# Class 8 Maths Formula Sheets

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Most of us gradually start disliking Math formulas and equations at some point as they seem difficult to grasp. But if you understand the logic behind them instead of mugging it, you will realize they help you solve complex problems easily and quickly!

Our team of Math experts have created a list of Class 8 Maths formulas for you with logical explanations as well as the method of how and where to use them. Success is said to be the sum of small efforts that are repeated daily and by using this list of important formulas in your exam preparations, you will be able to easily understand their logic, solve complex problems faster and score higher marks in your school exams!

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## Important Maths Formulas for Class 8

### 1. Rational Numbers Formulas

 Additive Identity/Role of Zero \begin{align} a + 0 = a \end{align} Multiplicative Identity/Role of One \begin{align} a \times 1 = a \end{align} Reciprocal or Multiplicative Inverse \begin{align} \left( {\frac{a}{b}} \right) \times \left( {\frac{b}{a}} \right) = 1 \end{align} Distributive Property \begin{align} a\left( {b + c} \right) &= ab + ac \\ a\left( {b - c} \right) &= ab-ac \end{align} Additive Inverse of \begin{align} \frac{a}{b} \end{align} is \begin{align} -\frac{a}{b} \end{align} and vice-versa Commutative Property of Addition \begin{align} a + b = b + a \end{align} Commutative Property of Subtraction \begin{align} a - b \ne b - a \end{align} Commutative Property of Multiplication \begin{align} a \times b = b \times a \end{align} Commutativity of Division \begin{align} \frac{a}{b} \ne \frac{b}{a} \end{align} Associative Property of Addition \begin{align} (a + b) + c = a + (b + c) \end{align} Associative Property of Subtraction \begin{align} (a - b) - c \ne a - (b - c) \end{align} Associative Property of Multiplication \begin{align} (a \times b) \times c = a \times (b \times c) \end{align} Associative Property of Division \begin{align} \frac{{\left( {\frac{a}{b}} \right)}}{c} \ne \frac{a}{{\left( {\frac{b}{c}} \right)}} \end{align}

### 2. Algebraic Expressions Formulas

 \begin{align} \left( {x + y} \right)^2 = x^2 + y^2 + 2xy \end{align} \begin{align} \left( {x - y} \right)^2 = x^2 + y^2 - 2xy \end{align} \begin{align} \left( {x + y} \right)\left( {x - y} \right) = x^2 - y^2 \end{align} \begin{align} (x + y)(x + z) = x^2 + x\,(y + z) + yz \end{align} \begin{align} (x + y)(x - z) = x^2 + x\,(y - z) - yz \end{align} \begin{align} x^2 + y^2 = \left( {x + y} \right)^2 - 2xy \end{align} \begin{align} \left( {x + y} \right)^3 = x^3 + y^3 + 3xy\left( {x + y} \right) \end{align} \begin{align} \left( {x - y} \right)^3 = x^3 - y^3 - 3xy\left( {x - y} \right) \end{align} \begin{align} \left( {x + y + z} \right)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx \end{align} \begin{align} \left( {x - y - z} \right)^2 = x^2 + y^2 + z^2 - 2xy + 2yz - 2zx \end{align}

### 3. Mensuration Formulas

 Cuboid Volume of Cuboid (LSA) \begin{align} l \times b \times h \end{align} Lateral Surface Area of Cuboid (LSA) \begin{align} 2h\left( {l + b} \right) \end{align} Total Surface Area of Cuboid (TSA) \begin{align} 2\left( {lb + bh + hl} \right) \end{align} Cube Volume of Cube \begin{align} x^3 \end{align} Lateral Surface Area of Cube (LSA) \begin{align} 4x^2 \end{align} Total Surface Area of Cube (TSA) \begin{align} 6x^2 \end{align} Sphere Volume of Sphere \begin{align} \frac{4}{3} \times \pi r^3 \end{align} Lateral Surface Area of Sphere (LSA) \begin{align} 4\pi r^2 \end{align} Total Surface Area of Sphere (TSA) \begin{align} 4\pi r^2 \end{align} \begin{align} l &= \text{Length, } \\ h &= \text{Height,} \\ b &= \text{Breadth} \\ r &= \text{Radius of Sphere} \\ L &= \text{Slant Height} \end{align}

### 4. Probability Formulas

 \begin{align} \text{Probability} \end{align} \begin{align} = \frac{\text{No. of Favourable Outcomes}}{\text{Total No. of Outcomes}} \end{align}

### 5. Comparing Quantities Formulas

 \begin{align} \text{Cost Price (C.P.)} = \begin{bmatrix}\text{Actual }\\ \text{Price} \end{bmatrix} + \begin{bmatrix} \text{Overhead } \\ \text{Costs} \end{bmatrix} \end{align} \begin{align} \text{Selling Price (S.P.)} = \text{Cost Price} + \text{Profit} \end{align} \begin{align} \text{Profit (P)} = \begin{bmatrix} \text{Selling } \\ \text{Price (S.P.)} \end{bmatrix} - \begin{bmatrix} \text{Cost } \\ \text{Price (C.P.)} \end{bmatrix} \end{align} \begin{align} \text{Loss (L)} = \begin{bmatrix} \text{Cost } \\ \text{Price (C.P.)} \end{bmatrix} - \begin{bmatrix} \text{Selling } \\ \text{Price (S.P.)} \end{bmatrix} \end{align} \begin{align} \text{Profit }\left( \text{P} \right)\% = \left( {\frac{{\rm{P}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}}} \right) \times 100 \end{align} \begin{align} \text{Loss }\left( {\rm{L}} \right)\% = \left( {\frac{{\rm{L}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}}} \right) \times 100 \end{align} \begin{align} \text{Simple Interest (S.I.)} = \frac{{{\rm{P}} \times {\rm{R}} \times {\rm{T}}}}{{100}} \end{align} \begin{align} \text{Compound Interest (C.I.)} = {\rm{P}}\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^n \end{align} \begin{align} \text{P} &= \text{Princiapal Amount, } \\ \text{R} &= \text{Rate of Interest,} \\ \text{T} &= \text{Time,} \\ n &= \text{Duration} \end{align}

### 6. Exponents and Powers Formulas

 Laws of Exponents \begin{align} a^{ - m} = \frac{1}{a^m } \end{align} \begin{align} \frac{{a^m }}{{a^n }} = a^{m - n} \end{align} \begin{align} a^m \times a^n = a^{\left( {m + n} \right)} \end{align} \begin{align} \left( {a^m } \right)^n = a^{mn} \end{align} \begin{align} a^m \times b^m = \left( {ab} \right)^m \end{align} \begin{align} \frac{{a^m }}{{b^m }} = \left( {\frac{a}{b}} \right)^m \end{align} \begin{align} a^\circ = 1 \end{align} \begin{align} \left( {\frac{a}{b}} \right)^{ - m} = \left( {\frac{b}{a}} \right)^m \end{align} \begin{align} \left( 1 \right)^n = 1 \end{align}

### 7. Direct and Inverse Proportion Formulas

 Common factor method Example: \begin{align} 2x + 4 = 2(x + 2) \end{align} Factorization by regrouping terms Example: \begin{align} 2xy &\!+\! 3x \!+\! 2y \!+\! 3 \\&\!=\! 2\! \times\! x\! \times\! y \!+\! 3 \!\times\! x\! +\! 2\! \times\! y \!+ \!3 \\ &\!= \!x\! \times\! (2y \!+\! 3) \!+\! 1 \!\times\! (2y\! +\! 3) \\ &\!=\! (2y\! +\! 3) (x\! +\! 1) \end{align} Factorization using identities Example: \begin{align} (a + b)^2 &= a^2 + 2ab + b^2 \\ (a - b)^2 &= a^2 - 2ab + b^2 \\ a^2 - b^2 &= (a + b)(a - b) \end{align}

Our FREE CBSE Class 8 chapter-wise formulas PDF covers the following chapters:

• Chapter-1   Rational Numbers
• Chapter-2   Linear Equations in One Variable
• Chapter-4   Practical Geometry
• Chapter-5   Data Handling
• Chapter-6   Squares and Square Roots
• Chapter-7   Cubes and Cube Roots
• Chapter-8   Comparing Quantities
• Chapter-9   Algebraic Expressions and Identities
• Chapter-10 Visualising Solid Shapes
• Chapter-11 Mensuration
• Chapter-12 Exponents and Powers
• Chapter-13 Direct and Inverse Proportions
• Chapter-14 Factorisation
• Chapter-15 Introduction to Graphs
• Chapter-16 Playing with Numbers