We've compiled a comprehensive collection of
Math Formulas
that are part of the curriculum from Grade 6 to Grade 12. This resource is designed to enhance your understanding of the subject and provide you with a valuable tool to refer to. Explore the essential Math Formulas Chart here
This article provides a comprehensive compilation of math formulas spanning Grades 6 to 12, aiding in a deeper comprehension of the subject. Many students often encounter challenges when tackling math problems, but a solid foundation in basic math formulas can significantly enhance problem-solving efficiency. To navigate mathematical challenges effectively, students should commit to memorizing fundamental math formulas rooted in principles such as algebra, arithmetic, and geometry. Unlike many other subjects, mathematics demands consistent practice. Through diligent and regular practice, students can develop a robust command of math formulas, making them readily accessible when needed.
Math Formulas
Mathematical formulas serve as valuable tools for students, enabling them to navigate mathematical challenges with greater ease and efficiency. With a foundation in basic math formulas, students can approach complex problems using various strategies and techniques. Scoring well in mathematics is not an insurmountable task; it requires a combination of consistent hard work and smart work. The process involves carefully analyzing a problem to identify its requirements and then applying relevant math formulas to arrive at a solution. Additionally, individuals preparing for competitive exams can benefit from accessing a comprehensive collection of essential math formulas in one convenient resource, enhancing their understanding of the subject.
All Math Formulas
The primary challenge associated with math formulas lies in the task of memorization. It's undeniable that the Math Formulas Chart can be quite extensive, with the introduction of new concepts in each class. While addition, subtraction, multiplication, and division are relatively straightforward, more complex problems rooted in calculus, derivation, and geometry demand the application of math formulas for resolution. Fortunately, Adda247 offers a comprehensive compilation of fundamental math formulas. These resources are not only beneficial for board exams but also prove invaluable in preparing for competitive examinations.
Math Formulas for Basic Algebra
-
(a + b)2 = a2 + 2ab + b2
-
(a – b)2 = a2 – 2ab + b2
-
a2 – b2 = (a – b)(a + b)
-
a2 + b2 = (a + b)2 – 2ab
-
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
-
(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
-
(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)
-
x3+y3+z3−3xyz=(x+ y+ z)(x2+y2+z2−xy−yz−xz)
-
x3+y3=(x+ y)(x2−xy+y2)
-
x3−y3=(x−y)(x2+xy+y2)
-
(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)
-
x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]
-
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.
Math Formulas PDF
These Math Formulas are a valuable resource that can benefit students not only in their regular tests but also in a range of other contexts, including competitive exams. Additionally, students can make use of the chapter-wise Math Formulas PDFs designed for all class levels to aid in their board exam preparation. To ensure accessibility even when offline, we suggest that students download the Math Formula PDFs from these Math Formula Charts for convenient reference during their study sessions
All Math Formulas from Class 6 to Class 12
Explore the linked article to access comprehensive Math Formula Charts containing essential mathematics formulas tailored for Classes 6 to 12
Class 6 Math formulas
The Class 6 mathematics syllabus covers various topics, including Number Systems, Integers, Decimals, Fractions, Algebra, Mensuration, and more. Here are important concepts and math formulas to help you solve problems related to these topics:
-
'Undefined' refers to any value divided by zero.
-
If the sum of the digits in a number is a multiple of three, then the number itself is divisible by three.
-
A number is divisible by two if it contains any of the digits 0, 2, 4, 6, or 8.
-
In an equation, a variable represents a condition. An equation typically consists of two sides, known as the Left-Hand Side (LHS) and the Right-Hand Side (RHS), separated by an equal (=) sign.
-
A polygon is a closed geometric figure formed by line segments. A triangle is a polygon with three sides, while quadrilaterals have four sides.
-
The perimeter of a square is calculated as 4 times the length of its side.
-
To find the perimeter of a rectangle, you can use the formula: Perimeter = 2 × (Length + Breadth).
-
The perimeter of an equilateral triangle is determined by multiplying 3 by the length of one of its sides.
-
To calculate the area of a rectangle, use the formula: Area = Length × Breadth.
These concepts and formulas are fundamental for understanding and solving mathematical problems in Class 6 mathematics.
Class 7 Maths formulas.
In the Class 7 mathematics syllabus, several essential math topics are covered. Here, you'll find a compilation of important math formulas for Class 7 mathematics:
-
Profit Percentage = (Profit / Cost price) × 100
-
Loss Percentage = (Loss / Cost price) × 100
-
Simple Interest = (Principal × Rate × Time) / 100
-
Amount = Principal + Interest
-
Percentage Change = (Change / Original Amount) × 100
-
Product of rational numbers = (Product of Numerators) / (Product of Denominators)
-
Multiplication of a rational number by the reciprocal of another rational number.
-
Law of Product: a
m
× a
n
= a
m+n
-
Law of Quotient: a
m
/ a
n
= a
m-n
-
Law of Zero Exponent: a
0
= 1
-
Law of Negative Exponent: a
-m
= 1 / a
m
-
Law of Power of a Quotient: (a/b)^m = a
m
/ b
m
-
Law of Power of a Power: (a^m)^n = a
(mn)
-
Law of Power of a Product: (ab)
m
= a
m
* b
m
-
Perimeter of a Rectangle = 2 × (Length + Breadth)
-
Area of Rectangle = Length × Breadth
-
Area of a Square = Side
2
-
Area of Triangle = (1/2) × Base × Height
-
Perimeter of a Square = 4 × Side
-
Area of a Parallelogram = Base × Height
-
Area of a Circle = πr
2
-
Circumference of a Circle = πd, where 'd' is the diameter of the circle, and π ≈ 3.14 or 22/7.
These math formulas are crucial for Class 7 students to understand and apply in solving mathematical problems. For a more extensive list of formulas and details, you can refer to this resource
Class 8 Math formulas
To ensure efficient problem-solving, it is essential for Class 8 students to familiarize themselves with various arithmetic formulas. Here, you will find a compilation of the most common and relevant math formulas for Class 8:
-
Additive inverse of a rational number: a/b = -b/a
-
Multiplicative Inverse of a/b = c/d, if a/b × c/d = 1
-
Distributive property: a(b – c) = ab – ac
-
Simple Interest = (Principal × Rate × Time) / 100
-
Amount = Principal + Interest
-
Compound Interest formula = Amount – Principal. In the case of annual interest calculation, Amount = Principal × (1 + Rate/100)^n, where 'n' is the period.
-
Probability of the occurrence of an event = Number of outcomes comprising the event / Total number of outcomes
In addition to these arithmetic formulas, Class 8 introduces 2D and 3D geometry. You can explore important math formulas related to 2D and 3D geometric shapes in the resource provided here
Class 9 Math formulas
We have compiled a comprehensive collection of Class 9 Math formulas in alignment with the NCERT syllabus, encompassing various topics such as Algebra, Geometry, Polynomials, and more. Below, you'll find a selection of the most vital Class 9 Math formulas:
For the complete list and detailed information, you can refer to the resource provided here:
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
Geometrical Shapes
Area (A)
Perimeter
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 (b₁ x 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
Shape
Surface Area (A)
Volume (V)
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
Math Formulas Class 10
Discover an extensive array of significant math formulas tailored for Class 10 mathematics, categorized by chapter. To effectively address mathematical challenges, it is imperative for students to acquaint themselves with all Class 10 math formulas. Here, we present a compilation of the most critical and practical Class 10 Math formulas:
Mastery of these Class 10 Math formulas is essential for students, as they empower them to efficiently tackle mathematical problems and excel in their studies.
Algebra Formulas
-
(a + b)
2
= a
2
+ 2ab + b
2
-
(a - b)
2
= a
2
- 2ab + b
2
-
(a + b) (a – b) = a
2
– b
2
-
(x + a)(x + b) = x
2
+ (a + b)x + ab
-
(x + a)(x – b) = x
2
+ (a – b)x – ab
-
(x – a)(x + b) = x
2
+ (b – a)x – ab
-
(x – a)(x – b) = x
2
– (a + b)x + ab
-
(a + b)
3
= a
3
+ b
3
+ 3ab(a + b)
-
(a - b)
3
= a
3
- b
3
- 3ab(a - b)
-
(x + y + z)
2
= x
2
+ y
2
+ z
2
+ 2xy + 2yz + 2xz
-
(x + y – z)
2
= x
2
+ y
2
+ z
2
+ 2xy – 2yz – 2xz
-
(x – y + z)
2
=x
2
+ y
2
+ z
2
– 2xy – 2yz + 2xz
-
(x – y – z)
2
= x
2
+ y
2
+ z
2
– 2xy + 2yz – 2xz
-
x
3
+ y
3
+ z
3
– 3xyz = (x + y + z)(x
2
+ y
2
+ z
2
– 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 – cos2θ ⇒ cos2θ = 1 – sin2 θ
-
Cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cosec2θ – 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 x
2
+ y
2
= a
2
for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2].
-
The tangent to a circle equation x
2
+ y
2
= a
2
at (a1,b1) is xa1 + yb1 = a2
Area and Volume Formulas
-
The volume of Sphere = 4/3 ×π r
3
-
Lateral Surface Area of Sphere (LSA) = 4π r
2
-
Total Surface Area of Sphere (TSA) = 4πr
2
-
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 (πr
3
)
-
Lateral Surface Area of Hemisphere (LSA) = 2π r
2
-
Total Surface Area of Hemisphere (TSA) = 3π r
2
-
The volume of Prism = B × h
-
Lateral Surface Area of Prism (LSA) = p × h
Class 11 Math formulas
Class 11 Mathematics often poses challenges for students due to its extensive syllabus encompassing various new topics. Nevertheless, by grasping the underlying concepts and essential math formulas, students can secure high grades in their Class 11 Math examinations. Here is a compilation of the most crucial Class 11 Math formulas:
For a comprehensive list and further details, please refer to the resource provided here:
Familiarity with these Class 11 Math formulas is instrumental for students, enabling them to navigate the subject effectively and achieve success in their exams.
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 – cos 2 θ ⇒ cos 2 θ = 1 – sin2 θ
-
cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cosec 2 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)
Class 12 Math formulas
The Class 12 mathematics syllabus encompasses challenging topics such as Vectors, Matrices, Trigonometry, and 3-Dimensional Geometry. Securing a strong performance in Mathematics is crucial as the Class 12 board result significantly impacts a student's undergraduate admission prospects. To excel in the Class 12 mathematics examination, it is imperative to review and practice relevant math formulas and concepts. Below, you'll find a comprehensive table containing all the important Class 12 Math formulas:
For an extensive list and further details, please consult the resource provided here:
Mastery of these Class 12 Math formulas is essential for students, as they play a pivotal role in achieving success in the examination and facilitating admission into undergraduate programs.
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
-
∫ sec2x dx = tan x + C
-
∫ cosec2x 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 for Class 6 to 12 for CBSE (NCERT) Board
I
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