Math Formulas

Mathematics Formulas

Mathematics is an abstract subject that needs a firm grasp of different Mathematical formulas. In-depth 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:

  1. Algebra Formula
  2. Algebraic Expressions Formula
  3. Angle Formula
  4. Area Formula of Quadrilaterals
  5. Area Formula
  6. Area of a Pentagon Formula
  7. Area of an Octagon Formula
  8. Area Under the Curve Formula
  9. Arithmetic Sequence Explicit Formula
  10. Arithmetic Sequence Recursive Formula
  11. Binary Formula
  12. Calculus Formula
  13. Change of Base Formula
  14. Cofactor Formula
  15. Complex Number Division Formula
  16. Complex Number Power Formula
  17. Conditional Probability Formula
  18. Cos Inverse Formula
  19. Cosine Formula
  20. Cube Formula
  21. Cubic Equation Formula
  22. Daily Compound Interest Formula
  23. Decay Formula
  24. Decimal to Fraction Formula
  25. Derivative Formula
  26. Diagonal Formula
  27. Equation Formula
  28. Exponential Formula
  29. Factorial Formula
  30. Function Formulas
  31. Geometric Distribution Formula
  32. Graphs of Trigonometric Formula
  33. HYPERBOLA FORMULA
  34. Integral Formula
  35. Lateral Area Formula
  36. Limit Formula
  37. LCM Formula
  38. Newton’s Method Formula
  39. Parabola Formula
  40. Parallelogram Formula
  41. Percentile Formula
  42. Perimeter Formulas
  43. Probability Distribution Formulas
  44. Proportion Formula
  45. Pythagorean Triples Formulas
  46. Radius Formula
  47. Ratio Formula
  48. Rhombus Formula
  49. Sequence Formula
  50. Sin Tan Formula
  51. Sin Cos Formula
  52. Surface Areas Formula
  53. Statistics Formulas
  54. Tangent Formula
  55. Tan Theta Formula
  56. Volume Charge Density Formula
  57. The volume of a Cone Formula
  58. The volume of a Cylinder Formula
  59. The volume of a Rectangular Prism Formula
  60. The volume of a Square Pyramid Formula
  61. The volume of A Triangular Prism Formula
  62. 30-60-90 Formulas
  63. Vertex Formula
  64. X and Y Intercept Formula
  65. Z Score Formula

BODMAS Formula

B = Bracket 

O = Of

D = Division

M = Multiplication 

A = Addition

S = Subtraction 

Basic Algebra Formulas

  1. a2 – b2 = (a – b)(a + b)
  2. (a + b)2 = a2 + 2ab + b2
  3. a2 + b2 = (a + b)2 – 2ab
  4. (a – b)2 = a2 – 2ab + b2
  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)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  8. (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
  9. a3 – b3 = (a – b)(a2 + ab + b2)
  10. a3 + b3 = (a + b)(a2 – ab + b2)
  11. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  12. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
  13. a4 – b4 = (a – b)(a + b)(a2 + b2)
  14. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  15. (a +b+ c)2=a2+b2+c2+2ab+2bc+2ca
  16. (a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯
  17. (x+ y+ z)2=x2+y2+z2+2xy+2yz+2xz
  18. (x +y−z)2=x2+y2+z2+2xy−2yz−2xz
  19. (x− y+ z)2=x2+y2+z2−2xy−2yz+2xz
  20. (x−y−z)2=x2+y2+z2−2xy+2yz−2xz
  21. x3+y3+z3−3xyz=(x+ y+ z)(x2+y2+z2−xy−yz−xz)
  22. x2+y2=1/2[(x+ y)2+(x−y)2]
  23. (x +a)(x +b)(x +c)=x3+(a +b+ c)x2+(ab +bc+ ca)x+ abc
  24. x3+y3=(x+ y)(x2−xy+y2)
  25. x3−y3=(x−y)(x2+xy+y2)
  26. 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 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 Mathematics formulas are available for every chapter allocated in the latest syllabus of respective standards. 

Class 6 Mathematics formulas

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

Class 7 Mathematics formulas

  1. Product of rational numbers = (Product of Numerators) / (Product of Denominators)
  2. First Rational Number × (Reciprocal of other Rational Number)
  3. Area of a Square = Side2
  4. The perimeter of a Square = 4 × Side
  5. Area of Rectangle = Length × Breadth
  6. Perimeter of a Rectangle = 2 × (Length + Breadth)
  7. Area of a Parallelogram = Base × Height
  8. Area of Triangle = 1/ 2 × Base × Height
  9. Circumference of a circle = π d, where ‘d’ is the diameter of a circle and π = 22/7 or 3.14
  10. Area of a circle = πr2
  11. Law of Product: am × an = am+n
  12. Law of Quotient: am/an = am-n
  13. Law of Zero Exponent: a0 = 1
  14. Law of Negative Exponent: a-m = 1/am
  15. Law of Power of a Power: (am)n = amn
  16. Law of Power of a Product: (ab)m = ambm
  17. Law of Power of a Quotient: (a/b)m = am/bm
  18. (a-b) 2 = a2 – 2ab + b2 
  19. (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 Mathematics formulas

  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. Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes
  5. Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal ( 1 + Rate/100)n, where ‘n’ is the period.
  6. (a – b)2 = a2 – 2ab + b2
  7. (a + b) (a – b) = a2 – b2  
  8. Euler’s Formula: For any polyhedron, Number of faces + Number of vertices – Number of edges = 2
  9. Volume of a Cone = (1 / 3 )πr2h
  10. Volume of a Sphere = (4/3) π r3

Class 9 Mathematics formulas

Real Numbers 

  1. √ab = √a √b
  2. √(a/b) = √a / √b
  3. (√a + √b) (√a – √b) = a – b 
  4. (√a + √b)2 = a + 2√ab + b
  5. (a + √b) (a – √b) = a2 – b
  6. (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 Mathematics formulas

Algebra Formulas

  1. (a + b)2 = a2 + 2ab + b2
  2. (a – b)2 = a2 – 2ab + b2
  3. (a + b) (a – b) = a2 – b2
  4. (x + a)(x + b) = x2 + (a + b)x + ab
  5. (x + a)(x – b) = x2 + (a – b)x – ab
  6. (x – a)(x + b) = x2 + (b – a)x – ab
  7. (x – a)(x – b) = x2 – (a + b)x + ab
  8. (a + b)3 = a3 + b3 + 3ab(a + b)
  9. (a – b)3 = a3 – b3 – 3ab(a – b)
  10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
  11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – xz)

Arithmetic Formulas 

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

Trigonometry Formulas

  1. sin(90° – A) = cos A
  2. cos(90° – A) = sin A
  3. tan(90° – A) = cot A
  4. cot(90° – A) = tan A
  5. sec(90° – A) = cosec A
  6. cosec(90° – A) = sec A
  7. sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
  8. cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1
  9. sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
  10. sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Circle Formula

  1. 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].
  2. The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2

Area and Volume Formulas 

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

Class 11 Mathematics formulas

Algebra Formulas

  1. a × (b + c) = a × b + a × c (Distributive property)
  2. a + b = b + a (Commutative Property of Addition)
  3. a × b = b × a (Commutative Property of Multiplication)
  4. a + (b + c) = (a + b) + c (Associative Property of Addition)
  5. a × (b × c) = (a × b) × c (Associative Property of Multiplication)
  6. a + 0 = a (Additive Identity Property)
  7. a × 1 = a(Multiplicative Identity Property)
  8. a + (-a) = 0 (Additive Inverse Property)
  9. a⋅(1/a) = 1 (Multiplicative Inverse Property)
  10. a × (0) =0 (Zero Property of Multiplication)

Trigonometry Formulas

  1. sin(90° – A) = cos A
  2. cos(90° – A) = sin A
  3. tan(90° – A) = cot A
  4. cot(90° – A) = tan A
  5. sec(90° – A) = cosec A
  6. cosec(90° – A) = sec A
  7. sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
  8. cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1
  9. sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
  10. sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Calculus Formulas

  1. d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]
  2. d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)]
  3. d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)]
  4. 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 

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

Class 12 Mathematics Syllabus  

Vector Formulas

  1. A + B = B + A (Commutative Law)
  2. A + (B + C) = (A + B) + C (Associative Law)
  3. (A • B )= |P| |Q| cos θ ( Dot Product )
  4. (A × B )= |P| |Q| sin θ (Cross Product)
  5. k (A + B )= kA + kB
  6. A + 0 = 0 + A (Additive Identity)

Trigonometry Formulas

  1. sin-1(-x) = – sin-1x 
  2. tan-1x + cot-1x = π / 2
  3. sin-1x + cos-1 x = π / 2
  4. cos-1(-x) = π – cos-1x
  5. cot-1(-x) = π – cot-1x

Calculus Formulas

  1. ∫ f(x) dx = F(x) + C
  2. Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1)
  3. Exponential Rules: ∫ ex dx = ex + C 
  4. ∫ ax dx = ax / ln(a) + C
  5. ∫ ln(x) dx = x ln(x) – x + C
  6. Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant. 
  7. Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C 
  8. Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
  9. Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
  10. ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
  11. Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
  12. ∫cos x dx = sin x + C
  13. ∫ sin x dx = -cos x + C
  14. ∫ sec2 x dx = tan x + C
  15. ∫ cosec2 x dx = -cot x + C
  16. ∫ sec x tan x dx = sec x + C
  17. ∫ cosec x cot x dx = – cosec x + C

Geometry Formulas 

  1. Cartesian equation of a plane: lx + my + nz = d 
  2. 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. 

  1. Make it easy to memorize the formulas
  2. Perform and score better in all examinations.
  3. Allocate extra time for board exams.
  4. Finish the Mathematics syllabus before time.
  5. Aware of the strengths and weaknesses.
  6. Prepare for the high-level entrance examinations.
FAQs (Frequently Asked Questions)
1. Where do I get all basic Mathematics formulas for Class 6 to Class 12?

You will get all the basic Mathematics formulas for classes 6 to 12 in Extramarks.

2. How to memorise the Mathematics formulas?

The students can memorise the Mathematics formulas through regular practise and revision.