Some Quick Maths Formulas | Fraction (Mathematics) | Elementary Geometry

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  SOME QUICK MATHS FORMULASFormulas1. Sum of rst n natural numbers  n!n 1#$%%. Sum of t&e s'uares of rst n natural numbers  n!n 1#!%n 1#$(). Sum of t&e *ubes of rst n natural numbers  +n!n 1#$%,-%. Sum of rst n natural o// numbers  n-%0. Aera2e  !Sum of 3tems#$4umber of 3temsAr3t&met3* 5ro2ress3on !A.5.#6An A.5. 3s of t&e form a7 a /7 a %/7 a )/7 89&ere a 3s *alle/ t&e :rst term; an/ / 3s *alle/ t&e :*ommon /3<eren*e;1. nt& term of an A.5. tn  a !n=1#/%. Sum of t&e rst n terms of an A.5. Sn  n$%+%a !n=1#/, or Sn  n$%!rst term last term#>eometr3*al 5ro2ress3on !>.5.#6A >.5. 3s of t&e form a7 ar7 ar%7 ar)7 89&ere a 3s *alle/ t&e :rst term; an/ r 3s *alle/ t&e :*ommon rat3o;.1. nt& term of a >.5. tn  arn=1%. Sum of t&e rst n terms 3n a >.5. Sn  a?1=rn?$?1=r?5ermutat3ons an/ Comb3nat3ons 6n5r  n@$!n=r#@n5n  n@n51  nnCr  n@$!r@ !n=r#@#nC1  nnC  1  nCnnCr  nCn=rnCr  n5r$r@4umber of /3a2onals 3n a 2eometr3* 2ure of n s3/es  nC%=n Tests of B33s3b3l3t 6A number 3s /33s3ble b % 3f 3t 3s an een number.A number 3s /33s3ble b ) 3f t&e sum of t&e /323ts 3s /33s3ble b ).A number 3s /33s3ble b  3f t&e number forme/ b t&e last t9o /323ts 3s /33s3ble b .A number 3s /33s3ble b 0 3f t&e un3ts /323t 3s e3t&er 0 or .A number 3s /33s3ble b ( 3f t&e number 3s /33s3ble b bot& % an/ ).A number 3s /33s3ble b D 3f t&e number forme/ b t&e last t&ree /323ts 3s /33s3ble b D.A number 3s /33s3ble b  3f t&e sum of t&e /323ts 3s /33s3ble b .A number 3s /33s3ble b 1 3f t&e un3ts /323t 3s .A number 3s /33s3ble b 11 3f t&e /3<eren*e of t&e sum of 3ts /323ts at o//  la*es an/ t&e sum of 3ts /323ts at een la*es7 3s /33s3ble b 11.H.C.F an/ L.C.M 6H.C.F stan/s for H32&est Common Fa*tor. T&e ot&er names for H.C.F are >reatest Common B33sor !>.C.B# an/ >reatest Common Measure !>.C.M#. T&e H.C.F. of t9o or more numbers 3s t&e 2reatest number t&at /33/es ea*& one of t&em eGa*tl. T&e least number 9&3*& 3s eGa*tl /33s3ble b ea*& one of t&e 23en numbers 3s *alle/ t&e3r L.C.M. T9o numbers are sa3/ to be *o=r3me 3f t&e3r H.C.F. 3s 1.H.C.F. of fra*t3ons  H.C.F. of numerators$L.C.M of /enom3natorsL.C.M. of fra*t3ons  >.C.B. of numerators$H.C.F of /enom3nators5ro/u*t of t9o numbers  5ro/u*t of t&e3r H.C.F. an/ L.C.M.5ERCE4TA>ES 6If A 3s R more t&an 7 t&en  3s less t&an A b R $ !1 R# J 1If A 3s R less t&an 7 t&en  3s more t&an A b R $ !1=R# J 1If t&e r3*e of a *ommo/3t 3n*reases b R7 t&en re/u*t3on 3n *onsumt3on7 not to 3n*rease t&e eGen/3ture 3s 6 R$!1 R#J1If t&e r3*e of a *ommo/3t /e*reases b R7 t&en t&e 3n*rease 3n *onsumt3on7 not to /e*rease t&e eGen/3ture 3s 6 R$!1=R#J15ROFIT  LOSS 6>a3n  Sell3n2 5r3*e!S.5.#  Cost 5r3*e!C.5#Loss  C.5.  S.5.>a3n   >a3n J 1 $ C.5.Loss   Loss J 1 $ C.5.S.5.  !1 >a3n#$1JC.5.S.5.  !1=Loss#$1JC.5.If C5!G#7 >a3n!#7 >a3n!#. T&en   GJ$1. +Same 3n *ase of Loss,RATIO  5RO5ORTIO4S6 T&e rat3o a 6 b reresents a fra*t3on a$b. a 3s *alle/ ante*e/ent an/ b 3s *alle/*onse'uent. T&e e'ual3t of t9o /3<erent rat3os 3s *alle/ roort3on.If a 6 b  * 6 / t&en a7 b7 *7 / are 3n roort3on. T&3s 3s reresente/ b a 6 b 66 *6 /.In a 6 b  * 6 /7 t&en 9e &ae aJ /  b J *.If a$b  *$/ t&en ! a b # $ ! a  b #  ! * / # $ ! *  / #. TIME  NORK 6If A *an /o a 3e*e of 9or 3n n /as7 t&en A;s 1 /a;s 9or  1$nIf A an/  9or to2et&er for n /as7 t&en !A #;s 1 /as;s 9or  1$nIf A 3s t93*e as 2oo/ 9orman as 7 t&en rat3o of 9or /one b A an/   %615I5ES  CISTER4S 6  If a 3e *an ll a tan 3n G &ours7 t&en art of tan lle/ 3n one &our  1$GIf a 3e *an emt a full tan 3n  &ours7 t&en art emt3e/ 3n one &our  1$If a 3e *an ll a tan 3n G &ours7 an/ anot&er 3e *an emt t&e full tan 3n &ours7 t&en on oen3n2 bot& t&e 3es7t&e net art lle/ 3n 1 &our  !1$G=1$# 3f PGt&e net art emt3e/ 3n 1 &our  !1$=1$G# 3f GP TIME  BISTA4CE 6B3stan*e  See/ J T3me1 m$&r  0$1D m$se*1 m$se*  1D$0 m$&rSuose a man *oers a *erta3n /3stan*e at G m& an/ an e'ual /3stan*e at m&. T&en7 t&e aera2e see/ /ur3n2 t&e 9&ole ourne 3s %G$!G # m&.5ROLEMS O4 TRAI4S 6 T3me taen b a tra3n G metres lon2 3n ass3n2 a s32nal ost or a ole or a stan/3n2 man 3s e'ual to t&e t3me taen b t&e tra3n to *oer G metres. T3me taen b a tra3n G metres lon2 3n ass3n2 a stat3onar obe*t of len2t&  metres 3s e'ual to t&e t3me taen b t&e tra3n to *oer G  metres.Suose t9o tra3ns are mo3n2 3n t&e same /3re*t3on at u m& an/  m& su*& t&at uP7 t&en t&e3r relat3e see/  u= m&.If t9o tra3ns of len2t& G m an/  m are mo3n2 3n t&e same /3re*t3on at u m& an/  m&7 9&ere uP7 t&en t3me taen b t&e faster tra3n to *ross t&e slo9er tra3n  !G #$!u=# &ours.Suose t9o tra3ns are mo3n2 3n oos3te /3re*t3ons at u m& an/  m&.  T&en7 t&e3r relat3e see/  !u # m&.If t9o tra3ns of len2t& G m an/  m are mo3n2 3n t&e oos3te /3re*t3ons atu m& an/  m&7 t&en t3me taen b t&e tra3ns to *ross ea*& ot&er  !G #$!u #&ours.If t9o tra3ns start at t&e same t3me from t9o o3nts A an/  to9ar/s ea*& ot&er an/ after *ross3n2 t&e tae a an/ b &ours 3n rea*&3n2  an/ A rese*t3el7 t&en A;s see/ 6 ;s see/  !b 6 a#SIM5LE  COM5OU4B I4TERESTS 6Let 5 be t&e r3n*3al7 R be t&e 3nterest rate er*ent er annum7 an/ 4 be t&e t3me er3o/.S3mle Interest  !5J4JR#$1Comoun/ Interest  5!1 R$1#-4  5Amount  5r3n*3al Interest9&en rate of 3nterest t3me n r3n*3al are *onstant /en r3n*3al!C.I.=S.I.#J!1$R#-4  LO>ORITHMS 6If a-m  G 7 t&en m  lo2a!G#.5roert3es 6lo2G!G#  1lo2G!1#  lo2a!GJ#  lo2a!G# lo2a!#lo2a!G$#  lo2 aG  lo2 alo2a!G#  1$lo2G!a#lo2a!G-#  !lo2a!G##lo2a!G#  lo2b!G#$lo2b!a#4ote 6 Lo2ar3t&ms for base 1 /oes not eG3st.AREA  5ERIMETER 6S&ae Area 5er3meterC3r*le  !Ra/3us#% %!Ra/3us#S'uare !s3/e#% !s3/e#Re*tan2le len2t&Jbrea/t& %!len2t& brea/t&#Area of a tr3an2le  1$%JaseJHe32&t orArea of a tr3an2le   !s!s=!s=b#!s=*## 9&ere a7b7* are t&e len2t&s of t&e s3/es an/ s  !a b *#$%Area of a arallelo2ram  ase J He32&tArea of a r&ombus  1$%!5ro/u*t of /3a2onals#Area of a trae3um  1$%!Sum of arallel s3/es#!/3stan*e bet9een t&e arallel s3/es#Area of a 'ua/r3lateral  1$%!/3a2onal#!Sum of s3/es#Area of a re2ular &eGa2on  (!)$#!s3/e#%Area of a r3n2  !R%=r%# 9&ere R an/ r are t&e outer an/ 3nner ra/33 of t&e r3n2.Area of a *3r*ler-% or /-%$Area of sem3=*3r*ler-%$%Area of a 'ua/rant of a *3r*ler-%$Area en*lose/ b t9o *on*entr3* *3r*les!R-%=r-%#Area of a se*tor$1D /e2ree Jr4o of reolut3ons *omlete/ b a rotat3n2 9&eel 3n 1 m3nute/3stan*e moe/ 3n 1 m3nute$*3r*umferen*eVOLUME  SURFACE AREA 6Cube 6Let a be t&e len2t& of ea*& e/2e. T&en7Volume of t&e *ube  a) *ub3* un3tsSurfa*e Area  (a% s'uare un3tsB3a2onal   ) a un3ts
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