4. Menu Bar View Auto /Automatically Scroll ( ) pdf Options
View Go To ( Adobe Reader Foxit Reader ), Page number ; OK 1 Math
Shortcut Techniques with Formulas 4
5. + Plus / add [ Sum / Total ] Minus / Subtract /Deduct [
Difference ] Times / Into/ dot /of /Multiply [Product /
Multiplication ] , /, Division , Divisible , Remainder a(dividend-)
b(Divisor-) = c(Quotient-) Plus or Minus = Equal / Is Approximately
Equal Is not Equal < Is Less then {5 < 10} Is not less then {
10} Is less than or equal to { x X } > Is greater then {5> 2}
Is not greater then {5 20} Is greater than or equal to ( / ) %
Percentage( 100 ) Infinity / Varies as / is Proportional Implies/or
If and only if Pi 1,2,3...n [,,] Constant / x,y,z Variable / Math
Shortcut Techniques with Formulas 5
6. 2x x + x = a +bx+c Expression [a , bx,c Term] 0 n0 =n , n0
=0 , 0/n =0 , n/o = (anything 0) = Undefined () |x| [x] Absolute
Value ( ) Negative Positive Square Root , =2, =3 Cube Root , =3, =4
n Root n x 1/n X y = Summation ,X n ,*( )+- Bracket Logarithmsa x (
n= ) [ + , ] 10 n! n Factorial n n (n-1) (n-2)1 [ 5!=54321] n pr
Permutation [ n n pr , n pr= n(n-1) (n-2) (n-3) ..(n-r+1) Ex:- 6
p3=654 ] n cr Combination / / , n cr = ( ) Math Shortcut Techniques
with Formulas 6
7. A=*, , , + A , a,b,c,d Intersection /cap [ / ] [AB={x:xA
xB}] Union/cup [ ]=> ( ) [AB={x:xA xB}] Element of / Belongs to
/ [Ex: bA] Is not an Element of/not Belongs to / Subset of [A / B /
] / Superset Empty Set AB [B A , A / A ] A-B={x:xA xB} A
Complementary set [UA=U-A={xU : xA } P(A) Power Set [A n P(A) 2 n ]
NZQR N( / +n), Z( +n,0,+n) Q(0,+n, ), R ( ), ( ) Q=R-Q Straight
line ( ) Ray ( ) Line Segment ( ) Similar to Almost Equal to Is
Equivalent to / Congruent Math Shortcut Techniques with Formulas
7
20. n Let the Numbers =x and (x+1) According to the Question,
(x+1) 2 x 2 = n x = , = + = ( a , b , c d) .. = ( a , b , c d) .. +
= ( a , b , c d) .. + / = .. .. .. = .. .. = .. = Math Shortcut
Techniques with Formulas 20
21. - (a) 2 (b) 3 = 6 1 = 6 10 =(610) = .. = = - M A , M = M A
[ A = ] N B , N = N B = M + N = AM +BN = 1.3 Math Shortcut
Techniques with Formulas 21
22. Varies as / is Proportional - ( , , , ) , = = , = a, b, c ,
a:b =b:c a+b+c = S () a = S a:b = x:y = (xl): (yl) = xl : yl b:c
=l:m = (ly): (my)= yl : my a:b:c = xl : yl : my Formula:-- = a + b
+ c = n ( ) 1.4 Math Shortcut Techniques with Formulas 22
24. 100 (100) x % = N (90) P % (75% ) Formula:-- Let the Number
be = x X P% = N X 75% = 90 What Percentage % is R(90) of N(120)? N
X% =R 120 x% =90 : 100 100 , 100 , , 100 - 25% = (100 + 25 ) = 125
125 = 100 ,, 100 ,, ,, ,, = = 80 = ( 00 80)% =20% 1.5 Math Shortcut
Techniques with Formulas 24
32. Formula:- T = Formula:- T = Formula:- T = Formula:- T = [ ]
Solution X 20 = 1 X 1 = Y 1 = Z 1 = X , Y Z 1 = ( ) = 1 ,, 1 ,, ,,
,, = 8 Math Shortcut Techniques with Formulas 32
33. Formula:-- 1 = 1/8 ,, 6 ,, ,, ,, = 6/8 = (1 ) = X 1 = 20 ,,
,, ,, = (20 ) =20/4 = 5 Formula:-- X 1 = 1/ 20 5 ,, ,, = 0 X 5 X ,
Y Z = (1 ) = X , Y Z 1/8 = 1 ,, 1 ,, ,, ,, = 8 ,, ,, ,, ,, = = 6 =
X , Y Z + X 5 = 6 + 5 = 11 Math Shortcut Techniques with Formulas
33
35. Formula:- T = ( ) t U = Up , D = Down T = ( ) ( ) 1= 77Min
Formula:-- ( ) n = 1 ( ) = = = + = , U V [ U > V ] , (Relative
Speed) = U +V , (Relative Speed) = U V / / X T T X ,, 1 ,, ,, ,, =
= Math Shortcut Techniques with Formulas 35
36. p Lt T =( Lp + Lt) ,, 1 ,, ,, ,, = ( ) = ( ) Formula:-- , 1
(60 60) = 45 = (45 1000) 60 ,, ,, = 0 0 750 60 , = + 750 = + 100 =
650 Formula:- = ( ) 45 = ( ) [ T C nver S eed in km/hr to m/sec
multiply speed by ] =650 x T = , (Relative Speed) = , (Relative
Speed) = T = ( ) = 11 Second [1 km/hr = meter/second ] Math
Shortcut Techniques with Formulas 36
37. Formula:- T = = 0 T = 0 0 ( ) = 9 Second [1 km/hr =
meter/second ] Formula:- T = T = 0 0 0 (Principal / Capital / Sum
)[ Invested] / / ( Interest / Extra money for Interest) [ ] / [
Per-annum ] (Rate of Interest) [ , 100 1 ] /-/ (Amount/
Interest-principal/Increased Principal) = + P t = p t 1 1.7 Math
Shortcut Techniques with Formulas 37
38. r , 100 1 r 1 1 P 1 P t n I = I = npr [r = r% = r/100] [ ]
A = P + I A = P + nPr = P (1 + nr) P = [r = r% = r/100] P = [ , , ]
Math Shortcut Techniques with Formulas 38
39. P r n C = p ( ) = (C) (P) = P ( ) P = ( ) = ( ) Solution-
700 5 = 105 100 ,, 1 ,, ,, = Formula:- I = 105 = r = , X 5 - = 2X =
- = 2X X = X X 5 = X 100 ,, 1 ,, ,, = = 20 = 20% Math Shortcut
Techniques with Formulas 39
43. (Cost Price ) CP :- / (Selling Price )SP:- (Profit) = (SP)
- (CP)/ (Profit /Gain) P:- (loss) = (CP) - (SP)/ (Loss)L:- , - X %
x % x C x % , = X % c = ( C + ) X % C = ( C ) C P , = Furmula: 1
(Profit %) = 00 ( ) Profit % = 00 % 1.8 Math Shortcut Techniques
with Formulas 43
44. Furmula: 1 (Loss %) = ( ) loss % = 00 0 Furmula: (n) ,
(n+1) (n+2) , , ? (loss) = ( , / -) loss % = 00 ( 0) Formula:- =n ,
First Value=F%, Second Value=S% = n [ + , ] = 12 Formula:- = ( ) (
) = 00 00 0 Math Shortcut Techniques with Formulas 44
54. Solution: , 5 = x 1 ,, ,, ,, = 4 = x 1 ,, ,, ,, = 1 = = = =
,, 100 ,, ,, 25 Math Shortcut Techniques with Formulas 54
55. 1 Lac = 10 5 1 Million = 10 6 = 10 lac 1 Crore =10 7 =10
million 1 Billion = 10 9 (USA) =10 12 (Eu) 1 Trillion = 10 12 (USA)
= 10 18 (Eu) 1 kilogram= 2.2 (lbs) pounds 1 Seer = .93 kg 1 mound =
40 seer = 37.2 kg 1 quintal = 100 kg 1 ton = 1000 kg S.I
International Systems of Units 1960 CGS Centimeter . Gram .Second
M.K.S Meter . Kilogram . Second F.P.S Foot .Pound .Second 12 Inch =
1 foot , 3 foot = 1 Yard , 1760 Yard = 1 mile Relationship Distance
Area Volume 1 Inch = 2.54 Centimeter 1 Inchs2= 6.45 cm 2 1 liter =
1000 Cubic Centimeter 1 Meter = 39.37 Inch 1 Hectare = 10000 meter
2 1 Cubic meter = 1000 liters 1 mile = 1.61 kilometer 1 Katha = 720
feet 2 1 Cubic foot = 28.31 liters 1 Nautical Mile = 1.853km 1 Acre
= 4047 meter 2 1 gallon = 3.78 liters(us) = 4.54 liters(uk) 1 km2 =
247 Acres 1 Cubic Centimeter= 1 gram 1 m_t_r = 100 C_ntim_t_r =
39.37 In]hs = 3.28 `__t = 1.0936 Y[r^s = 0.00062 mil_s 1 kilogram =
1000 grams = 2.2 pounds = 35.27 Ounces = 0.157 Stone(uk) 1 meter 2
= 10.76 feet 2 =1550 Inchs 2 = 10000 centimeter 2 1 Square
kilometer = .3861 mile2 = 100 hectares = 247 acres 1 mile 2 = 2.589
kilometers 2 = 259 hectare = 640 acres 1 Celsius = 33.8 Fahrenheit
= 274.15 kelvin 1.9 Math Shortcut Techniques with Formulas 55
56. Want more Updates facebook /gmail/skype: -
http://tanbircox.blogspot.com Metric relationships Length Area
Volume Capacity I em 10mm 10 em 100 mm Im 100 em 1 em 1cmB 10 em
1cm I em~ 1000 mm3 10cmB 100 em! IOOOO mm2 1m tanbir.cox 11m 1000
em3 I 000000 mm3 I m3 1000000 em' Website (J):- 10 em I mL One 1 em
cube (cubic Centimetre) has a capacicy of 1 millilitre. IL One 10
em cube (1000 cm3) has a capacity of 1 lirre. Ikl One cuhic metre
ha~ a capacity of 1 kilolitre. These 5 drums each hold 1 kilolirre.
Math Shortcut Techniques with Formulas 56
57. F S F + S ( F S) F S = F S = 30 = 20 + 15 (F S ) (F S ) 1
12 12 = 3600 ,, ,, ,, ,, = 0 N = n 0 1 0 ( ) H M = ( ) ( ) HM = [
() ] 0 / 0 Examples: ( ) ( ) = ( ) ( ) = [ > 0 ] = 0 ( ) ( ) = 0
1.10 Math Shortcut Techniques with Formulas 57
58. : ( ) ( ) ( x ) x ( ) ( ) () x : , A= q n , q = n = ( , , W
= q x n , q = , n = x = w = n x , d = v t. , v = t= , Q(t) = Q0 q t
, Q0= q = t= Q(t) = t ( + ) P = b r , b = r = = = S% P= = b S% Math
Shortcut Techniques with Formulas 58
73. pdf Menu Bar View Auto /Automatically Scroll ( Ctrl + Shift
+ H ) up Arrow down Arrow Straight line ( ) Ray ( ) Line Segment (
) Similar to Almost Equal to Is Equivalent to / Congruent Angle
Right Angle Measured Angle Perpendicular To Is Parallel to
Therefore / Hence Since / Because / Triangle Rectangle/Square
Circle 3 Math Shortcut Techniques with Formulas 73
74. Euclids (): Elements 13 , 300 , Math Shortcut Techniques
with Formulas 74
75. Want more Updates http://facebook.com/tanbir.ebooks
facebook /gmail/skype: - http://tanbircox.blogspot.com angle of
depression (of an object) angle of elevation An angle formed
between the horizontal line and the line of sight to an object
below. An angle formed between the horizontal line and the line
ofsight to an object above. +---------.---,.-------,r.,r-- ------.
horizontaI line D object The angle of depression is a0 The angle of
elevation is b0 Angles are measured in degrees (0 ), minutes (')
and seconds ("). b acute right obtuse angle angle angle 0
76. AOD = COD AOC = BOD = 180 ADB = ADC = = 90 , = 90 Math
Shortcut Techniques with Formulas 76
77. 0 < AOC < 90 90 < AOD < 180 180 < AOB <
360 AOB = 360 X Math Shortcut Techniques with Formulas 77
78. 90 , 180 , DEF ACB AB || CD EF (Transversal) , AGF = DHE
DGF = CHE Math Shortcut Techniques with Formulas 78
79. AB || CD EF (Transversal) , AGF = CHF DGF = DHF ABC , BAC
=B , ABC = B , ACB = C AB= c , BC = a AC = b 3.1 Math Shortcut
Techniques with Formulas 79