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Home > News & Articles > List of Important Maths Formulas and Solved Examples | Class 6 to 12

Kasturi Talukdar

Updated on 22nd June, 2023 , 12 min read

List of Important Maths Formulas and Solved Examples | Class 6 to 12

Q: "What are some commonly used math formulas?"

"Some commonly used math formulas include the Pythagorean theorem, quadratic formula, area and perimeter formulas for geometric shapes, trigonometric identities, and formulas for arithmetic and geometric sequences."

Q: "How can I remember math formulas more easily?"

"To remember math formulas, practice applying them in various problems, create flashcards or cheat sheets, break formulas into smaller parts for better understanding, and try to understand the logic behind each formula."

Q: "Where can I find a comprehensive list of math formulas?"

"You can find comprehensive lists of math formulas in textbooks, educational websites, math reference books, or by searching online math resources."

Q: "Are there any shortcuts or tricks for learning math formulas?"

"Yes, some tips include identifying patterns in formulas, understanding the derivations or proofs of formulas, and connecting formulas to real-world applications to enhance understanding and memory."

Q: "How can I use math formulas effectively in problem-solving?"

"To use math formulas effectively, read the problem carefully, identify the relevant formula(s) needed, substitute the given values into the formula, and solve step-by-step using proper mathematical operations."

Q: "Can I derive math formulas by myself?"

"Yes, some math formulas can be derived using logical reasoning, algebraic manipulations, or geometric principles. Deriving formulas can deepen your understanding of the underlying concepts."

Q: "What are the essential math formulas for geometry?"

"Essential geometry formulas include those for area and perimeter of shapes (rectangle, triangle, circle), volume and surface area of solids (cuboid, cylinder, sphere), and trigonometric ratios for angles and triangles."

Q: "Are there any formulas to calculate statistical measures?"

"Yes, statistical measures like mean, median, mode, and standard deviation have specific formulas. For example, mean is calculated by dividing the sum of all observations by the total number of observations."

Q: "Can I use calculators to find math formulas?"

"Calculators can help in performing calculations involved in math formulas, but understanding the concepts behind the formulas and knowing when and how to apply them is crucial."

Maths formulas Overview

Maths formulas are the building blocks for solving complex problems and unlocking the secrets of the universe. Whether you're a student, a professional in a STEM field, or simply someone who wants to sharpen their analytical skills, understanding and applying mathematical formulas is essential. In this article, we will delve into the world of mathematical formulas, exploring their significance, and providing a comprehensive guide to help you master them. Let's embark on this exciting journey of mathematical discovery!

Basic Maths Formulas

A mathematical formula is a precise representation or rule that emerges from the relationship between multiple quantities, and its outcome is expressed using symbolic notation. Math formulas consist of various elements, such as constants, which are specific numbers, variables that represent unknown values, mathematical signs and symbols, and occasionally exponential powers.

BODMAS Formula

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

Basic Algebra Formulas

a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
(a +b+ c)2=a2+b2+c2+2ab+2bc+2ca
(a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯
(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=1/2[(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=1/2[(x−y)2+(y−z)2+(z−x)2]

Maths Formulas Table

The table below has all the basic maths formulas:

Perimeter	Square Rectangle	P = 4a P = 2(l+b)
Circumference	Circle	C = 2 (pi) r
Area	Square Rectangle Triangle Trapezoid Circle	A = a2 A = l x b A = ½(b x h) A = ((b1 +b2 ) x h) / 2 A = π x r 2
Surface Area	Cube Cylinder Cone Sphere	S = 6l2 CSA = 2 x π x r x h CSA = π x r x l S = 4 x π x r 2
Volume	Cylinder Cone Sphere	V = πr 2h V =1/3 πr 2h V = 4/3 x π x r3
Pythagoras Theorem	a2 + b2 = c2
Distance Formula	d = √[(x2 – x1)2 +(y2 – y1)2]
Slope of a line	m = y2 – y1 / x2 – x1
Mid- Point Formula	M = [(x1 + x2 )/ 2 , (y1 + y2 )/ 2]
Algebraic Formula	Pythagorean theorem Slope-intercept form of the equation of a line Distance formula Total cost Quadratic formula Laws of Exponents Fractional Exponents	a2 + b2 = c2 y = mx + c d = rt total cost = (number of units) × (price per unit) X = [-b ± √(b2 – 4ac)] /2a am x b m = (a x b)m; am x a n = (a)m+n a1/2 = √a
Trigonometric Formulas	Sine Function Cosine Function Tangent Function	Sin x = Opposite Side/ Hypotenuse Cos X = Adjacent Side/ Hypotenuse Tan x = Opposite Side/ Adjacent Side

Important Maths Formulas from Class 6-12

Gaining a comprehensive understanding of mathematics formulas significantly enhances students' performance in examinations across all academic levels, be it class tests, final exams, or board exams. Most of the chapters within the mathematics syllabus are interconnected, meaning that mastering the formulas of one chapter simplifies comprehension of subsequent chapters. Noteworthy examples of interrelated chapters include percentage and profit-loss, percentages and fractions, real numbers and complex numbers, among others.

To truly grasp the formulas, students must allocate sufficient time and effort to systematically analyze and comprehend them. Detailed lists of math formulas are readily available for each chapter as per the latest syllabus of respective academic standards.

Maths Formulas: Class 6

1,000,000,000 is called one billion.
Anything divided by zero is called ‘undefined'.
A number is divisible by 2 if it has 0, 2, 4, 6 or 8 in one place.
A number is divisible by 3 if the sum of the digits is a multiple of 3.
A simple closed figure formed by line segments is a polygon. Triangle is a three-sided Polygon. Quadrilaterals are four-sided polygons.
An equation is a condition represented on a variable. An equation is composed of two sides, known as the Left-Hand Side and Right Hand Side, separated by an equal (=) sign.
The perimeter of a Square = 4 × Length of its side
Perimeter of a Rectangle = 2 × (Length + Breadth)
The perimeter of an Equilateral triangle = 3 × Length of a side
Area of a Rectangle = length × breadth
Variable refers to a value that is not fixed. It can take different values.
An equation is a condition represented on a variable.
An equation is composed of two sides, known as the Left-Hand Side and Right Hand Side, separated by an equal (=) sign.

Maths Formulas: Class 7

Product of rational numbers = (Product of Numerators) / (Product of Denominators)
First Rational Number × (Reciprocal of other Rational Number)
Area of a Square = Side2
The perimeter of a Square = 4 × Side
Area of Rectangle = Length × Breadth
Perimeter of a Rectangle = 2 × (Length + Breadth)
Area of a Parallelogram = Base × Height
Area of Triangle = 1/ 2 × Base × Height
Circumference of a circle = π d, where ‘d' is the diameter of a circle and π = 22/7 or 3.14
Area of a circle = πr2
Law of Product: am × an = am+n
Law of Quotient: am/an = am-n
Law of Zero Exponent: a0 = 1
Law of Negative Exponent: a-m = 1/am
Law of Power of a Power: (am)n = amn
Law of Power of a Product: (ab)m = ambm
Law of Power of a Quotient: (a/b)m = am/bm
(a-b) 2 = a2 – 2ab + b2
(a-b-c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ac

If their two ratios are equivalent for any four quantities, those four quantities are said to be proportionate.

Increase in Percentage = (Change / Original Amount) × 100

Profit Percentage = (Profit / Cost price) × 100

Simple Interest = (Principal × Rate × Time) / 100

Amount = Principal + Interest

Maths Formulas: Class 8

Additive inverse of rational number: a/b = -b/a
Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
Distributives a(b – c) = ab – ac
Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes
Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal (1 + Rate/100)n, where ‘n' is the period.
(a – b)2 = a2 – 2ab + b2
(a + b) (a – b) = a2 – b2
Euler's Formula: For any polyhedron, Number of faces + Number of vertices – Number of edges = 2
Volume of a Cone = (1 / 3)πr2h
Volume of a Sphere = (4/3) π r3

Maths Formulas: Class 9

Topic	Shapes/Statistics	Maths Formulas
Real Numbers	-	√ab = √a √b √(a/b) = √a / √b (√a + √b) (√a – √b) = a – b (√a + √b)2 = a + 2√ab + b (a + √b) (a – √b) = a2 – b (a + b) (a – b) = a2 – b2
Geometry Formulas	Rectangle	A = Length x Width P = 2(Length + Width)
	Triangle	A = ½ x Breadth x Height P = Sum of all the three sides of a triangle
	Trapezoid	A = ½ x Height x (b₁x b₂) P = Sum of all the sides of a trapezoid
	Parallelogram	A = Breadth x Height P = 2( a+ b) Here. a = side B = base
	Circle	A = πr² P = 2 πr
Algebra Identities	-	(x + β)² = x² + β² + 2 x β (x – β)² = x² + β² – 2 x β (x + θ) (x – θ) = x² – θ² (x + α)(x + θ) = x² + (α + θ)x + αθ (x + α)(x – θ) = x² + (α – θ)x – αθ (x – α)(x + θ) = x² + (θ – α)x – xθ (x – α)(x – θ) = x² – (α + θ)x + αq (α + θ)³ = α³ + θ³ + 3αθ(α + θ) (α – θ)³ = α³ + θ³ – 3αθ(α – θ) (α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ (α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ (α – β + θ)² = α² + β² + θ²- 2αβ – 2βθ + 2αθ (α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ (x)³ + (β)³ = ( x + β) (x² – xβ + β) (x)³ – (β)³ = ( x + β) (x² – xβ + β)
Surface Area and Volume	Cuboid	2 = (lb + bh + hl), Here, l = length, b = Breadth, h = height V = Length x Breadth x Height
	Cube	A = 6 side² V = Side³ Cylinder A = 2πr( h + r) Here, r = radius of circular cylinder H = height of a cylinder V = πr²H
	Cone	A = πr( L + r) Here, l = slant height r = Radius of base Also, l² = h² + r², where h is the cone's height V = ½ πr²
	Sphere	A = 4πr² V = 4/3πr³
Heron's Formula	-	Area of Triangle with 3 sides √s(s-a)(s-b)(s-c) Here, s = semi perimeter A,b, c are the sides of a triangle. Semi Perimeter S = ( a + b + c)/2
Polynomial Formula	-	P (x) = anxn + an- 1xn- 1 – an- 2xn- 1 + …… ax + a0
Statistics (Measure of Central Tendency)	Mean	Sum of all the observations/ Total Number of Observations
	Median	For odd observations = ((n+1)/2)th observations For even Observations – ((n/2)th + ((n/2) +1)th)/2 observations
	Mode	The value which occurs most frequently in a data

Maths Formulas: Class 10

Algebra Formulas

(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(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)

Arithmetic Formulas

an = a + (n – 1) d, where an is the nth term.
Sn= n/2 [2a + (n – 1)d]

Trigonometry Formulas

sin(90° – A) = cos A
cos(90° – A) = sin A
tan(90° – A) = cot A
cot(90° – A) = tan A
sec(90° – A) = cosec A
cosec(90° – A) = sec A
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

Circle Formula

The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2].
The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2

Area and Volume Formulas

The volume of Sphere = 4/3 ×π r3
Lateral Surface Area of Sphere (LSA) = 4π r2
Total Surface Area of Sphere (TSA) = 4πr2
The volume of the Right Circular Cylinder = πr2h
Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
The volume of Hemisphere = ⅔ x (πr3)
Lateral Surface Area of Hemisphere (LSA) = 2πr2
Total Surface Area of Hemisphere (TSA) = 3πr2
The volume of Prism = B × h
Lateral Surface Area of Prism (LSA) = p × h

Maths formulas: Class 11

Algebra Formulas

a × (b + c) = a × b + a × c (Distributive property)
a + b = b + a (Commutative Property of Addition)
a × b = b × a (Commutative Property of Multiplication)
a + (b + c) = (a + b) + c (Associative Property of Addition)
a × (b × c) = (a × b) × c (Associative Property of Multiplication)
a + 0 = a (Additive Identity Property)
a × 1 = a(Multiplicative Identity Property)
a + (-a) = 0 (Additive Inverse Property)
a⋅(1/a) = 1 (Multiplicative Inverse Property)
a × (0) =0 (Zero Property of Multiplication)

Trigonometry Formulas

sin(90° – A) = cos A
cos(90° – A) = sin A
tan(90° – A) = cot A
cot(90° – A) = tan A
sec(90° – A) = cosec A
cosec(90° – A) = sec A
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

Calculus Formulas

d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]
d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)]
d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)]
d/dx [f(x) / g (x)] = {d/dx [f(x)] × [g(x)] – [f(x)] × d/dx [g(x)]} / g(x)2

Geometry and Lines Formulas

Slope m = rise/run = Δy/Δx = y2−y1/x2−x1
Point-Slope Form y−y1 = m (x−x1)

Maths Formulas: Class12

Vector Formulas

A + B = B + A (Commutative Law)
A + (B + C) = (A + B) + C (Associative Law)
(A • B )= |P| |Q| cos θ ( Dot Product )
(A × B )= |P| |Q| sin θ (Cross Product)
k (A + B )= kA + kB
A + 0 = 0 + A (Additive Identity)

Trigonometry Formulas

sin-1(-x) = – sin-1x
tan-1x + cot-1x = π / 2
sin-1x + cos-1 x = π / 2
cos-1(-x) = π – cos-1x
cot-1(-x) = π – cot-1x

Calculus Formulas

∫ f(x) dx = F(x) + C
Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1)
Exponential Rules: ∫ ex dx = ex + C
∫ ax dx = ax / ln(a) + C
∫ ln(x) dx = x ln(x) – x + C
Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant.
Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C
Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
∫cos x dx = sin x + C
∫ sin x dx = -cos x + C
∫ sec2 x dx = tan x + C
∫ cosec2 x dx = -cot x + C
∫ sec x tan x dx = sec x + C
∫ cosec x cot x dx = – cosec x + C

Geometry Formulas

Cartesian equation of a plane: lx + my + nz = d
Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x1 – x2)2 + (y1 – y2)2 + (z1 – z2)2)

Maths Formulas Conclusion

Mathematical formulas serve as powerful tools for solving problems across various disciplines. Understanding and mastering these formulas can significantly enhance your problem-solving skills and analytical thinking. From algebraic equations to geometric measurements, trigonometric identities to calculus operations, and probability to statistics, the world of mathematical formulas is vast and interconnected. By familiarizing yourself with these formulas, you gain the confidence to tackle complex mathematical challenges and unlock new realms of knowledge. So, embrace the power of mathematics and let the formulas guide you on your journey of exploration and success.

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Frequently Asked Questions

What are some commonly used math formulas?

Some commonly used math formulas include the Pythagorean theorem, quadratic formula, area and perimeter formulas for geometric shapes, trigonometric identities, and formulas for arithmetic and geometric sequences.

How can I remember math formulas more easily?

To remember math formulas, practice applying them in various problems, create flashcards or cheat sheets, break formulas into smaller parts for better understanding, and try to understand the logic behind each formula.

Where can I find a comprehensive list of math formulas?

You can find comprehensive lists of math formulas in textbooks, educational websites, math reference books, or by searching online math resources.

Are there any shortcuts or tricks for learning math formulas?

Yes, some tips include identifying patterns in formulas, understanding the derivations or proofs of formulas, and connecting formulas to real-world applications to enhance understanding and memory.

How can I use math formulas effectively in problem-solving?

To use math formulas effectively, read the problem carefully, identify the relevant formula(s) needed, substitute the given values into the formula, and solve step-by-step using proper mathematical operations.

Can I derive math formulas by myself?

Yes, some math formulas can be derived using logical reasoning, algebraic manipulations, or geometric principles. Deriving formulas can deepen your understanding of the underlying concepts.

What are the essential math formulas for geometry?

Essential geometry formulas include those for area and perimeter of shapes (rectangle, triangle, circle), volume and surface area of solids (cuboid, cylinder, sphere), and trigonometric ratios for angles and triangles.

Are there any formulas to calculate statistical measures?

Yes, statistical measures like mean, median, mode, and standard deviation have specific formulas. For example, mean is calculated by dividing the sum of all observations by the total number of observations.

Can I use calculators to find math formulas?

Calculators can help in performing calculations involved in math formulas, but understanding the concepts behind the formulas and knowing when and how to apply them is crucial.

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SGPA Calculator	Volume of Cuboid Formula
Place Value and Face Value	SGPA to CGPA
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