Formulas in maths for all graded students

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 This is a comprehensive list of mathematical formulas for students. These are very important for school exams and competitive tests.

1. ALGEBRAIC IDENTITIES

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

(a + b) (a - b) = a^2 - b^2

(x + a) (x + b) = x^2 + (a + b)x + ab

(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

(a + b)^3 = a^3 + b^3 + 3ab(a + b)

(a - b)^3 = a^3 - b^3 - 3ab(a - b)

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

a^3 - b^3 = (a - b) (a^2 + ab + b^2)

2. GEOMETRY: AREA AND PERIMETER (2D)

SQUARE:

Area = Side × Side (a^2)

Perimeter = 4 × Side (4a)

RECTANGLE:

Area = Length × Breadth (l × b)

Perimeter = 2 × (Length + Breadth)

TRIANGLE:

Area = 1/2 × Base × Height

Perimeter = Side1 + Side2 + Side3

CIRCLE:

Area = π × r^2 (pi = 3.14 or 22/7)

Circumference = 2 × π × r

PARALLELOGRAM:

Area = Base × Height

Perimeter = 2 × (Side1 + Side2)

3. MENSURATION: VOLUME AND SURFACE AREA (3D)

CUBE:

Volume = a^3

Total Surface Area = 6a^2

Lateral Surface Area = 4a^2

CUBOID:

Volume = length × breadth × height

Total Surface Area = 2(lb + bh + hl)

CYLINDER:

Volume = π × r^2 × h

Curved Surface Area = 2 × π × r × h

Total Surface Area = 2 × π × r × (r + h)

SPHERE:

Volume = (4/3) × π × r^3

Surface Area = 4 × π × r^2

CONE:

Volume = (1/3) × π × r^2 × h

Curved Surface Area = π × r × l (l = slant height)

4. TRIGONOMETRY RATIOS

Sin Theta = Opposite Side / Hypotenuse

Cos Theta = Adjacent Side / Hypotenuse

Tan Theta = Opposite Side / Adjacent Side

Cosec Theta = Hypotenuse / Opposite Side

Sec Theta = Hypotenuse / Adjacent Side

Cot Theta = Adjacent Side / Opposite Side

Trigonometric Identities:

Sin^2 Theta + Cos^2 Theta = 1

1 + Tan^2 Theta = Sec^2 Theta

1 + Cot^2 Theta = Cosec^2 Theta

5. ARITHMETIC FORMULAS

Simple Interest = (Principal × Time × Rate) / 100

Compound Interest = P [ (1 + r/100)^n - 1 ]

Profit = Selling Price - Cost Price

Loss = Cost Price - Selling Price

Speed = Distance / Time

Average = Sum of Values / Number of Values

STUDY TIPS FOR MATH:

Always memorize the units (cm, m, sq.cm, cubic.m).

Write each formula 5 times to remember it forever.

Draw the shape next to the formula while solving problems.

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