50 Maths Formulas PDF

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

• Area of Rectangle A = Length x Width
• Perimeter of Rectangle P = 2(Length + Width)

• Area of Circle,  A = πr²
• The perimeter of circle, P = 2 πr

• Area of Parallelogram, A = Breadth x Height
• Perimeter of Parallelogram,  P = 2( a+ b) (Here. a = side, b = base )

• Area of Trapezoid A = ½ x Height x (b₁ x b₂)
• Perimeter of Trapezoid, P = Sum of all the sides of a trapezoid

• Surface Area (A) = (lb + bh + hl), ([l = length,  b = Breadth, h = height]
• Volume V = Length x Breadth x Height

• 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

• The surface area of Cube. A = 6 side²
• Volume of a Cube V = Side³

• Surface Area of a Sphere A = 4πr²
• The volume of a Cube V = 4/3πr³

• Surface area of a Cone (A) = πr( L + r) [l = slant height , r = Radius of base]
• Volume of a Cone (V )= ½ πr²

• 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

• (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)

• 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

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

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

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

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

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

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

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)

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)