# Maharashtra State Board Class 10 Maths Formula

Maths Formula for Class 10

In this story, the “chicken” is the high level in the equation, the “chicken” is the basic operation and the bottom level in the equation is called what it is; “chicken”.

Two-term matrices. A formula that can be hard to understand? For some, it might make more sense.

Another relation is called “hit rate” or the “hit chance”. There is an equation called

What is the “hit chance”?

For an athlete to possibly reach the highest level of fitness in sports, there is a low chance of failure during training. Of course, as an athlete, I have a low chance of gaining the same degree of physical fitness that my guru has.

I want you to understand that our basic methods (usually G-S-R-R) must equal the lowest total (like a higher number of men are at the top) while we add a source of added maintenance (like an increase in height or weight).

The symbol for this equation is “gens.” In the simplest way to explain this equation, the addition of basic operations (basketball, football, baseball) adds four current operations. If we are at the bottom middle of the class (yours) we gain the +2 +2 +1 + 4. So, the number of groups (foreground picture) equal +2 +2 + 2 + 4 + 2.

Each individual requires their own form of Gens, which is a minimum specified for what their playstyle is. Remember the usages of math; in many cases, the lower version of the equation also provides the standard of the larger than larger extreme (1 gens means -1 per 10,000 people).

Mathematics is hard.

Class 10 Maths Formula

### Linear Equation

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

Two Variable : ax + by + c = 0 : a ≠ 0 & b ≠ 0 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.

Pair of Linear Equation in Two Variable :

a₁x + b₁ + c₁ = 0  a₂x + b₂ + c₂  = 0

where

a₁, b₁, c₁, a₂, b₂ and c₂ are all real numbers and

a₁² + b₁²  ≠ 0 & a₂² + b₂²  ≠ 0

Algebra or Algebraic Equations :-

The standard form of Quadratic Equation :

ax + by + c = 0 where a ≠ 0

And x = [ -b ± √ (b²-4ac)] / 2a

## Algebraic Formulas

(a+b)² = a² + 2ab + b²

(a-b)² = a² – 2ab + b²

a²-b² = (a+b) (a-b)

(a+b)³ = a³ + 3a²b + 3ab² + b³

(a-b)³ = a³ – 3a²b + 3ab² – b³

a³+b³ = (a+b) (a² – ab + b²)

a³-b³ = (a-b) (a² + ab + b²)

(x+a) (x+b) = x² + (a+b)x + ab

(x+a) (x-b) = x² + (a-b)x – ab

(x-a) (x+b) = x² + (b-a)x – ab

(x-a) (x-b) = x² – (a+b)x + ab

(x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz

(x+y-z)² = x² + y² + z² + 2xy – 2yz – 2xz

(x-y+z)² = x² + y² + z² – 2xy – 2yz + 2xz

(x-y-z)² = x² + y² + z² – 2xy + 2yz – 2xz

x³ + y³ + z³ -3xyz = (x + y + z)(x² + y² + z² -xy – yz – xz)

x² + y²  = ½ [(x + y)² + (x – y)²]

x² + y² + z² – xy + yz – xz = ½ [(x – y)² + (y – z)²  + (z – x)²]

## Basic Formulas for Powers

• pm x pn = pm+n
• {pm}/{pn} = pm-n
• (pm)n = pmn
• p-m = 1/pm
• p1 = p
• P0 = 1

## Arithmetic Progression (AP) Formulas

If a₁, a₂, a₃, a₄, a₅, a₆,……are the terms of AP and d is the common difference between each term, then we can write the sequence as; a, a+d, a+2d, a+2d, a+4d, a+5d,…..,nth term…. where a is the first term. Now, nth term for arithmetic progression.

nth term = a + (n-1) d

Sum of nth term in Arithmetic Progression;

Sn = n/2 [a + (n-1) d]

## Trigonometry Formulas

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

cot θ = Adjacent Side/Opposite Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

cot θ = 1/tan θ

sec θ = 1/cos θ

cosec θ = 1/sin θ

### Other Trigonometric Formulas :

sin (90⁰- θ ) = cos θ

cos (90⁰- θ ) = sin θ

tan (90⁰- θ ) = cot θ

cot (90⁰- θ ) = tan θ

sec (90⁰- θ ) = cosec θ

cosec (90⁰- θ ) = sec θ

sin² θ + cos² θ = 1

sec² θ = 1 + tan² θ

cosec² θ = 1 + cot² θ

## Circles Formulas

Circumference of the circle = 2πr

Area of the circle = πr²

Area of the sector of angle θ = (θ /360) x πr²

Length of an arc of a sector of angle θ  = (θ /360) x 2πr

( r = radius of the circle)

## Surface Area and Volumes Formulas

### Sphere Formulas:

Diameter of sphere = 2r

Circumference of sphere = 2πr

The surface area of sphere = 4πr²

Volume of cylinder = 4/3 πr²

## Cylinder Formulas

Circumference of cylinder = 2πrh

The curved surface area of cylinder = 2πr²

The total surface area of cylinder = Circumference of cylinder + Curved surface area of cylinder = 2πrh + 2πr²

Volume of cyclinder = πr²h

## Cone Formulas

Slant height of cone : l = √(r² + h²)

Curved surface area of cone = πrl

Total surface area of cone = πr (l + r)

Volume of cone = 1/3 πr²h

## Cuboid Formulas

Perimeter of cuboid = 4(l + b + h)

Length of the longest diagonal of a cuboid = √(l² + b² + h²)

Total surface area of cuboid = 2(l x b + b x h + l x h)

Volume of cuboid = l x b x h

Here, l  = length, b = breadth and h = height in case of cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes.

## Statistics Formulas for Class 10

In class 10, the chapter statistics mostly deals with finding the mean median and standard deviation of grouped data.

i.      The mean of the grouped data can be found by 3 methods.

1.    Direct Method: x̅ = ∑ni=1fixi∑ni=1fi, where ∑fi xi is the sum of observations from value i = 1 to n And ∑fi is the number of observations from value i = 1 to n

2.    Assumed mean method : x̅ = a+∑ni=1fidi∑ni=1fi

3.    Step deviation method : x̅ = a+∑ni=1fiui∑ni=1fi×h

ii.     The mode of grouped data : Mode = l + f₁ – f₀ / 2f₁ – f₀ – f₂ x h.

iii.    The median for a grouped data :

Median = l + n/2 – cf /f x h.