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:

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

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.

Quadratic Equation and Formula

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]

Click here to check all algebra formulas

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 ∠θ.

\(\begin{array}{l}sin\ \theta = \frac{Side\ opposite\ to\ angle\ \theta}{Hypotenuse}=\frac{Perpendicular}{Hypotenuse}= \frac{P}{H}\end{array} \)
\(\begin{array}{l}Cos\ \theta = \frac{Adjacent\ side\ to\ angle\ \theta}{Hypotenuse}= \frac{Base}{Hypotenuse} = \frac{B}{H}\end{array} \)
\(\begin{array}{l}Tan\ \theta = \frac{Side\ opposite\ to\ angle\ \theta}{Adjacent\ side\ to\ angle\ \theta} = \frac{P}{B}\end{array} \)
\(\begin{array}{l}Sec\ \theta =\frac{1}{cos\, \theta }\end{array} \)
\(\begin{array}{l}Cot\ \theta = \frac{1}{tan\, \theta }\end{array} \)
\(\begin{array}{l}Cosec\ \theta = \frac{1}{sin\, \theta }\end{array} \)
\(\begin{array}{l}Tan\ \theta = \frac{Sin\ \theta }{Cos\ \theta }\end{array} \)

Trigonometry Table:

Angle 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

26 Comments

  1. REALLY HELPFUL

  2. Sir plz. Class 10 Mathematics all chapters formulas.

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

  4. This is help full

  5. sir i want chapter wise all formulas of class 10 maths

  6. I wAnt chapter wise formula

  7. I want chapter wise formula only of 10

  8. Sir I want chapter wise formula plz

  9. Sir I want chapter wise formula

  10. 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. thanks you so much

  15. Very helpful during exams thanks byjus

  16. REALLY HELPFUL THANKS FOR THESE FORMULAS

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

  18. Yes it is really helpful for solving the problem

  19. It is really helpful to solve the question 🤗🤗

  20. It is really helpful to solve the question

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