Maths General FunDAS

7/24/2019 Maths General FunDAS

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Info to nail GMAT quant – compiled by dreamz and tictaktoe/piyusht

QUAT T!"#$%

1) nPr = n!/(n-r)!

2) nPn = n!

3) nCr = n!/(n-r)!r!

4) nCn = 1

5) nP0 = 1

6) nC0 = 1

7) A& An = a + (n-1)d

Sn = n/2[2a + (n-1)d]

8) G& An = ar(n-1)

Sn = a(rn – 1 )/ (r-1)

S∞ = a/(1-r)

9) 1 m" = 1760 #ard$

10) 1 #ard = 3 %""&

11) 1 m"2 = 640 a'r"$

12) a*n = 4 ,ar&$ '* 4228

13) 1 ,ar& = 2 n&$

14) 1 n& = 2 ',$

15) 1 ', = 8 *,n'"$

16) 1 *,nd = 16 *,n'"$17) 1 *,n'" = 16 dram$

18) 1 . = 22 *,nd$

19) 30-60-90 &ran" 132 $d"$

20) 45-45-90 &ran" 112 $d"$

21) a33 a

22) % A &an = n*& &an n*& A

23) "r* dd"d # an# n*n"r* n&""r $ "r*

24) $*n # 0 $ ,nd"%n"d

25)



Tan'ent (hord An'le)An an" %*rm"d # an n&"r$"'&n &an"n&

and '*rd a$ &$ "r&": ;*n; &" 'r'"

<an"n& C*rd An" =

n&"r'"&"d Ar'

AC $ an an" %*rm"d # a &an"n& and'*rd

&$ intercepted arc $ &" mn*r ar' %r*m A &*

mAC = 60>

An'le *ormed Inside of a (ircle by T+o

Intersectin' (hords)

?"n &@* '*rd$ n&"r$"'& ;n$d"; a 'r'"%*,r an"$ ar" %*rm"d A& &" *n& *%

n&"r$"'&*n &@* $"&$ *% "r&'a an"$ 'an "$""n n &" '*rn"r$ *% &" B &a& $ %*rm"d *n&" '&,r" "m"m"r "r&'a an"$ ar"

",a

An" D*rm"d In$d" # <@* C*rd$ =

,um *% n&"r'"&"d Ar'$

En'" #*, a" %*,nd EFG *% &"$"an"$ #*, a,&*ma&'a# .n*@ &"

$"$ *% &" *&"r &r"" # ,$n #*,r.n*@"d" *% "r&'a an"$ ("n

",a) and adHa'"n& an"$ %*rmn a$&ra& n" (addn &* 180)

G $ %*rm"d # &@* n&"r$"'&n'*rd$

&$ intercepted arcs ar" [F*&" &" n&"r'"&"d ar'$ "*n

&* &" $"& *% "r&'a an"$]

a$* mCGA = 120> ("&'a an")

mGC and mGA = 60> # $&ra&n"

An'le *ormed #utside of a (ircle by the Intersection of)

;<@* <an"n&$; *r ;<@* S"'an&$; *r ;a <an"n& and a S"'an&;



<" %*rm,a$ %*r a <IGG *% &"$" $&,a&*n$ ar" &" $am"

An" D*rm"d E,&$d" = -ifference *% n&"r'"&"d Ar'$

(?"n $,&ra'&n $&ar& @& &" ar"r ar')

T+o Tan'ents)AC $ %*rm"d # &@* &an"n&$ n&"r$"'&n

*,&$d" *% 'r'" E<" intercepted arcs ar" mn*r ar' AC and

maH*r ar' AC <"$" &@* ar'$ &*"&"r'*mr$" &" "n&r" 'r'"

Special situation for this set up & 'an " r*"n &a& AC and '"n&raAEC ar" $,"m"n&ar# <,$ &" an" %*rm"d # &" &@* &an"n&$ and

&$ %r$& n&"r'"&"d ar' a$* add &* 180>

T+o ,ecants)

ACG $ %*rm"d # &@* $"'an&$ n&"r$"'&n*,&$d" *% 'r'" E

<" intercepted arcs ar" mn*r ar'$ and

AG

a Tan'ent and a ,ecant)A $ %*rm"d # a &an"n& and a $"'an&

n&"r$"'&n *,&$d" *% 'r'" E<" intercepted arcs ar" mn*r ar'$ AC and

A

26) <" $&andard d"a&*n $ a $&a&$&' &a& &"$ #*, *@ &&# a &" ar*,$

":am"$ ar" ',$&"r"d ar*,nd &" m"an n a $"& *% da&a ?"n &" ":am"$ ar"



r"&&# &&# ,n'"d &*"&"r and &" "-$a"d ',r" $ $&"" &" $&andard

d"a&*n $ $ma ?"n &" ":am"$ ar" $r"ad aar& and &" " ',r" $

r"a&"# %a& &a& &"$ #*, a" a r"a&"# ar" $&andard d"a&*n

27) n(A ∪ ∪ C) = n(A) + n ()+ n(C)– n(A ∩ ) – n(A ∩ C) – n( ∩ C)

+ n(A ∩ ∩ C)

28) n(A*n#) = n(A) – n(A ∩ C) – n(A ∩ ) + n(A ∪ ∪ C)

29) d"nd = $*r J K,*&"n& + "mand"r

30) LCM J ICD = Pr*d,'& *% 2 n,m"r$

31) 1 + 2 + 3 NNNNNNn = n J n+1 / 2

32) S,m *% $,ar"$ *% 1$& n na&,ra n,m"r$ = n (n+1)(2n+1) / 6

33) S,m *% ',"$ *% 1$& n na&,ra n,m"r$ = [n (n+1)/2]2

34)

,quares and (ubes

umber . 0 ,quare . 1 0 (ube . 2 0

1 1 12 4 83 9 274 16 645 25 125

6 36 2167 49 -8 64 -9 81 -10 100 -11 121 -12 144 -13 169 -14 196 -15 225 -16 256 -17 28918 32419 36121 44122 48423 52924 57625 625

35)*ractions and &ercenta'e)



*raction -ecimal &ercenta'e1 / 2 05 501 / 3 033 33 1/32 / 3 066 66 2/31 / 4 025 253 / 4 075 75

1 / 5 02 202 / 5 04 403 / 5 06 604 / 5 08 801 / 6 0166 16 2/35 / 6 0833 83 2 / 31 / 8 0125 12 1 / 23 / 8 0375 37 1 / 25 / 8 0625 62 1 / 27 / 8 0875 87 1 / 21 / 9 0111 112 / 9 0222 221 / 10 01 10

1 / 20 005 51 / 100 001 1

36) A"ra" $""d = <*&a d$&an'" / <*&a <m"

34 5hen equal distances are co6ered in different speed then +e take the

harmonic mean

A6 ,peed 7 1ab / a 8 b

14 -ifferent distances in same time +e take AM

A6 ,peed is 7 a 8 b / 1

37) Simple Interest: SI = PRT / 100, A = P + SI

38) 1 F'." = 5 '"n&$1 dm" = 10 '"n&$1 ,ar&"r = 25 '"n&$1 a% = 50 '"n&$1 d*ar = 100 '"n&$

39) G,a&"ra &ran" Ar"a = (3 J a2) /4

40) Ar"a *% &ra",m = O (I"& J S,m *% ara" $d"$)

41) Ar' L"n& = ( / 360) 2 r

42) Ar"a *% $"'&*r = ( / 360) r 2

43) G,a '*rd$ ar" ",d$&an& %r*m &" '"n&"r

44) (:+#) 8 = 8C8:8 + 8C7:7# + 8C6:6#2 + 8C5:5#3 + N + 8C2:2#6 + 8C1:#7 + 8C0#8

45) S*m"&m"$ @" "& $* n*"d @& &" n&&#-r&&"$ *% ma&"ma&'$ &a& @"$&ar& %,n'&*nn ." a,&*ma&*n$ and $&* thinkin *n& %a r"# &* &$



&ra D*r ":am" @a& $ &" r*a&# &a& a n,m"r am*n$& &" %r$&1000 *$&" n&""r$ $ d$" # 8Q *n& $&ar& '*,n&n &" m,&"$ *%8! <" %,r" *% 1000 $ a r"d "rrn R$" a &&" '*mm*n $"n$" <"n,m"r$ @ " 8162432NS* 1 n ""r# 8 n,m"r$ $ a m,&" *% 8 ""n% #*, '*n$d"r &" %r$& m*n n&""r$ S* Pr*a&# $ 1/8

46) <" n,m"r *% n&""r$ %r*m A &* n',$" $ = -A +1

47) A"ra" *% '*n$"',&" n,m"r$G %r*m 13 &* 77 = (13+77)/2

48) S*" = ('an" n #)/('an" n :)

49) 00 = ,nd"%n"d

50)

S*" = -1 S*" =2 S*" = 1

S*" = 0

S*" = n%n&#

51) S,m *% n&"r*r an"$ *% a *#*n @& n $d"$ = (n-2)J180

52) "r"" m"a$,r" *% *n" an" n a r",ar *#*n @& n $d"$

= (n-2)J180 T/n

53) ?"n multiplyin' *r di6idin' *& $d"$ *% an n",a&# # a ne'ati6e

n,m"r &" n",a&# $n re6erses4

–: # = -(-:) # = : -#

54) Dra'&*n (%ra'&*n)2 %*r a *$&" %ra'&*n$

55) Dra'&*n (%ra'&*n ) %*r a *$&" %ra'&*n$

56) % n $ a *$&" n&""r (n6)/2 = (n12 / 4)

57) % 1 2 3 N n ar" '*n$"',&" *$&" n&""r$ and &"r a"ra" $ an *dd

n&""r = n $ *dd = $,m *% $"r"$ $ *dd



58)n a &ran" @& $d"$ *% m"a$,r" a and ' a-'a+

59)"%*r" '*n%rmn &r# and a'. $*" and ma." $,r" &a& , a" an$@"r"d @a&

a$ ""n a$."d

60)?"n &" ,"$&*n m"n&*n$ rm" n,m"r r"m"m"r &* &n. *% 2 &**

61)n a &ran" % &" $,m *% &@* an"$ = &rd an" &"n & $ a r& an"d&ran"

62)* n*& &ran$*r& n%*rma&*n %r*m an*&"r $&a&"m"n& ,n"$$ '*n$d"rn *&

'*"'&"#

63)A- = *dd = a + = *dd

64)

65)



66) % a S ,"$&*n $m# a$.$ @"&"r a ' and d ar" '*n$"',&" n&""r$U ,$"#*,r ran & a$ H,$& a$."d , &* an$@"r % &"# ar" '*n$"',&" n*& % &"# ar"'*n$"',&" n *rd"r

67) M"a$,r" *% an an" *% a '#'' *#*n = 180 – 360/n @"r" n $ &" n,m"r*% $d"$ *% &" *#*n

68) S*m"&m"$ m$&a."$ m& a$* " '*mm&&"d # $m# m$r"adn &"$&a&"m"n& G

*& <m and Iarr# r"'""d an a'r" *% and m*r" &an F"" = & = n + 1 = n + 1<m and Iarr# r"'""d an a'r" m*r" &an F"" = & + = n+1

69)

A

C

L"& <ran" AC " ",a&"ra @& "a' $d" *% m"a$,r" Va and AC ⊥ A = = A = a ∠a = ∠ = ∠' = 600

AC = (a2 + a/2 2)= 3Ja/2

Ar"a = 3 J a2 /4

P"rm"&"r = 3a ad,$ *% 'r'" E = a/3 = AC J 2/3 ad,$ *% 'r'" E = 3a/6 = AC J 1/3

E E

70) <@* 'r'"$ @ &*,' "a' *r n&"r$"'& "a' *&"r % &" d$&an'" "&@""n &"r'"n&"r$ d $ $,' &a&

– r ≤ d ≤ + r @"r" and r ar" &" rad *% &" &@* 'r'"$

71) "mand"r *% "$$ &an &@* m"an$ n*& H,$& *n"U & a$* m"an$ r"mand"r *% "r*



72) * n*& ma." ,n@arran&"d a$$,m&*n$ 12 mdn& &* 12 n**n d*"$ n*&m"n&*n @a& da#$ and "n'" #*, 'ann*& %nd *,& &" &m" "r*d

73) S&andard d"a&*n *% a $"& $ a@a#$ n"a&" and ",a$ "r* *n# % a""m"n&$ *% &" $"& ar" ",a

74) % &" d%%"r"n'" "&@""n &" ar"$& and &" $ma"$& d$*r *% a n,m"r $ B&" n,m"r $ B + 1

75) A@a#$ r"m"m"r &" $"'a @a&' *,& 'a$"$ n S ,"$&*n$ % &" ,"$&*nm"n&*n$ m"an *% a $"& &" m"an 'an " GE a$*

76) % ar"a *% a r"'&an" $ .n*@n da*na $ .n*@n "rm"&"r 'an " %*,nd

a2 + 2 = da*na2

a2 + 2 + 2a = da*na2+ 2a(a + )2 = da*na2+ 2Jar"a

77) (#2) = W#W = # % # $ *$&" -# % # $ n"a&"

78) an" = m*d [(60I - 11M) /2 ]

I = a," *% *,r andM = a," *% mn,&" and

" % &m" $ 230 &"n I =2 and M =30

79) G"r# n,m"r ra$"d &* *@"r 5 a$ &" n,m"r &$"% a$ ,n& d&

80) % a + + ' = &an &" ar"$& *% a and ' 'ann*& " r"a&"r &an &" m"an*% &" *&"r &@*

81) <" r," &a& *n" $d" *% a &ran" 'ann*& " $,m *% *&"r &@* *n# a"$ &*$d"$ not an'les

82) DFALLX MAYG SRG ED ?IA< <IG KRGS<EF SAXS – F<GZG MGAFSF<GZAL LGFZ<I And FZ A ?G F<E PGCGS EGS FE< FGCGSSALXMPLX <IA< <IGX ?LL G F<GZAL LGFZ<IS Smar# &a& a *a& '*"r$ ad$&an'" ,$&r"am n 3 *,r$ $&a&"$ *n# &" &m" ""n % & a$ ""n m"n&*n"d&a& & '*"r$ a a d$&an'" 12 .m d*@n$&r"am n 2 *,r$

83) :2 = 9J#2 d*"$ n*& n"'"$$ar# m# &a& :2 #2 (In& '*n$d"r :=#=0)

84) ?"n @" $a# m,&"$ "&@""n 16 and 260 and n',$"/":',$" $ n*&

m"n&*n"d &a." 16 and 260 &* " ":',$"

85) <" $&a&"m"n& m"$

<" *,r# @a" %*r "a' "m*#"" ran"$ %r*m \5 an *,r &* \20 an *,r

mnm,m a"ra" = (20 + 5 + 5 + 5 + 5)/5



ma:m,m a"ra" = (5 + 20 + 20 + 20 + 20)/5

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Maths General FunDAS