In mathematics, we generally solve various types of problems and for that, we also need a maths formulas list.

All formulas of maths make our problems easy.

And in this article, we are going to cover class 10th maths formulas chapter-wise for CBSE and MP Board students.

Let's start the list of maths formulas for class 10 (chapter-wise)

## Real Numbers (Math formula class 10 chapter 1)

### Euclid Division Lemma *(Euclid's Division Algorithm)*

→ Dividend = (Divisor × Quotient) + Remainder

Or

→ a = bq + r, 0 ≤ r < b

### HCF and LCM

→ HCF(a,b) × LCM(a,b) = a × b

Or

→ HCF × LCM = Product of both numbers

### Algebraic Identities

→ (a+b)² = a² + 2ab + b²→ (a+b)³ = a³ + b³ + 3a²b + 3ab²

### Law of Exponents (Exponents formulas list)

→ aᵐ × aⁿ = aᵐ⁺ⁿ

→ aᵐ ÷ aⁿ = aᵐ⁻ⁿ

→ aᵐ × bᵐ = (ab)ᵐ

## Polynomials

### The general form of Quadratic polynomial

ax² + bx + c = 0

### Relationship between zeroes and coefficients-

→ Sum of zeroes-

α+β = (-b/a)

→ Product of zeroes

αβ = (c/a)

### Division Algorithm

→ Dividend = (Divisor×Quotient) + Remainder

Or

→ p(x)=g(x)×q(x) + r(x)

### Algebraic Identities

→ (a² - b²) = (a+b)(a-b)

→ (a² + b²) = (a+b)² - 2ab

## Pair of linear equations in two variables

## (Class 10 chapter 3 maths formula)

### The general form of linear equation in two variables

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

### Graphical Representation and Algebraic Interpretation

(a₁/a₂)≠(b₁/b₂)

→ Coincident lines and infinitely many solutions

(a₁/a₂)=(b₁/b₂)=(c₁/c₂)

→ Parallel lines and no solution

(a₁/a₂)=(b₁/b₂)≠(c₁/c₂)

### Cross-multiplication method

→ x/(b₁c₂ - b₂c₁) = y/(c₁a₂ - c₂a₁) = 1/(a₁b₂ - a₂b₁)

→ Sum of two supplementary angles = 180°

### Pythagoras theorem

→ H² = P² + B²

### Speed, Distance, and Time Formulas

→ Speed = Distance/Time

→ Time = Distance/Speed

→ Distance = Speed×Time

## Quadratic Equations (Class 10 maths chapter 4 all formula)

### The general form of Quadratic Equation

ax² + bx + c = 0

### Completing the Square method and List of Algebraic Identities (Class 10 algebra all formula)

→(a+b)² = a² + 2ab + b²

→ (a-b)² = a² - 2ab + b²

→ (a+b)³ = a³ + b³ + 3a²b + 3ab²

→ (a-b)³ = a³ + b³ + 3a²b - 3ab²

### Quadratic Formula

{-b±√(b²-4ac)} / 2a

### Nature of roots / Discriminant

→ Two distinct real roots, if

b² - 4ac > 0

→ Two equal real roots, if

b² - 4ac = 0

→ No real roots, if

b² - 4ac < 0

### Formulas of Speed, Distance, and Time

Speed = Distance/Time

Time = Distance/Speed

Distance = Speed×Time

## Arithmetic Progression (A.P.) (Arithmetic formula class 10)

### The general form of A.P.

a, a+d, a+2d, a+3d, ..........a+(n-1)d

### Nth term or Last term of A.P.

→ an = a + (n-1)d

Or

→ l = a + (n-1)d

### Sum of n terms of an A.P.

→ Sn = (n/2){2a + (n-1)d}

Or

→ Sn = (n/2){a + an}

Or

→ Sn = (n/2){a + l}

### Sum of first n positive integer

→ Sn = (n/2){n + 1}

### Simple Interest

→ S. I. = (P×R×T)/100

### Quadratic Formula

→ {-b±√(b²-4ac)} / 2a

## Coordinate Geometry

### Distance formula

√ {(x₂-x₁)² + (y₂-y₁)²}

### Section Formula

x = (m₁x₂ + m₂x₁) / (m₁+m₂)

y = (m₁y₂ + m₂y₁) / (m₁+m₂)

### Mid-point formula

x = (x₂ + x₁)/2

y = (y₂ + y₁)/2

### Area of a triangle

(1/2){x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)}

Or

(1/2)×Base×Height

### Area of rhombus

=(1/2)D₁×D ₂

### If points are collinear

(1/2){x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)}=0

## Introduction to Trigonometry

## Some applications of Trigonometry

### Trigonometry ratio formula class 10

sin, cos, tan, cosec, sec, and cot.

→ sinθ = (1/cosecθ )

→ cosθ = (1/secθ )

→ tanθ = (1/cotθ)

→ cosecθ = (1/sinθ)

→ secθ = (1/cosθ)

→ cotθ = (1/tanθ )

→ tanθ = (sinθ/cosθ)

→ cotθ = (cosθ/sinθ)

### Pythagoras theorem

H² = P² + B²

### Trigonometric Ratio of Complementary Angles

→ sinθ = cos(90-θ)

→ cosθ = sin(90-θ)

→ tanθ = cot(90-θ)

→ cotθ = tan(90-θ)

→ cosecθ = sec(90-θ)

→ secθ = cosec(90-θ)

### Trigonometric Identities

→ sin²θ + cos²θ = 1

→ sin²θ = 1 - cos²θ

→ cos²θ = 1 - sin²θ

→ sec²θ - tan²θ = 1

→ sec²θ = 1 + tan²θ

→ tan²θ = sec²θ - 1

→ cosec²θ - cot²θ = 1

→ cosec²θ = 1 + cot²θ

→ cot²θ = cosec²θ - 1

→ Sum of two complementary angles = 90°

## Class 10 Areas related to circle formula

→ Area of Circle = πr²

→ Area of semi-circle = πr²/2

→ Circumference of circle = 2πr

→ Area of right-angled triangle = (1/2)×base×height

→ Area of equilateral triangle = √3side²/4

→ Area of square = side×side

→ Area of rectangle = Length×Breadth

→ Area of minor/major sector = (πr²θ)/360°

→ Length of Arc = (2πrθ)/360°

→ Area of minor/major segment = r²{πθ/360° - sin(θ/2)cos(θ/2)}

→ Perimeter of sector = (2πrθ)/360° + 2r

→ Area of circular ring = π(R²-r²)

→ Area of quadrant = πr²/4

## Surface Area and Volume

→ Area of Circle = πr²

→ Area of circular ring = π(R²-r²)

### Curved/Lateral Surface Area

→ Lateral surface area of cube = 4×edge²

→ Lateral surface area of cuboid = 2(bh+hl)

→ Curved surface area of cylinder = 2πrh

→ Curved surface area of hemisphere = 2πr²

→ Curved surface area of sphere = 4πr²

→ Curved surface area of cone = πrl

→ Slant Height of Cone l = √{h² + r²}

→ Curved surface area of a frustum of cone = πl(r₁ + r₂)

### Total Surface Area

→ Total surface area of cube = 6×edge²

→ Total surface area of cuboid = 2(lb+bh+hl)

→ Total surface area of cylinder = 2πr(r+h)

→ Total surface area of sphere = 4πr²

→ Total surface area of hemisphere = 3πr²

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

→ Total surface area of frustum of cone = πl(r₁ + r₂) + π(r₁² + r₂²)

### Volume

→ Volume of cube = edge³

→ Volume of cuboid = L×B×H

→ Volume of cylinder = πr²h

→ Volume of sphere = (4/3)πr³

→ Volume of hemisphere = (2/3)πr³

→ Volume of cone = (1/3)πr²h

→ Volume of frustum of cone = (1/3)πh(r₁² + r₂² + r₁r₂)

→ Slant height of frustum of cone = √{(h²) + (r₁ - r₂)²}

→ 1 litre = 1000 cm³

→ 1000 litre = 1 m³

→ Speed = Distance / Time

## Statistics class 10 formulas

→ Class Mark = (Upper class limit + Lower class limit) / 2

### Mean

→ Direct method

x = ∑(fᵢxᵢ) / ∑(fᵢ)

→ Assumed mean method

x = a + ∑(fᵢdᵢ) / ∑(fᵢ)

→ Step-deviation method

x = a + {∑(fᵢuᵢ)/∑(fᵢ)}×h

### Mode

l + {(f₁ - f₀)}h/{2f₁ - f₀ - f₂)

### Median

l + {(n/2) - cf}×h / f

### Empirical Formula

3 Median = Mode + 2 Mean

## Probability

→ P(E) = (Number of outcomes favorable to E) / (Number of all possible outcomes of the experiments)

→ P(E) = 1 - P(not E)

→ Every Probability P(E) is-

0 ≤ P(E) ≤ 1

### Total possible outcomes in two dice

Here we are discussing the possible outcomes for two dice.

When we throw any two dice simultaneously, then we get the below results-

Face cards, Spades, Clubs, Diamond, Hearts, Ace, Jack, King, and Queen are shown in below picture-

### How many playing cards are in one deck?

There are 52 playing cards in a deck.

### How many face cards are there in a deck of 52 cards?

There are 12 face cards in a deck of 52 cards.

### How many ace cards are in a deck of 52 cards?

There are 4 ace cards in a deck of 52 cards.

Now use the important formula of maths and solve your problems without any difficulties.