1923510th Formula

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Sample Paper 2013Class XSubject Mathematics Formulae

1.Compound Interest ( Imp chapter) S.I = PTR

100. Amt = Pri ( 1 + Rat )Time

100 Note: If you are asked to compute the interest semiannua!!y ( "a!f year!y) the

a#o$e formu!a is to #e modified% #y taking time x 2, and rate 2 If the rates are &i$en different!y for the consecuti$e years% then

'or eamp!e if the rates are * % 1 * and 1, * respecti$e!y% then Amt = Pri ( 1 + ) ( 1 + 1 ) ( 1 +1, ) 100 100 100. "ere% you need not mention time as

eponent. -epreciation ertain items $a!ue /i!! #e diminished as the time passes% then it is

kno/n as depreciation. 'or eamp!e the $a!ue of a car% refri&erator% machinery etc.

in that case.

'ina! a!ue of machine = Actua! $a!ue ( 1 Rat )Time100

In popu!ation &ro/th pro#!ems% If present popu!ation is &i$en and askin& for

i) The popu!ation n2 yrs a&o% then take Amount as Present popu!ation2% and !ind

"#rincipa$%

ii) The popu!ation after n2 yrs% then take Principa! as Present popu!ation2% and !ind

"&mount%

2.'a$es Tax &T.

Se!!in& price = 3arked price + * of sa!es ta.

Se!!in& price = 3arked price 4 * -iscount . Ta * = Ta 100

3P -iscount * = -iscount 100

3P.

5hi!e computin& AT

In step1 6 Take manufacturin& cost and a!cu!ate AT on*anu!acturing

Cost

In step 6 Take Profit 1% and a!cu!ate AT on #ro!it 1 on$+

In step7 6 Take Profit % and a!cu!ate AT on #ro!it 2 on$+

In step8 6 Take Profit 7% and a!cu!ate AT on #ro!it on$+

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Add a!! to &et Tota$AT

Se!!in& price = 3anufacturin& cost +Profit 1 +Profit + Profit 7 etc.% + Tota! AT

.-ankingSa$in&s 9ank account 5hi!e takin& the entries you ha$e to #ear in mind that

5hi!e computin& the interest a!/ays take time as 1/12% irrespecti$e of the tota!

num#er of months &i$en. i.e in PTR /100% take time as 1/1% instead of tota! no ofmonths.

If entry of a particu!ar month is not &i$en% then you ha$e to take the !ast entry of the

pre$ious month ("ere at times there is chance of makin& mistake% choose the $a!ue

from the :uestion.) I f you are asked to find the amount that /i!! #e o#tained on c!osin& the account

Then take $ast entr+from the ;uestion + Interest o#tained

( 9ut -<

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a84 #8 = (a )4 (# ).

(a+ # ) (a4 # )

(a+ # ) (a 4 #) (a + #)

( a + #)7 = a7 + #7+ 7a# (a +#)

a7+ #7 = (a+ #)(a+ a# + #)

( a 4 #)7 = a74 #74 7a# (a 4 # )

a74 #7 = (a4 #)(a+ a# + #) (or)

Tria$ 5rror method.

In step 6 Take the product of ommon terms2 as their "'.

In step7 6 Take the product of A!! the terms %

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ote6 /hen = y% is &i$en% then use ru!er to measure the $ertica! distance of the point

from the !ine% and then take the same distance on the other side to o#tain it2s ref!ection.

9.atio #roportion.

-up!icate ratio of a :# is a2:#2 ( Incase of Su#dup!icate ratio you ha$e to takeS:uare root2)

Trip!icate ratio of a :# is a:# ( Incase of Su#trip!icate ratio you ha$e to takeu#e root2)

Proportion a : # = c :d% ontinued Proportion a : # = # : c%(3idd!e $a!ue to#e repeated)

1st nd 7rd 8th proportiona!s 1st nd nd 7rdproportiona!s

Product of 3eans2(3idd!e $a!ues) = Product of tremes2(ither end $a!ues)

If a = c is &i$en% then omponendo D -i$idendo is a + # = c + d

# d a 4 # c 4 d

-o you ha$e a :uestion F 5here to take FGE method HE ou may adopt it in the

fo!!o/in& situations

Cen&th on the map J mode! = k times the ori&ina! !en&th.

Area on the map J mode! = k2

times the ori&ina! Area.o!ume of the mode! = k times the ori&ina! o!ume.

;.emainder theorem.

If ( 4 ) is a !actorof the &i$en epression% then

1

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Some times% you may #e asked to find A + A9 + K is &i$en% you ha$e to assume it

as A + A9 + K I, "ere% I is the Identity matri.

in /hich a!! the principa! dia&ona! $a!ues are 1% and the rest

are Lero2.

11.istance 'ection 3ormu$ae

-istance = =/(4 1) + (y4 y1) . ( The same formu!a is to #e used to find the!en&th of !ine

se&ment% sides of a trian&!e% s:uare% rectan&!e%

para!!e!o&ram etc.%)

To pro$e co!inearity of the &i$en three points A%9% and % ou ha$e to find

The distance of A9 + The distance of 9 = The distance of A.

Section formu!a6 point (% y) = m1 + m1 % m1 y+ my1

m1 + m m1 + m

3id point = 1 + % y1 + y

entroid of a trian&!e = 1 + + 7 % y1 + y + y7

7 7

12.58uation o! a $ine.

If t/o points are &i$en% then S!ope (m) = y 4 y1

4 1

If a point% and s!ope are &i$en% then S!ope (m) = y 4 y1

4 1

If t/o !ines are Para!!e!2 to each other then their s!opes are e:ua! i.e m 1 = m



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If t/o !ines are Perpendicu!ar2 to each other then product of their s!opes is 4 1. i.em1 m= 4 1

-ependin& upon the :uestion ou may ha$e to use a) y = m + c% /here c2 is the y

intercept.

1.'imi$arit+. If t/o trian&!es are simi!ar then% ratio of their sides are e:ua!.

i.e if M A9 >M P;R then A9 = 9 = A P; ;R PR. If M A9 >M P;R then Area of M A9 = Side2 = A92= 92 = A2

Area of M P;R Side2 P;2 ;R2 PR2

Si@e transformation6

Cen&th of the mode! = k2 times the actua! !en&th. >"ere k2 is to #e taken as 1 J 10000 ?



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Area of the mode! = k

2

2 times the actua! area. >"ere k

2

2 is to #e taken as (1 J 10000)

2

?o!ume of the mode! = k2 times the actua! $o!ume. >"ere k2 is to #e taken as (1 J

10000)?

1.'+mmetr+.

A !ine /hich di$ides the &i$en fi&ure into t/o identica! parts is kno/n as !ine of

Symmetry2

1. An an&!e has

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The sum of opposite an&!es of a cyc!ic :uadri!atera! is a!/ays 10 0.

1?.Circum!erence &rea o! a Circ$e.

Area of a irc!e = r2.

Perimeter of a irc!e = r Area of sector = . r2. 7N0

Cen&th of an arc = . r. 7N0

Area of rin& = ( R24 r2) -istance mo$ed #y a /hee! in one re$o!ution = ircumference of the /hee!.

um#er of re$o!utions = . Tota! distance mo$ed .

ircumference of the /hee!.

Area of an e:ui!atera! trian&!e = =J7 Side2.

8

Note:5hi!e so!$in& 3ensuration2 pro#!ems% take care of the fo!!o/in&.

1. If diameter of a circ!e is &i$en% then find the radius first

("a$e you made mistake ear!ier #y takin& d2 as radius2 and so!$ed the

pro#!em H)

. heck the units of the entire data. If the units are different% then con$ert them to

the same units.

'or amp!e6 -iameter = 18 cm% and "ei&ht = 7 m

Therefore -iameter = 18 cm% and "ei&ht = 700 cm ("a$e you e$er

committed such mistake H)



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19.'o$ids.1. C+$inder6 o!ume of a cy!inder = r2h

ur$ed surface area = rh

Tota! surface area = rh + r2 r (h +r)

o!ume of ho!!o/ cy!inder = R2h 4 r2h ( R24 r2) hTSA of ho!!o/ cy!inder = R24r2?

(

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#) Surface area = SA of one + SA of hemisphere (usua!!y Surface area /i!! not

#e asked)

1;.Trigonometric Identities.

5here$er S:uare2 appears think of usin& the identities i) Sin2 + os2 = 1

ii) Sec2 4 Tan2 = 1

iii) oseec2 4 ot2 = 1

Try to con$ert a!! the $a!ues of the &i$en pro#!em in terms of Sin and os

osec may #e /ritten as 1JSin

Sec may #e /ritten as 1/os

ot may #e /ritten as 1/Tan

Tan may #e /ritten as Sin /os

5here$er fractiona! parts appears then think takin& their C32

Think of usin& ( a + # )2% ( a 4 # )2% ( a + # )% ( a 4 # )formu!ae etc.%

Rationa!i@e the denominator > If a + #% (or) a 4 # format is &i$en in the denominator?

ou may separate the denominator 'or 6 Sin + os as Sin + os

Sin Sin Sin

1 + ot

If you are not a#!e to so!$e the C"S part comp!ete!y% -o the pro#!em to such an

etent you can so!$e% then start /orkin& /ith R"S% and fina!!y you /i!! end up the

pro#!em at a step /here C"S = R"S Sin ( O0 4 ) = os 6 os ( O0 4 ) = Sin .

Sec( O0 4 ) = osec 6 osec ( O0 4 ) = Sec

Tan ( O0 4 ) = ot 6 ot ( O0 4 ) = Tan

2

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-on2t for&et to /rite the sca!e on ais% and on yais. To find the Co/er :uarti!e2 take /8 >"ere is f? then take the correspondin& point

on Uais

To find the Bpper :uarti!e2 take 7/8% then take the correspondin& point on Uais

To find the 3edian2 take /% then take the correspondin& point on Uais

22.*easures o! Centra$ Tendenc+.3or unBgrouped data

Arithmetic 3ean = Sum of o#ser$ations

o of o#ser$ations

3ode = The most fre:uent!y occurred $a!ue of the ra/ data.

To find the 3edian first of a!! arran&e the data in Ascendin&2 or -escendin&2 order%then

3edian = (+1)J term $a!ue of the &i$en data% in case of the data is ha$in& odd no ofo#ser$ations.

3edian = >(J) + (+1)J)? / term $a!ue of the &i$en data% in case of the data isha$in&

e$en num#er of o#ser$ations.3or grouped data

Arithmetic 3ean = f (-irect method)

fArithmetic 3ean = a + fd (short cut method)

f

Arithmetic 3ean = a + fu c (stepde$iation method) f

2.#roai$it+.

Pro#a#i!ity of an e$ent 6 P(e$ent) = um#er of fa$ora#!e outcomes

Tota! num#er of outcomes

In a deck of p!ayin& cards% there are four sym#o!s

V(Spades in 9!ack co!our) ha$in& A% %7%8%,%N%K%%O%10%W%G% and ; tota! 17 cards

X(!u#s in 9!ack co!our) ha$in& A% %7%8%,%N%K%%O%10%W%G% and ; tota! 17 cards

Y("earts in Red co!our) ha$in& A% %7%8%,%N%K%%O%10%W%G% and ; tota! 17 cards

Z(-iamond in Red co!our) ha$in& A% %7%8%,%N%K%%O%10%W%G% and ; tota! 17 cards, cards

Wack% Gin& and ;ueen are kno/n as 'ace ards2 % As these cards are ha$in& some

pictures on.



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Note:-ra/in& rou&h sketches is a!/ays ad$isa#!e% thou&h% you may not &et marks for

them% #ut% they /i!!

&i$e a c!ear cut idea to so!$e the pro#!em.

A!! The 9est

Chintan 'hah

h+e+ Institute

( &mawadi/ Cg road, 'ate$$ite, Dudges -ung$ow)

;92

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1923510th Formula