What are the most important formulas in Class 8 Maths?

The most important formulas are the five algebraic identities, the compound interest formula, and the mensuration formulas for 2D and 3D shapes. The laws of exponents are also essential as they are used throughout higher classes. Focus on these first and the rest will follow.

What is the difference between simple interest and compound interest?

Simple interest is calculated on the original principal only. Compound interest is calculated on the principal plus previously accumulated interest. The SI formula is P*R*T/100. The CI formula is P(1+R/100)^n - P. Over multiple years, CI always gives a higher amount than SI (for the same rate and principal).

How many algebraic identities are there in Class 8?

There are five standard identities in Class 8: (a+b)^2, (a-b)^2, a^2-b^2, (a+b+c)^2, and (x+a)(x+b). These are the foundation for the additional identities introduced in Class 9 involving cubes.

What is the formula for the area of a trapezium?

The area of a trapezium is (1/2) x (sum of parallel sides) x height. If the parallel sides are a and b, and the height is h, then Area = (1/2)(a+b)h. This formula is frequently asked in exams and is also useful for finding areas of irregular quadrilaterals.

How do I remember all the mensuration formulas for Class 8?

Group them by shape. For 2D: learn rectangle, square, triangle, parallelogram, trapezium, rhombus, and circle. For 3D: learn cuboid, cube, and cylinder. Notice the patterns: TSA includes all faces, LSA/CSA excludes top and bottom. Write each formula three times and solve one problem for each.

What are the most important formulas in Class 8 Maths?

The most important formulas are the five algebraic identities, the compound interest formula, and the mensuration formulas for 2D and 3D shapes. The laws of exponents are also essential as they are used throughout higher classes. Focus on these first and the rest will follow.

What is the difference between simple interest and compound interest?

Simple interest is calculated on the original principal only. Compound interest is calculated on the principal plus previously accumulated interest. The SI formula is P*R*T/100. The CI formula is P(1+R/100)^n - P. Over multiple years, CI always gives a higher amount than SI (for the same rate and principal).

How many algebraic identities are there in Class 8?

There are five standard identities in Class 8: (a+b)^2, (a-b)^2, a^2-b^2, (a+b+c)^2, and (x+a)(x+b). These are the foundation for the additional identities introduced in Class 9 involving cubes.

What is the formula for the area of a trapezium?

The area of a trapezium is (1/2) x (sum of parallel sides) x height. If the parallel sides are a and b, and the height is h, then Area = (1/2)(a+b)h. This formula is frequently asked in exams and is also useful for finding areas of irregular quadrilaterals.

How do I remember all the mensuration formulas for Class 8?

Group them by shape. For 2D: learn rectangle, square, triangle, parallelogram, trapezium, rhombus, and circle. For 3D: learn cuboid, cube, and cylinder. Notice the patterns: TSA includes all faces, LSA/CSA excludes top and bottom. Write each formula three times and solve one problem for each.

Study Guide

Class 8 Maths All Formulas: The Complete CBSE Formula Sheet (2026)

Every formula from all chapters of Class 8 CBSE Maths. Algebraic identities, mensuration, compound interest, exponents, and more, organised for quick revision.

CBSEClass 8

The SparkEd Authors (IITian & Googler)15 March 202612 min read

How to Use This Formula Sheet

$Class 8 is where Maths starts getting serious. Algebraic identities, compound interest, mensuration formulas for 3D shapes, and exponents all appear for the first time. This page compiles every important formula so you have one reliable reference.$

$Jump to any chapter using the headings. Each formula includes a brief explanation of when to use it. For the best results, write these out by hand and solve at least one problem per formula.$

Rational Numbers

$Rational numbers extend whole numbers and integers to include fractions and decimals.$

Properties of Rational Numbers

$\frac{p}{q}$

$Closure: Rational numbers are closed under addition, subtraction, and multiplication. Division is closed except when dividing by zero.$

$a + 0 = a$

$a \times 1 = a$

$\frac{a}{b}$

\frac{a}{b} + \frac{-a}{b} = 0

$\frac{a}{b}$

\frac{a}{b} \times \frac{b}{a} = 1

$Distributive property:$

a \times (b + c) = a \times b + a \times c

$\frac{a}{b}$

$Memory tip: Rational numbers follow all the properties that whole numbers follow for addition and multiplication, plus they have multiplicative inverses (except zero).$

Linear Equations in One Variable

$Class 8 extends linear equations to include variables on both sides and more complex forms.$

Solving Linear Equations

$ax + b = 0$

$x = \frac{-b}{a}$

$Equations with variables on both sides: Collect variable terms on one side and constants on the other.$

$5x + 3 = 3x + 11$

5x - 3x = 11 - 3

2x = 8

x = 4

$Equations involving fractions:Multiply both sides by the LCM of all denominators to clear fractions.$

$\frac{a}{b} = \frac{c}{d}$

a \times d = b \times c

$Memory tip: Whatever you do to one side, do to the other. This keeps the equation balanced.$

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Squares, Cubes, and Their Roots

$This chapter introduces perfect squares, perfect cubes, and methods to find their roots.$

Square and Square Root Formulas

$1, 4, 9, 16, 25, 36, \ldots$

n^2 = n \times n

$2, 3, 7,$

$Useful patterns:$

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

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

(n + 1)^2 - n^2 = 2n + 1

$n$

1 + 3 + 5 + \ldots + (2n - 1) = n^2

$m > 1$

(2m)^2 + (m^2 - 1)^2 = (m^2 + 1)^2

$2m$

Cube and Cube Root Formulas

$Perfect cube: A number that is the cube of an integer.$

n^3 = n \times n \times n

$1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, \ldots$

$n^3 = n \times n^2$

$Cube root:$

\sqrt[3]{n^3} = n

$To find the cube root of a number by prime factorisation, group the prime factors in triples.$

$1$

Comparing Quantities: CI and SI

$This chapter covers percentages, profit/loss, and the crucial compound interest formula.$

Percentage, Profit, and Loss

$Percentage:$

\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

$Profit and Loss:$

\text{Profit} = \text{SP} - \text{CP}

\text{Loss} = \text{CP} - \text{SP}

\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100

\text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100

$Selling Price formulas:$

\text{SP} = \text{CP} \times \frac{100 + \text{Profit\%}}{100}

\text{SP} = \text{CP} \times \frac{100 - \text{Loss\%}}{100}

$Discount:$

\text{Discount} = \text{Marked Price} - \text{Selling Price}

\text{Discount \%} = \frac{\text{Discount}}{\text{Marked Price}} \times 100

$Sales Tax / VAT / GST:$

\text{Billing Amount} = \text{SP} + \text{Tax on SP}

Simple and Compound Interest

$Simple Interest (SI):$

\text{SI} = \frac{P \times R \times T}{100}

$P$

\text{Amount} = P + \text{SI} = P\left(1 + \frac{RT}{100}\right)

$Compound Interest (CI):$

A = P\left(1 + \frac{R}{100}\right)^n

\text{CI} = A - P = P\left[\left(1 + \frac{R}{100}\right)^n - 1\right]

$n$

$CI compounded half-yearly:$

A = P\left(1 + \frac{R}{200}\right)^{2n}

$R_1\%$

A = P\left(1 + \frac{R_1}{100}\right)\left(1 + \frac{R_2}{100}\right)

$P_{\text{new}} = P_{\text{old}}\left(1 + \frac{R}{100}\right)^n$

$n$

Algebraic Expressions and Identities

$The algebraic identities in this chapter are used throughout Classes 9 and 10.$

Standard Algebraic Identities

$Identity 1:$

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

$Identity 2:$

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

$Identity 3:$

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

$Identity 4:$

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

$Identity 5:$

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

$Useful rearrangements:$

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

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

(a + b)^2 - (a - b)^2 = 4ab

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

$Multiplication of polynomials: Multiply each term of the first polynomial by each term of the second, then combine like terms.$

$+2ab$

Mensuration: Perimeter, Area, and Volume

$Class 8 Mensuration extends to 3D shapes. This is a formula-heavy section.$

2D Figures: Perimeter and Area

$l$

\text{Perimeter} = 2(l + b)

\text{Area} = l \times b

$a$

\text{Perimeter} = 4a

\text{Area} = a^2

$b$

\text{Area} = \frac{1}{2} \times b \times h

$b$

\text{Area} = b \times h

$a, b$

\text{Area} = \frac{1}{2}(a + b) \times h

$d_1, d_2$

\text{Area} = \frac{1}{2} \times d_1 \times d_2

$r$

\text{Circumference} = 2\pi r

\text{Area} = \pi r^2

3D Figures: Surface Area and Volume

$l$

\text{TSA} = 2(lb + bh + hl)

\text{LSA} = 2h(l + b)

\text{Volume} = l \times b \times h

$a$

\text{TSA} = 6a^2

\text{LSA} = 4a^2

\text{Volume} = a^3

$r$

\text{CSA} = 2\pi rh

\text{TSA} = 2\pi r(r + h)

\text{Volume} = \pi r^2 h

$= 2\pi r$

Exponents and Powers

$Exponents are essential for expressing very large or very small numbers.$

Laws of Exponents

$Product rule:$

a^m \times a^n = a^{m+n}

$Quotient rule:$

\frac{a^m}{a^n} = a^{m-n}

$Power of a power:$

(a^m)^n = a^{mn}

$Power of a product:$

(ab)^n = a^n \cdot b^n

$Power of a quotient:$

\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}

$Zero exponent:$

a^0 = 1 \quad (a \ne 0)

$Negative exponent:$

a^{-n} = \frac{1}{a^n}

\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n

$a \times 10^n$

$300{,}000{,}000 = 3 \times 10^8$

$0.000045 = 4.5 \times 10^{-5}$

$Memory tip: For the product rule, bases must be the same. When multiplying same bases, add exponents. When dividing same bases, subtract exponents.$

Direct and Inverse Proportion

$Proportion problems appear frequently in real-life applications and exam questions.$

Proportion Formulas

$x$

\frac{x_1}{y_1} = \frac{x_2}{y_2}

$\frac{x}{y} = k$

$x$

x_1 \times y_1 = x_2 \times y_2

$x \times y = k$

$How to identify: - If doubling one quantity doubles the other, it is direct proportion. - If doubling one quantity halves the other, it is inverse proportion.$

$\text{speed} \times \text{time} = \text{distance}$

$Memory tip: Direct = same direction (both increase or both decrease). Inverse = opposite directions (one increases, other decreases).$

Factorization

$Factorization is the reverse of expansion. You break an expression into a product of simpler factors.$

Methods of Factorization

$Method 1: Taking out the common factor$

6x^2 + 12x = 6x(x + 2)

$Method 2: Regrouping terms$

ax + bx + ay + by = x(a + b) + y(a + b) = (a + b)(x + y)

$Method 3: Using identities$

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

x^2 + 6x + 9 = (x + 3)^2

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

x^2 - 10x + 25 = (x - 5)^2

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

49x^2 - 16 = (7x + 4)(7x - 4)

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

x^2 + 7x + 12 = (x + 3)(x + 4)

(since

3 + 4 = 7

and

3 \times 4 = 12

)

$Division of algebraic expressions:$

\frac{a^m}{a^n} = a^{m-n}

$Divide by factoring both numerator and denominator, then cancel common factors.$

$Memory tip: Factorization is "undoing" multiplication. If you can expand identities forward, you can also use them backward to factorise.$

Quick Revision Strategy

$Class 8 Maths has around 45 to 50 important formulas. The chapters that carry the most weight are Comparing Quantities (CI/SI), Algebraic Identities, and Mensuration.$

$1. Start with the identities. The five algebraic identities appear in almost every exam. Write them out, expand them, and use them to factorise expressions. If you know these cold, you will save time across multiple chapters.$

$2. Master the CI formula. Compound interest is one of the most commonly tested topics. Practice with different compounding periods (annual, half-yearly) and applications (population growth, depreciation).$

$3. Mensuration needs practice, not just memory. Knowing the formula is not enough. You need to identify which formula to use from the problem description. Practice mixed problems where you do not know in advance whether it is a trapezium, rhombus, or cylinder problem.$

$This page covers the complete CBSE Class 8 Maths syllabus. Use it alongside regular practice on SparkEd for the best results.$

$www.sparkedmaths.com | info@sparkedmaths.com$

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