50 Maths Formulas PDF

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50 Maths Formulas

50 Maths Formulas

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
  • sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
  • Cosec2 θ = 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)

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