CBSE · Class 8
Maths Formulas — Class 8
All key Maths formulas for CBSE Class 8 — algebraic identities, mensuration, exponents, linear equations and rational numbers.
For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.
Ch 1.Rational Numbers
| Formula / Relation | Expression |
|---|---|
| Additive inverse | Additive inverse of a/b = −a/b |
| Multiplicative inverse (reciprocal) | Multiplicative inverse of a/b = b/a |
| Distributive property | a × (b + c) = a × b + a × c |
| Division of rational numbers | (a/b) ÷ (c/d) = (a/b) × (d/c) |
Ch 2.Algebraic Identities
| Formula / Relation | Expression |
|---|---|
| Square of sum | (a + b)² = a² + 2ab + b² |
| Square of difference | (a − b)² = a² − 2ab + b² |
| Difference of squares | (a + b)(a − b) = a² − b² |
| Cube of sum | (a + b)³ = a³ + 3a²b + 3ab² + b³ |
| Cube of difference | (a − b)³ = a³ − 3a²b + 3ab² − b³ |
| Sum of cubes | a³ + b³ = (a + b)(a² − ab + b²) |
| Difference of cubes | a³ − b³ = (a − b)(a² + ab + b²) |
Ch 3.Linear Equations in One Variable
| Formula / Relation | Expression |
|---|---|
| Linear equation form | ax + b = c → x = (c − b)/a |
| Cross-multiplication | If a/b = c/d then ad = bc |
Ch 4.Exponents and Powers
| Formula / Relation | Expression |
|---|---|
| Product rule | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Quotient rule | aᵐ ÷ aⁿ = aᵐ⁻ⁿ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ |
| Power of a product | (ab)ⁿ = aⁿ × bⁿ |
| Zero exponent | a⁰ = 1 (a ≠ 0) |
| Negative exponent | a⁻ⁿ = 1/aⁿ |
Ch 5.Mensuration — Area and Perimeter
| Formula / Relation | Expression |
|---|---|
| Area of trapezium | Area = ½ × (sum of parallel sides) × height = ½(a + b)h |
| Area of rhombus | Area = ½ × d₁ × d₂ |
| Area of general quadrilateral | Area = ½ × d × (h₁ + h₂) |
| Area of polygon (using triangles) | Divide polygon into triangles; sum all triangle areas |
Ch 6.Mensuration — Surface Area and Volume
| Formula / Relation | Expression |
|---|---|
| Lateral surface area of cube | LSA = 4a² |
| Total surface area of cube | TSA = 6a² |
| Volume of cube | V = a³ |
| Lateral surface area of cuboid | LSA = 2h(l + b) |
| Total surface area of cuboid | TSA = 2(lb + bh + lh) |
| Volume of cuboid | V = l × b × h |
| Lateral surface area of cylinder | LSA = 2πrh |
| Total surface area of cylinder | TSA = 2πr(r + h) |
| Volume of cylinder | V = πr²h |
Ch 7.Understanding Quadrilaterals
| Formula / Relation | Expression |
|---|---|
| Angle sum of a polygon | Sum of interior angles = (n − 2) × 180° |
| Each exterior angle of a regular polygon | Exterior angle = 360° / n |
| Number of diagonals | Diagonals = n(n − 3)/2 |
Frequently Asked Questions
Which algebraic identities are most important for Class 8?
The four most important are: (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; (a + b)(a − b) = a² − b²; and the cube identities (a + b)³ and (a − b)³. These identities underpin multiplication, factorisation and simplification problems throughout Class 8–10 and appear in almost every Maths exam.
What is the formula for the area of a trapezium?
Area of trapezium = ½ × (sum of parallel sides) × perpendicular height = ½(a + b)h, where a and b are the two parallel sides and h is the perpendicular distance between them. For example, if the parallel sides are 8 cm and 5 cm and the height is 4 cm: Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm².
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