maths formulas for class 6 to 10

 Maths Formulas for Class 6 to 10

We have summarized all the Math Formulas which are included in the

curriculum in Classes 6 to 10th help you have a at can better grasp of

the subject. Check out most important Math formulas chart here

Math Formulas: In this article, We have summarized all the Math

Formulas that are included in the curriculum in Classes 6 to 12. It will

help you have a better grasp of the subject. Generally, Most Students

have difficulty solving Math problems, but Basic Math formulas help you

to solve that problems efficiently and faster. Students should study and

recall basic Math Formulas based on principles such as algebra,

arithmetic, and geometry in order to answer mathematical issues

efficiently. Math is quite different from other subjects, as it requires

practice. Proper and regular practice helps students to build a strong

grasp of math Formulas at their fingertips.

Math Formulas

Math formulas assist students in better tackling any mathematical

difficulties problems in an easier and faster way. By implementing basic

Math formulas, students may answer complex problems using a variety

of ways and tactics. It is not an impossible subject to achieve high

marks in. All you need is consistent hard work and smart work. We use

them by first carefully reading our problem to discover what it is asking

for, and then seeking math formulas that provide us with the solution to

our problem. Candidates preparing for competitive ms can also

review all of the important math formulas in one spot to help them

understand the topic better.

All Math Formulas

The main problem with Math formulas is about Memorizing Them.

There is no doubt the Math Formulas Chart is very long as every class

there is an introduction of new concepts. Addition, subtraction,

multiplication, and division are simple; nevertheless, issues dependent

on derivation, calculus, and geometry require math formulas to solve.

But Adda247 provides you with a comprehensive list of the Basic Math

Formulas which will help learners not only in boards but also in

competitive exams with their preparation

Math Formulas for Basic Algebra

Following Basic maths formulas are used to solve Algebraic problems in all Classes. Check out the math formulas chart given below:

1. (a + b)2 = a2 + 2ab + b2
2. (a – b)2 = a2 – 2ab + b2
3. a2 – b2 = (a – b)(a + b)
4. a2 + b2 = (a + b)2 – 2ab
5. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
6. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
7. (a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯
8. (x+ y+ z)2=x2+y2+z2+2xy+2yz+2xz
9. (x +y−z)2=x2+y2+z2+2xy−2yz−2xz
10. (x− y+ z)2=x2+y2+z2−2xy−2yz+2xz
11. (x−y−z)2=x2+y2+z2−2xy+2yz−2xz
12. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
13. (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
14. a3 + b3 = (a + b)(a2 – ab + b2)
15. a3 – b3 = (a – b)(a2 + ab + b2)
16. x3+y3+z3−3xyz=(x+ y+ z)(x2+y2+z2−xy−yz−xz)
17. x3+y3=(x+ y)(x2−xy+y2)
18. x3−y3=(x−y)(x2+xy+y2)
19. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
20. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
21. a4 – b4 = (a – b)(a + b)(a2 + b2)
22. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
23. x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]
24. x2+y2=1/2[(x+ y)2+(x−y)2]
25. (x +a)(x +b)(x +c)=x3+(a +b+ c)x2+(ab +bc+ ca)x+ abc

All Math Formulas from Class 6 to Class 12

Read the following article for all of the necessary Math Formula Charts related to Maths Formulas for Classes 6 to 12.

Math formulas for Class 6

Topics Like Number Systems, Integers, Decimals, Fractions, Algebra, Mensuration, etc are included in the Class 6 maths Syllabus. Check important concepts and math formulas for class 6 to solve the problems as follows:

1. ‘Undefined’ refers to anything divided by zero
2. If the total of the digits is a multiple of three, the number is divisible by three.
3. A number is divisible by two if it contains the digits 0, 2, 4, 6, or 8.
4. A variable represents a condition in an equation. An equation has two sides, known as the Left-Hand Side and the Right-Hand Side, which are separated by an equal (=) sign.
5. A polygon is a simple closed figure created by line segments. A triangle is a polygon with three sides. Quadrilaterals are polygons with four sides.
6. The perimeter of a Square = 4 × Length of its side
7. Perimeter of a Rectangle = 2 × (Length + Breadth)
8. The perimeter of an Equilateral triangle = 3 × Length of a side
9. Area of a Rectangle = length × breadth

Maths formulas for Class 7

There are some math topics that are included in the class 7 Maths syllabus. Check out all of the important math formulas for class 7 maths listed below

1. Profit Percentage = (Profit / Cost price) × 100
2. Loss Percentage = (Loss/ Cost price) × 100
3. Simple Interest = (Principal × Rate × Time) / 100
4. Amount = Principal + Interest
5. Percentage Change= (Change / Original Amount) × 100
6. Product of rational numbers = (Product of Numerators) / (Product of Denominators)
7. First Rational Number × (Reciprocal of other Rational Number)
8. Law of Product: am × an = am+n
9. Law of Quotient: am/an = am-n
10. Law of Zero Exponent: a0 = 1
11. Law of Negative Exponent: a-m = 1/am
12. Law of Power of a Quotient: (a/b)m = am/bm
13. Law of Power of a Power: (am)n = amn
14. Law of Power of a Product: (ab)m = ambm
15. Perimeter of a Rectangle = 2 × (Length + Breadth)
16. Area of Rectangle = Length × Breadth
17. Area of a Square = Side2
18. Area of Triangle = 1/ 2 × Base × Height
19. The perimeter of a Square = 4 × Side
20. Area of a Parallelogram = Base × Height
21. Area of a circle = πr2
22. Circumference of a circle = π d, where ‘d’ is the diameter of a circle and π = 22/7 or 3.14

Math formulas For Class 8

Students must study all arithmetic formulae for Class 8 in order to solve the problem quickly. The most common and relevant class 8 Math formulas are listed below.

1. Additive inverse of rational number: a/b = -b/a
2. Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
3. Distributives a(b – c) = ab – ac
4. Simple Interest = (Principal × Rate × Time) / 100
5. Amount = Principal + Interest
6. Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal ( 1 + Rate/100)n, where ‘n’ is the period.
7. Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes

Apart from the athematic math formulas 2d and 3d geometry has been introduced, Check out all the important math formulas related to 2D and 3D geometric shapes in the below table:

Math Formulas for 2D Geometric Shapes

2 Dimensional shapes	Geometric Area Formula
Rectangle	Area of Rectangle A = Length x Width Perimeter of Rectangle P = 2(Length + Width)
Triangle	Area of Triangle, A = ½ x Breadth x Height Perimeter of Triangle, P = Sum of all the three sides of a triangle
Circle	Area of Circle,  A = πr² The perimeter of circle, P = 2 πr

Math Formulas for 3D Geometric Shapes

3 Dimensional shapes	Total Surface Area	Lateral / Curved Surface Area	Volume
Cuboid	2 (lb + bh + hl)	2h (l + b)	l × b × h
Cube	6a2	4a2	a3
Cylinder	2πr (r + h)	2 (π × r × h)	πr2h
Sphere	4πr2	4πr2	4/3 (πr3)
Hemisphere	3πr2	2πr2	⅔ (πr3)
Right Pyramid	Lateral Surface Area + Area of the Base	½ (Perimeter of Base × Slant Height)	⅓ (Area of the Base) × Height
Right Circular Cone	πr (l + r)	πrl	⅓ (πr2h)
Right Prism	Lateral Surface Area + 2(Area of One End)	Perimeter of Base × Height	Area of Base × Height

Math formulas For Class 9th

All Class 9 Math formulas are provided here in accordance with the NCERT syllabus for all courses such as Algebra, Geometry, Polynomials, and so on. The most essential class 9 Math formulas are listed below.

Topics	Math 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	Area of Rectangle A = Length x Width Perimeter of Rectangle P = 2(Length + Width)
Triangle	Area of Triangle, A = ½ x Breadth x Height Perimeter of Triangle, P = Sum of all the three sides of a triangle
Circle	Area of Circle,  A = πr² The perimeter of circle, P = 2 πr
Parallelogram	Area of Parallelogram, A = Breadth x Height Perimeter of Parallelogram,  P = 2( a+ b) (Here. a = side, b = base )
Trapezoid	Area of Trapezoid A = ½ x Height x (b₁ x b₂) Perimeter of Trapezoid, P = Sum of all the sides of a trapezoid
Cuboid	Surface Area (A) = (lb + bh + hl), ([l = length,  b = Breadth, h = height] Volume V = Length x Breadth x Height
Cylinder	Surface area of Cylinder A = 2πr( h + r) [r = radius of the circular cylinder, H = height of a cylinder] The volume of Cylinder  V = πr²H
Cube	The surface area of Cube. A = 6 side² Volume of a Cube V = Side³
Sphere	Surface Area of a Sphere A = 4πr² The volume of a Cube V = 4/3πr³
Cone	Surface area of a Cone (A) = πr( L + r) [l = slant height , r = Radius of base] Volume of a Cone (V )= ½ πr²
Heron’s Formula	Area of Triangle with 3 sides = √s(s-a)(s-b)(s-c) Here, s = semi-perimeter, and A,b, and 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
Algebra Identities	(x + θ) (x – θ) = x² – θ² (x + β)² = x² + β² + 2 x β (x – β)² = x² + β² – 2 x β (x – α)(x + θ) = x² + (θ – α)x – xθ (x – α)(x – θ) = x² – (α + θ)x + αq (x + α)(x + θ) = x² + (α + θ)x + αθ (x + α)(x – θ) = x² + (α – θ)x – αθ (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 (α + θ)³ = α³ + θ³ + 3αθ(α + θ) (x)³ + (β)³ = ( x + β) (x² – xβ + β) (x)³ – (β)³ = ( x + β) (x² – xβ + β)
Statistics	Mean : Total number of observations/sum of all observations Median: ((n+1)/2)th observations = odd observations ((n/2)th + ((n/2)+1)th)/2 observations for even observations Mode: The most often occurring value in a data set

Math Formulas For Class 10th

Explore all of the important math formulas for class 10 maths by chapter. To swiftly solve the problem, students must learn all math formulas for class 10. Check out the most essential and useful class 10 Math formulas listed below.

Topics	Math Formulas
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 sin θ cosec θ = 1 cos θ sec θ = 1 tan θ cot θ = 1 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
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
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

Math formulas For Class 11th

Students struggle the most with Class 11 Maths because the syllabus covers a wide range of new topics. However, by comprehending the concept and the relevant math formulas, applicants can easily earn good grades in the Class 11 Math exams. Check out the most important class 11 Math formulas listed below.

Topics	Math formula
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)
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)
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

Math formulas For Class 12th

Topics Like Vectors, Matrices, Trigonometry, and 3-dimensional geometry are included in the Class 12 maths Syllabus. Scoring well in Maths is very essential as the Class 12 board result will determine the UG admission of a Student. However, revising and practicing related math formulas and concepts will help you score well in the Class 12 mathematics exam. Check out the table below for all of the Imp[orat Class 12 Math formulas.

Topics	Math formulas
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
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)
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)

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