**Maths Formulas for Class 8 **

Most of the students consider mathematics as a nightmare and math formulas are generally difficult to grasp when you don’t understand them well. The negative attitude towards any of your subjects will make you reluctant to study that particular subject.

Most of the time, students feel nervous during their exams and they are not able to give their best shot. To make you more confident in the study and help you through different concepts in Maths, we will discuss the important maths formulas for class 8 here.

When you understand the logic behind each mathematics topics then it would be easier to solve the most complex problems too. For a perfect idea, we will explain to you the formulas chapter-wise and we will give you topics on how can you score maximum marks in class 8^{th} exams.

#### Class 8 Rational Numbers Formulas

\[\ Additive\;Identity=> a + 0 = a \] |

\[\ Multiplicative\;Identity=> a \times 1 = a \] |

\[\ Reciprocal\;or\;Multiplicative\;Inverse=> \left( {\frac{a}{b}} \right) \times \left( {\frac{b}{a}} \right) = 1 \] |

\[\ Distributive\;Property=> a(b + c) = ab + ac \;and\; a(b-c) = ab-ac \] |

\[\ Additive\; Inverse\; of\; \frac{a}{b} \;is \; \frac{a}{b} \;and\; vice-versa\] |

\[\ Commutative\;Property\;of\;Addition=> a + b = b + a \] |

\[\ Commutative\;Property\;of\;Subtraction=> a-b \ne b-a \] |

\[\ Commutative\;Property\;of\;Multiplication=> a \times b = b \times a \] |

\[\ Commutativity\;of\;Division=> \frac{a}{b} \ne \frac{b}{a} \] |

\[\ Associative\;Property\;of\;Addition=> (a + b) + c = a + (b + c) \] |

\[\ Associative\;Property\;of\;Subtraction=> (a-b)-c \ne a-(b-c) \] |

\[\ Associative\;Property\;of\;Multiplication=> (a \times b) \times c = a \times (b \times c) \] |

\[\ Associative\;Property\;of\;Division=> \frac{{\left( {\frac{a}{b}} \right)}}{c} \ne \frac{a}{{\left( {\frac{b}{c}} \right)}} \] |

#### Class 8 Understanding Quadrilaterals Formulas

- Sum of angles of a quadrilateral is equal to 360 degree
- Opposite sides of a parallelogram are equal.
- Opposite angles of a parallelogram are equal.
- Diagonals of a parallelogram bisect each other.
- Diagonals of a rectangle are equal and bisect each other.
- Diagonals of a rhombus bisect each other at right angles.
- Diagonals of a square are equal and bisect each other at right angles.

#### Class 8 Data Handling Formulas

\[\ Arithmetic\;Mean = \frac{Sum\;of \;Observation}{Number\; of\; Observation} \] |

\[\ Range = Largest\;Observation – Smallest\;Observation \] |

\[\ Mode = Large\;Number\;of \;Observations \] |

\[\ Median = (\frac{n + 1}{2})^{th} Obserbation \] |

\[\ Probability = \frac{No. \;of\; Favorable \;outcome}{No.\; of\; all\; possible\; outcome} \] |

#### Class 8 Comparing Quantities Formulas

\[\begin{align} \text{Cost Price (C.P.)} = \begin{bmatrix}\text{Actual }\\ \text{Price} \end{bmatrix} + \begin{bmatrix} \text{Overhead } \\ \text{Costs} \end{bmatrix} \end{align}\] |

\[\begin{align} \text{Selling Price (S.P.)} = \text{Cost Price} + \text{Profit} \end{align}\] |

\[\begin{align} \text{Profit (P)} = \begin{bmatrix} \text{Selling } \\ \text{Price (S.P.)} \end{bmatrix} – \begin{bmatrix} \text{Cost } \\ \text{Price (C.P.)} \end{bmatrix} \end{align}\] |

\[\begin{align} \text{Loss (L)} = \begin{bmatrix} \text{Cost } \\ \text{Price (C.P.)} \end{bmatrix} – \begin{bmatrix} \text{Selling } \\ \text{Price (S.P.)} \end{bmatrix} \end{align}\] |

\[\begin{align} \text{Profit }\left( \text{P} \right)\% = \left( {\frac{{\rm{P}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}}} \right) \times 100 \end{align}\] |

\[\begin{align} \text{Loss }\left( {\rm{L}} \right)\% = \left( {\frac{{\rm{L}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}}} \right) \times 100 \end{align}\] |

\[\begin{align} \text{Simple Interest (S.I.)} = \frac{{{\rm{P}} \times {\rm{R}} \times {\rm{T}}}}{{100}} \end{align}\] |

\[\begin{align} \text{Compound Interest (C.I.)} = {\rm{P}}\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^n \end{align}\] |

\[\begin{align} \text{P} &= \text{Princiapal Amount, } \\ \text{R} &= \text{Rate of Interest,} \\ \text{T} &= \text{Time,} \\ n &= \text{Duration} \end{align}\] |

#### Class 8 Algebraic Expressions and Identities Formulas

- (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 - (x + a)(x – b)=x
^{2}+ (a – b)x – ab - (x – a)(x + b)=x
^{2}+ (b – a)x – ab - (x – a)(x – b)=x
^{2}– (a + b)x + ab - (a + b)
^{3}=a^{3}+ b^{3}+ 3ab(a + b) - (a – b)
^{3}=a^{3}– b^{3}– 3ab(a – b) - (x + y + z)
^{2}=x^{2}+ y^{2}+ z^{2}+ 2xy + 2yz + 2xz - (x + y – z)
^{2}=x^{2}+ y^{2}+ z^{2}+ 2xy – 2yz – 2xz - (x – y + z)
^{2}=x^{2}+ y^{2}+ z^{2}– 2xy – 2yz + 2xz - (x – y – z)
^{2}=x^{2}+ y^{2}+ z^{2}– 2xy + 2yz – 2xz - x
^{3}+ y^{3}+ z^{3}– 3xyz=(x + y + z)(x^{2}+ y^{2}+ z^{2}– xy – yz−xz) - (x + a)(x + b)(x + c)=x
^{3}+ (a + b + c)x^{2}+ (ab + bc + ca)x + abc - x
^{3}+ y^{3}=(x + y)(x^{2}– xy + y^{2}) - x
^{3}– y^{3}=(x – y)(x^{2}+ xy + y^{2}) - (a + b)
^{4}= a^{4}+ 4a^{3}b + 6a^{2}b^{2}+ 4ab^{3}+ b^{4}) - (a – b)
^{4}= a^{4}– 4a^{3}b + 6a^{2}b^{2}– 4ab^{3}+ b^{4}) - a
^{4}– b^{4}= (a – b)(a + b)(a^{2}+ b^{2}) - a
^{5}– b^{5}= (a – b)(a^{4}+ a^{3}b + a^{2}b^{2}+ ab^{3}+ b^{4})

#### Class 8 Mensuration Formulas

\[\ Area\;of\;Square = l^{2} \] \[\ Perimeter\;of\;Square = 4 \times l \]Where, l : length of side |

\[\ Area\;of\;Rectangle = l \times w \] \[\ Perimeter\;of\;Rectangle = 2 (l+w) \]Where, L = Length w = Width |

\[\ Area\;of\;Circle = \pi r^{2} \] \[\ Perimeter\;of\;Circle = 2 \pi r \]Where, 𝒓 = Radius d = Diameter d = 2𝒓 |

\[\ Area\;of\;Scalene\;Triangle = \sqrt{s(s-a)(s-b)(s-c)} \] \[\ Perimeter\;of\;Scalene\;Triangle = a+b+c \]Where, a, b, c are Side of Scalene Triangle |

\[Area\;of\;Isoscele\;Triangle =\frac{1}{2}bh\] \[Altitude\;of\;an\;Isosceles\;Triangle=\sqrt{a^{2}-\frac{b^{2}}{4}}\] Where, b = Base of the isosceles triangle h = Height of the isosceles triangle & a = length of the two equal sides \[\large Perimeter\;of\;Isosceles\;Triangle,P=2\,a+b\] Where, |

\[ Area \;of \;an \;Right\;Triangle = \frac{\sqrt{1}}{2}bh\] \[ Perimeter \;of \;an \;Right \;Triangle = a+b+c\] \[ semi\;Perimeter \;of \;an \;Right \;Triangle = \frac{a+b+c}{2}\] |

\[ Area \;of \;an \;Equilateral \;Triangle = \frac{\sqrt{3}}{4}a^{2}\] \[ Perimeter \;of \;an \;Equilateral \;Triangle = 3a\] \[ Semi \;Perimeter \;of \;an \;Equilateral \;Triangle = \frac{3a}{2}\] \[ Height \;of \;an \;Equilateral \;Triangle = \frac{\sqrt{3}}{2}a\] |

\[\large perimeter\;of\;a\;rhombus =4\times Side\] \[\large Area\;of\;a\;Rhombus = A = \frac{1}{2} \times d_{1} \times d_{2}\] Where, d1 and d2 are the diagonals of the rhombus bisect each other 90-degree angle. |

\[\ Area\;of\;a\;Parallelogram = b\times h\] \[\ Perimeter\;of\;Parallelogram = 2\left(b+h\right)\] Where, b: Base h: Height. |

\[\large Perimeter\;of\;a\;Trapezoid\;=a+b+c+d\] Where, a, b, c, d are the lengths of each side. \[\large Area\;of\;a\;Trapezoid\; = \frac{1}{2} \times h \times (a + b)\] Where:, h = height a = the short base b = the long base |

\[\large Surface\;area\;of\;Cube=6a^{2}\] \[\large Volume\;of\;a\;cube=a^{3}\] Where, a is the side length of the cube. |

\[\large Surface\;area\;of\;Cuboid = 2(lb + bh + hl)\] \[\large Volume\;of\;a\;Cuboid = h \times l \times w\] Where, l: Height h: Legth w: Depth |

\[\large Diameter\;of\;a\;sphere=2r\] \[\large Circumference\;of\;a\;sphere=2\pi r\] \[\large Surface\;area\;of\;a\;sphere=4\pi r^{2}\] \[\large Volume\;of\;a\;sphere=\frac{4}{3}\: \pi r^{3}\] Where, r: Radius |

\[\large Curved\;Surface\;area\;of\;a\;Hemisphere =4\pi r^{2}\] \[\large Total\;Surface\;area\;of\;a\;Hemisphere =3\pi r^{2}\] \[\large Volume\;of\;a\;Hemisphere =\frac{2}{3}\: \pi r^{3}\] Where, r: Radius |

\[\large Curved\;Surface\;area\;of\;a\;Cylinder =2\pi rh\] \[\large Total\;Surface\;area\;of\;a\;Cylinder =2\pi r(r+h)\] \[\large Volume\;of\;a\;Cylinder = \pi r^{2} h\] Where, r: Radius h: Height |

\[\large Total\;Surface\;Area\;of\;cone=\pi r \left (s+r \right )\] \[\large Vomule\;of\;cone=\frac {1}{3}\pi r^{2}h\] \[\large Curved\;Surface\;Area\;of\;cone=\pi rs\] Where, r is the radius of cone.h is the height of cone.s is the slant height of the cone. |

#### Class 8 Exponents and Powers Formulas

\[\ Power\; zero = a^{ 0 } = 1\] |

\[\ Power \;one = a^{ 1 } = a\] |

\[\ Fraction\; formula = \sqrt{ a } = a^{ \frac{ 1 }{ 2 }}\] |

\[\ Reverse \;formula = \sqrt{ n } { a } = a^{\frac{ 1 } { n }}\] |

\[\ Negative \;power \;value = a^{ -n } = \frac{ 1 }{ a^{n} }\] |

\[\ Fraction\; formula = a^{n} = \frac{1}{ a^{ -n } }\] |

\[\ Product \;formula = a^{m}a^{n} = a^{ m + n }\] |

\[\ Division\; Formula = \frac{ a^{ m }}{ a^{ n }} = a ^{ m-n }\] |

\[\ Power\; of \;Power formula = (a^{ m })^{ p } = a^{ mp }\] |

\[\ Power \;distribution Formula = (a^ { m }c^{ n })^{ x } = a ^ { mx } c ^{ nx }\] |

\[\ The\; Power\; distribution \;Formula = \left ( \frac {a ^{ m }}{c^{ n }} \right )^{x} = \frac{a^{ mx }}{c^{ nx }}\] |

(-1)^{Even Number} = 1 |

(-1)^{Odd Number} = -1 |

(a^{m})(a^{n}) = a^{m+n
} |

(ab)^{m} = a^{m}b^{m
} |

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

**Chapter-wise Marks in Exam **

The first step on how to start your study in 8^{th} class is checking the complete syllabus and where to start to ease out the preparation. Class 8^{th} is a very crucial stage in your life where students learn the maximum number of concepts for different subjects and apply them later for real-life applications too. This is the right time to make a foundation for future studies.

To prepare for class 8^{th} exams, you first check the complete syllabus from NCERT book and chapter-wise weightage. Spend more time on the topics having high weightage of marks. Obviously, your class teacher also helps you at every stage but don’t forget to prepare your own strategy and work on the same norms. Before we move ahead, here is a quick look at chapter-wise marks in exams for class eighth.

**NCERT Solutions Class 8 Maths By Chapters**

- Chapter 1 – Rational Numbers
- Chapter 2 – Linear Equations in One Variable
- Chapter 3 – Understanding Quadrilaterals
- 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

**Chapter-wise Maths Formulas for Class 8**

Maths play a vital role in preparing you for the competitive exams and higher studies too. As we know that CBSE board has changed the curriculum for class 8^{th} after many years. So, this is necessary for you to understand the different topics and their weightage as discussed earlier. Also, you should be mentally prepared on how to score well in the exam with the right strategy.

- Chapter 1 – Rational Numbers
- Chapter 3 – Understanding Quadrilaterals
- Chapter 5 – Data Handling
- Chapter 8 – Comparing Quantities
- Chapter 9 – Algebraic Expressions and Identities
- Chapter 11 – Mensuration
- Chapter 12 – Exponents and Powers

#### Summary

Here, we will discuss the tips that will be helpful for you for exams and scores as well as needed.

- First of all, you should prepare a notebook where all important mathematical formulas are noted down and revise them from time to time especially before your exams.
- The practice is the key to success. The more will you practice, there is a huge chance of getting success in your career.
- Try to solve the maximum CBSE papers in one sitting and check your level where you need to improve to score well.
- Also, spend more time on the topics having more weightage.
- When you solve previous year sample papers, it will increase your overall confidence and makes you the right candidate for tough mathematics problems. Also, you will get a chance to brush up all concepts quickly.
- Also, don’t just read the topic but practice them wisely. Keep always in your mind that reading maths could not help you. Instead set a fixed time to practice mathematical concepts daily.