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Mathematics Formulas
Mathematics is an abstract subject that needs a firm grasp of different Mathematical formulas. Indepth knowledge of Mathematics formulas prepares the students of Cass 6 to Class 12 to solve complex mathematical 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 Mathematics 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
 306090 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]
Mathematics Formulas from Class 6 to Class 12
A detailed understanding of the Mathematics 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 Mathematics 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 profitloss, 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 Mathematics formulas are available for every chapter allocated in the latest syllabus of respective standards.
Class 6 Mathematics 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 threesided Polygon. Quadrilaterals are foursided polygons.
 An equation is a condition represented on a variable. An equation is composed of two sides, known as the LeftHand 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 LeftHand Side and Right Hand Side, separated by an equal (=) sign.
Class 7 Mathematics 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 = amn
 Law of Zero Exponent: a0 = 1
 Law of Negative Exponent: am = 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
 (ab) 2 = a2 – 2ab + b2
 (abc)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 Mathematics 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 Mathematics 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(sa)(sb)(sc)
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 Mathematics 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 Mathematics 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
 PointSlope Form y−y1 = m (x−x1)
Class 12 Mathematics 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
 sin1(x) = – sin1x
 tan1x + cot1x = π / 2
 sin1x + cos1 x = π / 2
 cos1(x) = π – cos1x
 cot1(x) = π – cot1x
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)
Mathematics Formulas for Class 6 to 12 for CBSE (NCERT) Board
If a student is searching for exciting ways to understand Mathematics formulas easily, Extramarks is the right place. The academic experts’ mathematics formula list helps the students of classes 6 to 12 understand the basics. The mentors carefully design the most significant Mathematics 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 mathematics 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 Mathematics syllabus before time.
 Aware of the strengths and weaknesses.
 Prepare for the highlevel entrance examinations.
FAQs (Frequently Asked Questions)
You will get all the basic Mathematics formulas for classes 6 to 12 in Extramarks.
The students can memorise the Mathematics formulas through regular practise and revision.