# Class 10 math formula PDF

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
• 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)

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,

• a1x+b1y+c=0
• a2x+b2y+c=0

Then,

• (a1/a2)=(b1/b2)≠(c1/c2

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

• (a1/a2)=(b1/b2)=(c1/c2)

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

• (a1/a2)≠(b1/b2)=(c1/c2)

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

an =Tn=a+(n-1)d

Where  an & Tn 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=(x2-x1)²+(y2-y1
Area of triangle formed by three points is ????=½[x1(y2-y3)+x2(y3-y1)+x3(y3-y1)]

Where x and y with different variants are Coordinate points.

Section formula for the division in line is given by

x=(mx2+nx1)/(m+n)
y=(my2+ny1)/(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.

class 10 math formula pdf