Formula sheet for class 9th:
Algebraic Formula:
1. (a + b)2 = a2 + 2ab + b2
2. (a – b)2 = a2 -2ab + b2
3. (a + b) (a – b) = a2 -b2
4. (x + a)(x + b) = x2 + (a + b) x + ab
5. (x + a)(x – b) = x2 + (a – b) x -ab
6. (x – a)(x + b) = x2 + (b – a) x -ab
7. (x – a)(x – b) = x2 – (a + b) x + ab
8. (a + b)3 = a3 + b3 + 3ab(a + b)
9. (a – b)3 = a3 – b3 – 3ab (a – b)
10. (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
15. x2 + y2 = 1212 [(x + y)2 + (x – y)2]
16. (x + a) (x + b) (x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
17. x3 + y3 = (x + y) (x2 – xy + y2)
18. x3 – y3 = (x – y) (x2 + xy + y2)
19. x2 + y2 + z2 -xy -yz -zx = 1212 [(x-y)2+(y-z)2+(z-x)2]
Pythagorean Theorem:
a2 + b2 = c2
Distance formula:
- d = (x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√(x2−x1)2+(y2−y1)2.
- Slope of a line m = y2−y1x2−x1y2−y1x2−x1.
- Midpoint Formula : (x1+x22,y1+y22)(x1+x22,y1+y22).
- Slope of an Equation y = mx + b
Quadratic Equation:
- Quadratic Equation: x = −b±b2−4ac√2a−b±b2−4ac2a.
- Standard form of equation ax2 + bx + c = 0
| Geometry Shapes Formulas for Class 9 | ||
| Geometric Figure | Area | Perimeter |
| Rectangle | A=l×w | P=2(l+w) |
| Triangle | A=12bh | P=a+b+c |
| Trapezoid | A = 12h(b1+b2) | P=a+b+c+d |
| Parallelogram | A=bh | P=2(b+h) |
| Circle | A=πr2 | C=2πr |
Summary
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CBSE class 9th
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