 # 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 higher-level 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:

### 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

 a1x+b1y+c1=0 a2x+b2y+c2=0

Where

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

It should be noted that linear equations in two variables can also be represented in graphical form.

The standard form of a Quadratic Equation is:

 ax2+bx+c=0 where a ≠ 0 and $$\begin{array}{l}x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end{array}$$

### Algebraic formulas

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

### Basic formulas for powers

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

### Arithmetic Progression(AP) Formulas

If a1, a2, a3, a4, a5, a6, 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, nth term for arithmetic progression is given as;

 nth term = a + (n-1) d

Sum of the first n terms in Arithmetic Progression;

 $$\begin{array}{l}S_{n}=\frac{n}{2}[2a+(n-1)d]\end{array}$$

### Trigonometry Formulas For Class 10

Trigonometry maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle 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 right-angled triangle ABC is right-angled at point B and have

$$\begin{array}{l}\angle \theta\end{array}$$
.

Sin θ=

$$\begin{array}{l}\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\end{array}$$
=
$$\begin{array}{l}\frac{Perpendicular}{Hypotenuse}\end{array}$$
= P/H

Cos θ =

$$\begin{array}{l}\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\end{array}$$
=
$$\begin{array}{l}\frac{Base}{Hypotenuse}\end{array}$$
= B/H

Tan θ =

$$\begin{array}{l}\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\end{array}$$
= P/B

Sec θ =

$$\begin{array}{l}\frac{1}{cos\, \theta }\end{array}$$

Cot θ =

$$\begin{array}{l}\frac{1}{tan\, \theta }\end{array}$$

Cosec θ =

$$\begin{array}{l}\frac{1}{sin\, \theta }\end{array}$$

Tan θ =

$$\begin{array}{l}\frac{Sin\, \theta }{Cos\, \theta }\end{array}$$

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
• sin2θ + cos2 θ = 1
• sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
• Cosec2 θ = 1 + cot2 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 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

(r = radius of the circle)

### Surface Area and Volumes Formulas For Class 10

The common formulas from the surface area and volumes chapter in 10th class include the following:

• Sphere Formulas
 Diameter of sphere 2r Surface area of sphere 4 π r2 Volume of Sphere 4/3 π r3
• Cylinder Formulas
 Curved surface area of Cylinder 2 πrh Area of two circular bases 2 πr2 Total surface area of Cylinder Curved surface area of Cylinder + Area of Circular bases = 2 πrh + 2 πr2 Volume of Cylinder π r2 h
• Cone Formulas
 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 π r2 h
• Cuboid Formulas
 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 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:

$$\begin{array}{l}\bar{x}=\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\end{array}$$

where ∑fi xi is the sum of observations from value i = 1 to n

And ∑fi is the number of observations from value i = 1 to n

Assumed mean method :

$$\begin{array}{l}\bar{x}=a+\frac{\sum_{i=1}^{n}f_{i}d_{i}}{\sum_{i=1}^{n}f_{i}}\end{array}$$

where a is assumed mean and di is deviation of a from each of the xi.

Also, di = xi – a

Step deviation method :

$$\begin{array}{l}bar{x}=a+\frac{\sum_{i=1}^{n}f_{i}u_{i}}{\sum_{i=1}^{n}f_{i}}\times h\end{array}$$

where

$$\begin{array}{l}u_{i}=\frac{x_{i}-a}{h}\end{array}$$
and h is class size

(II) The mode of grouped data:

$$\begin{array}{l}Mode = l + \frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\end{array}$$

l=lower limit of modal class.

h= size of the class interval

f1= frequency of modal class.

f0= frequency of the class preceding the modal class.

f2= frequency of the class succeeding the modal class.

(III) The median for a grouped data:

$$\begin{array}{l}Median = l + \frac{\frac{n}{2}-cf}{f}\times h\end{array}$$

l=lower limit of median class.

n= number of observations.

cf= cumulative frequency of class preceding the median class.

f= frequency of median class

h= class size

## More Formulas for Class 10

Check out more important Class 10 maths resources from below:

Quiz on Maths Formulas for Class 10

1. SUBAS LENKA

2. Keshav Mittal

Sir plz. Class 10 Mathematics all chapters formulas.

1. lavanya

Please visit: https://byjus.com/maths/maths-formulas-for-class-10/, to get all formulas for Class 10 Maths.
Thank you!

1. Anushka Mittal

is this for icse grade 10 also

2. Nitish raj

I have problems any one solve

2. vartika rai

sir pls give all the formulas of class 10

3. thats very cool its very easy to learn formulas i thank byju s app members

4. Mrinmoy

This is help full

5. MEGHANA REDDY

sir i want chapter wise all formulas of class 10 maths

6. Farhan khan

I wAnt chapter wise formula

7. Divansh

I want chapter wise formula only of 10

8. Priya jha

Sir I want chapter wise formula plz

9. Roja Jasmine

Sir I want chapter wise formula

10. Roja jasmine

I want chapterwise formulas

11. Gud eving sir i want chapter wise formula only of 10 plz sir

12. Sir may i get all formulas of class 10 by chapterwise

13. it is very useful

14. kishore

thanks you so much

15. Very helpful during exams thanks byjus

16. REALLY HELPFUL THANKS FOR THESE FORMULAS

17. kendrick lamar

where is arithmetic progressions? thats like the one most confusing topic for me atleast

1. Hi,
Learn all about Arithmetic progressions here in detail.

2. lavanya

Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. Learn more here: Arithmetic Progression.

18. Yes it is really helpful for solving the problem

19. Sabira khan

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