# Maths Formulas for Class 9

Maths formulas for Class 9 are provided here for the students who consider Mathematics subject as a nightmare and difficult to understand. This may cause them to feel reluctant and lose interest from studies. Therefore, to help them understand Maths in a simple way, we have accumulated all the important formulas for 9th standard Maths subject, which students can easily remember.

The formulas are given here as per the NCERT syllabus for all the topics such as Algebra, Geometry, Polynomials, etc.

## Class 9 Math Formulas Tables

When you are clear with the logic behind every formula, solving any kind of problem become easier. If you are perfect with all the below-mentioned formulas in Maths for Class 9 that is listed chapter-wise, nothing can stop you from scoring maximum marks in the final examination.

### Geometry

Geometry Shapes Formulas for Class 9 | ||
---|---|---|

Geometric Figure |
Area |
Perimeter |

Rectangle | A= l × w | P = 2 × (l+w ) |

Triangle | A = (1⁄2) × b × h | P = a + b + c |

Trapezoid | A = (1⁄2) × h × (b_{1}+ b_{2}) |
P = a + b + c + d |

Parallelogram | A = b × h | P = 2 (a+b) |

Circle | A = π r^{2} |
C = 2 π r |

### Algebra

Algebraic Identities For Class 9 |

\((a+b)^{2}=a^2+2ab+b^{2}\) |

\((a-b)^{2}=a^{2}-2ab+b^{2}\) |

\(\left (a + b \right ) \left (a – b \right ) = a^{2} – b^{2}\) |

\(\left (x + a \right )\left (x + b \right ) = x^{2} + \left (a + b \right )x + ab\) |

\(\left (x + a \right )\left (x – b \right ) = x^{2} + \left (a – b \right )x – ab\) |

\(\left (x – a \right )\left (x + b \right ) = x^{2} + \left (b – a \right )x – ab\) |

\(\left (x – a \right )\left (x – b \right ) = x^{2} – \left (a + b \right )x + ab\) |

\(\left (a + b \right )^{3} = a^{3} + b^{3} + 3ab\left (a + b \right )\) |

\(\left (a – b \right )^{3} = a^{3} – b^{3} – 3ab\left (a – b \right )\) |

\( (x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz\) |

\( (x + y – z)^{2} = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz\) |

\( (x – y + z)^{2} = x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz\) |

\( (x – y – z)^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz\) |

\( x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz)\) |

\( x^{2} + y^{2} = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]\) |

\( (x + a) (x + b) (x + c) = x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc\) |

\( x^{3} + y^{3} = (x + y) (x^{2} – xy + y^{2})\) |

\( x^{3} – y^{3} = (x – y) (x^{2} + xy + y^{2})\) |

\( x^{2} + y^{2} + z^{2} -xy – yz – zx = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]\)< |

### Surface Area and Volumes

Shape |
Surface Area |
Volume |

Cuboid | 2(lb + bh +lh)
l= length, b=breadth, h=height |
lbh |

Cube | 6a^{2} |
a^{3} |

Cylinder | 2πr(h+r)
r = radius of circular bases h = height of cylinder |
πr^{2}h |

Cone | πr(l+r)
r=radius of base l=slant height Also, l |
(1/3)πr^{2}h |

Sphere | 4πr^{2} |
(4/3)πr^{3} |

### Heron’s Formula

\(Area ~of~ triangle~ using~ three~ sides =\sqrt{s(s-a)(s-b)(s-c)} \\) | |

Semi-perimeter, s = (a+b+c)/2 |

### Polynomial

Polynomial Formula |

\(P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}-a_{n-2} x^{n-2}+\ldots \ldots+a x+a_{0}\) |

### Statistics

Measure of Central Tendency | |

Mean | Sum of Observation/Total number of observation = ∑ x/n |

Median | [(n+1)/2]th term [For odd number of observation]
Mean of (n/2)th term and (n/2+1)th term [For even number of observation] |

Mode | Value which is repeated maximum time in a data set |

### Probability

Empirical Probability = Number of trials with expected outcome/Total number of Trials |

### Class Related Formulas

Maths Formulas for Class 8 | Maths Formulas for Class 10 | Maths Formulas for Class 11 | Maths Formulas for Class 12 |