Class 8 Maths Formula Sheets

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

\begin{aligned} {(x + y)}^{2} = x^{2} + y^{2} + 2 x y \end{aligned}

\begin{aligned} {(x - y)}^{2} = x^{2} + y^{2} - 2 x y \end{aligned}

\begin{aligned} (x + y) (x - y) = x^{2} - y^{2} \end{aligned}

\begin{aligned} (x + y) (x + z) = x^{2} + x (y + z) + y z \end{aligned}

\begin{aligned} (x + y) (x - z) = x^{2} + x (y - z) - y z \end{aligned}

\begin{aligned} x^{2} + y^{2} = {(x + y)}^{2} - 2 x y \end{aligned}

\begin{aligned} {(x + y)}^{3} = x^{3} + y^{3} + 3 x y (x + y) \end{aligned}

\begin{aligned} {(x - y)}^{3} = x^{3} - y^{3} - 3 x y (x - y) \end{aligned}

\begin{aligned} {(x + y + z)}^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x \end{aligned}

\begin{aligned} {(x - y - z)}^{2} = x^{2} + y^{2} + z^{2} - 2 x y + 2 y z - 2 z x \end{aligned}

Cuboid
Volume of Cuboid (LSA)	$\begin{aligned} l \times b \times h \end{aligned}$
Lateral Surface Area of Cuboid (LSA)	$\begin{aligned} 2 h (l + b) \end{aligned}$
Total Surface Area of Cuboid (TSA)	$\begin{aligned} 2 (l b + b h + h l) \end{aligned}$
Cube
Volume of Cube	$\begin{aligned} x^{3} \end{aligned}$
Lateral Surface Area of Cube (LSA)	$\begin{aligned} 4 x^{2} \end{aligned}$
Total Surface Area of Cube (TSA)	$\begin{aligned} 6 x^{2} \end{aligned}$
Sphere
Volume of Sphere	$\begin{aligned} \frac{4}{3} \times π r^{3} \end{aligned}$
Lateral Surface Area of Sphere (LSA)	$\begin{aligned} 4 π r^{2} \end{aligned}$
Total Surface Area of Sphere (TSA)	$\begin{aligned} 4 π r^{2} \end{aligned}$
$\begin{aligned} l & = Length, \\ h & = Height, \\ b & = Breadth \\ r & = Radius of Sphere \\ L & = Slant Height \end{aligned}$

\begin{aligned} Probability \end{aligned}

\begin{aligned} = \frac{No. of Favourable Outcomes}{Total No. of Outcomes} \end{aligned}

\begin{aligned} Cost Price (C.P.) = [\begin{matrix} Actual \\ Price \end{matrix}] + [\begin{matrix} Overhead \\ Costs \end{matrix}] \end{aligned}

\begin{aligned} Selling Price (S.P.) = Cost Price + Profit \end{aligned}

\begin{aligned} Profit (P) = [\begin{matrix} Selling \\ Price (S.P.) \end{matrix}] - [\begin{matrix} Cost \\ Price (C.P.) \end{matrix}] \end{aligned}

\begin{aligned} Loss (L) = [\begin{matrix} Cost \\ Price (C.P.) \end{matrix}] - [\begin{matrix} Selling \\ Price (S.P.) \end{matrix}] \end{aligned}

\begin{aligned} Profit (P) % = (\frac{P}{C . P .}) \times 100 \end{aligned}

\begin{aligned} Loss (L) % = (\frac{L}{C . P .}) \times 100 \end{aligned}

\begin{aligned} Simple Interest (S.I.) = \frac{P \times R \times T}{100} \end{aligned}

\begin{aligned} Compound Interest (C.I.) = P {(1 + \frac{R}{100})}^{n} \end{aligned}

\begin{aligned} P & = Princiapal Amount, \\ R & = Rate of Interest, \\ T & = Time, \\ n & = Duration \end{aligned}

Laws of Exponents

\begin{aligned} a^{- m} = \frac{1}{a^{m}} \end{aligned}

\begin{aligned} \frac{a^{m}}{a^{n}} = a^{m - n} \end{aligned}

\begin{aligned} a^{m} \times a^{n} = a^{(m + n)} \end{aligned}

\begin{aligned} {(a^{m})}^{n} = a^{m n} \end{aligned}

\begin{aligned} a^{m} \times b^{m} = {(a b)}^{m} \end{aligned}

\begin{aligned} \frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m} \end{aligned}

\begin{aligned} a^{\circ} = 1 \end{aligned}

\begin{aligned} {(\frac{a}{b})}^{- m} = {(\frac{b}{a})}^{m} \end{aligned}

\begin{aligned} {(1)}^{n} = 1 \end{aligned}

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

Student E Knowledge