All Maths Formulas For Class 10

In the class 10 math formulas include formulas related to real numbers, polynomials, quadratic equations, triangles, circles, statistics, probability, etc. These all math formulas will be extremely helpful for students to be able to solve questions more accurately and quickly.

List of Maths Formulas for Class 10

Here The basic maths class 10 formulas are almost the same for all the boards. The list of maths formulas are:

• Linear Equation Formulas
• Algebra and Quadratic Equation Formulas
• Arithmetic Progression Formulas
• Trigonometry Formulas
• Circle Formulas
• Surface Area and Volume Formulas
• Statistics Formulas

Class 10 Maths Formulas PDF

Linear Equations for class 10

One Variable	ax+b=0	Here a≠0 and a&b are real numbers
Two variable	ax+by+c = 0	Here 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

linear equations in one variable

ax+b=0

Linear Equations in two variables

a2x+b2y+c2=0

a3x+b3y+c3=0

Where

• a₁, b₁, c₁, a₂, b₂, and c₂ all are the real numbers
• a₁²+b₁² ≠ 0 & a₂² + b₂² ≠ 0

Quadratic Equation and Formula for Class 10

Standard form of Quadratic Equation is:

ax²+bx+c=0 where a ≠ 0

Basic formulas for powers

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

Algebraic formulas for Class 10

• (a+b) (a-b) = a2 – b2
• (a+b)2 = a2 + b2 + 2ab
• (a-b)2 = a2 + b2 – 2ab
• (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
• (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – b3 – 3ab(a – b)
• x2 + y2 =½ [(x + y)2 + (x – y)2]
• x3 + y3= (x + y) (x2 – xy + y2)
• x3 – y3 = (x – y) (x2 + xy + y2)
• (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
• x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
• x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
• (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc

Arithmetic Progression (AP) Formulas

If a₁, a₂, a₃, a_4,…… are the terms of AP (Arithmetic Progression) and d is common difference between each term, then we can write the sequence as; a_, a+d, a+2d, a+3d, a+4d,….,nth term.

Here a is the first term. Now, n^th term for AP (arithmetic progression) is given as follow:

nth term = a + (n-1) d

The Sum of first n terms in Arithmetic Progression (AP)

Circles Formulas For Class 10

• Circumference of circle = 2 π r
• Area of circle = π r²
• Area of the sector of angle θ = (θ/360) × π r²
• Length of an arc of a sector of angle θ = (θ/360) × 2 π r

In above points (r = radius of the circle)

Trigonometry Formulas For Class 10

Trigonometry formulas are based on these functions and can be used to solve various equations and problems related to triangles.

• sin(90° – θ) = cos θ
• cos(90° – θ) = sin θ
• tan(90° – θ) = cot θ
• cot(90° – θ) = tan θ
• sec(90° – θ) = cosecθ
• cosec(90° – θ) = secθ
• sin²θ + cos² θ = 1
• sec² θ = 1 + tan²θ for 0° ≤ θ < 90°
• Cosec² θ = 1 + cot² θ for 0° ≤ θ ≤ 90°

Trigonometry Table

Angles (In Degrees)	0°	30°	45°	60°	90°	180°
sin	0	1/2	1/√2	√3/2	1	0
cos	1	√3/2	1/√2	1/2	0	-1
tan	0	1/√3	1	√3	∞	0
cot	∞	√3	1	1/√3	0	∞
cosec	∞	2	√2	2/√3	1	∞
sec	1	2/√3	√2	2	∞	-1

Click here to know all things about trigonometry table

Surface Area and Volumes Formulas For Class 10

Here we are adding common formulas of surface area and volumes for 10th class.

Sphere Formulas

Diameter of the sphere	2r
Surface area of the sphere	4 π r2
Volume of the Sphere	4/3 π r3

Cylinder Formulas

Curved surface area of the Cylinder	2 πrh
Area of the two circular bases	2 πr2
Total surface area of the Cylinder	Curved surface area of Cylinder + Area of Circular bases = 2 πrh + 2 πr2
Volume of The Cylinder	π r2 h

Cone Formulas

Slant height of cone	l = √(r2 + h2)
Curved surface area of the cone	πrl
Total surface area of the cone	πr (l + r)
Volume of the cone	⅓ π r2 h

Cuboid Formulas

Perimeter of the cuboid	4(l + b +h)
Length of the longest diagonal of a cuboid	√(l2 + b2 + h2)
Total surface area of the cuboid	2(l×b + b×h + l×h)
Volume of the Cuboid	l × b × h

Where, l = length, b = width and h = height. In case of the 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

Mean:

Mean = (Sum of all values) / (Total number of values)

Variance:

Variance = (Sum of (value – mean) squared) / (Total number of values – 1)

Standard Deviation:

Standard deviation = Square root of variance

Range:

Range = (Largest value) – (Smallest value)

Mode:

Mode = L+h(fm−f1)(fm−f1)−(fm−f2) L + h ( f m − f 1 ) ( f m − f 1 ) − ( f m − f 2 )

Median:

median = [l + ((n/2) – cf)/f)h ] , Where

l=lower limit of median class, n= number of observations, cf= cumulative frequency, f= frequency of median class, h= class size