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CBSE CLASS X

Mathematics

1. Mathematics (Paper) - Mr. Ajai Kumar Shukla

Algebra

1. (a + b)² = a² + 2ab + b²
2. a² – b² = (a + b) (a – b)
3. (a – b)² = a² – 2ab + b²
4. (a – b)³ = a³ – 3a²b + 3ab² – b³
5. (a + b)³ = a³ + 3a²b + 3ab² + b³
6. a³ – b³ = (a – b) (a² + ab + b²)
7. a³ + b³ = (a + b) (a² – ab + b²)
8. x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + y² – xy – yz – zx) = ½ (x + y + z) [ (x – y)² + (y – z)² + (z – x) ²]
9. a³ – b³ + c³ + 3abc = (a – b + c) (a² + b² + c² + ab + bc – ca)

Comparing Quantities

1. Profit = S.P. – C.P.
2. Loss = C.P. – S.P
3. Profit % = (Profit / C.P.) x 100
4. Loss % = (Loss / C.P.) x 100
5. C.P. = S.P. / (1+P%)
6. S.P. = C.P. – (Loss% x C.P.)
7. Amount = Principal + Interest1
8. S.I. = (P x R x T)/100, P = Principal, R = Rate, T = Time, S.I. = Simple intrest for yearly
9. A = P (1 + R/100)n A = Amount, R = Rate, n = Numbers of years
10. Discount = Marked Price – Sale Price.
11. Discount % = (Discount / Marked Price) x 100
12. A = P (1 + R/200)2n A = Amount, R = Rate, n = Number of years, for half yearly.

Mensuration

1. Perimeter of a regular Polygon = Number of sides x length of one side.
2. Area of Parallelogram = base x height
3. Area of trapezium = half of the sum of the length of parallel sides x perpendicular distance between them.
4. Area of rhombus – half the product of its diagonal
5. Volume of cube = (I)³
6. 1 cm³ = 1ml
7. 1 L = 1000 cm³
8. 1 m³ = 1000000 cm³
9. a⁰ = 1

Submitted By Mr. Ajai Kumar Shukla, Rachna Tutorials
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