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**I will put here all formulas from maharashtra board .**

One Variable | ax+b=0 | a≠0 and a&b are real numbers |

Two variable | ax+by+c = 0 | a≠0 & b≠0 and a,b & c are real numbers |

Three variable | ax+by+cz+d=0 | a≠0 , b≠0, c≠0 and a,b,c,d are real numbers |

The pair of linear equations in two variables are given as:

a_{1}x+b_{1}+c_{1}=0 and a_{2}x+b_{2}+c_{2}=0

Where a_{1}, b_{1}, c_{1}, & a_{2}, b_{2}, c_{2} are real numbers & a_{1}^{2}+b_{1}^{2} ≠ 0 & a_{2}^{2 }+ b_{2}^{2} ≠ 0

**The Quadratic Formula:** For a quadratic equation p*x*^{2} + q*x* + r = 0, the values of *x* which are the solutions of the equation are given by:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

If a1, a2, a3, a4….. be the terms of an AP and d be the common difference between each term, then the sequence can be written as: a, a + d, a + 2d, a + 3d, a + 4d…… a + nd. where a is the first term and (a + nd) is the (n – 1) th term. So, the formula to calculate the nth term of AP is given as:

**n ^{th} term = a + (n-1) d**

The sum for the nth term of AP where **a** is the 1st term, **d** is the common difference, and **l** is the last term is given as:

**S _{n} = n/2 [2a + (n-1) d]** or

taxable value = output tax - input tax

Probability Range | 0 ≤ P(A) ≤ 1 |

Bayes Formula | P(A|B) = P(B|A) ⋅ P(A) / P(B) |

Rule of Addition | P(A∪B) = P(A) + P(B) – P(A∩B) |

Disjoint Events – Events A and B are disjoint if | P(A∩B) = 0 |

Independent Events – Events A and B are independent iff | P(A∩B) = P(A) ⋅ P(B) |

Statistics in Class 10 is mostly about finding the Mean, Median, and Mode of the given data .

Mean formulas

1.Direct Method ** x̅ **=\(\sum _i^n=fixi\over \sum_i^n=fi\)

2.Assume Mean method ** x̅= a+\(\sum_i^n=fidi\over \sum_i^n=fi\)**

**3. step deviation method x̅= a+\(\sum_i^n=fidi\over \sum_i^n=fi\) **×h

Mode = I+\({fi-f0\over 2f1-f0-f2}\times h\)

Median =I+\({{n\over2}-cf\over f}\times h\)

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