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Latest Class 8 Mathematics NCERT Solutions
Chapter 1: Rational Numbers
Rational Numbers extend the number system beyond integers by including fractions of the form $\dfrac{p}{q}$, where $q \ne 0$. Learn about closure, commutative, associative, and distributive properties under addition and multiplication. Understand the additive inverse and multiplicative inverse of numbers, and how rational numbers are used in comparing, ordering, and performing daily life calculations.
Chapter 2: Linear Equations in One Variable
This chapter focuses on equations that can be written in the form $ax + b = c$. Learn to solve equations involving brackets, variables on both sides, and word problems. Real-life contexts like age problems and price comparisons are included to make algebra meaningful and applicable.
Chapter 3: Understanding Quadrilaterals
Dive into the fascinating world of four-sided figures such as parallelograms, trapeziums, rectangles, rhombuses, and squares. Understand internal angle sums and how they always equal $360^\circ$. Learn to identify properties like equal sides, diagonals, and parallel lines through visual reasoning.
Chapter 4: Data Handling
Learn how to collect, organize, and interpret data using graphs, bar diagrams, and pie charts. Understand probability in simple experiments and calculate measures of central tendency — mean ($\bar{x} = \dfrac{\text{sum of observations}}{\text{number of observations}}$), median, and mode — to summarize large data sets effectively.
Chapter 5: Squares and Square Roots
Discover perfect squares and the patterns they form. Learn shortcuts such as using prime factorization or long division method to find square roots. Understand properties like $(a+b)^2 = a^2 + 2ab + b^2$ and $(a-b)^2 = a^2 - 2ab + b^2$ to simplify calculations efficiently.
Chapter 6: Cubes and Cube Roots
Explore cubes of numbers and learn the identity $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$. Study methods for finding cube roots through prime factorization and estimation. Understand how cubes and cube roots appear in volume calculations of 3D shapes.
Chapter 7: Comparing Quantities
Strengthen your skills in dealing with percentages, ratios, and proportions. Learn to calculate profit and loss, discounts, simple interest ($SI = \dfrac{P \times R \times T}{100}$), and compound interest through practical examples involving financial transactions.
Chapter 8: Algebraic Expressions and Identities
Learn to handle expressions involving variables and constants. Understand operations on algebraic expressions and the application of standard identities like:
$ (a+b)^2 = a^2 + 2ab + b^2 $,
$ (a-b)^2 = a^2 - 2ab + b^2 $, and
$ (a+b)(a-b) = a^2 - b^2 $.
These identities help simplify complex algebraic problems and factorization tasks.
Chapter 9: Mensuration
This chapter extends your understanding of area and volume to three-dimensional shapes. Learn formulas like:
$\text{Surface Area of a Cube} = 6a^2$,
$\text{Volume of a Cylinder} = \pi r^2h$,
and $\text{Volume of a Sphere} = \dfrac{4}{3}\pi r^3$.
These concepts are applied to solve real-world measurement problems involving packaging, tanks, and construction.
Chapter 10: Exponents and Powers
Learn to represent very large or very small numbers using scientific notation. Understand and apply the laws of exponents, such as $a^m \times a^n = a^{m+n}$, $\dfrac{a^m}{a^n} = a^{m-n}$, and $(a^m)^n = a^{mn}$. These rules make complex calculations much simpler and faster.
Chapter 11: Direct and Inverse Proportions
Understand how quantities are related through direct proportion ($\dfrac{x_1}{y_1} = \dfrac{x_2}{y_2}$) or inverse proportion ($x_1y_1 = x_2y_2$). Apply these relationships to solve problems involving speed, distance, and time, or work and workers.
Chapter 12: Factorisation
Develop strong factoring skills using common factors, grouping terms, and special identities. Learn to simplify expressions such as $x^2 + 5x + 6 = (x + 2)(x + 3)$, and solve polynomial equations efficiently.
Chapter 13: Introduction to Graphs
Visualize data and equations on the Cartesian plane. Learn to plot coordinates $(x, y)$, draw linear graphs, and interpret information from different types of graphs such as bar graphs, histograms, and line graphs. Understand the relationship between algebra and geometry through visual representation.