# Maths Formula PDF

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### Maths Formula PDF

Basic Algebra Formula

• 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 – 3a2b + 3ab2 – b3
• 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)
• (am)(an) = am + n
• (ab)m = ambm
• (am)n = amn

2-D Formulas

• Rectangle
• Perimeter of Rectangle = 2(l + b)
• Area of Rectangle  = l × b

Where
l’ is Length

• Square
• Area of Square = a2
• Perimeter of Square = 4a

Where
a’ is the length of sides of a Square

• Triangle
• Area of Triangle= 1/2 × b × h

Where
b’ is the base of the triangle and
h’ is the height of the triangle

• Trapezoid
• Area of Trapezoid = 1/2 × (b1 + b2) × h

Where
b1 and b2 are the bases of Trapezoid
h is height of Trapezoid

• Circle
• Area of Circle = π × r2
• Circumference of Circle = 2πr

Where
r’ is radius of a Circle

3-D Formulas

• Cube
• Surface Area of Cube = 6a2
• Volume of Cube = a3

Where
a’ is the length of sides of Cube

• Cylinder
• Curved Surface Area of Cylinder = 2πrh
• Total Surface Area of Cylinder = 2πr(r + h)
• Volume of Cylinder = V = πr2h

Where
r’ is the radius of base of Cylinder
h’ is the height of Cylinder

• Cone
• Curved Surface Area of Cone = πrl
• Total Surface Area of Cone = πr(r + l) = πr[r + √(h2 + r2)]
• Volume of Cone = V = 1/3× πr2h

where,
r’ is the Radius of base of Cone
h is the Height of the Cone

• Sphere
1. Surface Area of a Sphere = S = 4πr2
2. Volume of a Sphere = V = 4/3 × πr3

Where,
is the Radius of Sphere

Basic Fractions Formula

• (a + b/c) = [(a × c) + b]/c
• (a/b + d/b) = (a + d)/b
• (a/b + c/d) = (a × d + b × c)/(b × d)
• a/b × c/d = ac/bd
• (a/b)/(c/d) = a/b × d/c

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)

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