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CBSE CLASS X
Mathematics
 Mathematics (Paper)  Mr. Ajai Kumar Shukla
Algebra
 (a + b)^{2} = a^{2} + 2ab + b^{2}
 a^{2} – b^{2} = (a + b) (a – b)
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
 a^{3} – b^{3} = (a – b) (a^{2} + ab + b^{2})
 a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2})
 x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z) (x^{2} + y^{2} + y^{2} – xy – yz – zx) = ½ (x + y + z) [ (x – y)^{2} + (y – z)^{2} + (z – x) ^{2}]
 a^{3} – b^{3} + c^{3} + 3abc = (a – b + c) (a^{2} + b^{2} + c^{2} + ab + bc – ca)
Comparing Quantities
 Profit = S.P. – C.P.
 Loss = C.P. – S.P
 Profit % = (Profit / C.P.) x 100
 Loss % = (Loss / C.P.) x 100
 C.P. = S.P. / (1+P%)
 S.P. = C.P. – (Loss% x C.P.)
 Amount = Principal + Interest1
 S.I. = (P x R x T)/100, P = Principal, R = Rate, T = Time, S.I. = Simple intrest for yearly
 A = P (1 + R/100)n A = Amount, R = Rate, n = Numbers of years
 Discount = Marked Price – Sale Price.
 Discount % = (Discount / Marked Price) x 100
 A = P (1 + R/200)2n A = Amount, R = Rate, n = Number of years, for half yearly.
Mensuration
 Perimeter of a regular Polygon = Number of sides x length of one side.
 Area of Parallelogram = base x height
 Area of trapezium = half of the sum of the length of parallel sides x perpendicular
distance between them.
 Area of rhombus – half the product of its diagonal
 Volume of cube = (I)^{3}
 1 cm^{3} = 1ml
 1 L = 1000 cm^{3}
 1 m^{3} = 1000000 cm^{3}
 a^{0} = 1
Submitted By Mr. Ajai Kumar Shukla, Rachna Tutorials
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