mathematics short cut techniques with formulas

1. Math Shortcut Techniques with Formulas 1

2. Math Shortcut techniqueS with ForMulaS Contents 1. Arithmetic ...................................................... 4 1.1. Divisibility Rules ............................................ 8 1.2. Square Root .................................................... 17 1.3. Average............................................................ 21 1.4. Ratio and Proportion............................................ 22 1.5. Percentage(%)...................................................... 24 1.6. Unitary Method.................................................... 30 1.7. Calculation of Interest.......................................... 37 1.8. Profit Loss............................................................ 43 1.9. Measurement and Unit......................................... 55 1.10. Miscellaneous...................................................... 57 2. Algebra.............................................................. 62 2.1. Exponents/Indices............................................... 65 2.2. Logarithms.......................................................... 66 2.3. Simultaneous Linear Equation............................ 67 2.4. Series/ Progression.............................................. 68 3. Geometry.............................................................. 73 3.1. Triangle................................................................ 79 3.2. Quadrilateral......................................................... 85 3.3. Circle.................................................................... 88 3.4. Mensuration.......................................................... 91 3.5. Solid Geometry..................................................... 98 3.6. Trigonometry......................................................... 102 Math Shortcut Techniques with Formulas 2

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

8. Angle / Right Angle Measured Angle Perpendicular To Is Parallel to Therefore / Hence Since / Because / Triangle Rectangle/Square Circle (Unit) () 3 (Digits) / 3 Ex:- 318 3+1+8=12 , (Unit) (tens) 4 Ex:- 544 , 4 44 4 (Unit) () 5 3 2 (Unit) , (tens) (Hundredth) 8 Ex:- 77 264 , 264 8 , 77264 8 (Digits) / 9 Ex:- 288 2+8+8=18 , 9 , 288 9 (Unit) () 2, 5, 10 (oo ) , 4, 25, 100 (000) , 8, 125, 1000 1.1 Math Shortcut Techniques with Formulas 8

9. 0,1,2,3,4,5,6,7,8,9 1 100 0 11 2 9 (2,3,4,5,6,7,8,9) 20 1 21 87654321 8(Crores) 7(Nijut) 6(lacs) 5(Ajut) 4(Thousands) 3(Hundreds) 2(Tens) 1(Units) 4321=41000+3100+210+1 Math Shortcut Techniques with Formulas 9

10. { -n.-5,-4,-3,-2,-1, 0, +1,+2,+3,+4,+..+n} 2 {0, 2, 4, 6, 8,.2n} 2 {1, 3, 5, 7, 9.(2n+1)} Even Even= Even , Odd Odd=Odd , Even Odd=Even Even + Even=Even , Odd + Odd=Even , Even Odd=Odd Even / Even= Even , Even /Odd=Odd , Odd/Even= Odd Odd Odd =Odd , Odd Even =Odd , Even Even =Even , Even Odd =Even (2,4,6.) (3,5,7..) { n,n+1,n+2,n+3,.} ( even prime number) (Odd Prime number) 1 100 25 1060 1 200 46 1 500 95 1 1000 168 ( 2 ,3 3 , ) Math Shortcut Techniques with Formulas 10

11. 1 100 1-10 2,3,5,7 4 11-20 11,13,17,19 4 21-30 23,29 2 31-40 31,37 2 41-50 41,43,47 3 51-60 53,59 2 61-70 61,67 2 71-80 71,73,79 3 81-90 83,87 2 91-100 97 1 (4422322321) (1232232244) / Fraction ()= ( ) () ( , x y ) , = Rules of fractions + = - = + = = + - = = - = = = Math Shortcut Techniques with Formulas 11

12. = a c = b 2 > ( Ex:- , ) < ( Ex:- , ) Math Shortcut Techniques with Formulas 12

14. , , , , , , , , Math Shortcut Techniques with Formulas 14

15. - , - (0,1,2,3.n ), ()-16 , ( a/b - a b ) , - a/b - a b ) , ( ) , ( ) , , , , , e Ex:- , , , , , I1, V5, X10, L50, C100, O500, M1000 Greek Alphabet Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Kai Psi Omega , , 20 =5221 , Ex:- 35/5=7 , 35/7=5 5 7 35 35 7 5 , Math Shortcut Techniques with Formulas 15

16. , - .. Math Shortcut Techniques with Formulas 16

17. 2304 (Square Root ) 74 28 1) 2) , 3) 74 64 , = 8 : 4) 8 74 64 5) 74 64 10 28 1028 ( ) 6) 8 82 = 16 ( ) 7) 16 1028 1028 8) 6 16 6 6 =996 7 ( 16 7 7 = 1169) 1028 9) 1028 996 32 862 = 172 32 10) , 86 11) 74 28 32 7396 86 1.2 Math Shortcut Techniques with Formulas 17

18. facebook /gmail/skype: - http://tanbircox.blogspot.com ~~ ~~C x= Formula:-- = 1008 = 2222337=243271 = (4+1)(2+1)(1+1)=30 Formula:-- x =am bn cl =(m+1)(n+1)(l+1) 21008 2504 2252 2126 363 321 7 Math Shortcut Techniques with Formulas 19

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

23. Formula:- Required Amount: = Required ratio Water = 3 =6 Formula:-- = 7 + 3 = 10 30 = 30 ( ) ( ) = 21 30 = 30 ( ) ( ) = 9 , = 3 : 7 x 3 : 7 21 : (9 + x) = 3 : 7 x = 40 7 : 5 10 = 30 0/ 0 3 = 7 : (3+2) = 7 :5 1 = 3 6 Math Shortcut Techniques with Formulas 23

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

25. Formula:- [ % = ] [ % = ]] (Increase ) + (Decrease ) , % % 25% , % 25% % , 25% Formula:- % Change = 100% Result + Increase Result Decrease = 0 0 0 100% =100% [ ] Math Shortcut Techniques with Formulas 25

26. Formula:-- 5% , 100 + 5 =105 100 = 105 ,, 1000 ,, ,, ,, = = 1050 5 = 1050 1000 = 50 1 ,, ,, ,, = 50/5 = 10 Formula:- = 10 Solution: = 100x = 100y = = 10000 xy 20% = (100+20)x =120x 10% = (100-10) = 90y = 120x 90y = 10800xy = 10800xy 10000xy = 800xy 10000xy = 800xy ,, ,, 100 ,, ,, ,, = =8% Formula:- x First Value ( ) % y Second Value ( ) % , / (Increase) + / (Decrease) (Answer) + , (Answer) , Math Shortcut Techniques with Formulas 26

27. Formula:-- + C% = (+5) + (+5) + ( ) ( ) Formula:-- , F = S = 10 C% = (10) + (10) + ( ) ( ) Formula:-- , F = S = 5 , + C% = (+5) + (+5) + ( ) ( ) F= + 25% S = 5% C% = (+25) + (5) + ( ) ( ) C% = (-20) + (+20) + ( ) ( ) Math Shortcut Techniques with Formulas 27

28. C% = (+20) + (+20) + ( ) ( ) C% = (+10) + (+20) + ( ) ( ) Formula:- Mix % = Formula:- - Rest (n) = 100x (f% + s% + t% )x Formula:- -pass = n x% (a/b) , = 100 = (100+25 ) 125 125 =100 ,, ,, 100 ,, ,, ,, ,, 80 = (100 80 ) = 20 Math Shortcut Techniques with Formulas 28

29. , 100 =25 ,, 64 ,, ,, ,, ,, = , = (6416) 48 , 40 = 100 ,, 48 ,, ,, ,, ,, = 120 = (12048) 72 , = (72 16) 56 , , Formula:-- = (100 70 10)% = 20% = (100 80 10)% = 10% = (20 + 10 + 10)% = 40% = (100 40)% = 60% 60 , = 100 ,, ,, 360 ,, ,, ,, ,, ,, ,, = Math Shortcut Techniques with Formulas 29

30. = (60 40)% = 20% = (70 40)% = 30% = (40 + 30 + 20)% = 90% = (100 90)% = 10% [1 10% ] 100 = 10 ,, 200 ,, ,, ,, ,, ,, ,, = , , , , , () [ , ] X = Y 1 = (X Y) [ , ] Z = ( ) [ , ] 1.6 Math Shortcut Techniques with Formulas 30

31. 1 1 2 , Formula:- M1 D1 = M2 D2 1) M2 = 2) D2 = Solution : 100 =(500 100) = 400 5 , 500 = (20 5) 15 1 ,, ,, ,, ,, ,, = (15 500) 400 ,, ,, ,, ,, ,, = ( ) 00 [ 500 , , ] Formula:-- X m = 1 1 ,, ,, = Y 1 = X Y 1 = ( + ) = = 1 ,, 1 ,, ,, ,, = Formula:- T = Math Shortcut Techniques with Formulas 31

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

34. 1 1 1 2 2 2 Formula:-- 3 20 = 1 3 ,, ,, 1 ,, ,, = 0 1 ,, ,, 1 ,, ,, = 0 4 ,, ,, 1 ,, ,, = 0 = [ , , ] , 5 20 = 1 1 ,, ,, 1 ,, ,, = 0 10 ,, ,, 1 ,, ,, = 0 0 = 0 4 10 , 1 = ( + 0 ) = = 1 1 ,, ,, ,, = 6 Formula : T2 = ( ) ( ) Math Shortcut Techniques with Formulas 34

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

40. Formula:- ( ) = = r 0 1 2 Formula:-- 100 1 = (10 8 ) = 2 100 ,, ,,, ,, 5 ,, ,, ,, = (5 2 ) = 10 10 = 100 ,, 200 ,, ,, ,, = 00 00 0 Formula:- I = 200 = p =2000 Formula:-- 5% , 100 10 = ( 5 10) = 50 100 10 = ( 100 + 50 ) = 150 150 = 100 ,, 5000 ,, ,, ,, = 00 000 0 Formula:- P = ( ) P = ( ) Math Shortcut Techniques with Formulas 40

41. ) Formula:-- 300 4 = 1200 1 500 5 = 2500 1 (1200 + 2500 ) = 3700 1 3700 1 148 100 ,, ,, 1 ,, ,, = 00 00 = x % = x/100 , I1 = 00 00 , I2 = 00 00 , I1 + I2 =148 00 00 + 00 00 = 148 x = 4% Formula:- I = ( ) r = r = 00 ( 00 ) ( 00 ) = 4% Math Shortcut Techniques with Formulas 41

42. + 5 = 500 + 5 = 460 [ ] 2 = 40 1 ~ ~ = = 20 3 ~ ~ = 203 = 60 = (46060) = 400 400 1 20 1 ~ 1 ~ ~ 20/400 100 ~ 1 ~ ~ 20 400 00 Formula:- C = p ( ) C = 600 ( ) C = 726 Math Shortcut Techniques with Formulas 42

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

45. Solution = (150 + 20 ) =170 170 = 20 ,, 100 ,, ,, ,, = 0 00 0 Formula:- = + [ = ] = Cost = 150 +20 =170 % = 0 00 0 Formula:- = Cost = 00 00 00 0 Formula:- = ( ) ( ) Cost = 00 00 00 0 Solution: 100 , 100 P% , 100 = (100 + P ) ,, n ,, ,, ,, = ( 00 ) 00 L% , 100 = (100 - L ) ( 00 ) 00 ,, ,, ,, = ( 00 ) 00 ( 00 ) 00 [ P% , L% p% 5%(L%) ] Math Shortcut Techniques with Formulas 45

46. Formula:-- 15% , 100 = (100 +15 ) =115 ,, 280 ,, ,, ,, = = 322 8% , (100 - 8 ) 92 = 100 ,, 322 ,, ,, ,, ,, = = 350 Formula : ( ) = 30 30 20% =24 (Profit) =( ) Profit = ( 0) Formula:- = R% ( ) Cost= 00 0 0 Math Shortcut Techniques with Formulas 46

47. Solution % 10% = (100 10) = 90 20% = (100 + 20 ) = 120 (120 90) = 30 30 100 ,, ,, 40 ,, ,, ,, ,, Formula:- = 40 10% 20% , 10% + 20% =40 15% = 40 1% = 0 100% = 0 00 Formula:- = = 00 0 0 Math Shortcut Techniques with Formulas 47

48. Solution: 3 % 20% = (100 20) = 80 40% = (100 + 40 ) = 140 40% 100 = 140 ,, 80 ,, ,, ,, 0 0 00 = 112 10% , = (100 10 ) =90 = (112 -90) = 22 22 = 100 ,, 50 ,, ,, ,, = 00 0 Formula: 10% , Sells1 = (100 10) = 90 20% = (100 20 ) = 80 , profit , 80 40% =32 ,Sells2 = + = 80 + 32 = 112 = [ Absolute Value Negative Positive ] Cost = 00 0 Math Shortcut Techniques with Formulas 48

49. Solution: 5 = 4 1 ,, ,, = , 4 = 5 1 ,, ,, = = - = = 0 [ ] = 0 ,, ,, 100 ,, ,, ,, = Formula Math Shortcut Techniques with Formulas 49

50. Solution: X = 1 1 ,, ,, = Y = 1 1 ,, ,, = = = = ,, ,, 100 ,, ,, ,, = ( ) 00 Formula = ( ) = ( ) 00 Solution: = (380+20) 400 400 =20 ,, 100 ,, ,, ,, Solution: 10% = (100-10) 90 5% = (100+5) 105 = (105 90) 15 15 100 ,, 45 ,, ,, ,, ,, 300 Math Shortcut Techniques with Formulas 50

51. Solution: 20% = (100+20) 120 10% = (100-10) 90 20% , 100 = 120 ,, 90 ,, ,, ,, = ( ) =108 % , = (100 ) = (100 ) 31 2 =100 ,, 31 ,, ,, ,, ,, = 200 Solution: x % , = 00 ( 00 ) = 100 ,, n ,, ,, ,, = y % , = 00 100 = ( 00 ) ,, ,, ,, ,,= ( ) ( ) = n ( ) ( ) Math Shortcut Techniques with Formulas 51

52. Solution: 36 =12 100 ,, ,, ,, 20% , 100 = (100 + 20) 120 20% , = 120 20 ,, ,, ,, Solution: 15% 1200 + 1200 15% (1200 15 100 ) 1200+180 = 1380 5% 1380 1380 5% 1380 69 = 1311 Solution: 5 = 2 100 ,, ,, = 40 40% , 100 (100+40) 140 140 =40 35 ,, ,, ,, ,, = 10 Math Shortcut Techniques with Formulas 52

53. Solution: 12 =20 1 ,, ,, ,, = 5 3 1 = = 2 5 3 = 1 3 5 3 = 1 3 ,, 100 ,, ,, 20 [ ] Solution: 3 = 1 1 ,, ,, ,, = 2 = 1 1 ,, ,, ,, = 2 1 = = 1 2 1 3 = 1 6 [ ] 1 3 = 1 6 ,, 100 ,, ,, 50 Math Shortcut Techniques with Formulas 53

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

60. Numerical prefixes Prefix M ~eaning Ex,ample mono l monorail hi 2 bicycle, binary . 3 trieye]e, trjangletrJ tetra. 4 tetrahedron, tetrapack quad 4 quadri]ateral quads . 5penta) qutn pentagon hexa 6 hexagon hepta, septi 7 heptagon octa 8 octagon nona, non 9 nonagon deca 10 decagon decahedron undeca 1l undecagon dodeca 12 dodecagon, dodecahedron . 20 icosahedronlCOSa hect 100 hectare kilo 1000 kilogramn n1ega l 000 000 tnegalicre) megawatt . l000 n1~Uion gigabytegga tanbir.cox (J):- Math Shortcut Techniques with Formulas 60

62. pdf Menu Bar View Auto /Automatically Scroll ( Ctrl + Shift + H ) up Arrow down Arrow ( )( ) ( ) ( ) (x) ( ) . / . / ( ) (y) ( ) . / . / ( ) ( ) ( ) [ (x) +(y)] ( ) ( ) ( ) ( ) [ (x) (y)] ( ) ( ) ( ) ( ) ( ) ( ) 2 Math Shortcut Techniques with Formulas 62

63. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) *( ) ( ) ( ) + ( ) ( ) ( ) ( )( )( ) ( )( ) ( )( ) ( )( ) Math Shortcut Techniques with Formulas 63

64. , q (a b ) x q (q= a+b) r (r=ab) ( ) ( )( ) 1) q>0, r>0 ( )( ) 2) q0 ( )( ) 3) q>0, r0 1 r , n r < 0 1 r (.1 -.9 ) , n -1

70. 1, 4, 9, 16. 5, 5 ] 1 , 9 , 25, 49, 81 , 5 7 9 ] 9 36 81 144 .. 5, ( ) ( ) ] 81, 27, . 3, 1 9 , ] 1, 2, 3, 5, 8 , 13 , 21 , 34. 55[ = ] 8, 11, 17, 29, 53,.. 101 [8, 8+(11-8),11+(17-11), ] 1, 3, 6, 10, 15, 21,. 28 [ 1,(1+2),(3+3),(6+4), (10+5)] 2, 8, 18, 32, 50 [ 2,(2+6),(8+6+4),(18+6+4+4), (32+6+4+4+4)] 2, 4, 8, 14, 22, 32. 44 [ 2,(2+2),(4+2+2),(8+2+2+2), (14+2+2+2+2)] 0, 5, 12, 21, 32.. 45 [ 0,(0+5),(5+5+2),(12+5+2+2), (21+5+2+2+2)] 13, 17, 25, 41,.. 73 [ 13,(13+22 ),(17+23 ),(25+24 ), (41+25 )] 5, 7, 11, 19,.. 5 [ 5,(5+21)(7+22 ),(11+23 ),(19+24 )] 8 [ 4,(4+21)(6+22 ),(10+23 ),(18+24 )] 3, 6, 4, 9, 5, 12, 6,. 5 , t1:t3:t5:t7 5 | t2:t4:t6:t8 9 5- 8 9 7 , (t1 +4),(t2+8)(t3+4)(t4+8)] 7 5 5 8 9 , t3:t5:t7 ( 7-2),(27-4),(27-6),(27-8)| t4:t6:t8 (5 ) (5 ) (5 9)- Math Shortcut Techniques with Formulas 70

71. 0, 9, 17, 2435, 39, 42 . 5 8 1, 3, 6 9 5 8 7 7 5 7 9 5 9 7 8 5 5 9 7 7 5 9 7 5 15, 13, 12, 11, 9, 9.. 7 8 8 7 8 5 8 9 9 7 5 8 9 5 7 99 5 7 5 7 7 5 8 7 8 9 7 5 5 8 21, 18, 9 7 8 5 5 9 5 9 7 7 5 5 5 9 5 5 5 7 7 8 8 8 8 3, 7, 28, 32, 8, 12, 48, 5 Math Shortcut Techniques with Formulas 71

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

80. ACD = ACB = , 180 Vertex (Exterior angel) 360 0 , ( ) Math Shortcut Techniques with Formulas 80

81. , , 2:1 ( ) (In-Centre): ( ) (Circumcentre): ( ) (Centroid):

mathematics short cut techniques with formulas

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