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Microsoft Word - Bank Exams-Math Formulae Booklet-Final-A4-Size.doc Flipbook PDF

Microsoft Word - Bank Exams-Math Formulae Booklet-Final-A4-Size.doc

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INDEX PAGE 1. Types of Numbers....................................................................................... 4 2. Surds............................................................................................................ 9 3. Divisibility Test .......................................................................................... 11 4. Factors....................................................................................................... 13 5. Theorems on Numbers ............................................................................. 15 6. H.C.F & L.C.M ............................................................................................ 18 7. Ratio & Proportions .................................................................................. 20 8. Time, Work, Speed and Distance.............................................................. 21 9. Percentage ................................................................................................ 22 10. Profit and Loss........................................................................................... 24 11. Interest...................................................................................................... 26 12. Sales Tax.................................................................................................... 27 13. Miscellaneous ........................................................................................... 29 14. Partnership................................................................................................ 30 15. Chain Rule ................................................................................................. 31 16. Pipes and Cisterns..................................................................................... 32 17. Problem on Trains..................................................................................... 33 18. Boats and Streams .................................................................................... 34 19. Alligation or Mixture................................................................................. 35 20. Area‐Circle & Triangle............................................................................... 36 21. Volme and Surface Area ........................................................................... 39 22. Clocks ........................................................................................................ 42 23. True Discount............................................................................................ 43 24. Banker’s Discount ..................................................................................... 44 25. Co‐ordinate Geometry.............................................................................. 46 26. Point & Plane ............................................................................................ 48 27. Angles between Lines ............................................................................... 51 28. Types of Triangles ..................................................................................... 52 29. Polygons.................................................................................................... 54 30. Properties of Triangles.............................................................................. 56 31. Perimeter and Area of Plane Figures........................................................ 63 32. Area Theorems.......................................................................................... 68 33. Theorems on Circles.................................................................................. 71 34. Co‐ordinate Geometry‐Lines .................................................................... 79 35. Trigonometry ............................................................................................ 82 36. Progression ............................................................................................... 85 37. Quadratic Equations ............................................................................... 102 38. Permutations and Combinations............................................................ 116 39. Logarithm................................................................................................ 128 40. Angle & Trigonometric Ratio .................................................................. 130 41. Properties of Triangles............................................................................ 136 42. Solutions of Triangles.............................................................................. 151 43. Probability............................................................................................... 157

Types of Numbers Natural Numbers:  Counting numbers are known as natural numbers. 1, 2, 3, 4, 5,…., etc., are all natural numbers. Whole Numbers:  All natural numbers together with 0 form the set of all whole numbers. Clearly, every natural number is a whole number. And, 0 is the only whole number that is not a natural number. Integers:  All natural numbers, 0 and negatives of natural numbers form the set of all integers. so, …., –4, –3, –2, –1, 0, 1, 2, 3, 4, …. etc., are all integers. (i) Even Integers:  Integers which are divisible by 2 are called even integers. e.g., 0, ± 2, ± 4, ….. (ii) Odd Integers:  Integers, which are not divisible by 2 are called as odd integers. e.g., ±1, ±3, ±5, ±7 …. Prime Number:  Let ‘p’ be a natural number ‘p’ is said to be prime if it has exactly two distinct factors, namely 1 and itself. e.g., 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ….. www.learnersplanet.com

(iii) Composite Number:  Let ‘a’ be a natural number, ‘a’ is said to be composite if, it has atleast three distinct factors. Note: (i) ‘1’ is neither prime nor composite. (ii) ‘2’ is the only even prime number. (iii) Number which are not prime are composite numbers (except 1). (iv) ‘4’ is the smallest composite number. (iv) Co‐Prime Numbers:  Two natural numbers (not necessarily prime) are co‐prime, if there H.C.F. (Highest Common Factor) is one. e.g., (1, 2), (1, 3), (3, 4), (3, 10), (3, 8), (5, 6), (7, 8) etc. These numbers are also called as relatively prime numbers. Note: (a) Two distinct prime numbers are always co‐prime but converse need not be true. (b) Consecutive numbers are always co‐prime numbers. (v) Twin Prime Numbers:  If the difference between two prime numbers is two, then the numbers are called as twin prime numbers. e.g., {3, 5}, {5, 7}, {11, 13}, {17, 19}, {29, 31}. www.learnersplanet.com