# 50 Maths Formulas PDF

REPORT THIS PDF ⚐

## 50 Maths Formulas

50 Maths Formulas PDFs for all the concepts covered under different classes (6, 7, 8, 9, 10, 11, and 12), as per the CBSE syllabus are provided here by our expert teachers. To solve mathematical problems easily, students should learn and remember the basic formulas based on certain fundamentals such as algebra, arithmetic, and geometry.

The basic Math formulas include arithmetic operations, where we learn to add, subtract, multiply and divide. Also, algebraic identities help to solve equations. The important formulas are related to algebra, Pythagoras theorem, series and sequence, mensuration, calculus, probability and statistics, trigonometry, matrices, etc.

## 50 Maths Formulas for Classes 6 to 12th

### Math formulas for Class 6

• ‘Undefined’ refers to anything divided by zero
• If the total of the digits is a multiple of three, the number is divisible by three.
• A number is divisible by two if it contains the digits 0, 2, 4, 6, or 8.
• 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.
• 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.
• 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

### Maths formulas for Class 7

• 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)
• First Rational Number × (Reciprocal of other Rational Number)
• 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 Quotient: (a/b)m = am/bm
• Law of Power of a Power: (am)n = amn
• Law of Power of a Product: (ab)m = ambm
• Perimeter of a Rectangle = 2 × (Length + Breadth)
• Area of Rectangle = Length × Breadth
• Area of a Square = Side2
• Area of Triangle = 1/ 2 × Base × Height
• The perimeter of a Square = 4 × Side
• Area of a Parallelogram = Base × Height
• Area of a circle = πr2
• 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

• 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
• Simple Interest = (Principal × Rate × Time) / 100
• Amount = Principal + Interest
• Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal ( 1 + Rate/100)n, where ‘n’ is the period.
• Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes

### Maths Formulas for Class 9

Topics Math 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
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

### 10th Class Maths Formulas List

Topics Math Formulas
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. sin θ cosec θ = 1
8. cos θ sec θ = 1
9. tan θ cot θ = 1
10. sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
11. cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1
12. sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
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
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

### 11th Maths Formulas

• (a+b)2 = a2 + b2 + 2ab
• (a-b)2 = a2 + b2 – 2ab
• (a+b) (a-b) = a2 – b2
• (x + a)(x + b) = x2 + (a + b)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 – a)(x + b) = x2 + (b – a)x – ab
• (x – a)(x – b) = x2 – (a + b)x + ab
• (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 =½ [(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 = ½ [(x-y)2 + (y-z)2 + (z-x)2]
• sin (90° – θ) = cos θ
• cos (90° – θ) = sin θ
• tan (90° – θ) = cot θ
• cot (90° – θ) = tan θ
• sec (90° – θ) = cosecθ
• cosec (90° – θ) = secθ
• sin2θ + cos2 θ = 1
• secθ = 1 + tan2θ for 0° ≤ θ < 90°
• Cosecθ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

### Math formulas For Class 12th

Topics Math formulas
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
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)
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)