Maths Formulas For Class 10
Maths formulas for Class 10 are the general formulas that are not only crucial for Class 10 but also form the base for higherlevel maths concepts. The maths formulas are also important in various higher education fields like engineering, medical, commerce, finance, computer science, hardware, etc. In almost every industry, the most common formulas introduced in class 10 are used.
The class 10 maths formulas include formulas related to real numbers, polynomials, quadratic equations, triangles, circles, statistics, probability, etc. These maths formulas will be extremely helpful for students to be able to solve questions more accurately and quickly.
List of Maths Formulas for Class 10 (Chapterwise)
The basic maths class 10 formulas are almost the same for all the boards. The list of maths formulas are:
 Pair of Linear Equation in Two Variables 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
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Linear Equations
One Variable  ax+b=0  a≠0 and a&b are real numbers 
Two variable  ax+by+c = 0  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 
Pair of Linear Equations in two variables
a_{1}x+b_{1}y+c_{1}=0 a_{2}x+b_{2}y+c_{2}=0 
Where
 a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, and c_{2} are all real numbers and
 a_{1}^{2}+b_{1}^{2} ≠ 0 & a_{2}^{2 }+ b_{2}^{2} ≠ 0
It should be noted that linear equations in two variables can also be represented in graphical form.
Quadratic Equation and Formula
The standard form of a Quadratic Equation is:
ax^{2}+bx+c=0 where a ≠ 0 And x = [b ± √(b^{2} – 4ac)]/2a 
Algebraic formulas
 (a+b)^{2 }= a^{2 }+ b^{2 }+ 2ab
 (ab)^{2 }= a^{2 }+ b^{2 }– 2ab
 (a+b) (ab) = a^{2 }– b^{2}
 (x + a)(x + b) = x^{2} + (a + b)x + ab
 (x + a)(x – b) = x^{2} + (a – b)x – ab
 (x – a)(x + b) = x^{2} + (b – a)x – ab
 (x – a)(x – b) = x^{2} – (a + b)x + ab
 (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
 (a – b)^{3} = a^{3} – b^{3} – 3ab(a – b)
 (x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz
 (x + y – z)^{2} = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz
 (x – y + z)^{2} = x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz
 (x – y – z)^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz
 x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz xz)
 x^{2 }+ y^{2} =½ [(x + y)^{2} + (x – y)^{2}]
 (x + a) (x + b) (x + c) = x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc
 x^{3} + y^{3}= (x + y) (x^{2} – xy + y^{2})
 x^{3} – y^{3} = (x – y) (x^{2} + xy + y^{2})
 x^{2} + y^{2} + z^{2} xy – yz – zx = ½ [(xy)^{2} + (yz)^{2} + (zx)^{2}]
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Basic formulas for powers
 p^{m }x p^{n }= p^{m+n}
 {p^{m}}⁄{p^{n}} = p^{mn}
 (p^{m})^{n }= p^{mn}
 p^{m} = 1/p^{m}
 p^{1} = p
 P^{0 }= 1
Arithmetic Progression(AP) Formulas
If a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6},_{…} 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+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, n^{th} term for arithmetic progression is given as;
n^{th} term = a + (n1) d 
Sum of the first n terms in Arithmetic Progression;
S_{n} = n/2 [2a + (n1) d] 
Trigonometry Formulas For Class 10
Trigonometry maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a rightangle triangle. Also, in trigonometry, the functions sec, cosec and cot formulas can be derived with the help of sin, cos and tan formulas.
Let a rightangled triangle ABC is rightangled at point B and have \(\angle \theta\).
Sin θ= \(\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\)=\(\frac{Perpendicular}{Hypotenuse}\) = P/H
Cos θ = \(\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Base}{Hypotenuse}\) = B/H
Tan θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\) = P/B
Sec θ = \(\frac{1}{cos\, \theta }\)
Cot θ = \(\frac{1}{tan\, \theta }\)
Cosec θ = \(\frac{1}{sin\, \theta }\)
Tan θ = \(\frac{Sin\, \theta }{Cos\, \theta }\)
Trigonometry Table:
Angle  0°  30°  45°  60°  90° 
Sinθ  0  1/2  1/√2  √3/2  1 
Cosθ  1  √3/2  1/√2  ½  0 
Tanθ  0  1/√3  1  √3  Undefined 
Cotθ  Undefined  √3  1  1/√3  0 
Secθ  1  2/√3  √2  2  Undefined 
Cosecθ  Undefined  2  √2  2/√3  1 
Other Trigonometric formulas:
 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
 sin^{2}θ + cos^{2} θ = 1
 sec^{2 }θ = 1 + tan^{2}θ for 0° ≤ θ < 90°
 Cosec^{2 }θ = 1 + cot^{2} θ for 0° ≤ θ ≤ 90°
Get complete Trigonometry Formulas list here
Circles Formulas For Class 10
 Circumference of the circle = 2 π r
 Area of the circle = π r^{2}
 Area of the sector of angle θ = (θ/360) × π r^{2}
 Length of an arc of a sector of angle θ = (θ/360) × 2 π r
(r = radius of the circle)
Surface Area and Volumes Formulas For Class 10
The common formulas from the surface area and volumes chapter in 10^{th} class include the following:
 Sphere Formulas
Diameter of sphere  2r 
Surface area of sphere  4 π r^{2} 
Volume of Sphere  4/3 π r^{3} 
 Cylinder Formulas
Curved surface area of Cylinder  2 πrh 
Area of two circular bases  2 πr^{2} 
Total surface area of Cylinder  Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr^{2} 
Volume of Cylinder  π r^{2 }h 
 Cone Formulas
Slant height of cone  l = √(r^{2} + h^{2}) 
Curved surface area of cone  πrl 
Total surface area of cone  πr (l + r) 
Volume of cone  ⅓ π r^{2 }h 
 Cuboid Formulas
Perimeter of cuboid  4(l + b +h) 
Length of the longest diagonal of a cuboid  √(l^{2} + b^{2} + h^{2}) 
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 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 mode of grouped data.
(I) The mean of the grouped data can be found by 3 methods.
 Direct Method: x̅ = \(\frac{\sum_{i=1}^{n}f_i x_i}{\sum_{i=1}^{n}f_i}\), where ∑f_{i }x_{i } is the sum of observations from value i = 1 to n And ∑f_{i }is the number of observations from value i = 1 to n
 Assumed mean method : x̅ = \(a+\frac{\sum_{i=1}^{n}f_i d_i}{\sum_{i=1}^{n}f_i}\)
 Step deviation method : x̅ = \(a+\frac{\sum_{i=1}^{n}f_i u_i}{\sum_{i=1}^{n}f_i}\times h\)
(II) The mode of grouped data:
Mode = \(l+\frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h\)
(III) The median for a grouped data:
Median = \(l+\frac{\frac{n}{2} – cf}{f} \times h\)
More Formulas for Class 10
 Geometry Formulas For Class 10
 Algebra Formulas for Class 10
 Mensuration Formulas Class 10
 Trigonometry Formulas For Class 10
Check out more important Class 10 maths resources from below:
Class 10 Maths Important Questions  Revision Notes For Class 10th Maths 
Sample Papers For Class 10 Maths  Previous Year Question Papers For Class 10 Maths 