✅ Maths Formulas For Class 10 ⭐️⭐️⭐️⭐️⭐

General Maths Formulas for Class 10

Here is a list of other important formulas for class 10-

1. (a+b)2 = a2 + b2 + 2ab
2. (a-b)2 = a2 + b2 – 2ab
3. (a+b) (a-b) = a2 – b2
4. (x + a)(x + b) = x2 + (a + b)x + ab
5. (x + a)(x – b) = x2 + (a – b)x – ab
6. (a + b)3 = a3 + b3 + 3ab(a + b)
7. (a – b)3 = a3 – b3 – 3ab(a – b)
8. (x – a)(x + b) = x2 + (b – a)x – ab
9. (x – a)(x – b) = x2 – (a + b)x + ab
10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
15. x2 + y2 =½ [(x + y)2 + (x – y)2]
16. (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
17. x3 + y3= (x + y) (x2 – xy + y2)
18. x3 – y3 = (x – y) (x2 + xy + y2)
19. x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]

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 x = [-b ± √(b2 – 4ac)]/2a

Basic formulas for powers

• p^m x pⁿ = p^m+n
• {p^m}⁄{pⁿ} = p^m-n
• (p^m)ⁿ = p^mn
• p^-m = 1/p^m
• 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, n^th term for arithmetic progression is given as;

nth term = a + (n-1) d

Sum of the first n terms in Arithmetic Progression;

Sn = n/2 [2a + (n-1) d] or Sn = n/2 [a + l]

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.

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°

Relations between trigonometric identities are given below:

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)

Important properties related to circles:

• Equal chords of a circle are equidistant from the centre.

• The perpendicular drawn from the centre of a circle, bisects the chord of the circle.

• The angle subtended at the centre by an arc = Double the angle at any part of the circumference of the circle.

• Angles subtended by the same arc in the same segment are equal.

• To a circle, if a tangent is drawn and a chord is drawn from the point of contact, then the angle made between the chord and the tangent is equal to the angle made in the alternate segment.

 The sum of opposite angles of a cyclic quadrilateral is always 180^o.

Important formulas related to circles:

Area of a Segment of a Circle: If AB is a chord which divides the circle into two parts, then the bigger part is known as major segment and smaller one is called minor segment.

Here, Area of the segment APB = Area of the sector OAPB – Area of ∆ OAB

Mensuration

Check below the important formulas for areas and volumes of solids:

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 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	Circumference of Cylinder + Curved surface area of Cylinder = 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.

For Ungrouped Data:

Mean: The mean value of a variable is defined as the sum of all the values of the variable divided by the number of values.

Median: The median of a set of data values is the middle value of the data set when it has been arranged in ascending order.  That is, from the smallest value to the highest value.
Median is calculated as

Where n is the number of values in the data. If the number of values in the data set is even, then the median is the average of the two middle values.
Mode: Mode of a statistical data is the value of that variable which has the maximum frequency

For Grouped Data:

Mean: If x₁, x₂, x₃,……x_n are observations with respective frequencies f1, f2, f3,…..fn then mean is given as:

Median: For the given data, we need to have class interval, frequency distribution and cumulative frequency distribution. Then, median is calculated as

Where 
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 (assuming class size to be equal)

Mode: Modal class: The class interval having highest frequency is called the modal class and Mode is obtained using the modal class.

Where 
l = lower limit of the modal class, 
h = size of the class interval (assuming all class sizes to be equal), 
f₁ = frequency of the modal class, 
f₀ = frequency of the class preceding the modal class, 
f₂ = frequency of the class succeeding the modal class.

List of Important Class 10 Math Formulas

A list of some basic class 10 maths formulas related to most important topics covered under various school boards is given below:

• (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
• an = a + (n – 1) d
• Sn= n/2 [2a + (n – 1)d]
• sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ ⇒ cos² θ = 1 – sin² θ
• cosec² θ – cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ – 1
• sec² θ – tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1
• Vol of Sphere = 4/3 ×π r³
• Surface Area of Sphere = 4πr²

Similarity of Triangles:                                                                  

• If two triangles are similar then ratio of their sides are equal.

Theorem on the area of similar triangles: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Coordinate Gemetry:

• Distance Formulae: Consider a line having two point A(x₁, y₁) and B(x₂, y₂), then the distance of these points is given as:

 Section Formula: If a point p divides a line AB with coordinates A(x₁, y₁) and B(x₂, y₂), in ratio m:n, then the coordinates of the point p are given as:

Mid Point Formula: The coordinates of the mid-point of a line AB with coordinates A(x₁, y₁) and B(x₂, y₂), are given as:

Area of a Triangle: Consider the triangle formed by the points A(x₁, y₁) and B(x₂, y₂) and C(x₃, y₃) then the area of a triangle is given as-

Probability

Class 10 Maths Formulas Examples

Example 1: Check whether the equation is a quadratic equation or not: x + 1/x = 2

Solution: x + 1/x = 2

 x + x^-1 = 2

x + x^-1 – 2 = 0

Since x + x^-1 – 2 = 0 is not a quadratic polynomial, therefore, x + 1/x = 2 is not a quadratic equation. 

Example 2: Find the zeros of the quadratic polynomial 6x² – 3 – 7x

Solution :

Here, p (x) = 6x² – 3 – 7x = 6x² – 7x – 3

= 6x² – 9x + 2x – 3 = 3x (2x – 3) + 1 (2x – 3) 

= (2x – 3) (3x + 1)

= 6(x – 3/2)[x − (−1/3)]

∴ Zeros of p (x) are 3/2 and −1/3

Some FAQs on Maths Formulas Class 10

Here are some frequently asked questions that students ask regarding Class 10 Maths Formulas.

Q: How should students memorise Maths formula? Ans: Learning and memorising maths formulas require a lot of effort and practice. Students must be familiar with the chapters and the concepts and then try to understand how a formula is derived.

Q: How can students learn Maths formulas for Class 10? Ans: For learning Maths formulas, students must take the help of formulas provided in the above segment in this article.

Q: What are the important topics of NCERT Class 10 Maths syllabus? Ans: The important topics of NCERT Class 10 Maths syllabus includes statistics & probability, Geometry, and Algebra.

Q: Is NCERT Syllabus for Class 10 Maths difficult to study? Ans: The difficulty level of Maths is moderate and topics and in a flow from basic to advanced. The candidate must be acquainted with the formulas for making Maths easy to study and solve.

Q: Where can students get the Maths formula for Surface area and volume? Ans: Students who are looking to be well versed with the Maths formula must view them in this article.

What are the Important Formulas for Class 10 Math?

Some of the most important formulas for Class 10 math are based on topics like polynomials, trigonometry, quadratic equations, pairs of linear equations in two variables, statistics and probability. These important class 10 math formulas from above topics are listed below:

• (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
• an = a + (n – 1) d
• Sn= n/2 [2a + (n – 1)d]
• sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos²θ ⇒ cos²θ = 1 – sin²θ
• cosec² θ – cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ – 1
• sec² θ – tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec²θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1
• Vol of Sphere = 4/3 ×πr³
• Surface Area of Sphere = 4πr²

What are the Basic Formulas in Class 10 Maths?

The basic formulas in class 10 maths are covered in the topics like real numbers, polynomials, geometry, statistics and probability. Memorizing class 10 real numbers basic formulas will equip students to understand a variety of concepts related to natural numbers, whole numbers and real numbers, etc. The polynomial formulas are helpful in finding the roots of equations. In geometry, it is important that the students must memorize the basic formulas related to the area and volume of different three dimensional shapes and objects like spheres, cones, prisms, etc.

What are the important formulas covered in class 10 Algebra?

Some of the most important formulas covered in class 10 Algebra are related to polynomials including linear, and quadratic equations. All these important formulas are provided on this page. Students can also download and revise these class 10 algebra formulas through the pdf link provided on this page.

How Many Formulas are there in Class 10 Maths?

There are approximately 40 formulas in class 10 maths based on chapters like real numbers, polynomial quadratic equations, pair of linear equations in two variables, arithmetic progressions, triangles, coordinate geometry, Introduction to trigonometry, applications of trigonometry, circles, surface area and volume, statistics, probability.

How can I Memorize Class 10 Maths formulas?

Memorizing class 10 Maths formulas is important for students to solve problems easily. Students can revise formulas by repeatedly writing or applying them to various problems. Studying and learning math formulas necessitates students to put a lot of time and effort in practicing them. Students must also have a familiarity with the chapters and the concepts to understand how to derive formulas.

✅ Math Formulas ⭐️⭐️⭐️⭐️⭐