Principal(P)=Rs.60,000,



Time(n)=6months=1year(compoundedhalfyearly)


Amount(A)=

=

=

=

=

=Rs.63,600

After6monthsVasudevanwouldgetamountRs.63,600.

(ii)Here,Principal(P)=Rs.60,000,

Time(n)=1year=2year(compoundedhalfyearly)


Amount(A)=

=

=



=

=

=Rs.67,416

After1yearVasudevanwouldgetamountRs.67,416.

6.AriftookaloanofRs.80,000fromabank.Iftherateofinterestis10%perannum,

findthedifferenceinamountshewouldbepayingafter yearsiftheinterestis:

(i)compoundedannually.

(ii)compoundedhalfyearly.

Ans.(i)Here,Principal(P)=Rs.80,000,Time(n)= years,Rateofinterest(R)=10%

Amountfor1year(A)=

=

=

=

=Rs.88,000

Interestfor year=



=Rs.4,400

Totalamount=Rs.88,000+Rs.4,400=Rs.92,400

(ii)Here,Principal(P)=Rs.80,000,

Time(n)= year=3/2years(compoundedhalfyearly)


Amount(A)=

=

=

=

=

=Rs.92,610

Differenceinamounts

=Rs.92,610–Rs.92,400=Rs.210

7.MariainvestedRs.8,000inabusiness.Shewouldbepaidinterestat5%perannum

compoundedannually.Find:

(i)Theamountcreditedagainsthernameattheendofthesecondyear.

(ii)Theinterestforthethirdyear.



Ans.(i)Here,Principal(P)=Rs.8000,RateofInterest(R)=5%,Time(n)=2years

Amount(A)=

=

=

=

=

=Rs.8,820

(ii)Here,Principal(P)=Rs.8000,RateofInterest(R)=5%,Time =3years

Amount(A)=

=

=

=

=



=Rs.9,261

Interestfor3rdyear=A–P

=Rs.9,261–Rs.8,820=Rs.441

8.FindtheamountandthecompoundinterestonRs.10,000for yearsat10%per

annum,compoundedhalfyearly.

Wouldthisinterestbemorethantheinteresthewouldgetifitwascompounded

annually?

Ans.Here,Principal(P)=Rs.10000,RateofInterest(R)=10%=5%(compoundedhalfyearly)

Time(n)= years=3years(compoundedhalfyearly)

Amount(A)=

=

=

=

=

=Rs.11,576.25


=Rs.11,576.25–Rs.10,000=Rs.1,576.25



Ifitiscompoundedannually,then

Here,Principal(P)=Rs.10000,RateofInterest(R)=10%,Time(n)= years

Amount(A)for1year=

=

=

=

=

=Rs.11,000

Interestfor year= =Rs.550

Totalamount=Rs.11,000+Rs.550

=Rs.11,550

Now,C.I.=A–P=Rs.11,550–Rs.10,000

=Rs.1,550

Yes,interestRs.1,576.25ismorethanRs.1,550.

9.FindtheamountwhichRamwillgetonRs.4,096,ifhegaveitfor18monthsat



perannum,interestbeingcompoundedhalfyearly.

Ans.Here,Principal(P)=Rs.4096,

RateofInterest(R)=

= (compoundedhalfyearly)

Time(n)=18months= years=3years(compoundedhalfyearly)

Amount(A)=

=

=

=

=

=Rs.4,913

10.Thepopulationofaplaceincreasedto54,000in2003atarateof5%perannum.

(i)Findthepopulationin2001.

(ii)Whatwouldbeitspopulationin2005?

Ans.(i)Here,A2003=Rs.54,000,R=5%, =2years



Populationwouldbelessin2001than2003intwoyears.

Herepopulationisincreasing.

A2003=

54000=

54000=

54000=

54000=

=48,979.5

48,980(approx.)

(ii)Accordingtoquestion,populationisincreasing.Thereforepopulationin2005,

A2005=

=

=



=

=

=59,535

Hencepopulationin2005wouldbe59,535.

11.Inalaboratory,thecountofbacteriainacertainexperimentwasincreasingatthe

rateof2.5%perhour.Findthebacteriaattheendof2hoursifthecountwasinitially

5,06,000.

Ans.Here,Principal(P)=5,06,000,RateofInterest(R)=2.5%,Time(n)=2hours

After2hours,numberofbacteria,

Amount(A)=

=

=

=

=

=



=5,31,616.25

Hence,numberofbacteriaaftertwohoursare531616(approx.).

12.AscooterwasboughtatRs.42,000.Itsvaluedepreciatedattherateof8%per

annum.Finditsvalueafteroneyear.

Ans.Here,Principal(P)=Rs.42,000,RateofInterest(R)=8%,Time(n)=1years

Amount(A)=

=

=

=

=

=Rs.38,640

Hence,thevalueofscooterafteroneyearisRs.38,640.




NCERTSolutions

CHAPTER-9

AlgebraicExpressionsandIdentities(Ex.9.1)

1.Identifytheterms,theircoefficientsforeachofthefollowingexpressions:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Ans.(i)Terms: and

Coefficientin is5andin is

(ii)Terms: and

Coefficientof andof is1.

(iii)Terms: and

Coefficientin is4,coefficientof is andcoefficientof is1.

(iv)Terms: and

Coefficientof is ,coefficientof is1andcoefficientof is

(v)Terms: and



Coefficientof is coefficientof is andcoefficientof is

(vi)Terms: and

Coefficientof is0.3,coefficientof is andcoefficientof is0.5.

2.Classifythefollowingpolynomialsasmonomials,binomials,trinomials.Which

polynomialsdonotfitinanyofthesethreecategories:

Ans.(i)Since containstwoterms.Thereforeitisbinomial.

(ii)Since1000containsoneterms.Thereforeitismonomial.

(iii)Since containsfourterms.Thereforeitisapolynomialanditdoesnot

fitinabovethreecategories.

(iv)Since containsthreeterms.Thereforeitistrinomial.

(v)Since containstwoterms.Thereforeitisbinomial.

(vi)Since containsthreeterms.Thereforeitistrinomial.

(vii)Since containsthreeterms.Thereforeitistrinomial.

(viii)Since4z-15z2containstwoterms.Thereforeitisbinomial.

(ix)Since containsfourterms.Thereforeitisapolynomialanditdoes

notfitinabovethreecategories.

(x)Since containsoneterms.Thereforeitismonomial.

(xi)Since containstwoterms.Thereforeitisbinomial.

(xii)Since containstwoterms.Thereforeitisbinomial.



3.Addthefollowing:

(i)

(ii)

(iii)

(iv)

Ans.(i)

(ii)

Hencethesumif0.

Hencethesumis

(iii)

(iv)



Hencethesumis

.

4.(a)Subtract from

(b)Subtract from

(c)Subtract from

Ans.(a)

(b)

(c)




NCERTSolutions

CHAPTER-9


1.Findtheproductofthefollowingpairsofmonomials:

(i)

(ii)

(iii)

(iv)

(iv)

Ans.

(i) = =

(ii) =

=

(iii) =

=

(iv) =

=

(v) = =0

2.Findtheareasofrectangleswiththefollowingpairsofmonomialsastheirlengths



andbreadthsrespectively:

Ans.

(i)Areaofrectangle

=

= sq.units

(ii)Areaofrectangle

=

=

= sq.units

(iii)Areaofrectangle=

=

= sq.units

(iv)Areaofrectangle=

=

= sq.units

(v)Areaofrectangle=

=

= sq.units



3.Completethetableofproducts:

(i)

Ans.

(i)

4.Obtainthevolumeofrectangularboxeswiththefollowinglength,breadthand

heightrespectively:

(i)

(ii)



(iii)

(iv)

Ans.(i)Volumeofrectangularbox

=

= cubicunits

(ii)Volumeofrectangularbox

=

= cubicunits

(iii)Volumeofrectangularbox

=

= cubicunits

(iv)Volumeofrectangularbox

=

= cubicunits

5.Obtaintheproductof:



(i)

(ii)

(iii)

(iv)

(v)

Ans.

(i)

=

(ii) =

=

(iii)

=

(iv)

=

(v) =(-1)(mxmxmxnxnxp)

=




NCERTSolutions

CHAPTER-9


1.Carryoutthemultiplicationoftheexpressionsineachofthefollowingpairs:

(i) (ii) (iii)

(iv)

(v)

Ans.

(i)

=

(ii)

=

(iii) =

(iv) =

(v) =

=0+0+0=0

2.Completethetable:

First

expression

Second

expressionProduct



(i) …..

(ii) …..

(iii) …..

(iv) …..

(v) …..

Ans.

First

expression

Second

expressionProduct

(i) =

=

(ii) =

=

(iii) =

=

(iv) =

=

(v) =

=



3.Findtheproduct:

(i)

(ii)

(iii)

(iv)

Ans.

(i)

=

(ii)

=

=

(iii)

=

=



(iv) =

4.(a)Simplify: andfindvaluesfor

(i)

(ii)

(b)Simplify: andfinditsvaluefor

(i)

(ii)

(iii)

Ans.(a)

=

(i)For

=

=108–45+3=66

(ii)For

=

=



=

(b)

=

(i)For

=

=0+0+0+5=5

(ii)For

=

=1+1+1+5=8

(iii)For

=

= = =4

5.(a)Add: and

(b)Add: and

(c)Subtract: from

(d)Subtract: from

Ans.(a)



=

=

(b)

=

=

=

(c)

=

=

=

(d)

=

=

=

=

=

=




NCERTSolutions

CHAPTER-9


1.Multiplythebinomials:

(i)(2x+5)and(4x-3)

(ii) and

(iii) and

(iv) and

(v) and

(vi) and

Ans.

(i)

=

=

=

(ii)

=



=3y2-4y-24y+32

=3y2-28y+32

(iii)

=2.5lx2.5l+2.5lx0.5m-0.5mx2.5l-0.5mx0.5m

=

=

(iv)

=

=

(v)

=

=

=

=

(vi)



=

=

=

2.Findtheproduct:

(i)

(ii)

(iii)

(iv)

Ans.(i)

=

= =

(ii)

=

=

=

(iii)



=

=

(iv)

=

=

3.Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Ans.(i)



=

=

=

(ii)

=

=

=

(iii)

=

=

(iv)

=

=

=

=

(v)

=



=

=

(vi)

=

=

=

(vii)

=

=

=

(viii)

=

=

=




NCERTSolutions

CHAPTER-9


1.Useasuitableidentitytogeteachofthefollowingproducts:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Ans.(i)

[Usingidentity ]



=

(ii)

=

[Usingidentity ]

=

(iii)

=

[Usingidentity ]

=

(iv)

=

[Usingidentity ]

=

(v)

[Usingidentity ]

=



(vi)

=

[Usingidentity ]

=

(vii)

[Usingidentity ]

=

(viii)

=

[Usingidentity ]

=

(ix)

=

[Usingidentity ]

=



(x)

=

[Usingidentity ]

=

2.Usetheidentity tofindthefollowingproducts:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Ans.(i)

[Usingidentity ]

=

(ii)



[Usingidentity ]

=

(iii)

=

[Usingidentity ]

=

(iv)

=(4x)2+{5+(-1)}(4x)+(5)(-1)

[Usingidentity ]

=

=

=

(v)

[Usingidentity ]

=

=

(vi)



[Usingidentity ]

=

=

(vii)

[Usingidentity ]

=

3.Findthefollowingsquaresbyusingidentities:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Ans.(i)

[Usingidentity ]



=

(ii)

[Usingidentity ]

=

(iii)

[Usingidentity ]

=

(iv)

[Usingidentity ]

=

(v)

[Usingidentity ]

=



(vi)

[Usingidentity ]

=

4.Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Ans.(i)

[Usingidentity ]

=

(ii)



={(2x+5)+(2x-5)}{(2x+5)-(2x-5)}

[Usingidentity(a2-b2)=(a+b)(a-b)]

={4x}{2x+5-2x+5}

=(4x)(10)

=40x

(iii)

[Usingidentities and ]

=

=

=

(iv)

[Usingidentity ]

=

=

=

(v)



[Using

identity ]

=

=

=

(vi)

[Usingidentity ]

=

=

(vii)

=

[Usingidentity ]

=

=

5.Showthat:

(i)

(ii)



(iii)

(iv)

(v)

Ans.(i)L.H.S.=

[Usingidentity ]

=

=

= [ ]

=R.H.S.

(ii)L.H.S.=

[Usingidentity ]

=

=

= [ ]

(iii)L.H.S.=



[Usingidentity ]

=

=

=R.H.S.

(iv)L.H.S.=

= [Usingidentities

and ]

= =

=

=R.H.S.

(v)L.H.S.= =

[Usingidentity ]

=0

=R.H.S.

6.Usingidentities,evaluate:

(i)

(ii)



(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Ans.(i)

[Usingidentity ]

=4900+140+1=5041

(ii)

[Usingidentity ]

=10000–200+1=9801

(iii)

[Usingidentity ]

=10000+400+4=10404



(iv)

[Usingidentity ]

=1000000–4000+4=996004

(v)

[Usingidentity ]

=25+2.0+0.04=27.04

(vi)

=

=

[Usingidentity ]

=90000–9=89991

(vii) =

=

[Usingidentity ]

=6400–4=6396

(viii)



[Usingidentity ]

=64+14.4+0.81=79.21

(ix)10.05x9.5=

=

[Usingidentity ]

=100–0.25=99.75

7.Using find

(i)

(ii)

(iii)

(iv)

Ans.(i)

[Usingidentity ]

= =200

(ii)

[Usingidentity ]



= =0.08

(iii)

[Usingidentity ]

= =1800

(iv)

[Usingidentity ]

= =84.0=84

8.Using ,find

(i)

(ii)

(iii)

(iv)

Ans.(i) =

=

[Usingidentity ]

=

=10000+700+12=10712

(ii)

=



[Usingidentity ]

=

=25+1.5+0.02=26.52

(iii)

=

[Usingidentity ]

=

=10000+100–6=10094

(iv)

= [Usingidentity

]

=

=

=100–5+0.06=95.06




NCERTSolutions

CHAPTER-10

VisualisingSolidShapes(Ex.10.1)

1.Foreachofthegivensolid,thetwoviewsaregiven.Matchforeachsolidthe

correspondingtopandfrontviews.Thefirstoneisdoneforyou.

Ans.(a) (iii) (iv)

(b) (i) (v)

(c) (iv) (ii)

(d) (v) (iii)

(e) (ii) (i)



2.Foreachofthegivensolid,thethreeviewsaregiven.Identifyforeachsolidthe

correspondingtop,frontandsideviews.



Ans.(a) (i) Front

(ii) Side

(iii) Topview

(b) (i) Side

(ii) Front

(iii) Topview

(c) (i) Front

(ii) Side

(iii) Topview

(d) (i) Front

(ii) Side

(iii) Topview

3.Foreachgivensolid,identifythetopview,frontviewandsideview.



Ans.(a) (i) Topview(ii) Frontview(iii) Sideview

(b) (i) Sideview(ii) Frontview(iii) Topview

(c) (i) Topview(ii) Sideview(iii) Frontview

(d) (i) Sideview(ii) Frontview(iii) Topview

(e) (i) Frontview(ii) Topview(iii) Sideview

4.Drawthefrontview,sideviewandtopviewofthegivenobjects:



Ans.






NCERTSolutions

CHAPTER-10

VisualisingSolidShapes(Ex.10.2)

1.Canapolygonhaveforitsfaces:

(i)3triangles

(ii)4triangles

(iii)asquareandfourtriangles

Ans.(i)No,apolyhedroncannothave3trianglesforitsfaces.

(ii)Yes,apolyhedroncanhavefourtriangleswhichisknownaspyramidontriangularbase.

(iii)Yes,apolyhedronhasitsfacesasquareandfourtriangleswhichmakesapyramidon

squarebase.

2.Isitpossibletohaveapolyhedronwithanygivennumberoffaces?(Hint:Thinkofa

pyramid)

Ans.Itispossible,onlyifthenumberoffacesaregreaterthanorequalto4.

3.Whichareprismsamongthefollowing:

Ans.Figure(ii)unsharpenedpencilandfigure(iv)aboxareprisms.

4.(i)Howareprismsandcylindersalike?

(ii)Howarepyramidsandconesalike?



Ans.(i)Aprismbecomesacylinderasthenumberofsidesofitsbasebecomeslargerand

larger.

(ii)Apyramidbecomesaconeasthenumberofsidesofitsbasebecomeslargerandlarger.

5.Isasquareprismsameasacube?Explain.

Ans.Yes,asquareprismissameasacube,itcanalsobecalledacuboid.Acubeandasquare

prismarebothspecialtypesofarectangularprism.Asquareisjustaspecialtypeof

rectangle!Cubesarerectangularprismswhereallthreedimensions(length,widthand

height)havethesamemeasurement.

6.VerifyEuler’sformulaforthesesolids.

Ans.(i)Here,figure(i)contains7faces,10verticesand15edges.

UsingEucler’sformula,wesee

F+V–E=2

PuttingF=7,V=10andE=15,

F+V–E=2

7+10–15=2

17–15=2

2=2

L.H.S.=R.H.S.HenceEucler’sformulaverified.

(ii)Here,figure(ii)contains9faces,9verticesand16edges.


F+V–E=2

F+V–E=2

9+9–16=2

18–16=2

2=2



L.H.S.=R.H.S.

HenceEucler’sformulaverified.

7.UsingEuler’sformula,findtheunknown:

Faces ? 5 20

Vertices 6 ? 12

Edges 12 9 ?

Ans.Infirstcolumn,F=?,V=6andE=12


F+V–E=2

F+V–E=2

F+6–12=2

F–6=2

F=2+6=8

Hencethereare8faces.

Insecondcolumn,F=5,V=?andE=9


F+V–E=2

F+V–E=2

5+V–9=2

V–4=2

V=2+4=6

Hencethereare6vertices.

Inthirdcolumn,F=20,V=12andE=?


F+V–E=2

F+V–E=2

20+12–E=2

32–E=2

E=32–2=30

Hencethereare30edges.



8.Canapolyhedronhave10faces,20edgesand15vertices?

Ans.IfF=10,V=15andE=20.

Then,weknowUsingEucler’sformula,

F+V–E=2

L.H.S.=F+V–E

=10+15–20

=25–20

=5

R.H.S.=2

L.H.S. R.H.S.

Therefore,itdoesnotfollowEucler’sformula.

Sopolyhedroncannothave10faces,20edgesand15vertices.




NCERTSolutions

CHAPTER-11

Mensuration(Ex.11.1)

1.Asquareandarectangularfieldwithmeasurementsasgiveninthefigurehavethe

sameperimeter.

Whichfieldhasalargerarea?

Ans.Given:Thesideofasquare=60mandthelengthofrectangularfield=80m


Perimeterofrectangularfile=Perimeterofsquarefield

2(l+b)=4XSide

(80+b)=

(80+b)=120

b=120-80

b=40m

Hence,thebreadthoftherectangularfieldis40m.

Now,AreaofSquarefield=(Side)2

=(60)2sq.m=3600sq.m



AreaofRectangularfield=(length breadth)

=80 40sq.m=3200sq.m

Hence,areaofsquarefieldislarger.

2.Mrs.Kaushikhasasquareplotwiththemeasurementasshowninthefigure.She

wantstoconstructahouseinthemiddleoftheplot.Agardenisdevelopedaroundthe

house.FindthetotalcostofdevelopingagardenaroundthehouseattherateofRs.55

perm2.

Ans.Sideofasquareplot=25m

Areaofsquareplot=(Side)2=(25)2=625m2

LengthandBreadthofthehouseis20mand15mrespectively

Areaofthehouse=(lengthxbreadth)

=20 15=300m2

Areaofgarden=Areaofsquareplot–Areaofhouse

=(625–300)=325m2

CostofdevelopingthegardenaroundthehouseisRs.55

TotalCostofdevelopingthegardenofarea325sq.m=Rs.(55 325)

=Rs.17,875



3.Theshapeofagardenisrectangularinthemiddleandsemi-circularattheendsas

showninthediagram.Findtheareaandtheperimeterofthisgarden

[Lengthofrectangleis20–(3.5+3.5meters]

Ans.Given:Totallengthofthediagram=20m

Diameterofsemicircleonboththeends=7m

Radiusofsemicircle= = =3.5m

Lengthofrectangularfield=[Totallength-(radiusofsemicircleonbothside)]

={20–(3.5+3.5)}

=20–7=13m

Breadthoftherectangularfield=7m

Areaofrectangularfield=(lxb)

=(13 7) 91

Areaoftwosemicircles=

= =38.5m2

TotalAreaofgarden=(91+38.5) 129.5m2

Perimeteroftwosemicircles=

=22m



Hence,Perimeterofgarden=(22+13+13)m=48m

4. A flooring tile has the shape of a parallelogram whose base is 24 cm and the

correspondingheight is 10 cm.Howmany such tiles are required to cover a floor of

area1080 ?[Ifrequiredyoucansplit thetiles inwhateverwayyouwanttofillup

thecorners]

Ans.Baseofflooringtile=24cm 0.24m

heightofaflooringtile=10cm 0.10m[1cm=1/100m]

Now,Areaofflooringtile=Base Altitude

=0.24 0.10sq.m

=0.024m2

Numberoftilesrequiredtocoverthefloor=

=

=45000tiles

Hence45000tilesarerequiredtocoverthefloor.

5.Anantismovingaroundafewfoodpiecesofdifferentshapesscatteredonthefloor.

For which food-piece would the ant have to take a longer round? Remember,

circumferenceofacirclecanbeobtainedbyusingtheexpression where is

theradiusofthecircle.



Ans.(a)Radius=

=1.4cm

Circumferenceofsemicircle=

= 4.4cm

Totaldistancecoveredbytheant=(Circumferenceofsemicircle+Diameter)

=(4.4+2.8)cm

=7.2cm

(b)Diameterofsemicircle=2.8cm

Radius= =1.4cm


= 4.4cm

Totaldistancecoveredbytheant=(1.5+2.8+1.5+4.4) 10.2cm

(c)Diameterofsemicircle=2.8cm



Radius=

=1.4cm


= 4.4cm

Totaldistancecoveredbytheant=(2+2+4.4)=8.4cm

Henceforfigure(b)foodpiece,theantwouldtakealongerround.




NCERTSolutions

CHAPTER-11


1.Theshapeofthetopsurfaceofatableisatrapezium.Finditsareaifitsparallelsides

are1mand1.2mandperpendiculardistancebetweenthemis0.8m.

Ans.

ParallelsideofthetrapeziumAB=1m,CD=1.2mandheight ofthetrapezium(AM)=

0.8m

Areaoftopsurfaceofthetable= (sumofparallelsides)Height

= x(AB+CD)xAM

=

=

=0.88m2

Thussurfaceareaofthetableis0.88

2.Theareaofatrapeziumis34 andthelengthofoneoftheparallelsidesis10cm

anditsheightis4cm.



Findthelengthoftheotherparallelside.

Ans.Letthelengthoftheotherparallelsidebe=bcm

Lengthofoneparallelside=10amandheight =4cm

Areaoftrapezium= (sumofparallelsides)Height

=>34= (a+b)h

=>

=>

=>

=>

=>

=>

=>

Henceanotherrequiredparallelsideis7cm.

3.LengthofthefenceofatrapeziumshapedfieldABCDis120m.IfBC=48m,CD=17m

andAD=40m,findtheareaofthisfield.SideABisperpendiculartotheparallelsides

ADandBC.



Ans.Given:BC=48m,CD=17m,

AD=40mandperimeter=120m

PerimeteroftrapeziumABCD=Sumofallsides

120=(AB+BC+CD+DA)

120=AB+48+17+40

120=AB+105

(120–105)=AB

AB=15m

NowAreaofthefield= x(Sumofparallelsides)xHeight

= x(BC+AD)xAB

= x(48+40)x15m2

= x(88)x15m2

= (1320)m2

=660

HenceareaofthefieldABCDis660 .

4.Thediagonalofaquadrilateralshapedfieldis24mandtheperpendicularsdropped

onitfromtheremainingoppositeverticesare8mand13m.Findtheareaofthefield.



Ans.Hereh1=13m,h2=8mandAC=24m

AreaofquadrilateralABCD=Areaof ABC+Areaof ADC

=

=

= x24(13+8)m2

= x24(21)m2

=12x21m2

=252

Hencerequiredareaofthefieldis252

5.Thediagonalsofarhombusare7.5cmand12cm.Finditsarea.

Ans.Given:d1=7.5cmandd2=12cm

Areaofrhombus= x(Productofdigonals)

= x(d1xd2)

= x(7.5x12)cm2

=45

Henceareaofrhombusis45 .



6.Findtheareaofarhombuswhosesideis6cmandwhosealtitudeis4cm.Ifoneof

thediagonalsis8cmlong,findthelengthoftheotherdiagonal.

Ans.RhombusisalsoakindofParallelogram.

Areaofrhombus=Base Altitude

=(6 4)cm2

=24

AlsoAreaofrhombus= x(d1xd2)

24= x(8xd2)

24=4d2

cm=d2

d2=6cm

Hence,thelengthoftheotherdiagonalis6cm.

7.Thefloorofabuildingconsistsof3000tileswhicharerhombusshapedandeachof

itsdiagonalsare45cmand30cminlength.Findthetotalcostofpolishingthefloor,if

thecostper is`4.

Ans.Here,d1=45cmandd2=30cm

Areaofonetile= x(d1xd2)

= x(45x30)

= (1350)

=675

So,theareaofonetileis675cm2

Areaof3000tiles=675 3000cm2



=2025000

= m2

[1cm= m,Herecm2=Cmxcm= x m2]

=202.50

Costofpolishingthefloorpersq.meter=Rs.4

Costofpolishingthefloorper202.50sq.meter=Rs.4 202.50=Rs.810

HencethetotalcostofpolishingthefloorisRs.810.

8.Mohanwantstobuyatrapeziumshapedfield.Itssidealongtheriverisparallelto

andtwicethesidealongtheroad.Iftheareaofthisfieldis10500m2andthe

perpendiculardistancebetweenthetwoparallelsidesis100m,findthelengthofthe

sidealongtheriver.

Ans.

Given:Perpendiculardistance(h)AM=100m

Areaofthetrapeziumshapedfield=10500

LetsidealongtheroadAB= m

sidealongtheriverCD= m

Areaofthetrapeziumfield= x(AB+CD)xAM



10500=

m

Hencethesidealongtheriver= =(2 70)=140m.

9.Topsurfaceofaraisedplatformisintheshapeofaregularoctagonasshowninthe

figure.Findtheareaoftheoctagonalsurface.

Ans.

Given:Octagonhavingeightequalsides,each5m.

Construction:JoinHCandGDItwilldividetheoctagonintotwoequaltrapezium.

AndAMisperpendicularonHCandENisperpendicularonGD

Areaoftrap.ABCD=Areaoftrap.GDFE....................................(1)

Areaoftwotrapeziums=(areaoftrap.ABCH+areaoftrap.GDFE)

=(areaoftrap.ABCH+areaoftrap.ABCH)(bystatement1).

=(2xareaoftrap.ABCH)



=(2x x(sumofparallelsides)xheight)

=(2x x(AB+CH)xAM)

=(11+5)x4m2

=(16)x4

=64

AndAreaofrectangle(HCDG)=length breadth

=HCxHG=11 5=55

Totalareaofoctagon=Areaof2Trapezium+AreaofRectangle

=64m2+55m2=119

10.Thereisapentagonalshapedparkasshowninthefigure.ForfindingitsareaJyoti

andKavitadivideditintwodifferentways.

Findtheareaofthisparkusingbothways.Canyousuggestsomeotherwayoffinding

itsarea?

Ans.Firstway:ByJyoti’sdiagram,

Areaofpentagon=AreaoftrapeziumABCP+AreaoftrapeziumAEDP

= (AP+BC)xCP+ (ED+AP) DP

= (30+15)xCP+ (15+30) DP



= (30+15)(CP+DP)

= 45 CD

=337.5m2

Secondway:ByKavita’sdiagram

Here,aperpendicularAMdrawntoBE.AM=30–15=15m

Areaofpentagon=Areaof ABE+AreaofsquareBCDE

={ 15 15}+(15 15)m2

=(112.5+225.0)m2

=337.5m2

Hencetotalareaofpentagonshapedpark=337.5 .

11.Diagramoftheadjacentpictureframehasouterdimensions=24cm 28cmand

innerdimensions16cm 20cm.Findtheareaofeachsectionoftheframe,ifthewidth

ofeachsectionissame.



Ans.Heretwoofgivenfigures(I)and(II)aresimilarindimensions.Andalsofigures(III)and

(IV)aresimilarindimensions.

Areaoffigure(I)=Areaoftrapezium

= =

= =96

AlsoAreaoffigure(II)=96cm2

NowAreaoffigure(III)

Areaoftrapezium=

=

=

=80

AlsoAreaoffigure(IV)=80




NCERTSolutions

CHAPTER-11


1.Therearetwocuboidalboxesasshownintheadjoiningfigure.Whichboxrequires

thelesseramountofmaterialtomake?

Sol.(a)Lengthofcuboidalbox =60cm

Breadthofcuboidalbox =40cm

Heightofcuboidalbox =50cm

Totalsurfaceareaofcuboidalbox=

=2(60 40+40 50+50 60)

=2(2400+2000+3000)

=2 7400

=14800

(b)Lengthofthecubeis50cm

Totalsurfaceareaofcuboidalbox=

=6(50)2

=6(2500)

=15000



Thus,thecuboidalbox(a)requiresthelesseramountofmateral.

2.Asuitcasewithmeasures80cm 48cm 24cmistobecoveredwithatarpaulin

cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such

suitcases?

Sol.Given:Lengthofsuitcasebox =80cm,Breadthofsuitcasebox =48cm

AndHeightofcuboidalbox =24cm

Totalsurfaceareaofsuitcasebox=

=2(80 48+48 24+24 80)

=2(3840+1152+1920)

=2 6912=13824

AreaofTarpaulincloth=Surfaceareaofsuitcase

=13824

=144cm

Requiredtarpaulinfor100suitcases=(144 100)cm

=14400cm

=144m[1cm= m]

Thus,144mtarpaulinclothrequiredtocover100suitcases.

3.Findthesideofacubewhosesurfaceareaid600 .



Sol.HereSurfaceareaofcube=600cm2

=600cm2

=100cm2

cm

=10cm

Hencethesideofcubeis10cm

4.Ruksharpaintedtheoutsideofthecabinetofmeasure1m 2m 1.5m.Howmuch

surfaceareadidshecoverifshepaintedallexceptthebottomofthecabinet?

Sol.Lengthofcabinet =2m

Breadthofcabinet =1m

Heightofcabinet =1.5m

Surfaceareaofcabinet=(AreaofBaseofcabinet(Cuboid)+Areaoffourwalls)

=

={2 1+2(1+2)1.5}

=2+2(3)1.5

=2+6(1.5)

=(2+9.0)

=11

Hencerequiredsurfaceareaofcabinetis11 .

5.Daniel is paining thewalls and ceiling of a cuboidal hallwith length, breadth and

heightof 15m, 10mand7mrespectively. Fromeach canofpaint 100 of area is



painted.Howmanycansofpaintwillsheneedtopainttheroom?

Sol.Lengthofwall =15m

Breadthofwall =10m

Heightofwall =7m

TotalSurfaceareaofclassroom=(AreaofBaseofceiling(Cuboid)+Areaoffourwalls)

=

=(15 10+2(10+15)(7))

=(150+2(25)(7))

=(150+350)

=500

Areaofonecanis100m2

NowRequirednumberofcans= =5cans

Hence5cansarerequiredtopainttheroom.

6.Describehowthetwofiguresbelowarealikeandhowtheyaredifferent.Whichbox

haslargerlateralsurfacearea?

Sol.Diameterofcylinder=7cm

Radiusofcylinder = cm

Heightofcylinder =7cm

Lateralsurfaceareaofcylinder=



=

=154cm2

Nowlateralsurfaceareaofcube=

=(4 49)

=196

Hencethecubehaslargerlateralsurfacearea.

7.Aclosedcylindricaltankofradius7mandheight3mismadefromasheetofmetal.

Howmuchsheetofmetalisrequired?

Sol.Radiusofcylindricaltank =7m

Heightofcylindricaltank =3m

Totalsurfaceareaofcylindricaltank=(Curvedsurfacearea+Areaofupperend

(circle)+AreaofLower(circle)end)

=

=

=

=

=44 10

=440

Hence440 metalsheetisrequired.



8.Thelateralsurfaceareaofahollowcylinderis4224 .Itiscutalongitsheightand

formedarectangularsheetofwidth33cm.Findtheperimeterofrectangularsheet?

Sol.Lateralsurfaceareaofhollowcylinder=4224

Heightofhollowcylinder=33cm

Curvedsurfaceareaofhollowcylinder=

4224=

= cm

NowLengthofrectangularsheet=

=128cm

Perimeterofrectangularsheet=

=2(128+33)

=2x161

=322cm

Henceperimeterofrectangularsheetis322cm.

9.Aroadrollertakes750completerevolutionstomoveonceovertolevelaroad.Find

theareaoftheroadifthediameterofaroadrolleris84cmandlength1m.



Sol.Diameterofroadroller=84cm

Radiusofroadroller

=42cm

Lengthofroadroller =1m=100cm

Curvedsurfaceareaofroadroller=

=

=26400cm2

Areacoveredbyroadrollerin750revolutions=26400 750

=1,98,00,000

=1980m2[ 1 =10,000 ]

Thus,theareaoftheroadis1980 .

10. A company packages its milk powder in cylindrical container whose base has a

diameterof14cmandheight20cm.Companyplacesalabelaroundthesurfaceofthe

container(asshowninfigure).Ifthelabelisplaced2cmfromtopandbottom,whatis

theareaofthelabel?

Sol.Diameterofcylindricalcontainer=14cm



Radiusofcylindricalcontainer =7cm

Heightofcylindricalcontainer=20cm

Heightofthelabel =(20–2–2)

=16cm

Curvedsurfaceareaoflabel=

=

=704cm2

Hencetheareaofthelabelof704cm2.




NCERTSolutions

CHAPTER-11


1.Givenacylindricaltank,inwhichsituationwillyoufindsurfaceareaandinwhich

situationvolume.

(a)Tofindhowmuchitcanhold.

(b)Numberofcementbagsrequiredtoplasterit.

(c)Tofindthenumberofsmallertanksthatcanbefilledwithwaterfromit.

Ans.(a)Volume(itismeasureoftheamountofspaceinsideofasolildfigures)

(b)Surfacearea(theoutsidepartoruppermostlayerofthesoildfigures)

(c)Volume

2.DiameterofcylinderAis7cmandtheheightis14cm.DiameterofcylinderBis14cm

andheight is 7 cm.Without doing any calculations can you suggestwhose volume is

greater? Verify it by finding the volume of both the cylinders. Check whether the

cylinderwithgreatervolumealsohasgreatersurfacearea.

Ans. Yes,we can say that volumeof cylinderB is greater, Because radius of cylinderB is

greaterthanthatofcylinderA.

DiameterofcylinderA=7cm

Radius(r)ofcylinderA= cmandHeight(h)ofcylinderA=14cm



VolumeofcylinderA=

=

=539

NowDiameterofcylinderB=14cm

RadiusofcylinderB= =7cmandHeightofcylinderB=7cm

VolumeofcylinderA=

= cm3

=1078

SincethecylinderAandcylinderBisopenfromupperendthenitwillexcludefromthe

Totalsurfacearea

TotalsurfaceareaofcylinderA=(Areaoflowerendcircle+curvedsurfaceareaofcyliner)

=( + )

=

= x ( +2x14)

=11( +28)

=11(31.5)cm2=346.5cm2

TotalsurfaceareaofcylinderB=

= x7(2x7+7)

=22 (14+7)



=22 21=462

Yes,cylinderwithgreatervolumealsohasgreatersurfacearea.

3.Findtheheightofacuboidwhosebaseareais180 andvolumeis900 ?

Ans.LettheLength,breadthandheightofthecuboidbel,b,h.

BaseofthecuboidisformaRecatangleso,thattheBase(Reactangle)Areais(Lengthx

Breadth)

Baseareaofcuboid=180

LxB=180cm2.......................................(1)

Volumeofcuboid=

Volumeofcuboid=900

=900(Fromeq.1)

(180)h=900

=5m

Hencetheheightofcuboidis5m.

4.Acuboidisofdimensions60cm 54cm 30cm.Howmanysmallcubeswithside6

cmcanbeplacedinthegivencuboid?

Ans.Given:Lengthofcuboid =60cm,

Breadthofcuboid =54cmand

Heightofcuboid =30cm



Weknowthat,Volumeofcuboid=

=(60 54 30)

AndVolumeofcube=(Side)3

=6 6 6

Numberofsmallcubes=

=450

Hencerequirednumberofsmallcubesare450.

5.Findtheheightofthecylinderwhosevolumeif1.54 anddiameterofthebaseis

140cm.

Ans.Given:Volumeofcylinder=1.54 andDiameterofcylinder=140cm

Radius = =70cm

= m=0.7m[

Volumeofcylinder=

1.54=

=1m

Henceheightofthecylinderis1m.



6.Amilktankisintheformofcylinderwhoseradiusis1.5mandlengthis7m.Findthe

quantityofmilkinlitersthatcanbestoredinthetank.

Ans.Given:Radiusofcylindricaltank =1.5m

Heightofcylindricaltank =7m

Volumeofcylindricaltank=

=

=49.5m3

=49.5 1000liters[ 1 =1000liters]

=49500liters

Hencerequiredquantityofmilkis49500litersthatcanbestoredinthetank.

7.Ifeachedgeofacubeisdoubled,

(i)howmanytimeswillitssurfaceareaincrease?

(ii)howmanytimeswillitsvolumeincrease?

Ans.Let unitsbetheedgeofthecube.

Surfacearea= andVolumeofthecube=



Whenitsedgeisdoubled=

(i)Surfacearea=6(side)2

= =

=

=4(Surfacearea)

Thesurfaceareaofthenewcubewillbe4timesthatoftheoriginalcube.

(ii)Volumeofcube(V)=

Whenedgeofcubeisdoubled= ,then

Volumeofcube(V’)=

V’=8(Volumeofcube)

Hencevolumewillincrease8times.

8.Waterispouringintoacuboidalreservoirattherateof60litersperminute.Ifthe

volumeofreservoiris108 ,findthenumberofhoursitwilltaketofillthereservoir.

Ans.Volumeofreservoir=108

=108x1000litres

=108000litres

Sincewaterispouringintoreservoir@60litresperminuteandin

Timetakentofillthereservoir= x hours

=30hours

Hence,30hoursitwilltaketofillthereservoir.




NCERTSolutions

CHAPTER-12

ExponentsandPowers(Ex.12.1)

1.Evaluate:

(i) (ii) (iii)

Ans.(i) =

=

(ii)

=

(iii) =

= =32



2.Simplifyandexpresstheresultinpowernotationwithpositiveexponent:

(i)

(ii)

(iii)

(iv)

(v)

Ans.(i) =

=

(ii)

=

(iii)

=



=

=

(iv)

= = =

=

(v)

= =

3.Findthevalueof:

(i)

(ii)

(iii)

(iv)

(v)



Ans.

(i) =

= =

=

(ii)

= =

=

=

(iii)

=

= =4+9+16=29

(iv)



=

(v)

=

=

4.Evaluate:

(i) (ii)

Ans.(i)

=

=

(ii)

=

5.Findthevalueof forwhich

Ans.



Comparingexponentsbothsides,weget

6.Evaluate:

(i) (ii)

Ans.

(i)

=

(ii)

=

= =

=



7.Simplify:

(i)

(ii)

Ans.(i)

= =

(ii)

=



=

= =

=1 1 3125

=3125




NCERTSolutions

CHAPTER-12

ExponentsandPowers(Ex.12.2)

1.Expressthefollowingnumbersinstandardform:

(i)0.0000000000085

(ii)0.00000000000942

(iii)6020000000000000

(iv)0.00000000837

(v)31860000000

Ans.(i)0.0000000000085

=0.0000000000085 =

(ii)0.00000000000942

=0.00000000000942 =

(iii)6020000000000000

=6020000000000000 =

(iv)0.00000000837

=0.00000000837 =

(v)31860000000



=31860000000 =

2.Expressthefollowingnumbersinusualform:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Ans.(i)

(ii) 4.5 10000=45000

(iii) =0.00000003

(iv) =1000100000

(v) =5.8x1000000000000

=5800000000000

(vi) =3.61492 1000000

=3614920

3.Expressthenumberappearinginthefollowingstatementsinstandardform:

(i)1micronisequalto m.



(ii)Chargeofanelectronis0.000,000,000,000,000,000,16coulomb.

(iii)Sizeofabacteriais0.0000005m.

(iv)Sizeofaplantcellis

0.00001275m.

(v)Thicknessifathickpaperis0.07mm.

Ans.(i)1micron

= m

(ii)Chargeofanelectronis

0.00000000000000000016coulombs.

=

= coulomb

(iii)Sizeofbacteria=0.0000005

m

(iv)Sizeofaplantcellis0.00001275m

=0.00001275 = m

(v)Thicknessofathickpaper=0.07mm

= mm= mm

4.Inastackthereare5bookseachofthickness20mmand5papersheetseachof

thickness0.016mm.Whatisthetotalthicknessofthestack?



Ans.Thicknessofonebook=20mm

Thicknessof5books=20 5=100mm

Thicknessofonepaper=0.016mm

Thicknessof5papers=0.016 5

=0.08mm

Totalthicknessofastack=100+0.08

=100.08mm

=100.08

mm




NCERTSolutions

CHAPTER-13

DirectandInverseProportions(Ex.13.1)

1.Followingarethecarparkingchargesneararailwaystationupto:

4hoursRs.60

8hoursRs.100

12hoursRs.140

24hoursRs.180

Checkiftheparkingchargesareindirectproportiontotheparkingtime.

Ans.Chargesperhour:

=Rs.15

=Rs.12.50

=Rs.11.67

=Rs.7.50

Here,thechargesperhourarenotsame,i.e.,



Therefore,theparkingchargesarenotindirectproportiontotheparkingtime.

2.Amixtureofpaintispreparedbymixing1partofredpigmentswith8partsofbase.

Inthefollowingtable,findthepartsofbasethatneedtobeadded.

Ans.Lettheratioofpartsofredpigmentandpartsofbasebe

Here

= (say)

When

When

When

When



3.InQuestion2above,if1partofaredpigmentrequires75mLofbase,howmuchred

pigmentshouldwemixwith1800mLofbase?

Ans.Letthepartsofredpigmentmixwith1800mLbasebe

Sinceitisindirectproportion.

parts

Hencewithbase1800mL,24partsredpigmentshouldbemixed.

4.Amachineinasoftdrinkfactoryfills840bottlesinsixhours.Howmanybottleswill

itfillinfivehours?

Ans.Letthenumberofbottlesfilledinfivehoursbe

Hours 6 5

Bottles 840 x

Hereratioofhoursandbottlesareindirectproportion.



bottles

Hencemachinewillfill700bottlesinfivehours.

5.Aphotographofabacteriaenlarged50,000timesattainsalengthof5cmasshownin

thediagram.Whatistheactuallengthofthebacteria?Ifthephotographisenlarged

20,000timesonly,whatwouldbeitsenlargedlength?

Ans.LetActuallengthofbacteriabe'a'

Itisenlarged50,000timesso50000xa=5cm

Actuallengthofbacteria

= cm= cm

Letenlargedlengthofbacteriabe

Herelengthandenlargedlengthofbacteriaareindirectproportion.



=2cm

Hencetheenlargedlengthofbacteriais2cm.

6.Inamodelofaship,themastis9cmhigh,whilethemastoftheactualshipis12m

high.Ifthelengthoftheshipis28m,howlongisthemodelship?

Ans.Letthelengthofmodelshipbe

Herelengthofmastandactuallengthofshipareindirectproportion.

=21cm

Hencelengthofthemodelshipis21cm.

7.Suppose2kgofsugarcontains9 crystals.Howmanysugarcrystalsaretherein

(i)5kgofsugar?(ii)1.2kgofsugar?



Ans.(i)Letsugarcrystalsbe

Hereweightofsugarandnumberofcrystalsareindirectproportion.

=

Hencethenumberofsugarcrystalsis

(ii)Letsugarcrystalsbe

Hereweightofsugarandnumberofcrystalsareindirectproportion.

=

Hencethenumberofsugarcrystalsis



8.Rashmihasaroadmapwithascaleof1cmrepresenting18km.Shedrivesonaroad

for72km.Whatwouldbeherdistancecoveredinthemap?

Ans.Letdistancecoveredinthemapbe

Hereactualdistanceanddistancecoveredinthemapareindirectproportion.

=4cm

Hencedistancecoveredinthemapis4cm.

9.A5m60cmhighverticalpolecastsashadow3m20cmlong.Findatthesametime

(i)thelengthoftheshadowcastbyanotherpole10m50cmhigh(ii)theheightofapole

whichcastsashadow5mlong.

Ans.Hereheightofthepoleandlengthoftheshadowareindirectproportion.

And1m=100cm

5m60cm=5 100+60=560cm

3m20cm=3 100+20=320cm

10m50cm=10 100+50=1050cm

5m=5 100=500cm

(i)Letthelengthoftheshadowofanotherpolebe



=600cm=6m

Hencelengthoftheshadowofanotherpoleis6m.

(ii)Lettheheightofthepolebe

=875cm=8m75cm

Henceheightofthepoleis8m75cm.

10.Aloadedtrucktravels14kmin25minutes.Ifthespeedremainsthesame,howfar

canittravelin5hours?

Ans.Letdistancecoveredin5hoursbe km.



1hour=60minutes

5hours=5 60=300minutes

Heredistancecoveredandtimeareindirectproportion.

=168km




NCERTSolutions

CHAPTER-13

DirectandInverseProportions(Ex.13.2)

1.Whichofthefollowingareininverseproportion:

(i)Thenumberofworkersonajobandthetimetocompletethejob.

(ii)Thetimetakenforajourneyandthedistancetravelledinauniformspeed.

(iii)Areaofcultivatedlandandthecropharvested.

(iv)Thetimetakenforafixedjourneyandthespeedofthevehicle.

(v)Thepopulationofacountryandtheareaoflandperperson.

Ans.(i)Thenumberofworkersandthetimetocompletethejobisininverseproportion

becauselessworkerswilltakemoretimetocompleteaworkandmoreworkerswilltakeless

timetocompletethesamework.

(ii)Timeanddistancecoveredindirectproportion.

(iii)Itisadirectproportionbecausemoreareaofcultivatedlandwillyieldmorecrops.

(iv)Timeandspeedareinverseproportionbecauseiftimeisless,speedismore.

(v)Itisainverseproportion.Ifthepopulationofacountryincreases,theareaoflandper

persondecreases.

2.InaTelevisiongameshow,theprizemoneyofRs.1,00,000istobedividedequally

amongstthewinners.Completethefollowingtableandfindwhethertheprizemoney

giventoanindividualwinnerisdirectlyorinverselyproportionaltothenumberof

winners:

Ans.Herenumberofwinnersandprizemoneyareininverseproportionbecausewinners

areincreasing,prizemoneyisdecreasing.



Whenthenumberofwinnersare4,eachwinnerwillget= =Rs.25,000





3.Rehmanismakingawheelusingspokes.Hewantstofixequalspokesinsuchaway

thattheanglesbetweenanypairofconsecutivespokesareequal.Helphimby

completingthefollowingtable:

(i)Arethenumberofspokesandtheanglesformedbetweenthepairsofconsecutive

spokesininverseproportion?

(ii)Calculatetheanglebetweenapairofconsecutivespokesonawheelwith15spokes.

(iii)Howmanyspokeswouldbeneeded,iftheanglebetweenapairofconsecutive

spokesis



Ans.Herethenumberofspokesareincreasingandtheanglebetweenapairofconsecutive

spokesisdecreasing.So,itisainverseproportionandangleatthecentreofacircleis

Whenthenumberofspokesis8,thenanglebetweenapairofconsecutivespokes=



(i)Yes,thenumberofspokesandtheanglesformedbetweenapairofconsecutivespokesis

ininverseproportion.

(ii)Whenthenumberofspokesis15,thenanglebetweenapairofconsecutivespokes=

.

(iii)Thenumberofspokeswouldbeneeded=

4.Ifaboxofsweetsisdividedamong24children,theywillget5sweetseach.Howmany

wouldeachget,ifthenumberofthechildrenisreducedby4?

Ans. Eachchildgets=5sweets

24childrenwillget24 5=120sweets



Totalnumberofsweets=120

Ifthenumberofchildrenisreducedby4,thenchildrenleft=24–4=20

Noweachchildwillgetsweets=

=6sweets

5.Afarmerhasenoughfoodtofeed20animalsinhiscattlefor6days.Howlongwould

thefoodlastiftherewere10moreanimalsinhiscattle?

Ans.Letthenumberofdaysbe

Totalnumberofanimals=20+10=30

Herethenumberofanimalsandthenumberofdaysareininverseproportion.

=4

Hencethefoodwilllastforfourdays.

6.Acontractorestimatesthat3personscouldrewireJasminder’shousein4days.If,he

uses4personsinsteadofthree,howlongshouldtheytaketocompletethejob?

Ans.Lettimetakentocompletethejobbe

Herethenumberofpersonsandthenumberofdaysareininverseproportion.



=3days

Hencetheywillcompletethejobin3days.

7.Abatchofbottleswaspackedin25boxeswith12bottlesineachbox.Ifthesame

batchispackedusing20bottlesineachbox,howmanyboxeswouldbefilled?

Ans.Letthenumberofboxesbe

Herethenumberofbottlesandthenumberofboxesareininverseproportion.

=15

Hence15boxeswouldbefilled.

8.Afactoryrequires42machinestoproduceagivennumberofarticlesin63days.How

manymachineswouldberequiredtoproducethesamenumberofarticlesin54days?



Ans.Letthenumberofmachinesrequiredbe

Herethenumberofmachinesandthenumberofdaysareininverseproportion.

=49

Hence49machineswouldberequired.

9.Acartakes2hourstoreachadestinationbytravellingatthespeedof60km/hr.How

longwillittakewhenthecartravelsatthespeedof80km/hr?

Ans.Letthenumberofhoursbe

Herethespeedofcarandtimeareininverseproportion.

= hrs.

Hencethecarwilltake hours



toreachitsdestination.

10.Twopersonscouldfitnewwindowsinahousein3days.

(i)Oneofthepersonsfellillbeforetheworkstarted.Howlongwouldthejobtakenow?

(ii)Howmanypersonswouldbeneededtofitthewindowsinoneday?

Ans.(i)Letthenumberofdaysbe


=6days

(ii)Letthenumberofpersonsbe


=6persons



11.Aschoolhas8periodsadayeachof45minutesduration.Howlongwouldeach

periodbe,iftheschoolhas9periodsaday,assumingthenumberofschoolhourstobe

thesame?

Ans.Letthedurationofeachperiodbe

Herethenumberofperiodsandthedurationofperiodsareininverseproportion.

=40minutes

Hencedurationofeachperiodwouldbe40minutes.




NCERTSolutions

CHAPTER-14

Factorisation(Ex.14.1)

1.Findthecommonfactorsofthegiventerms.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Ans.(i)

Hence,thecommonfactorsare2,2and3=2 2 3=12

(ii)

Hence,thecommonfactorsare2and =

(iii)



Hence,thecommonfactorsare

(iv)

Hence,thecommonfactoris1.

(v)

Hence,thecommonfactorsare

(vi)

Hencethecommonfactorsare

(vii)


(viii)




2.Factorizethefollowingexpressions.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Ans.

(i) =

Takingcommonfactorsfromeachterm,

=

=

(ii) =


=

=



(iii)


=

=

(iv)


=

=

(v)


=

=

(vi) changetheimagewithimage_3310_1


=

=

(vii)




=

=

(viii)


=

=4a(-a+b-c)

(ix)


=

=

(x)


=

=



3.Factorize:

(i)

(ii)

(iii)

(iv)

(v)

Ans.(i)

=

(ii)

=

(iii) =

=

(iv)

=

=

(v)

=

=

=




NCERTSolutions

CHAPTER-14


1.Factorizethefollowingexpressions:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

[Hint:Expand first]

(viii)

Ans.(i)

Usingidentity ,

Here and

=

(ii)

Usingidentity ,



Here and

(iii)

Usingidentity ,here

(iv)

Usingidentity ,here

(v)

Usingidentity ,here

(vi)

Usingidentity ,here

(vii)

=

=



=

=

(viii)

=

2.Factorize:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Ans.(i)

=

(ii)



=

(iii) =

=

(iv)

=

=

(v)

=

=(2l)(2m)=4lm

(vi)

=

(vii)

=

(viii)

=



=

=

=

=

3.Factorizetheexpressions:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Ans.(i) =

(ii) =

(iii) =

(iv)



=

=

(v) =

=

(vi) =

(vii)

=

=

=

(viii)

=

=

(ix)

=

=

=

4.Factorize:

(i) (ii)



(iii) (iv)

(v)

Ans.(i)

=

=

(ii)

=

=

=

(iii)

=

=

=(x-y-z)(x+y+z)[x2+(y+z)2]

(iv)

=

=[x-(x-z)][x+(x-z)][x2+(x-z)2]



=[x-x+z][x+x-z][x2+x2-2xz+z2]

=z(2x-z)(2x2-2xz+z2)

(v) =

=

=

=

5.Factorizethefollowingexpressions:

(i)

(ii)

(iii)

Ans.

(i)

=

=

=

(ii)

=



=

=

(iii)

=

=

=




NCERTSolutions

CHAPTER-14


1.Carryoutthefollowingdivisions:

(i)

(ii)

(iii)

(iv)

(v)

Ans.(i)

=

=

(ii)

=

=

(iii)



=

=

=

(iv)

=

=

(v)

=

=

2.Dividethegivenpolynomialbythegivenmonomial:

(i)

(ii)



(iii)

(iv)

(v)

Ans.(i)

= = =

(ii)

= =

(iii)

=

=

=

(iv)



=

= =

=

(v)

= =

3.Workoutthefollowingdivisions:

(i)

(ii)

(iii)

(iv)

(v)

Ans.(i)

= =



(ii)

=

(iii)

= =

(iv)

= =

(v)

=

=

4.Divideasdirected:



(i)

(ii)

(iii)

(iv)

(v)

Ans.(i)

=

= =

(iii)

=

=



(iv)

=

(v)

=

5.Factorizetheexpressionsanddividethemasdirected:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)



Ans.(i)

=

=

=

=

(ii)

=

=

=(m-16)

(iii)



=

=

=

=

(iv)

=

=

=

(v)

=

=



(vi)

=

=

=

(vii)

=

= changetheimagewithimage_3312_1

= changetheimagewith

image_3312_2

=




NCERTSolutions

CHAPTER-14


Findandcorrecttheerrorsinthefollowingmathematicalstatements:

1.

Ans.L.H.S.= R.H.S.

Hencethecorrectmathematicalstatementis

2.

Ans.L.H.S.= R.H.S.


3.

Ans.L.H.S.= R.H.S.


4.

Ans.L.H.S.= R.H.S.


5.

Ans.L.H.S.= R.H.S.




6.

Ans.L.H.S.= R.H.S.


7.

Ans.L.H.S.= R.H.S.


8.

Ans.L.H.S.= R.H.S.


9.

Ans.

L.H.S.= .

Hencethecorrectmathematicalstatementsis

10.Substituting in:

(a) gives



(b) gives

(c) gives

Ans.(a)L.H.S.=

Putting ingivenexpression,

= R.H.S.

Hence gives

(b)L.H.S.=


= R.H.S.

Hence gives

(c)L.H.S.=


= R.H.S.

Hence gives

11.

Ans.L.H.S.=

= R.H.S.

Hencethecorrectstatementis



12.

Ans.L.H.S.=

=


13.

Ans.L.H.S.=

=

= R.H.S.


14.(a+4)(a+2)=a2+8

Ans.L.H.S.=

= R.H.S.


15.

Ans.L.H.S.=

= R.H.S.




16.

Ans.L.H.S.= R.H.S.


17.

Ans.L.H.S.=

= R.H.S.

Hencethecorrectstatementis .

18.

Ans.L.H.S.= R.H.S.


19.

Ans.L.H.S.= R.H.S.




20.

Ans.L.H.S.= R.H.S.


21.

Ans.L.H.S.= R.H.S.





NCERTSolutions

CHAPTER-15

IntroductiontoGraphs(Ex.15.1)

1.Thefollowinggraphshowsthetemperatureofapatientinahospital,recordedevery

hour:

(a)Whatwasthepatient’stemperatureat1p.m.?

(b)Whenwasthepatient’stemperature38.5°C?

(c)Thepatient’stemperaturewasthesametwotimesduringtheperiodgiven.What

werethesetwotimes?

(d)Whatwasthetemperatureat1.30p.m.?Howdidyouarriveatyouranswer?

(e)Duringwhichperiodsdidthepatients’temperatureshowedanupwardtrend?

Ans.(a)Thepatient’stemperaturewas36.5oCat1p.m.

(b)Thepatient’stemperaturewas38.5oCat12noon.

(c)Thepatient’stemperaturewassameat1p.m.and2p.m.



(d)Thetemperatureat1.30p.m.is36.5oC.Thepointbetween1p.m.and2p.m., axisis

equidistantfromthetwopointsshowing1p.m.and2p.m.So,itrepresents01.30p.m.

Similarly,thepointon axis,between36oCand37oCwillrepresent36.5oC.

(e)Thepatient’stemperatureshowedanupwardtrendfrom9a.m.to11a.m.,11a.m.to12

noonand2p.m.to3p.m.

2.Thefollowinglinegraphshowstheyearlysalesfiguresforamanufacturing

company.

(a)Whatwerethesalesin(i)2002(ii)2006?

(b)Whatwerethesalesin(i)2003(ii)2005?

(c)Computethedifferencebetweenthesalesin2002and2006.

(d)Inwhichyearwastherethegreatestdifferencebetweenthesalesascompared

toitspreviousyear?

Ans.(a)Thesalesin:(i)2002wasRs.4croresand(ii)2006wasRs.8crores.

(b)Thesalesin:(i)2003wasRs.7crores(ii)2005wasRs.10crores.

(c)Thedifferenceofsalesin2002and2006=Rs.8crores–Rs.4crores=Rs.4crores

(d)Intheyear2005,therewasthegreatestdifferencebetweenthesalesascomparedtoits



previousyear,whichis(Rs.10crores–Rs.6crores)=Rs.4crores.

3.ForanexperimentinBotany,twodifferentplants,plantAandplantBwere

grownundersimilarlaboratoryconditions.Theirheightsweremeasuredattheendof

eachweekfor3weeks.Theresultsareshownbythefollowinggraph.

(a)HowhighwasPlantAafter(i)2weeks(ii)3weeks?

(b)HowhighwasPlantBafter(i)2weeks(ii)3weeks?

(c)HowmuchdidPlantAgrowduringthe3rdweek?

(d)HowmuchdidPlantBgrowfromtheendofthe2ndweektotheendofthe3rd

week?

(e)DuringwhichweekdidPlantAgrowmost?

(f)DuringwhichweekdidPlantBgrowleast?

(g)Werethetwoplantsofthesameheightduringanyweekshownhere?Specify.

Ans.(a)(i)TheplantAwas7cmhighafter2weeksand

(ii)after3weeksitwas9cmhigh.

(b)(i)PlantBwasalso7cmhighafter2weeksand

(ii)after3weeksitwas10cmhigh.

(c)PlantAgrew=9cm–7cm=2cmduring3rdweek.



(d)PlantBgrewduringendofthe2ndweektotheendofthe3rdweek

=10cm–7cm=3cm.

(e)PlantAgrewthehighestduringsecondweek.

(f)PlantBgrewtheleastduringfirstweek.

(g)Attheendofthesecondweek,plantAandBwereofthesameheight.

4.Thefollowinggraphshowsthetemperatureforecastandtheactualtemperaturefor

eachdayofaweek.

(a)Onwhichdayswastheforecasttemperaturethesameastheactualtemperature?

(b)Whatwasthemaximumforecasttemperatureduringtheweek?

(c)Whatwastheminimumactualtemperatureduringtheweek?

(d)Onwhichdaydidtheactualtemperaturedifferthemostfromtheforecast

temperature?

Ans.(a)OnTuesday,FridayandSunday,theforecasttemperaturewassameastheactual

temperature.

(b)Themaximumforecasttemperaturewas35oC.

(c)Theminimumactualtemperaturewas15oC.

(d)TheactualtemperaturedifferedthemostfromtheforecasttemperatureonThursday.



5.Usethetablesbelowtodrawlineargraphs.

(a)Thenumberofdaysahillsidecityreceivedsnowindifferentyears.

(b)Population(inthousands)ofmenandwomeninavillageindifferentyears.

Ans.(a)

(b)



6.Acourier-personcyclesfromatowntoaneighbouringsuburbanareatodelivera

parceltoamerchant.Hisdistancefromthetownatdifferenttimesisshownbythe

followinggraph.

(a)Whatisthescaletakenforthetimeaxis?

(b)Howmuchtimedidthepersontakeforthetravel?

(c)Howfaristheplaceofthemerchantfromthetown?

(d)Didthepersonstoponhisway?Explain.



(e)Duringwhichperioddidheridefastest?

Ans.(a)4units=1hour.

(b)Thepersontook hoursforthetravel.

(c)Itwas22kmfarfromthetown.

(d)Yes,thishasbeenindicatedbythehorizontalpartofthegraph.Hestayedfrom10amto

10.30am.

(e)Herodethefastestbetween8amand9am.

7.Cantherebeatime-temperaturegraphasfollows?Justifyyouranswer.

Ans.(i)Itisshowingtheincreaseintemperature.

(ii)Itisshowingthedecreaseintemperature.

(iii)Thegraphfigure(iii)isnotpossiblesincetemperatureisincreasingveryrapidlywhich

isnotpossible.

(iv)Itisshowingconstanttemperature.




NCERTSolutions

CHAPTER-15


1.Plotthefollowingpointsonagraphsheet.Verifyiftheylieonaline

(a)A(4,0),B(4,2),C(4,6),D(4,2.5)

(b)P(1,1),Q(2,2),R(3,3),S(4,4)

(c)K(2,3),L(5,3),M(5,5),N(2,5)

Ans.

(a)AllpointsA,B,CandDlieonaverticalline.

(b)P,Q,RandSpointsalsomakealine.Itverifiesthatthesepointslieonaline.

(c)Thesepointsdonotlieinastraightline.

2.Drawthelinepassingthrough(2,3)and(3,2).Findthecoordinatesofthepointsat

whichthislinemeetsthex-axisandy-axis.



Ans.

Thecoordinatesofthepointsatwhichthislinemeetsthe axisat(5,0)and axisat(0,

5).

3.Writethecoordinatesoftheverticesofeachoftheseadjoiningfigures.

Ans.VerticesoffigureOABC



O(0,0),A(2,0),B(2,3)andC(0,3)

VerticesoffigurePQRS

P(4,3),Q(6,1),R(6,5)andS(4,7)

VerticesoffigureLMK

L(7,7),M(10,8)andK(10,5)

4.StatewhetherTrueorFalse.Correctthatarefalse.

(i)Apointwhosexcoordinateiszeroandy-coordinateisnon-zerowilllieonthey-axis.

(ii)Apointwhoseycoordinateiszeroandx-coordinateis5willlieony-axis.

(iii)Thecoordinatesoftheoriginare(0,0).

Ans.(i)True(ii)False,itwilllieon axis.(iii)True




NCERTSolutions

CHAPTER-15


1.Drawthegraphsforthefollowingtablesofvalues,withsuitablescalesontheaxes.

(a)Costofapples

No.of

apples1 2 3 4 5

Cost(in

Rs.)5 10 15 20 25

(b)Distancetravelledbyacar

Time(in

hours)6a.m. 7a.m. 8a.m. 9a.m.

Distance(in

km)40 80 120 160

(i)Howmuchdistancedidthecarcoverduringtheperiod7.30a.m.to8a.m?

(ii)Whatwasthetimewhenthecarhadcoveredadistanceof100kmsinceit’sstart?

(c)Interestondepositsforayear.

Deposit(inRs.) 1000 2000 3000 4000 5000

Simple

Interest

(inRs.)

80 160 240 320 400

(i)Doesthegraphpassthroughtheorigin?

(ii)UsethegraphtofindtheinterestonRs2500forayear.



(iii)TogetaninterestofRs280peryear,howmuchmoneyshouldbedeposited?

Ans.(a)

(b)(i)Thecarcovered20kmdistance.

(ii)Itwas7.30am,whenitcovered100kmdistance.

(c)(i)Yes,thegraphpassesthroughtheorigin.

(ii)InterestonRs.2500isRs.200forayear.

(iii)Rs.3500shouldbedepositedforinterestofRs.280.



2.Drawagraphforthefollowing.

(i)

Sideof

Square(incm)2 3 3.5 5 6

Perimeter

(incm)8 12 14 20 24

Isitalineargraph?

(ii)

Sideof

Square(incm)2 3 4 5 6

Area(incm2) 4 9 16 25 36

Isitalineargraph?

Ans.(i)Yes,itisalineargraph.



(ii)No,itisnotalineargraphbecausethegraphdoesnotprovideastraightline.




NCERTSolutions

CHAPTER-16

PlayingwithNumbers(Ex.16.1)

Findthevaluesofthelettersineachofthefollowingandgivereasonsforthesteps

involved.

1.

Ans.OnputtingA=1,2,3,4,5,6,7andsoonandweget,7+5=12inwhichonesplaceis2.

A=7

Andputting2andcarryover1,weget

B=6

HenceA=7andB=6

2.

Ans.OnputtingA=1,2,3,4,5,6,7andsoonandweget,8+5=13inwhichonesplaceis3.

A=5

Andputting3andcarryover1,weget

B=4andC=1

HenceA=5,B=4andC=1



3.

Ans.OnputtingA=1,2,3,4,5,6,7andsoonandweget,AxA=6x6=36inwhichones

placeis6.

A=6

HenceA=6

4.

Ans.Here,weobservethatB=5

sothat7+5=12.

Putting2atonesplaceandcarryover1andA=2,weget

2+3+1=6

HenceA=2andB=5

5.

Ans.HereonputtingB=0,

weget0 3=0.

AndA=5,then5 3=15

A=5andC=1



HenceA=5,B=0andC=1

6.

Ans.OnputtingB=0,weget0,andA=5,then5 5=25

A=5,C=2

HenceA=5,B=0andC=2

7.

Ans.HereproductofBand6mustbesameasonesplacedigitasB.

6 1=6,6 2=12,6 3=18,

6 4=24

OnputtingB=4,wegettheonesdigit4andremainingtwoB’svalueshouldbe44.

For6 7=42andcarryover2=44

HenceA=7andB=4

8.

Ans.OnputtingB=9,weget9+1=10

Putting0atonesplaceandcarryover1,weget



ForA=7 7+1+1=9

HenceA=7andB=9

9.

Ans.OnputtingB=7,

7+1=8

NowA=4,then4+7=11

Putting1attensplaceandcarryover1,weget

2+4+1=7

HenceA=4andB=7

10.

Ans.PuttingA=8andB=1,weget

8+1=9

Nowagainweadd2+8=10

Tensplacedigitis‘0’andcarryover1.

Now1+6+1=8=A

HenceA=8andB=1




NCERTSolutions

CHAPTER-16

PlayingwithNumbers(Ex.16.2)

1.If21y5isamultipleof9,whereyisadigit,whatisthevalueofy?

Ans.Since21y5isamultipleof9.

Thereforeaccordingtothedivisibilityruleof9,thesumofallthedigitsshouldbeamultiple

of9.

Since21y5isamultipleof9.

2.If31z5isamultipleof9,wherezisadigit,whatisthevalueofz?Youwillfindthat

therearetwoanswersforthelastproblem.Whyisthisso?

Ans.Since31z5isamultipleof9.


of9.

If



Hence0and9aretwopossibleanswers.

3.If24xisamultipleof3,wherexisadigit,whatisthevalueofx?

(Since24xisamultipleof3,itssumofdigits6+xisamultipleof3;so6+xisoneof

thesenumbers:0,3,6,9,12,15,18,....Butsincexisadigit,itcanonlybethat

6+x=6or9or12or15.Therefore,x=0or3or6or9.Thus,xcanhaveanyof(four

differentvalues.)

Ans.Since isamultipleof3.


of3.

Since isadigit.

Thus, canhaveanyoffourdifferentvalues.

4.If31z5isamultipleof3,wherezisadigit,whatmightbethevaluesofz?

Ans.Since31z5isamultipleof3.


of3.

Since isadigit.



If

If

If

Hence0,3,6and9arefourpossibleanswers.



QuestionPaperFA-I2016-2017

CBSEClassVIIIMathematics(SET-A)

IndraprasthaInternationalSchool

GeneralInstruction:

Thisquestionpapercontains8questions.

Writeanswersneatlyandlegibly.

Allthequestionsarecompulsory.

Marksforeachquestionareindicatedagainstit.

1.a.Thestandardformof is__________.(1)

b.Ithinkofanumberandsubtract5fromfourtimesthenumber.Theresultis3more

thantwicethenumberthatIthoughtof.Thenumberis_________.(1)

Sol.(a)

(b)4

2.a.(2-1+3-1+4-1+5-1)0=__________.(1)

b.Diameterofthesunis14000×105m,thediameterinstandardformis_________.(1)

Sol.(a)1

(b)1.4×109

3.Findtheareaofarectangularboardwhichis mlongand mwide.(2)

Sol.Lengthofboard



Widthofboard

4.Bywhatnumbershould bemultipliedtogettheproductas ?(2)

Sol.Let bemultipliedbyx

Shouldbemultipliedby toget

5.Find6rationalnumbersbetween and (3)

Sol.

6Rationalnumbersbetween-3and5are (any6)(3)

a.Solveforx:33x+3=9x+4.



b.Findthevalueof

Sol.(a)33x+3=(32)x+4

33x+3=32x+8

Asbasesaresameequationpowers

3x+3=2x+8

(b)

7.Reenawantstodistributechocolatesonherbirthdaytochildrenstayinginan

orphanagesothattheyalsofeelgood.Ifthecostofachocolateis`10andthereare50

children,howmuchmoneywouldsheneed,ifshegives2chocolatestoeachchild?

Explainanytwovaluesshownbyher.(3)

Sol.Numberofchildren=50

Chocolategiventoeachchildren=2

Totalchocolaterequired=100

Costof100chocolates=100×10=Rs1000

Values:Anytwo

8.a.Findthevalueofxsuchthat(3-1+6-1+9-1+12-1)x (3)

b.1micronisequalto m.Expressthisstatementinstandardform.



Sol.(a)

(b)10-6



QuestionPaperFA-I2016-2017

CBSEClassVIIIMathematics(SET-B)

IndraprasthaInternationalSchool

GeneralInstruction:


Writeanswersneatlyandlegibly.



1.a.Ithinkofanumberandsubtract fromit.Imultiplytheresultby8andthe

resultIfinallyobtainis3timesthesamenumberIthoughtof.Thenumberis______.

(1)

b.Multiplicativeinverseof is____________.(1)

Sol.(a)4

(b)

2.a.(-1)112×(-1)113=________________.(1)

b.Usualformof1.25×10-6is________________.(1)

Sol.(a)-1

(b)0.00000125

3.Productoftworationalnumbersis Ifoneofthemis findtheother

number.(2)



Sol.productoftworationalnumbers

Onenumber

Secondnumber=Product÷Onenumber

∴Secondrationalnumber

4.Bywhatnumbershould bedividedsothatthequotientbecomes125?(2)

Sol.Let bedividebyx

or



shouldbedividedby

5.Findsixrationalnumbersbetween and .(3)

Sol.

Sixrationalnumberbetween and are: (anysix)

6.If findx3.(3)

Sol.

7.Agirlinsteadofdistributingsweetsonherbirthdaydecidestodistribute320apples

invariousorganizations.Halftheapplesshedistributedinanorphanage,threefourths

oftheremainingweredistributedinaschoolfordifferently-abledandremaining

applesweredistributedtothepoorchildren.Findthenumberofapplesshedistributed

tothepoorchildren.Explainanytwovaluesshownbyher.(3+1)

Sol.Totalapples=320

Giventoorphanage



Giventoschool

320=160+120+x

x=40

Shedistributed40applestothepoor.

Value:Anytwo

8.a.Findthevalueofthevariable:(3+1)

b.Thesizeofaplantcellisapproximately0.000013m.Convertthesizeinstandard

form.

Sol.(a)

(b)Sizeofcell=1.3×10-5m.



QuestionPaperSA-I,2016-2017

CBSEClassVIIIMathematics

PratibhaSchool

GeneralInstruction:

Allquestionsarecompulsory.

Thequestionpaperconsistsof32questionsdividedintofoursectionsA,B,CandD.

section‘A’comprisesof10questionsof1markeach.Section‘B’comprisesof8

questionsof2markseach.Section‘C’comprisesof8questionsof3markseach.

Section‘D’comprisesof6questionsof5markseach.

Internalchoicehasbeenprovidedinsomequestions.Attemptonlyoneoptioninsuch

questions.

Section-A

1.Writetheadditiveinverseof

2.Fillintheblanks:

3.Aregularpentagonhas……………………….sidesofequallength.

4.Aquadrilateralhas……………………diagonals.

5.Thesumofallangleofaquadrilateralis…………………

6.Findthevalueofyin3y–2=7.

7.Solve:



8.Writetwopositiverationalnumbersbiggerthan–2.

9.Ist=5thesolutionoftheequation5t+3=24?

10.Onemorethan ofanumbersis .Writetheequation.

Section–B

11.Express asarationalnumberwithdenominator12.

12.Nametheregularpolygonhaving:

(i)foursides

(ii)Threesides

13Solve:

8x+3=27+2x.

14Represent onnumberline.

15.Statewhetherthefollowingstatementsaretrueorfalse.

(i)0isawholenumberbutitisnotarationalnumber.

(ii) liesontherightsideof0onnumberline.

(iii)Everyintegerisarationalnumber.

(iv) isanegativerationalnumber.

16.Solve:



17.Anumberis10morethantheothernumberandtheirsum74.Findthenumbers.

OR

Theperimeterofarectangleis13cmanditsbreadthis cmFinditslength.

Q18.Findarationalnumberbetween .

Section–C

Solvethefollowingquestion(Question19-20)

19.

20.3(5x–7)-2(9x–11)=10

21.Find8rationalnumbersbetween

22.Findthevalueofx,yandzinthefollowingparallelogram.

23.Thebaseofanisoscelestriangleis cm.Iftheperimeterofthetriangleis cm.Find

thelengthoftwoequalsidesofthetriangle.

24Bywhatrationalnumbershouldwemultiply toget ?

25.ABCDisaparallelogram.Completethefollowingstatementwithreasons.



(i)AD=…………………

(ii)∠DCB=.................

(iii)∠DCB+∠CDA=..............

26.If10beaddedtofourtimesanumber,theresultis6timesthenumber.Findthenumber.

Section–D

27.Solve:

28.Solvetheequationandfindthevalueof‘m’:

29.RahulandSameerhadtovisittheirsisteronRakshabandhan,whowerelivingonthe

samerouteundertemplewhichwasatadistanceof33kmfromtheirhome.Sotheydecided

toshareaCNGcar.Rahul’ssisterwaslivingatadistanceof ofthedistancetothe

temple.Rahuldrovethecartohissister’shome.AftertheRakshbandhanceremony,theyleft

forSameer’ssisterhome,whichwas ofthetotaldistancetothetemple.NowSameer

drovetohissister’shomeasRahulwascompletelytired.

(i)Whatdistancewascoveredbyeachofthefriend?



(ii)CalculatethedistanceofthetemplefromSameer’ssister’shome.

(iii)Writeanyvaluewhichyoulearnfromthesefriends.

30.Dividethesumof and bytheirdifference.

Or

If ofanumberexceedsits by44.Findthenumber.

31.Rakhi’smotherisfourtimesasoldasRakhi.After4years,hermotherwillbethreeasold

asshewillbethen.Findtheirpresentages.

32.Thewidthofarectangleis ofit’slength.Iftheperimeteris180meters,findthe

dimensionsoftherectangle.

OR

Amanis10timesolderthanhisgrandson.Heisalso54yearsolderthanhim.Findtheir

ages.





PratibhaSchool

GeneralInstruction:



section‘A’comprisesof10questionsof1markeach.Section‘B’comprisesof8

questionsof2markseach.Section‘C’comprisesof8questionsof3markseach.

Section‘D’comprisesof6questionsof5markseach.

Internalchoicehasbeenprovidedinsomequestions.Attemptonlyoneoptioninsuch

questions.

Section-A

1.Writemultiplicativeinverseof

Fillintheblanks(Questions2-5)

2.

3.Arectanglewithsidesofequallengthiscalled_____________

4.Allrectanglesare_______________also.(parallelogram/square)

5.Asquarehasallsidesof_________length.

6.Solve:

7.Write2rationalnumberswhicharesmallerthan-4.

8.4morethantwiceanumberisequalto8.Writetheequation.



9.Findthevalueofzin7=z+4.

10.Isx=4thesolutionoftheequationx+2=8

SectionB

11.Solve:17+6p=9

12.Representonnumberline:

13.Statewhetherthefollowingstatementsaretrueorfalse.

(i)Allwholenumbersarerationalnumber.

(ii)0isanaturalnumber

(iii) liesontheleftsideof0onnumberline.

(iv)Thereciprocalofanegativenumberisalwaysanegativenumber.

14.Express asarationalnumberwithnumerator12.

15.Subtract from

16.Findarationalnumberbetween and

17.Thesumoftwonumbersare95.Ifonenumberis35,thenfindtheothernumber.

OR

Afterreading7/9thpartofabook40pagesareleft.Findthetotalnumberofpagesofthe

book.

18.NametheRegularPolygonhaving:

(i)Foursides

(ii)Threesides

SectionC




Solvethefollowingequations.(Question20-21)

20.

21.9x+5=4(x–2)+8

22.Twonumbersareintheratio5:8.Ifthesumofthenumbersis182.Findthenumbers.

23.Findthevalueofxinthegivenfigure.

24.Thesumoftwooppositeanglesofaparallelogramis130°.Findthemeasureofeachofits

angles.

25.Thesumofthreeconsecutiveintegersis51.Findtheintegers.

26.Bywhatnumbershould bedividedtoget ?

SectionD

27.Usingappropriateproperties,find:

28.Findthevalueof‘t’bysolvinglinearequationandcheckyouranswer.

8t+4=3(t–1)+7

29.ThemonthlyincomeofAmitisRs.16000.Hespent thofhisincomeonfood, thon

rentofhouseand thontheeducationofpoorchildren.Answerthefollowingquestions:



(i)Amountspentonfood.

(ii)Amountspentoneducationofpoorchildren

(iii)AmountleftwithAmit.

(iv)WhatvaluesdoyoulearnfromAmit?

30.CheckwhetherthefollowingstatementisTrueorFalse.

OR

Dividethesumof and bytheirdifference.

31.Monu’sfatheris26yearsyoungerthanMonu’sgrandfatherand29yearsolderthan

Monu.Thesumoftheagesofallthethreeis135years.Whatistheageofeachofthem?

32.Thedigitinthetensplaceofatwodigitnumberisthreetimestheotherdigit.Ifyou

interchangethedigitsofthistwodigitnumberandaddtheresultingnumbertotheoriginal

numberyouget88.Whatistheoriginalnumber?

OR

Twoanglesofatriangleareintheration4:5.Ifthesumoftheseanglesisequaltothethird

angle.Findtheanglesofthetriangle.





SHIKSHABHARATISCHOOL

GeneralInstruction:

SectionAcarry1markeachquestion.

SectionBcarry2markseachquestion.

SectionCcarry3markseachquestion.

SectionDcarry4markseachquestion.

SECTION:A

1.Therationalnumbernotequivalentto is

(a)

(b)

(C)

(d)

2.Thevalueof is

(a)

(b)



(C)

(d)

3.Aperfectsquarecannothavethedigit.

(a)9atonceplace

(b)1atonceplace

(c)8atonceplace

(d)4atonceplace

4.Thevalueof is

(a)34.25

(b)35.05

(c)35.75

(d)34.75

5.Thecuberootof4.096is

(a)34.25

(b)35.05

(c)35.75

(d)34.75

6.Thinkofanumber,adds,thenmultiplyby6.Theansweris180.Whatisthenumber?

(a)35

(b)25



(c)45

(d)50

7.Whichofthefollowingnumberisdivisiblebyboth3and2?

(a)1023

(b)4029

(c)1032

(d)2512

8.Theproductof7y5and10y20is

(a)70y25

(b)35y25

(c)-70y25

(d)-35y25

9.Thevalueof(537)2–(536)2is

(a)12436

(b)538

(c)1073

(d)2358

10.If thenthevalueofxis

(a)4



(b)

(c)-2

(d)1

SECTION:B

11.Ifthreeanglesofaquadrilateralare20o,90oand90o.Findthefourthangleofthe

quadrilateral.

12.Solve

13.Theproductoftworationalnumbersis Ifonethemis findtheother.

Q14.Simplify

(i)

(ii)

15.Findxandy(twopositivenumbers)suchthatx+y=340andthedifferenceb/wxandy

is60.

16.Divide:

(i)8x3–12x3+16x+by2x

(ii)5x3–15x2+25xby5x

17.Find:

(i)(a–2c)2



(ii)(3y–5)2

18.Thelongersideoftheparallelogramis8.4cm.andtheshortersideishalfofthelonger

side.Findtheparallelogram.

19.Insert6rationalnumbersb/3: and

20.Usingprimefactorizationstatewhichofthefollowingis/areperfectsquare(s)?

(i)729

(ii)445

SECTION:C

21.Findthesquareofthefollowingno.usingthecolumnmethod.

(i)25

(ii)53

22.Findthecubesofthefollowingno.usingthecolumnmethod.

(i)27

(ii)35

23.Forwhatpossiblevalueofbfollowingnumbersaredivisibleof3?

(i)7b23

(ii)83b49

24.Theanglesofaquadrilateralareintheratio1:2:3:4.Whatismeasureofthefourangles

separately?

25.Findthethreeconsecutivenumberswhosesumis183.

26.Findthesquarerootofthefollowingnumbersbylongdivisionmethod.



(i)194481

(ii)53361

27.Completethefollowingtablesbyfindinga,b,andc.

N 6n+10

a

b

30

22

40

c

28.Thesidesofatrianglearegivenbyx,2x+2and3x–2.Ifitsperimeteris30cm,thenfind

thesmallestsidesofthetriangle.

29.Findthevalueifm:

(i)

(ii)

30.Intheadjoiningfigure,ABCDisa11gm.If∠BAD=85oand∠CBD=60othancalculate

(i)∠CDB

(ii)∠ABD

SECTION:D

31.True/False:

I.Ifanumberisdivisiblebyboth3and6,itmuchbedivisibleby18.

II.Ifanumberisdivisibleby8,itmustbedivisibleby4.

III.Thesumoftwooddnumberisalwaysdivisibleby4.

IV.Thenumberformedbywritingnon–zerodigitsixtimes(e.g.555555)isalwaysdivisible



by11.

32.

ColumnA ColumnB

a.am×an p.am-n

b.0.000037 q.am+n

c.(75÷72)×33 r.3.7×(10)-5

d.am÷an,m>n s.(21)3

33.(a)Whatmustbesubtractedfrom4562togetaperfectsquare?Also,findthesquareroot

ofthisperfectsquare.

(b)Findthesquarerootbyfactorizationmethod14400.

34.Whatisthesmallestnumberbywhich1372mustbemultipliedsothattheproduct

becomesaperfectcube?Findtherequiredperfectcubesoobtained.

35.Fillintheblanks:

I.cubesofall____________nationalno’sareodd.

II.Thesumoftworationalnumbersisalwaysa____________.

III.Theproductofanyrationalnumberwith____________istherationalnumberitself.

IV.(425)2–(425)2=____________.



QuestionPaperSA-II,2014-2015


GeneralInstruction:

Thequestionspaperhasbeendividedinto4sections.

SecAcontains5questionsof1markeach

SecBcontains4questionsof2markseach

SecCcontains7questionsof3markseach

SecDcontains4questionsof4markseach

SecEOPENTEXTBASEDASSESSMENT(OTBA)contains10marks.

Anadditional15minutestimehasbeenallottedtoreadthisquestionpaperonly.

Useofcalculatorisnotpermitted.

SECTION–A

1.Whatistheareaofaparallelogram?

2.Evaluate3°+4°

3.Findtheproductof7pqand-6p

4.Whatisthevolumeofacubeofside1cm?

5.Findtheerrorin2(x-2)=2x–2

6.Factorize:2x+4

SECTION–B

7.Findtheproduct:

8.Findthevalueof310÷37

9.Amixtureofpaintispreparedbymixing1partofredpigmentswith8partsofthebase.



Nowinthefollowingtable.Fillintheblanks

Partofredpigments Partofbase

1 8

4 ………

12 ………

10.Factorize:x2+xy+8x+8y.

11.Express0.000035instandardform.

SECTION–C

12.Checkthedivisibilityof152875by9

13.Plotthefollowingpointsonthegraphsheet.Verifyiftheylieonaline.A(4,0),B(4,2),C

(4,6),D(4,2,5)

14.Simplify:(x2–5)(x+5)+25

15.Drawthefrontview,sideview,andtopviewofamilitarytent.

16.Atrainismovingatauniformspeedof75km/hr.Howfarwillittravelin20min?

17.Factorize:-a4–b4

SECTION–D

18.Thereare100studentsinahostel.Foodprovisionforthemisfor20days.Howlongwill

theseprovisionslast,if25morestudentsjointhegroup?

19.Drawthegraphforthefollowingtableofvalues,withsuitablescalesontheaxes.

Time(inhrs) Distance(inkm)

6am 40



7am 80

8am 120

9am 160

20.If21Y5isamultipleof9whereYisadigit,whatisthevalueofY?

21.Drawamapofyourclassroomusingproperscaleandsymbolsfordifferentobjects.

SECTIONE

OPENTEXTBASEDASSESSMENT(OTBA)

Theme1:ChildLabour

1.Whatistheprominentcauseforchildlabour?

2.Whatisthepercentageofchildlabourindomesticworkers?

3.PrepareaBarGraphbytakingstatesonx-axisand%ofchildrenony-axis(table1)3

Theme2:Children’sDay5Marks

1.a)AtwhattimeNehagotupinthemorning?

b)HowfarisNeha’sSchool?

2.a)AtwhattimeNeha’sschoolvancametoday?

b)Rehanachoosetotakewhichdrink?

c)Whowonthecricketmatch





GeneralInstruction:

Thequestionspaperhasbeendividedinto4sections.

SecAcontains10questionsof1markeach

SecBcontains8questionsof2markseach

SecCcontains8questionsof3markseach

SecDcontains4questionsof5markseach

Internalchoiceshavebeenprovidedinsomequestions.Attemptonlyoneoptionin

suchquestions.

SECTIONA

1Findthesumof5-2x2+4xand5x2–3x–4

2Thedifferencebetweentheupperandlowerclasslimitiscalled…………………oftheclass-

interval.

3Inhistogram,theheightofthebarsshowthe…………..ofclass-intervals.

4Numberoffacesinthegivenfigureare……………….

5Surfaceareaofacube……………………..

6Findtheareaofarhombuswhosediagonalsareoflength10cmand8.2cm.

7Simplify:

8Apointwhosey-coordinateiszeroandx-coordinateis7willlieon…………………..



9Findthecommonfactorsofthegiventerms:6abc,24ab2,12a2b

10‘Timetakentocoveradistance’andspeedofthecar’aresaidtobein……………………..

proportion.

SECTIONB

11Abaghas5bluecards,2orangecardsand4redcards.Acardisdrawnfromthebag

withoutlookingintothebag.Whatistheprobabilityofgetting.

a)aredcard?

b)anon-bluecard?

12Findtheproduct:

13Theweeklywages(inRs.)of30workersinafactoryaregivenbelow.Usingtallymarks,

makeafrequencytablewithintervalsas800-810,810-820andsoon.

804,808,812,840,885,835,835,836,878,840,868,890,806,840,830,835,890,810,835,863,

869,845,898,890,820,860,832,833,855,845

14UsingEuler’sformula,findtheunknown:

Faces ? 20

Vertices 6 ?

Edges 9 30

15Theareaofatrapeziumis34cm2andthelengthofoneoftheparallelsidesis10cmand

itsheightis4cm.Findthelengthoftheotherparallelside.

16Findtheheightofacuboidwhosevolumeis275cm2andbaseareais25cm2.

17Factorize:(2a+3)2–9b2

OR



Findthefactorsofy2–7y+12

18.Writethecoordinatesofthepoints‘P’and‘Q’

SECTIONC

19Drawapiechartshowingthefollowinginformation.Thetableshowsthecolours

preferredbyagroupofpeople.

Colours Blue Green Red Yellow Others

No.ofpeople 15 12 9 6 3

20Findthevalueof(3°+4-1)÷22

21Showthat:(4pq+3q)2–4(4pq–3q)2

22Drawthetopview,frontviewandsideviewofthegivensolid.

23Findtheheightofacylinderwhoseradiusis7cmandthetotalsurfaceareais968cm2

24.FindtheareaofthequadrilateralPQRSshowninthisfigure.

25.Drawthelinepassingthrough(4,2)and(2,4)findthecoordinatesofthepointsatwhich



thislinemeetsthex-axisandy-axis.

26.Thegraphshowsthepopulationofthecityin2007.

a)Whatwasthepopulationofthecityin2007?

b)Howmanypeoplelivedinthecityonanaverageduringthesixyears?

SECTIOND

27.WritetheEuler’sformulaandverifyitforthisfigure.

28Theinternalmeasuresofacuboidalroomare12m×8m×4m.Findthetotalcostof

whitewashingallfourwallofaroom,ifthecostofwhitewashingisRs.6perm2.Whatwill

bethecostofwhite-washing.

OR

Arectangularpaperofwidth14cmisrolledalongitswidthandacylinderofradius30cmis

formed.Findthevolumeofthecylinder.



29Atree15metreshigh,castsashadowof10metres.Findtheheightofanelectricpolethat

castsashadowof15metresundersimilarconditions.

OR

Factorizetheexpressionsanddividethemasdirected:(m2–14m–32)÷(m+2)

30Thegivendatashowsthenumberofaccidentsinvariousyearsofacity:

Year 2009 2010 2011 2012 2013 2014

No.ofaccidents 2300 2500 2750 3000 3100 3400

a)Representthedataintheformofalinegraph.

b)Inyouropinion,whatmaybethemaincauseofaccidents?

c)Whatqualitiesadrivershouldimbibetominimizetheno.ofaccidents?





GeneralInstruction:


TheQuestionPaperconsistsof26QuestionsdividedintofoursectionsA,B,CandD.

Section-Acomprisesof8questionsofonemarkeach.

Section-Bconsistsof6questionsoftwomarkseach.

Section-Ccomprisesof8questionsofthreemarkseach.

Section-Dcomprisesof4questionsoffourmarkseach.

Thereisnooverallchoice.However,aninternalchoicehasbeenprovidedin4

questionsoffourmarkseachand2questionsofsixmarkseach.Youhavetoattempt

onlyoneofthealternativesinallsuchquestions.

Theuseofcalculatorisnotpermitted.

Section–A

1.Themultiplicativeinverseof0.9is

a)

b)

c)

d)

2.Howmanyrationalnumbersexistbetween-2and1?

a)1



b)2

c)3

d)Infinite

3.Whichofthefollowingisthesolutionof223xx−=+?

a)x=4

b)x=5

c)x=7

d)x=-2

4.Whichofthefollowingisanexampleofregularpolygon?

a)Rhombus

b)Kite

c)Square

d)Rectangle

5.Intheclassinterval35-45,45iscalled

a)Upperlimit

b)Lowerlimit

c)Range

d)Frequency

6.Theunitesdigitofthesquareof327willbe

a)7

b)1



c)4

d)9

7.Bywhichdigitthecubeof27ends?

a)1

b)2

c)3

d)4

8.When35%isexpressedasfraction,weget

a)

b)

c)2.5

d)35

Section–B

9.Findthesquareof

a)32

b)46

10.Simplify:

11.Findthecuberootof64and512.

12.Findthevalueofxif20%ofxis40.



13.Sumoftwonumbersis95.Ifoneexceedstheotherby15,findthenumbers.

14.Howmanysidesdoesaregularpolygonhaveifthemeasureofeachofitsinteriorangleis

165°?

Section–C

15.Constructthequadrilateral“DEAR”withDE=4cm,EA=5cm,AR=4.5cm,

OR

Constructarhombuswhosediagonalsare5.2cmand6.4cmlong.

16.AtablemarkedatRs15,000isavailableforRs14,400.Findthediscountgivenandthe

discountpercent.

17.SimplifyandSolve15(y–4)-2(y–9)+5(y+6)=0

OR

Solve:


19.Theanglesofaquadrilateralareintheration3:5:7:9.Findtheanglesofthequadrilateral.

20.Numbers1to10arewrittenontenseparateslips(onenumberononeslip),keptinabox

andmixedwell.Oneslipischosenfromtheboxwithoutlookingintoit.Whatisthe

probabilityof

a)Gettinganumberlessthan6?

b)Gettinganumbergreaterthan6?

c)Gettingaonedigitnumber?



21.Findthesquarerootof100bythemethodofrepeatedsubtraction.

22.Findthesmallestnumberbywhich256mustbemultipliedtoobtainaperfectcube.

Section–D

23.ThecostofanarticlewasRs15,500.Rs450werespentonitsrepairs.Ifitissoldataprofit

of15%,findthesellingpriceofthearticle.

OR

Arunboughtapairofskatesofasalewherethediscountgivenwas20%.Iftheamounthe

paysisRs1,600,findthemarkedprices.

24.Drawapiechartofthedatagivenbelow.

Thetimespentbyachildduringaday:-

Sleep 8hours

School 6hours

Homework 4hours

Play 4hours

Others 2hours

25.Aman’sageisthreetimeshisson’sage.Tenyearsagohewasfivetimeshisson’sage.

Findtheirpresentages.

26.Theweeklywages(inRs.)of30workersinafactoryare.

830,835,890,810,835,836,869,845,

898,890,820,860,832,833,855,845,

804,808,812,840,885,835,835,836,

878,840,868,890,806,840

Usingtallymarksmakeafrequencytablewithintervalsas800-810,810-820andsoon.Also,



drawahistogramforthisdata





GeneralInstruction:

Allquestionarecompulsory.


SectionAconsistsof8questionsof1markeach.

SectionBconsistsof6questionsof2markseach.

SectionCconsistsOf10questionsof3markseach.

SectionDconsistsof4questionsof5markseach.

Thereisnooverallchoice.Howeveraninternalchoicehasbeenprovidedinsome

questions.Attemptonlyoneoptioninsuchquestions.

SECTIONA

1Writethenumericalcoefficientof

2.Findtheproduct:

Fillintheblanks:

3.Aprismisapolyhedronwhosebaseandtoparecongruentpolygonsandwhoselateral

facesare……...inshape.

4.AmountofregionoccupiedbyaSolidiscalledits.........................

5.7°=…………

6.am+an=…...........

7.ThecommonfactorofthetermsI0ab,5bC,20acis......................



8.Factorise:

5x2+15xy.

SECTIONB

9.Findthevalueofm:

(-2)m+2×(-2)5=(-2)10.

10.Expressthefollowingnumbersinususalform:

(a)5.15×10-4

(b)3614295×107.

11.Theareaofarhombusis240cm2andoneofitsdiagonalis30cm.Findtheother

diagonal.

12.Apyramidisapolyhedronwhosebaseisa......................andwhoselateralfaces

are......................withacommonvertex.

13.WriteEuler'sformulaandthenfindV,ifF=5,E=9.

14.Add:

5a(3–a),6a2–13a.

OR

Subtract13ab(a–b)from5ab(a+b).

SECTIONC

15.Constructafrequencydistributiontableforthedataonweights(inkg)of20studentsofa

classusingclassintervals30-35,35-40andsoon.

40,38,33,48,56,53,31,46,34,36,49,41,55,49,57,42,44,47,38,39.



16.Thenumberofstudentsinahostel,speakingdifferentlanguagesisgivenbelow.Display

thedatainapiechart.

Language Hindi English Marathi Tamil Bengali Total

No.of

students40 12 9 7 4 72

17,Classifythefollowingpolynomialsasmonomials,binomialsandtrinomials:

(a)5xyz2-3zy

(b)

(c)pqr.

OR

Simplify:

(a+b)(c–d)+(a–b)(c+d)+2(ac+bd).

18.Drawthelinepassingthrough(2,3)and(3,2).Findthecoordinatesofthepointsatwhich

thislinemeetsthex-axisandy-axis.

19.Factorise:

3a2+9a+6.

20.Simplify:

OR



21.Subtract3a(a+b-c)-2b(a–b+c)from4c(-a+b+c).

22.Anelectricpole,14mhigh,castsashadowof10m.Findtheheightofatreethatcastsa

shadowof15mundersimilarconditions.

23.Agodownisintheformofacubeofside40m.Howmanycubicalboxescanbestoredin

it,ifthevolumeofoneboxis8m?

OR

Acuboidisofdimensions60cm×54cm×30cm.Howmanysmallcubeswithside6cmcan

beplacedinthegivencuboid?

24.If15workerscanbuildawallin48hours,howmanyworkerswillberequiredtodothe

sameworkin30hours?

SECTIOND

25.Constructasquarewithside5cm(usecompass).

OR

Constructarectanglewithadjacentsidesoflengths5cmand4cm.

26.Drawagraphforthefollowing:

Sideofsquare 2 2.5 3.5 5 5.5 6

Perimeter 8 10 14 20 22 24

27.Arectangularpieceofpaper11cm×4cmisfoldedwithoutoverlappingtomakea

cylinderofheight4cm.Findthevolumeofthecylinder.

28.Find

4yz(z2+6z-16)+2y(z+8).





GeneralInstruction:


Thisquestionpaperconsistsof26questionsdividedintofoursectionsA,B,CandD.

SectionAcontains8questionsofmarkeachSection-Bcontain6questionsof2marks

each,Section-Ccontains8questionsof3markseachandSection-Dcontains4

questionsof4markseach.

Useofcalculatorsisnotallowed.

Section-A

MultipleChoiceQuestions:

l.Whichoneisbinomial:

(a)4l+5m

(b)2x

(c)3x2-5x+2

(d)

2.TherelationbetweenF,VandEarerepresentedbyEuler'sformulaasfollows:

(a)F-V+E=0

(b)F+E+V=1

(c)F+V-E=2

(d)F-V+E=2



3.Whatisthemultiplicativeinverseof3-1:

(a)

(b)37

(c)0

(d)2

4.Whichofthefollowingnumberisdivisibleof34:

(a)295

(b)432

(c)616

(d)1091

5.Theperimeterofasquareis4m.Itsareaisgivenby:

(a)1m2

(b)2m2

(c)4m2

(d)4m3

6.Thevalueof(5°+7)×7is:

(a)84

(b)36

(c)8

(d)35



7.Whatistheproductof4and0:

(a)4

(b)0

(c)2

(d)1

8.(a2–2ab+b2)isequalto:

(a)(a+b)2

(b)(a–b)2

(c)a2–b2

(d)a2+b2

Section-B

9.Findthevalueofmsothat:

3m+1×35=37

10.Plotthefollowingpointsonagraphpapersheet:

A(1,3),B(1,2),C(4,3),D(6,2)

11.AshirtismarkedatRs.850andsolditforRs.765.Whatisthediscountanddiscount

percentage.

12.Findthevalueusingsuitableidentity:

97×103

13.Findthecommonfactorsofthegiventerms:

12×36



14.Simplify:

(a+b)+(b-a)+(c-b)

Section-C

15.FindthecompoundinterestonRs.5000for2yearsattherateof0%perannum

compoundedannually.

16.Subtract5x2-4y2-6y-3from7x2-4xy+8y2+5x-3y.

17.Thediagonalofaquadrilateralshapedfieldis24mandtheperpendiculardroppedonit

fromtheremaining-oppositeverticesare8inand13m.Findtheareaofthefield.

18.Amachineinasoftdrinkfactoryfills840bottlesinhours.Howmanybottleswillitfillin

5hours.

19.Divide:

(7x2+4x)by(x+2)

20.Agodownisintheformofacuboidofmeasures60m×40m×30m.Howmanycuboidal

boxescanbestoredinit,ifthevolumeofoneboxis0.8m3.

21.Showthat:

(3x+7)2-84×=(3x–7)2

22.Ifanyobjecthas20faces,12verticesthenfindthevalueofEdgesbyusingEuler's

formula.

Section-D



23.Factorise:

(a)a2-2ab+b2–c2

(b)p2+6p+8

(c)x8+y8

24.Arectangularpaperofwidth15cmisrolledalongitswidthandacylinderofradius20

cmisformed.Findthevolumeofthecylinder.(Take

25.Thereare100studentsinaHostel.Foodprovisionforthemisfor20days.Howlongwill

theseprovisionlast,if25morestudentsjointhegroup.

26.Drawagraphforfollowingdata:

Slideofsquare(incm) 2 3 4 5 6

Area(incm2) 4 9 16 25 36

Isitalineargraph?



CBSETESTPAPER

CLASS–8Mathematics

LinearEquationsinonevariable

GeneralInstructions

ThisTestpapercontain43Questions.


1. Whenfiveisaddedtothreemorethanacertainnumber,theresultis19.Whatisthe

number?

2. Iffiveissubtractedfromthreetimesacertainnumber,theresultis10.Whatisthe

number?

3. When18issubtractedfromsixtimesacertainnumber,theresultis42.Whatisthe

number?

4. Acertainnumberaddedtwicetoitselfequals96.Whatisthenumber?

5. Anumberplusitself,plustwiceitself,plus4timesitself,isequalto104.Whatisthe

number?

6. Sixtymorethanninetimesanumberisthesameastwolessthantentimesthenumber.

Whatisthenumber?

7. Elevenlessthanseventimesanumberisfivemorethansixtimesthenumber.Findthe

number.

8. Fourteenlessthaneighttimesanumberisthreemorethanfourtimesthenumber.What

isthenumber?

9. Thesumofthreeconsecutiveintegersis108.Whataretheintegers?

10. Thesumofthreeconsecutiveintegersis-126.Whataretheintegers?

11. Findthreeconsecutiveintegerssuchthatthesumofthefirst,twicethesecondandthree

timesthethirdis-76.

12. Thesumoftwoconsecutiveevenintegersis106.Whataretheintegers?

13. Thesumofthreeconsecutiveoddintegersis189.Whataretheintegers?

14. Thesumofthreeconsecutiveoddintegersis255.Whataretheintegers?

15. Findthreeconsecutiveoddintegerssuchthatthesumofthefirst,twotimesthesecond,

andthreetimesthethirdis70.



16. Thesecondangleofatriangleisthesamesizeasthefirstangle.Thethirdangleis12

degreelargerthanthefirstangle.Findallthreeangles.

17. Twoanglesofatrianglearethesamesize.Thethirdangleis12degreessmallerthanthe

firstangle.Findallthreeangles.

18. Twoanglesofatrianglearethesamesize.Thethirdangleis3timeslargerasthefirst.

Findallthreeangles.

19. Thethirdangleofatriangleisthesameasfirst.Thesecondangleis4timesofthird

angle.Findallthreeangles.

20. Thesecondangleofatriangleis3timeslargerthanthefirstangle.Thethirdangleis30

degreemorethatfirstangle.Findallthreeangles.

21. Thesecondangleofatriangleistwiceaslargerasthefirst.Themeasurementofthethird

angleis20degreesgreaterthanthefirst.Findallthreeangles.

22. Thesecondangleofatriangleisthreetimeslargerthanfirst.Themeasurementofthird

angleis40degreegreaterthanthefirstangle.Findallangles.

23. Thesecondangleofatriangleisfivetimeslargerthanfirst.Themeasurementofthe

thirdangleis12degreemorethanthefirst.Findallangles.

24. Thesecondangleofatriangleisthreetimesthefirst,andthethirdis12degreelessthan

twicethefirst.Findallthreeangles.

25. Thesecondangleofatriangleisfourtimesthefirstandthethirdis5degreemorethan

twicethefirst.Findallthreeangles.

26. Theperimeterofarectangleis150cm.thelengthis15cmgreaterthanthewidth.Find

thedimensions.

27. Theperimeterofarectangleis304cm.thelengthis40cmlongerthanthewidth.Findthe

lengthandwidth.

28. Theperimeterofarectangleis152mtrs.Thewidthis22mtrslessthanthelength.Find

lengthandwidth.

29. Theperimeterofarectangleis280mtrs.Thewidthis26mtrslessthanthelength.Find

thelengthandwidth.

30. Theperimeterofacollegebasketballcourtis96mtrsandthelengthis14mtrsmorethan

thewidth.Whatarethedimensions?

31. Amountaincabinon1acreoflandcost30,000rupees.Ifthelandcost4timesasmuchas

thecabin,whatwasthecostofeach?

32. Ahorseandsaddlecost5000rupees.Ifthehorsecost4timesasmuchasthesaddle,what



isthecostofeach?

33. Abicycleandbicyclehelmetcost240rupees.Howmuchdideachcost,ifthebicyclecost5

timesasmuchasthehelmet?

34. Of240stampsthatHarryandhissistercollected,Harrycollected3timesasmanyashis

sister.Howmanystampsdideachofthemcollected?

35. IfMr.Brownandhissontogetherhas220rupees,andMr.Brownhad10timesasmuch

ashisson,howmuchmoneyhadeach?

36. Inaroomcontaining45studentsthereweretwiceboysascomparetogirls.Howmany

boyswerethere?

37. Aaronhas7timesasmanysheepasBerth,andbothtogetherhad608.Howmanysheep

hadeach?

38. Amanboughtacowandacalffor990rupees,paying8timesasmuchforthecowasfor

thecalf.Whatwasthecostofeach?

39. JamalandMonubeganabusinesswithacapitalof7500rupees.IfJamalfurnishedhalfas

muchcapitalasMonu,howmuchdideachfurnish?

40. Alabtechniciancuts12-inchpieceofatubeintotwopiecesinsuchawaythatonepiece

is2timeslongerthanother.Whatwillbethelengthofeachpiece?

41. A6ftboardiscutintotwopieces,ontwiceaslongastheother.Howlongarethepieces?

42. Aneightftboardiscutintotwopieces.Onepieceis2ftlongerthantheother.Howlong

arethepieces?

43. Anelectriciancuta30ftpieceofwireintotwopieces.Onepieceis2ftlongerthanother.

Howlongarethepieces?



Class–8LINEAREQUATION-VI

TESTPAPER[TOTALMARKS-25]

Note:-Allquestionsarecompulsory

Solvethese:-

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.



15.

16.

17.

18.

19.

20.



CBSEWorksheet-01

CLASS–VIIIMathematics(RationalNumbers)

Choosecorrectoptioninquestions1to5.

1.Findthereciprocalof-2.

a.

b.2

c.-2

d.noneofthese

2.Writetherationalnumberthatisequaltoitsnegative.

a.0

b.1

c.-1

d.2

3.Writetheadditiveinverseof .

a.

b.1

c.

d.0

4.Findthemultiplicativeinverseof-13.

a.-13

b.13

c.12

d.

5.Namethepropertyundermultiplicationusedin .

a.Reciprocal

b.Commutativeproperty



c.Associativeproperty

d.noneofthese

eMultiplicativeidentity

Fillintheblanks:

6.Anumberwhichcanbewrittenintheform ,wherepandqareintegersandq≠0is

calleda_________.

7.Sumoftworationalnumbersisa_______.

8.Foranythreerationalnumbersa,bandc,a+(b+c)=__________.

9._______=1×a=aforanyrationalnumbera.

10.Find

11.Findanytenrationalnumbersbetween



CBSEWorksheet-01


Answerkey:

1.a)

2.a)0

3.c)

4.d)

5.a)Reciprocal

6.rationalnumber

7.rationalnumber

8.(a+b)+c

9.a×1

10.

11.



CBSEWorksheet-02



1. Findthereciprocalof .

a. -5

b. 5

c.

d. Noneofthese

2. ×1=____

a. 1

b.

c. 0

d. 4

3. Writetheadditiveinverseof .

a.

b. 1

c.

d. 0

4. Findthemultiplicativeinverseof .

a. -4

b.

c.

d. 4



5. Namethepropertyundermultiplicationusedin .

a. Multiplicativeidentity

b. Commutativeproperty

c. Associativeproperty

d. Noneofthese

Fillintheblanks:

6. Anumberwhichcanbewrittenintheform ,wherepandqare_______andq≠0is

calledarationalnumber.

7. _________areclosedunderaddition.

8. ____________or___________isnotassociativeforrationalnumbers.

9. 1isthe__________forrationalnumbers.

10. Find:

11. Findarationalnumberbetween¼and½.



CBSEWorksheet-02


Answerkey

1. a)-5

2. b)

3. c)

4. d)4

5. a)Multiplicativeidentity

6. Integers

7. Rationalnumbers

8. SubtractionorDivision

9. multiplicativeidentity

10.

11. Therearemanyrationalnumbers.Foreg.3/8



CBSEWorksheet-03



1. Namethepropertyundermultiplicationusedin .

a. Commutativeproperty

b. Multiplicativeidentity

c. Associativeproperty

d. noneofthese

2. ×1=_______

a. 1

b.

c. 0

d. 2

3. Writetheadditiveinverseof .

a.

b. 1

c.

d. 0

4. Findthemultiplicativeinverseof .

a.

b.

c.



d.

5. StatetrueorFalse:

1and-1aretheonlyrationalnumbersthatisequaltoitsreciprocal.

Fillintheblanks:

6. Anumberwhichcanbewrittenintheform ,wherepandqareintegersand_____is


7. _________areclosedundersubtraction.

8. Theproductoftworationalnumbersisalwaysa_______.

9. Zerohas________reciprocal.

10. Find:

11. Findanythreerationalnumbersbetween¼and½.



CBSEWorksheet-03


Answerkey

1. Commutativeproperty

2.

3. c)

4. d)

5. True

6. q≠0

7. Rationalnumbers

8. Rationalnumber

9. no

10. -½

11. Thereareinfinitemanyrationalnumberslike



CBSEWorksheet-04



1.Writetherationalnumberthatdoesnothaveareciprocal.

a.0

b.1

c.-1

d.2

2.0×¼=_______

a.1

b.0

c.¼

d.4

3.Writetheadditiveinverseof .

a.

b.1

c.

d.0

4.Findthemultiplicativeinverseof .

a.

b.

c.

d.



5.Namethepropertyundermultiplicationusedin .

a.Commutativeproperty

b.Multiplicativeidentity

c.Associativeproperty

d.noneofthese

Fillintheblanks:

6.Anumberwhichcanbewrittenintheform_____,wherepandqareintegersandq≠0is


7.Foranytworationalnumbersaandb,a+b=_________.

8.Foranythreerationalnumbersa,bandc,a×(b×c)=_________.

9.Reciprocalof ,wherex≠0is________.

10.Tellwhatpropertyallowsyoutocompute

11.Findfiverationalnumbersbetween



CBSEWorksheet-04


Answerkey:

1.(a)0

2.(b)0

3.(c)

4.(d)

5.(a)Commutativeproperty

6.

7.b+a

8.(a×b)×c

9.x

10.Associativepropertyofmultiplication

11.



SILVEROAKACADEMY

SENIORSECONDARYSCHOOLBILARI

PERIODICASSESSMENT-1

SUBJECT-MATHEMATICS

CLASS-VIII

INSTRUCTIONS:-

Attemptallquestions,thereisnointernalchoice.

Drawneatdiagramifnecessary

Question1-4carry1markeach,question5-9carry2markseachand

question10-11carry3markseach.

1.Findthevalueof

2.Findtheareaofasquareofside

3.Findtheadditiveinverseof

4.4.Findthevalueof7-4X7

5.Verify:(x+y)+z=x+(y+z),ifx=6/12,y=9/4andz=2/3

6.Arrangeinascendingorder-1/2,-1/7,-1/11,-1/3

7.findthreerationalnumberbetween1/2and¾

8.simplify:

9.findthevalueofmif

10.Bywhichnumbershould bemultipliedtoget asproduct?

11.Represent onnumberline.



CBSEClass8Maths

AdditionwithExponents

Worksheet1

1. 9+72=_____________

2. 60+7=_____________

3. 9+23=_____________

4. 6+31=_____________

5. 70+4=_____________

6. 42+1=_____________

7. 9+43=_____________

8. 9+71=_____________

9. 32+4=_____________

10. 6+52=_____________

11. 5+93=_____________

12. 5+71=_____________

13. 3+93=_____________

14. 30+2=_____________

15. 32+8=_____________

16. 13+5=_____________

Total:16 Goal:_____ Complete:_____ Correct:_____



CBSEClass8Maths

AdditionwithExponents

Worksheet1

ANSWER

1. 9+72=______58______

2. 60+7=______8_______

3. 9+23=______17______

4. 6+31=______9_______

5. 70+4=______5_______

6. 42+1=______17______

7. 9+43=______73______

8. 9+71=______16______

9. 32+4=______13______

10. 6+52=______31______

11. 5+93=______734_____

12. 5+71=______12______

13. 3+93=______732_____

14. 30+2=______3_______

15. 32+8=______17______

16. 13+5=______6_______

Total:16 Goal:_____ Complete:_____ Correct:_____



CBSEClass-8th

CH-ALGEBRAICEXPRESSION

SAMPLEPAPER

1. Addthefollowingpolynomials:

a. 5x2–8xy,–3a2+2xyand–5x2+3xy

b. 2x3–9x2+8,3x2–6x–5,7x3–10x+1and3+2x–5x2–4x3

c. 6p+4q–r+3,2r–5p–6,11q–7p+2r–1and2q–3r+4

d. 4x2–7xy+4y2–3,5+6y2–8xy+x2and6–2x+2x2–5y2

e. 6ax–2by+3cz,6by–11ax–czand10cz–2ax–3by

2. Subtractthefollowing:

a. –6p+q+3r+8fromp–2c–5r–8

b. 5y4–3y3+2y2+y–1from4y4–2y3–6y2–y+5

c. 4y2+5q2–6r2+7from3p2–4q2–5r2–6

d. Thetwoadjacentsidesofarectangleare5x2–3y2andx2+2xy.Findtheperimeter.

e. Theperimeterofatriangleis6p2–4p+9andtwoofitssidesarep2–2p+1and3p2–

5p+3.Findthethirdsideofthetriangle.

3. Findeachofthefollowingproducts:

a. (x4+y4)×(x2–y2)

b. (9x+5y)×(4x+3y)

c. (3x2+5x–9)×(3x–5)

d. (2x+3x–7)×(3x2+5x+4)

4. Writethequotientandremainderwhenwedivide:

a. (x2+12x+35)by(x+7)

b. (15x2+x–6)by(3x+2)

c. (x3+1)by(x+1)

d. (5x3–12x2+12x+13)by(x2–3x+4)



e. (2x3–5x2+8x–5)by(2x2–3x+5)

5. Objectivetypequestion:

a. 6y4 (–2y3)is

(a)3y

(b)–3y

(c)3y3

(d)–3y3

b. (–72x2y3) (–8xy)is

(a)–9xy

(b)–9xy2

(c)9xy2

(d)9xy

c. Theremainderobtainedwhent4–3t3+t+5isdividedbyt–1is

(a)–4

(b)4

(c)1

(d)5

d. 8a2b3 (–2ab)=?

(a)4ab

(b)4ab

(c)–4ab

(d)–4ab2



Class:8MATHEMATICS

UNITTESTISESSION2013–14

INDRAPRASTHAINTERNATIONALSCHOOL

SETB

GENERALINSTRUCTIONS

Thisquestionpaperhas13questionsand2printedpages.


Marksarealongwithquestions.

1.(a) If,then______.

(i)-35(ii)-20(iii)35(iv)20(1)

(b)Reciprocalof is______.

(i) (ii) (iii) (iv)Noneofthese(1)

(c)Multiplicativeidentityofanyrationalnumber is______.

(i)1(ii)-1(ii)0(iv) (1)

(d)Whichofthefollowingstatementsisnottrue?

(i)5isarationalnumber.

(ii)Additiveinverseof is .

(iii) isarationalnumber.



(iv)Thereciprocalof is .(1)

(e)Multiplicativeinverseofanyrationalnumber is_____.

(i) (ii) (iii) (iv)0(1)

(f)If2x-2-x+4,thenequals_______.

(i)2(ii)3(iii)6(iv)-6(1)

(g)If then100xisequalto______.

(i)300(ii)330(iii)99(iv)990(1)

(h)Threeconsecutivemultiplesof7whosesumis777is________.

(i)245,259,273(ii)252,259,266

(iii)252,266,273(iv)238,259,280(1)

2.Write instandardform.(2)

3.Verifythecommutativepropertyforadditionof and .(2)

4.Verifythat–(-x)=forx=-5/13.(2)

5.Solve4(2x-5)+17=29.(2)

6.Solve .(2)

7.If ofanumberis13morethan ofthenumber,findthenumber.(2)



8.Verify andnamethe

propertyused.(3)

9.Findfiverationalnumbersbetween and .(3)

10.Solve .(3)

11.Fourfifthofanumberismorethanthreefourthofthenumberby4.Findthenumber.(3)

12.Thelengthofarectangleexceedsitsbreadthby4cm.Ifthelengthandthebreadthare

eachincreasedby3cm,theareaofthenewrectanglewillbe81cm2morethanthatofthe

givenrectangle.Findthelengthandbreadthofthegivenrectangle.(4)

13.(a)Rashmienjoyshelpingoutsmallchildrenwiththeirstudies.Onedaysheasks

themtofindanumberwhichwhenmultipliedbygives aproductas .

(i)Findthenumbershegavetothechildren.

(ii)Rashmidoesnotchargeanyfeefromthechildren.Mentionanytwovalues

displayedbyher.

(b)Represent onanumberline.(4)



Class–8(Mathematics)

FormativeAssessment–1(2014-2015)

GeneralInstructions


MarksarealongwithEachquestion.

SECTION:A(2X9=18)

Q.1Simplify:

Q.2Simplify:

Q.3Expressinstandardform0.000000000567.

Q.4Usingprimefactorizationmethodfindthesquarerootof63504.

Q.5Findthevalueof:5002−4992

Q.6Findthesquareusingidentity

Q.7findthesquarerootbylongdivisionmethod54756

Q.8If23%ofais46,thenfinda

Q.9Expressindecimalfractions6.5%

SECTION:B(3X8=24)

Q.10Acisterncanbefilledbyonetapin4hrs.andbyanotherin3hours.Howlongwillit

taketofillitifbothtapsareopenedtogether?

Q.11Abagcontains5redballs,8whiteballs,4greenballsand87blackballs,ifoneballis

drawnatrandom,findtheprobabilitythatitis:



(i)black(ii)red(iii)notgreen

Q.12Analloycontains36%zinc,40%copperandtherestisnickel,Findingramsthe

quantityofeachofthecontentsinasampleof1kgalloy.

Q.13Findthesquarebydiagonalmethod2574

Q.1415boysearnRs.900in5days,howmuchwill20boysearnin7days?

Q.15Thepopulationofatownincreasesby6%everyyearIfthepresentpopulationis15900,

finditspopulationayearago.

Q.16Bywhatnumbershould(-4)2bemultipliedsothattheproductmaybeequalto10−2?

Q.17If ,findthevalueofX-2

SECTION:C(4X2=8)

Q.18Findthesquarerootcorrecttothreeplacesofdecimal8.

Q.19Acandoapieceofworkin25daysandBcanfinishitin20days.Theyworktogether

for5daysandthenAgoesaway.InhowmanydayswillBfinishtheremainingwork?



FormativeAssessment–III(2014-2015)

Subject:Mathematics

Class:8

GeneralInstructions:

Answerallthequestions.

Beforealternatingthequestionwriteserialnumberofthequestion.

SECTIONA

1.

(a) (b)

(c) (d)

2.Thevalueof is

(a)1800(b)300

(c)1200(d)600

3.Acuboidhas

(a)6edges(b)12edges

(c)8edges(d)4edges

4.Areaoftriangleis

(a)Productofdiagonal

(b) ×base×height

(c)Length×breadth

(d) productofdiagonals

5. is

(a)15a7(b)105a7

(c)105(d)15a8



SECTIONB

6.Thediagonalsofarhombusare7.5cmand12cm.Finditsarea.

7.UsingEucler’sformula,findtheedgesofapolyhedronwhosefacesandverticesare8and6

respectively.

8.Findtheproduct

9.Findproduct(5-2x)(3+x)

SECTION–C

10.Simplify:

11.Theareaofatrapeziumis34cm2andthelengthofoneoftheparallelsidesis10cmand

itsheightis4cm.Findthelengthoftheotherparallelside.

12.FindthesideofCubewhosesurfaceareais600cm2.

13.Canapolyhedronhave10faces,20edgesand15vertices?Explainwithsuitablereason.

14.Simplify(a+b+c)(a+b-c)

SECTIOND

15.Thefloorofabuildingconsistsof3000files,whicharerhombusshaped,andeachofits

diagonalsis45cmand30cminlength.Findthetotalcostofpolishingthefloor,ifthecost

perm2isRs4.

16.Showthat:

17.Aclosedcylindricaltankofradius7mandheight3mismadefromasheetofmetal.How

muchsheetofmetalisrequiredandfinditscapacity.



UsersubmittedPaper2016-2017


INDRAPRASTHAINTERNATIONALSCHOOL

GeneralInstruction:




1.Multiply bythereciprocalof

2.Howmanysidesdoesaregularpolygonhaveifthemeasureofanexteriorangleis24°?

3.Theareaofsquarefieldis200sqm.Findthelengthofoneside.

4.AtablemarkedatRs15,000isavailableforRs14,400.Findthediscountpercent.

5.Thevalueofamachinedepreciatesby10%annually.Ifthepresentvalueofthemachineis

Rs100000,whatwillbeitsvalueafter2years?

6.Evaluate:

7.Thevolumeofacubeis9261cm3.Findthesideofthecube.

8.Theproductoftworationalnumbersis Ifoneofthenumbersis ,findtheother.

9.Bywhatnumbershould bedividedsothatthequotientmaybe ?

10.Findvalueof:

2x2+y3for

11.Outofthe162swimmerswhocametothepoolonMonday,2/3ofthemcameinthe



afternoon.Outofthis1/4ofthemwerewomen.Howmanywomencametothepoolon

Mondayafternoon?

12.Findxsothat

13.Findsixrationalnumbersbetween and

14.Findthegreatest4-digitnumberwhichisaperfectsquare.3

15.If findx3.

16.Aladderofheight20misplaced6mfromthewall.Findtheheightreachedbytheladder

onthewalluptotwodecimalplaces.

17.Is53240aperfectcube?Ifnot,thenbywhichsmallestnaturalnumbershould53240be

dividedsothatthequotientisaperfectcube?

18.AshopkeeperboughttwoTVsetsatRs10,000each.Hesoldoneataprofit10%andthe

otheratalossof10%.Findwhetherhemadeanoverallprofitorloss.

19.Findthesmallestsquarenumberthatisdivisiblebyeachofthenumbers4,9and10.

20.Express63asthesumofoddnumbers.

21.Verify‑

22.Thepopulationofatownincreases5%inthefirstyearand4%inthesecondyear.Ifthe

populationwas3,60,000atthebeginningofthefirstyear,whatisthepopulationattheend

of2years?

23.ThelistpriceofacolorTVsetis`14,500/-thedealerallowsadiscountof15%oncash

payment,therateofVATis10%.Howmuchmoneyincashcustomerhastopaytothedealer

fortheTVset.

24.a.Theanglesofaquadrilateralareintheratio3:4:6:7,findthefourangles.

b.Theratiooftwosidesofaparallelogramis3:5anditsperimeteris96cm.Findthesidesof



theparallelogram.

25.a.Withoutactuallysquaring,findthevalueof:1052–1042

b.Findthesquarerootof0.0625.

26.RajivinvestsRs10000at10.5%perannumcompoundedannuallyandRaviinveststhe

sameamountat10%compoundedsemiannually.Attheendofoneyearwhogainsmore

andbyhowmuch?

27.Sohanpurchasedtwofansfor`1500/-each.Hesoldoneatalossof5%andanotherata

gainof10%.Findthetotalprofitorloss.

28.Thediagonalsofarhombusare24cmand10cm.Findthelengthofeachsideofthe

rhombus.

29.24000blooddonorswereregisteredwithacharitablehospital.Thenumberofdonors

increasedattherateof5%everysixmonths.Findthetimeperiodattheendofwhichthe

totalnumberofblooddonorsbecome27783.Whatvaluedoyoulearnfromit?

30.InthegivenfigureABCDisarhombus.

a.IsAB=AD?Why?

b.IsBC=DC?Why?

c.Is∆ABC≅∆ADC?Why?

d.Is∠BAC=∠DAC?Why?

31.81%of4600studentsinaschoolavailtheschooltransport.Howmanystudentsdonot

availtheschooltransport?Theschoolprincipalofferedfreetransporttofewstudentswho

wereneedy.Whichvaluesaredepictedbytheprincipal?



Class8thMathematics

AlgebricExpression

UserSubmittedPaper

Q1.Addthefollowingpolynomials:

a.5x2-8xy,-3x2+2xyand-5x2+3xy

b.2x3-9x2+8,3x2-6x-5,7x3-10x+1and3+2x-5x2-4x3

c.6p+4q–r+3,2r–5p-6,11q-7p+2r-1and2q-3r+4

d.4x2-7xy+4y2-3,5+6y2-8xy+x2and6–2x+2x2−5y2

e.6ax-2by+3cz,6by–11ax-czand10cz-2ax-3by

Q2.Subtractthefollowing:

a.-6p+q+3r+8fromp–2q-5r–8

b.5y4-3y3+2y2+y-1from4y4−2y3−6y2-y+5

c.4y2+5q2-6r2+7from3p2-4q2-5r2-6

d.Thetwoadjacentsidesofarectangleare5x2−3y2andx2+2xy.Findtheperimeter.

e.Theperimeterofatriangleis6p2-4p+9andtwoofitssidesarep2–2p+1and3p2-5p+

3.Findthethirdsideofthetriangle.

Q3.Findeachofthefollowingproducts:

a.(x4+y4)X(x4−y2)

b.(9x+5y)X(4x+3y)

c.(3x2+5x–9)X(3x–5)

d.(2x2+3x–7)X(3x2+5x+4)

Q4.Writethequotientandremainderwhenwedivide:

a.(x2+12x+35)by(x+7)

b.(15x2+x–6)by(3x+2)

c.(x3+1)by(x+1)

d.(5x3+12x2+12x+13)by(x2-3x+4)

e.(2x3−5x2+8x–5)by(2x2-3x+5)



Q5.Objectivetypequestion:

a.6y4÷(−2y3)is

(a)3y

(b)-3y

(c)3y3

(d)−3y3

b.(−72x2y3)÷(-8xy)is

(a)–9xy

(b)-9xy2

(c)9xy2

(d)9xy

c.Theremainderobtainedwhen-+t+5isdividedbyt–1is

(a)-4

(b)4

(c)1

(d)5

d.8a2b3÷(-2ab)=?

(a)4ab2

(b)4a2b

(c)−4ab2

(d)-4a2b



Class–8Mathematics

LINEAREQUATION-III

TESTPAPER

Note:-Allquestionsarecompulsory.

Solvethefollowingequationsforx:

1.4x-5(2x-3)=1-2x

2.2.4x+1.35=3.75x+13.5

3. (x-5)=24+8x

4.5x-2(2x-7)=2(3x-1)+

5.

6.3x-2(2x-5)=2(x+3)-8

7.

8.

9.

10.

11.

12.




LINEAREQUATION-IV

TESTPAPER


Solvethefollowing:-

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.



11.

12.

13.

14.




LINEAREQUATION-V

TESTPAPER


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.



13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.




SquaresandSquareRoots

UserSubmittedPapers-01

1. Findthesquarerootof6400.

2. Is90aperfectsquare?

3. Is2352aperfectsquare?Ifnot,findthesmallestmultipleof2352whichisaperfect

square.Findthesquarerootofthenewnumber.

4. Findthesmallestnumberbywhich9408mustbedividedsothatthequotientisaperfect

square.Findthesquarerootofthequotient.

5. Withoutdoinganycalculation,findthenumberswhicharesurelynotperfectsquare.

i. 153

ii. 257

iii. 408

iv. 441

6. Findthesquarerootofthefollowingnumbersbytheprimefactorizationmethod.

i. 400

ii. 9604

iii. 8100

iv. 1764

v. 5929

vi. 9216

7. Foreachofthefollowingnumbers,findthesmallestwholenumberbywhichitshouldbe

multipliedsoastogetaperfectsquare.Alsofindthesquarerootofthesquarenumberso

obtained.

i. 252

ii. 2925

iii. 396

iv. 2028

v. 1458

vi. 7

8. Foreachofthefollowingnumber,findthesmallestwholenumberbywhichitshouldbe



dividedsoastogetaperfectsquare.Alsofindthesquarerootofthesquarenumberso

obtained.

i. 252

ii. 180

iii. 1008

iv. 2028

v. 1458

vi. 768

9. ThestudentsofclassviiiofaschooldonatedRs2401inall,forprimeminister’snational

relieffund.Eachstudentdonatedasmanyrupeesastheno:ofstudentsintheclass.Find

theno:ofstudentsintheclass.

10. 2118plantsaretobeplantedinagardeninsuchawaythateachrowcontainsasmany

plantsastheno:ofrows.Findtheno:ofrowsandtheno:ofplantsineachrow.

11. Findthesmallestsquarenothatisdivisiblebyeachofthenos:4,9and10.

12. Findthesmallestsquarenothatisdivisiblebyeachofthenos:8,15and20.

13. Findtheleastno.thatmustbesubtractedfrom5607soastogetaperfectsquare.Also

findthesquarerootoftheperfectsquare.

14. Findthegreatest4-digitno:whichisaperfectsquare.

15. Findtheleastno:thatmustbeaddedto1300soastogetaperfectsquare.Alsofindsthe

squarerootoftheperfectsquare.

16. Findthesquarerootof12.25.

17. Areaofasquareplotis2304m2.Findthesideofthesquareplot.Alsofindthesquare

rootoftheperfectsquare.

18. Findthesquarerootofeachofthefollowingno:bydivisionmethod.

i. 2304

ii. 4489

iii. 3481

iv. 529

v. 3249

vi. 1369

vii. 5776

viii. 7921

ix. 576



x. 1024

xi. 3136

xii. 900

19. Findthesquarerootofthefollowingdecimalno:

i. 2.56

ii. 7.29

iii. 51.84

iv. 42.25

v. 31.36

20. Findtheleastno.whichmustbesubtractedfromeachofthefollowingno.soastogeta

perfectsquare.Alsofindthesquarerootoftheperfectsquaresoobtained.

i. 402

ii. 1989

iii. 3250

iv. 825

v. 4000

21. Findtheleastno:whichmustbeaddedtoeachofthefollowingno:soastogetaperfect

square.Alsofindthesquarerootoftheperfectsquaresoobtained.

i. 525

ii. 1750

iii. 252

iv. 1825

v. 6412

22. Findthelengthofthesideofasquarewhoseareais441m2.

23. InarighttriangleABCangleB=90o

24. a.IfAB=6cm,BC=8cm,findAC

b.IfAC=13cm,BC=5cm,findAB

25. Agardenerhas1000plants.Hewantstoplantthisinsuchawaythattheno:ofrowsand

theno:ofcolumnsremainsame.Findtheminimumno:ofplantsheneedsmoreforthis.

26. Thereare500childreninaschool.foraFiredrill.Theyhavetostandinsuchamanner

suchthatasquarearrangementisformed,i.e.theno.ofrowsisequaltotheno.of

columns.Howmanychildrenwouldbeleftoutinthisarrangement?

27. Anaturalnumberiscalleda_____or_____ifitisthesquareofsomenaturalnumber.



28. =_________

29.

30. Is(1,2,3)aPythagoreantriplet?

31. Is2352aperfectsquare?Ifnot,findthesmallestnumberbywhich2352mustbe

multipliedsothattheproductisaperfectsquare.Findthesquarerootoftheperfect

squareobtained.

32. Findthesmallestnumberbywhich9408mustbedividedsothatthequotientisaperfect

square.Findthesquarerootoftheperfectsquareobtained.

33. Findtheleastnumberwhichmustbesubtractedfrom18265soastogetaperfectsquare.

34. Findtheleastnumberwhichmustbeaddedto893304toobtaina

35. perfectsquare.

36. Findthesquarerootof2.9correcttotwoplacesofdecimal.

37. Findthesquarerootof correcttotwoplacesofdecimal.

38. Findthesquarerootof .

39. Findtheleastperfectsquarewhichisdivisibleby5,6and8.

40. Findthesmallestfivedigitnumberwhichisaperfectsquare.

41. FindtheothertwomembersofaPythagoreantriplet,oneofthenumbersofwhichis16.

42. Check,is(12,35,37)aPythagoreantriplet?

ClassTestPaper

ByDipamSen


Documents

Sl No Topic Notes NCERT QA Video 1 Rational Numbers 8 32