In class X there are many vital chapters in Mathematics. As per NCERT book chapter names are

- REAL NUMBERS
- POLYNOMIAL
- PAIR OF LINEAR EQUATION IN TWO VARIABLES
- QUADRATIC EQUATIONS
- ARITHMETIC PROGRESSION
- TRIANGLES
- COORDINATE GEOMETRY
- INTRODUCTION TO TRIGONOMETRY
- CIRCLES
- SURFACE AREA AND VOLUMES
- STATISTICS
- PROBABILITY

**class 10 math formula**

Contents

In this article we are going to provide and read some necessary formulae of significant chapters which are given above.

**Real Numbers **

**Euclid Division Theorem**

Relation between Divisor(g), dividend(P) , quotient(q) and remainder(R) is given by:

P(x)= g(x)×q(x)+R

Where R is smaller than G(x) and G(x) is not equal to ZERO.

**HCF & LCM**

Relationship between HCF and LCM of two numbers(A & B) is given by

HCF×LCM=A×B

**Polynomials**

Suppose you are given an equation

ax²+bx+c=0 where a, b and c are not equal to zero at once*.

In this case if x-a=0 is the factor of the given equation then ‘a’ is the solution/zero of this equation also.

Also, ax²+bx+c=0 where a, b and c are not equal to zero at once*.

In this case, Sum of zeroes is given by **– b/a **

Product of zeroes is given by= **c/a**

**Similarly if we have cubic equation then **

ax³+bx²+cx+d=0 in which a, b, c and d are not equal to zero at once.

Sum of zeroes is given by=**(-b/a) **

Sum and product of zeroes =**(c/a) **

Product of roots =**(-d/a) **

**Quadratic Equations**

Equation having its variable with degree 2 with some constant is called a quadratic equation.

Ax²+Bx+C=0 (coefficient of X² should never be Zero)

**Zeros of this equation is given by **

X=(-B±√D)/2A

This formula is known as the Quadratic Formula of Dharacharya Sutra.

Where D is Discriminant given by D=B²-4AC

If D is negative then roots will be imaginary

If D is positive then roots will be real and distinct

If D is zero then an equal and real root will be obtained from the quadratic formula.

**Linear Equation in two variables **

Suppose there are two linear equations,

- a
_{1}x+b_{1}y+c=0 - a
_{2}x+b_{2}y+c=0

**Then, **

- (a
_{1}/a_{2})=(b_{1}/b_{2})≠(c_{1}/c_{2})

In this condition, the given equation will probably intersect at infinity thus there will be no zeroes of that equation.

- (a
_{1}/a_{2})=(b_{1}/b_{2})=(c_{1}/c_{2})

This condition is known as an overlapping condition where an infinite number of zeroes of the equation will be available.

- (a
_{1}/a_{2})≠(b_{1}/b_{2})=(c_{1}/c_{2})

In this case, only one solution of the equation will be available, meaning the lines of equations will cut at one point only.

**Arithmetic Progression **

Suppose you are given an AP a, a+d, a+2d, a+3d,……a+(n)d

Then last term or nth term is given by

**a _{n} =T_{n}=a+(n-1)d**

Where a_{n }& T_{n} are last or nth term, a is first term of AP, n is the number of terms in AP and d is the common difference of any two consecutive terms.

Sum of n terms of AP =n/2[2a+(n-1)d]=n/2(a+l)

Here also all terms a, n, d means the same as above but L means the last term of the AP.

**Coordinate Geometry **

Here Distance between two is given by D²=(x_{2}-x_{1})²+(y_{2}-y_{1})²

Area of triangle formed by three points is 🔽=½[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{3}-y_{1})]

Where x and y with different variants are Coordinate points.

**Section formula for the division in line is given by **

x=(mx_{2}+nx_{1})/(m+n)

y=(my_{2}+ny_{1})/(m+n)

Where m and n are ratios of division and x and y variants are points of/on line.

**Circles and Surface Area**

- Circumference of the circle = 2πr
- Area of the circle = πr²
- Area of the sector of angle θ = (θ/360)×πr²
- Length of an arc of a sector of angle θ = (θ/360) × 2πr

**(r = radius of the circle) **

- Diameter of sphere=2r
- Surface area of sphere=4πr²
- Volume of Sphere=4/3πr³
- Curved surface area of Cylinder 2 πrh
- Area of two circular bases 2πr²
- Total surface area of Cylinder Circumference of Cylinder + Curved surface area of Cylinder = 2πrh + 2πr²
- Volume of Cylinder πr2h
- Slant height of cone l = √(r2 + h2)
- Curved surface area of cone πrl
- Total surface area of cone=πr (l + r)
- Volume of cone=⅓ πr²h
- 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×b+b×h+l×h)
- Volume of Cuboid l×b×h

Here, l = length, b = breadth and h = height. In the case of Cube, put l = b = h = a, as the cube has all its sides of equal length, so you can treat the cube as a cuboid to find out the volume, surface area etc.

**Other useful links:**

- Class 10 science NCERT book PDF
- Life Processes class 10
- Nelson mandela class 10 PDF
- 10th class all subject books pdf

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