📘 Class 8 Maths Notes - Complete Guide

Chapter 1: Rational Numbers

Definition: A rational number is a number that can be written as a fraction where both the numerator and denominator are integers.

For example, ¾, 5/2, -7/8 are rational numbers. Every integer is a rational number because it can be written as a fraction with 1 in the denominator (e.g., 5 = 5/1).

Important Properties

• Rational numbers can be positive, negative, or zero.
• Fractions like ½, -4/3 are rational numbers.
• When expressed in decimal form, they either terminate (e.g., 0.5) or repeat (e.g., 0.666...).

Examples

• 1/2, 4/5, 6, -7/8

Chapter 2: Linear Equations in One Variable

A linear equation is an equation in which the highest power of the variable is one. These equations represent straight lines when graphed on a coordinate plane.

Example

• 2x + 3 = 7, solve for x: x = 2.
• 5y - 3 = 12, solve for y: y = 3.

Steps to Solve Linear Equations

• Move the constant terms to the other side of the equation.
• Divide or multiply to isolate the variable.

Chapter 3: Understanding Quadrilaterals

A quadrilateral is a polygon with four sides. The sum of all interior angles of a quadrilateral is 360°.

Types of Quadrilaterals

• Square: All sides equal, all angles are 90°.
• Rectangle: Opposite sides equal, all angles are 90°.
• Parallelogram: Opposite sides parallel and equal.
• Rhombus: All sides equal, opposite angles equal.
• Trapezium: Only one pair of opposite sides is parallel.

Properties of Parallelogram

• Opposite sides are equal and parallel.
• Opposite angles are equal.
• The diagonals bisect each other.

Chapter 4: Data Handling

Types of Data Representation

• Bar Graph: A graph that uses bars to represent data.
• Pictogram: Uses pictures or symbols to represent data.
• Pie Chart: A circular chart divided into sectors to represent data.

Steps to Draw a Bar Graph

• Draw the x and y axes.
• Label the axes with the appropriate categories.
• Draw bars with the correct heights corresponding to the data values.

Chapter 5: Squares and Square Roots

What is a Square Number?

A square number is a number that is the product of an integer multiplied by itself. Example: 1, 4, 9, 16, 25, 36.

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4, because 4 × 4 = 16.

Perfect Squares

• Perfect squares are numbers like 1, 4, 9, 16, etc., where their square roots are whole numbers.

Chapter 6: Cubes and Cube Roots

What is a Cube Number?

A cube number is a number that is the product of an integer multiplied by itself twice. Example: 1, 8, 27, 64, 125.

Cube Root

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Example: ∛27 = 3, because 3 × 3 × 3 = 27.

Chapter 7: Comparing Quantities

Percentage

Percentage is a way of expressing numbers as a fraction of 100. Example: 25% means 25 out of 100.

Ratio and Proportion

Ratio: A comparison of two quantities by division. Example: Ratio of 2:5 means for every 2 of one quantity, there are 5 of the other.

Proportion

Proportion is an equation that shows that two ratios are equal. Example: 2/3 = 4/6.

Chapter 8: Algebraic Expressions

What is an Algebraic Expression?

An expression consisting of variables, constants, and operators. Example: 2x + 3 is an algebraic expression.

Like and Unlike Terms

• Like terms: Terms with the same variables raised to the same powers. Example: 3x, 5x.
• Unlike terms: Terms with different variables or powers. Example: 2x and 3y.

Chapter 9: Visualizing Solid Shapes

3D Shapes

Solid shapes have three dimensions: length, breadth, and height. Examples include cuboids, cubes, and spheres.

Surface Area and Volume

• Volume of a cuboid: V = l × b × h
• Surface area of a cube: 6a²

Chapter 10: Mensuration

Surface Area and Volume

• Volume of cuboid: V = l × b × h
• Surface area of cube: 6a²
• Volume of cylinder: V = πr²h

Chapter 11: Exponents and Powers

Understanding Exponents

An exponent represents the number of times a number (called the base) is multiplied by itself. Example: 2³ = 2 × 2 × 2 = 8.

Chapter 12: Direct and Inverse Proportions

Direct Proportion

In direct proportion, as one quantity increases, the other quantity also increases. Example: If the price of 1 book is $5, then the price of 3 books is 3 × $5 = $15.

Chapter 13: Factorization

What is Factorization?

Factorization is the process of breaking down a number or expression into its factors. Example: Factorizing 12 = 2 × 2 × 3.

Chapter 14: Linear Graphs

What are Linear Graphs?

Linear graphs represent linear equations graphically. Each point on the graph corresponds to a solution of the equation.

Chapter 15: Probability

What is Probability?

Probability is the measure of the likelihood of an event happening. It is calculated as the number of favorable outcomes divided by the total number of outcomes.

Chapter 16: Statistics

Mean, Median, and Mode

• Mean: The average of a set of numbers.
• Median: The middle number in a set when arranged in order.
• Mode: The most frequent number in a set.