1. a²-b²= (a+b) (a - b)
2. (a+b)²= a²+2ab+b²
3. (a-b)²= a²-2ab+b²
4. (a+b)³ = a³+3ab(a+b)+b² Or a³+3a²b+3ab²+b²
5. (a-b)³= a³-3ab(a - b) - b³ Or a³ - 3a²b+3ab²-b³
6. a³+b³ = (a + b) (a²-ab+b²) Or (a + b)³ - 3ab (a + b)
7. a³-b³ = (a - b) (a²+ab+b²) Or (a - b)³ + 3ab (a - b)
8. (a+b+c)²= a²+b²+c²+2ab+2be+2ca Or a²+b²+c² + 2ab + 2be + 2ca
9. (-a-b-c)²= a²+b²+c²+2ab+2bc+2ca Or a²+b²+c² + 2(ab + be + ca)
10. a³+b³+c³-3abc = (a + b + c) (a² + b²+c² - ab - bc - ca)
11. (x+a) (x+b) = x²+(a+b) x+ab
12. (x+a) (x + b) (x+c)=x³+(a+b+c) x² + (ab + be + ca) x + abc
13. aᵐ x aⁿ = aᵐ+ⁿ
14. aᵐ ÷ aⁿ = aᵐ-ⁿ
15. a⁻ⁿ = 1/aⁿ
16. 1/a⁻ⁿ = aⁿ
17. LSA of a cuboid = 2h (l + b)
18. TSA of a cuboid = 2 (lb + bh + hl)
19. Volume of a cuboid = l.b.h
20. Diagonal of a cuboid = √(l² + b² + h²) ̅
21. LSA of a cube = 4a²
22. TSA of a cube = 6a²
23. Volume of a cube = a³
24. Diagonal of a cube = a√3 or √3.a
25. CSA of a cylinder = 2πrh
26. TSA of a cylinder = 2πr(h + r)
27. Volume of a cylinder = πr²h
28. CSA of a cone = πrl
29. TSA of a cone = πr(l + r)
30. Volume of a cone = 1/3 πr²h
31. CSA of a sphere = 4πr²
32. TSA of a sphere = 4πr²
33. Volume of a sphere = 4/3πr³
34. CSA of a hemisphere = 2πr²
35. TSA of a hemisphere = 3πr²
36. Volume of a hemisphere = 2/3πr³
37. LSA of a hollow cylinder = 2πh(R + r)
38. TSA of a hollow cylinder = 2πh(R + r) (h + R - r)
39. Volume of a hollow cylinder = πh (R² - r²)
40. Volume of a hollow sphere = 4/3 π(R³ - r³)
41. Volume of a hollow hemisphere = 2/3 π(R³ - r³)
42. Area (right triangle) = 1/2 × b × h
43. Area (isosceles triangle) = 1/2 × b × h
44. Area (equilateral triangle) = √3/4 × a²
45. Height (equilateral triangle) = √3/2 × a
46. Area (parallelogram) = bh
47. Area (rectangle) = lb
48. Area (Rhombus) = 1/2 × d₁ × d₂
49. Area (Square) = a²
50. Area (quadrilateral) = 1/2 × d(h₁ + h₂)
51. Area (trapezium) = 1/2 × h (a + b)
52. Perimeter (parallelogram) = 2 (l + b)
53. Perimeter (rectangle) = 2(l + b)
54. Perimeter (rhombus) = 4a
55. Perimeter (square) = 4a
56. Perimeter (equilateral triangle) = 3a
57. Diagonal (square) = √2 × a
58. Each interior angle (polygon) = ((2n-4))/n 90°
59. Each exterior angle (polygon) = 360°/ n
60. Sum of all interior angles (polygon) = (2n-4) 90°
61. Sum of all exterior angles (polygon) = 360°
62. Number of diagonals (polygon) = n(n-3) / 2
63. Area (circle) = πr²
64. Area (Semi-circle) = πr²/2
65. Area (quadrant of a circle) = πr²/4
66. Perimeter (circle) = 2πr
67. Perimeter (semi-circle) = 36/7 x r
68. Perimeter (quadrant of a circle) = 25/7 x r
69. 1km = 1000m.
70. 1m = 100cm.
71. 1cm = 10mm.
72. 1dm = 10cm.
73. 1hectare = 10,000 m².
74. 1m³ = 1000 litres.
75. 1litre = 1000cm³.
76. Standard form of a linear equation in one variable is ax + b = 0
77. Standard form of a linear equation in two variables is ax + by + c = 0
78. Standard form of a quadratic equation is ax² + bx + c = 0
79. Standard form of a cubic polynomial is f(x) = ax³ + bx² + ex + d
80. Standard form of an even number is 2x
81. Standard form of an odd number is 2x + 1
82. Standard form of an integer is x
83. Standard form of a fraction is x/y
84. Standard form of a two digit number is.xy (10x+y)
85. Standard form of two consecutive even numbers are 2x, 2x + 2
86. Standard form of two consecutive odd numbers are 2x - 1, 2x + 1
87. Standard form of three consecutive numbers are x - 1, x, x + 1
88. Standard form of two consecutive multiples of 3 are 3x, 3x + 3
89. Formula to find a quadratic polynomial is f(x) = k[x² - (α + β)x + αβ]
90. Formula to find a cubic polynomial is
f(x) = k [x³ - (α + β + γ)x² + (αβ + βγ + γα) x - αβγ]
91. SI = PRT / 100
92. CI = Amount – principle
93. Amount = P(1+ R/100)
94. Loss = CP - SP
95. Loss % = L/CP x 100
96. Profit = SP - CP
97. Loss % = P/CP x 100
98. SP (in case of loss) = ((100-L%))/100 CP
99. SP (in case of profit) = ((100+P%))/100 CP
100. CP(in case of loss) = (100 X SP)/((100-L%))
101. CP(in case of Profit) = (100 X SP)/(100+P%)
102. α+ β = -b/a
103. αβ = c/a
104. α β γ= -d/a
105. α+ β + γ = -b/a
106. αβ + βγ + γα = c/a
107. Sin0° = 0
108. Cos0° = 1
109. Tan0° = 0
110. Sec0° = 1
111. Cot0° = ∞
112. Sin30° = 1/2
113. Cos30° = √3/2
114. Tan30° = 1/√3
115. Cosec30° = 2
116. Sec30° = 2/√3
117. Cot30° = √3
118. Sin60° = √3/2
119. Cos60° = ½
120. Tan60° = √3 121. Cosec60° = 2/√3 122. Sec60° = 2
TRIGNOMETRIC IDENTITIES
179. Sin²θ + Cos²θ = 1
180. Sin²θ = 1 - Cos²θ
181. Sinθ = √(1 - Cos²θ) ̅
182. Cos²θ = 1 - Sin²θ
183. Cosθ = √(1 - Sin²θ) ̅
184. Sec²θ - Tan²θ = 1
185. Sec²θ = 1 + Tan²θ
186. Secθ = √(1 + Tan²θ) ̅
187. Tan²θ = Sec²θ - 1
188. Tanθ = √(Sec²θ - 1) ̅
189. (Secθ + Tanθ) (Secθ - Tanθ) = 1
190. Tan²θ - Sec²θ = -1
191. (Tanθ + Secθ) (Tanθ - Secθ) = -1
192. Cosec²θ - Cot²θ = 1
193. Cosec²θ = 1 + Cot²θ
194. Cosecθ = √(1 + cot²θ) ̅
195. Cot²θ = Cosec²θ - 1
196. Cotθ = √(Cosec²θ - 1) ̅
197. (Cosecθ + Cotθ) (Cosecθ - Cotθ) = 1
198. Cot²θ - Cosec²θ = -1
199. (Cotθ + Cosecθ) (Cotθ - Cosecθ) = -1
200. Additive Identity = 0 201. Multiplicative Identity = 1
202. Additive Inverse of -2/3 = 2/3 203. Multiplicative Inverse of -2/3 = -3/2
204. C = 100 205. L = 50 206. M = 1000 207. D = 500
208. Least composite number = 4 209. Least prime number = 2
210. Least even number = 2 211. Least whole number = 0
212. Least natural number = 1 213. Least odd number = 1
214. Marked price (MP)= (100 X SP)/(100-D%) 215. Discount % = D/MP X 100
All the best
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