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Maths Formulas
Maths is an abstract subject that needs a firm grasp of different Maths formulas. In-depth knowledge of Maths formulas prepares the students of Cass 6 to Class 12 to solve complex maths problems. Often students find it challenging to remember formulas and apply them in the right way. They only need to learn some tricks to memorize the formulas throughout their academic sessions.
List of Maths Formulas:
- Algebra Formula
- Algebraic Expressions Formula
- Angle Formula
- Area Formula of Quadrilaterals
- Area Formula
- Area of a Pentagon Formula
- Area of an Octagon Formula
- Area Under the Curve Formula
- Arithmetic Sequence Explicit Formula
- Arithmetic Sequence Recursive Formula
- Binary Formula
- Calculus Formula
- Change of Base Formula
- Cofactor Formula
- Complex Number Division Formula
- Complex Number Power Formula
- Conditional Probability Formula
- Cos Inverse Formula
- Cosine Formula
- Cube Formula
- Cubic Equation Formula
- Daily Compound Interest Formula
- Decay Formula
- Decimal to Fraction Formula
- Derivative Formula
- Diagonal Formula
- Equation Formula
- Exponential Formula
- Factorial Formula
- Function Formulas
- Geometric Distribution Formula
- Graphs of Trigonometric Formula
- HYPERBOLA FORMULA
- Integral Formula
- Lateral Area Formula
- Limit Formula
- LCM Formula
- Newton’s Method Formula
- Parabola Formula
- Parallelogram Formula
- Percentile Formula
- Perimeter Formulas
- Probability Distribution Formulas
- Proportion Formula
- Pythagorean Triples Formulas
- Radius Formula
- Ratio Formula
- Rhombus Formula
- Sequence Formula
- Sin Tan Formula
- Sin Cos Formula
- Surface Areas Formula
- Statistics Formulas
- Tangent Formula
- Tan Theta Formula
- Volume Charge Density Formula
- The volume of a Cone Formula
- The volume of a Cylinder Formula
- The volume of a Rectangular Prism Formula
- The volume of a Square Pyramid Formula
- The volume of A Triangular Prism Formula
- 30-60-90 Formulas
- Vertex Formula
- X and Y Intercept Formula
- Z Score Formula
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]
Math Formulas from Class 6 to Class 12
A detailed understanding of the Maths formulas makes the students of any standard perform better in examinations, whether it is class tests, final exams or board exams. Most of the chapters in the Maths syllabus are interrelated with each other. Therefore, if one understands the formulas of one chapter, the further chapters become simpler to them. Some of the interlinked chapters are percentage and profit-loss, percentages and fractions, real numbers and complex numbers, etc.
Students need to invest enough time and effort to analyse and understand the formulas methodically. The lists of Maths formulas are available for every chapter allocated in the latest syllabus of respective standards.
Class 6 Maths formulas
- 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.
Class 7 Maths formulas
- 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
Class 8 Math formulas
- 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
Class 9 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
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
Class 10 Math formulas
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
Class 11 Math formulas
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)
Class 12 Math Syllabus
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 for Class 6 to 12 for CBSE (NCERT) Board
If a student is searching for exciting ways to understand Maths formulas easily, Extramarks is the right place. The academic experts’ maths formula list helps the students of classes 6 to 12 understand the basics. The mentors carefully design the most significant Maths formulas list based on the chapters allotted to the current year syllabus. The following section presents the most vital formulas the students must study.
The Extramarks’ Advantage
Extramarks benefits the students of classes 6 to 12 by providing them with the basic maths formulas for free. The students can enjoy the following advantages with our assistance.
- Make it easy to memorize the formulas.
- Perform and score better in all examinations.
- Allocate extra time for board exams.
- Finish the Maths syllabus before time.
- Aware of the strengths and weaknesses.
- Prepare for the high-level entrance examinations.
FAQs (Frequently Asked Questions)
1. Where do I get all basic Maths formulas for Class 6 to Class 12?
You will get all the basic Maths formulas for classes 6 to 12 in Extramarks.
2. How to memorise the Maths formulas?
The students can memorise the Maths formulas through regular practise and revision.