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Class 8 Mathematics NCERT Solutions (Non-Rationalised)
Chapter 1 Rational Numbers
Rational numbers are numbers that can be expressed in the form $\frac{p}{q}$ where $q \ne 0$. In this chapter, students will explore properties such as the closure, commutative, associative, and distributive laws of rational numbers. Learn how to represent rational numbers on a number line and perform operations like addition, subtraction, multiplication, and division. These NCERT Class 8 Maths Solutions help in mastering rational number properties useful in higher algebra.
Chapter 2 Linear Equations in One Variable
This chapter teaches how to solve linear equations of the form $ax + b = c$ and apply them to real-life situations like finding ages, prices, and distances. Students learn to simplify expressions by balancing both sides and using inverse operations. The Non-Rationalised NCERT Solutions provide clear steps for problem-solving and concept reinforcement through practice questions.
Chapter 3 Understanding Quadrilaterals
Understand the different types of quadrilaterals like parallelograms, rhombuses, rectangles, and trapeziums. Learn their properties and the angle sum property where the sum of interior angles is $360^\circ$. This chapter builds the foundation for geometry by introducing key terms like diagonals, vertices, and sides.
Chapter 4 Practical Geometry
In Practical Geometry, students learn to construct quadrilaterals using given sides, angles, and diagonals with a ruler and compass. Step-by-step procedures are provided for figures like parallelograms, kites, and rhombuses. The chapter enhances spatial reasoning and accuracy in geometric constructions.
Chapter 5 Data Handling
Learn to organize and represent data using bar graphs, pie charts, and histograms. Understand concepts like probability and mean, median, and mode. Real-life examples such as sports data and weather statistics help visualize how mathematics is used in data interpretation.
Chapter 6 Squares and Square Roots
This chapter introduces squares and square roots and explains how to calculate them using prime factorization and division methods. Learn about perfect squares and shortcuts for finding the square of numbers like $(a + b)^2$. Examples using $\sqrt{64} = 8$ and $\sqrt{2}$ build strong numerical understanding.
Chapter 7 Cubes and Cube Roots
Discover the concept of cubes and cube roots of numbers. Practice calculations such as $5^3 = 125$ and find cube roots using the prime factorization method. This chapter also includes patterns in cubes and tricks for fast computation to boost number sense.
Chapter 8 Comparing Quantities
Strengthen your understanding of percentages, profit and loss, and simple and compound interest. Real-life applications such as calculating bank interest and discounts are explained clearly. Learn to solve problems where growth or depreciation is expressed using $A = P(1 + \frac{r}{100})^n$.
Chapter 9 Algebraic Expressions and Identities
This chapter explains algebraic expressions, coefficients, and identities like $(a + b)^2 = a^2 + 2ab + b^2$. Students learn to expand, simplify, and apply identities in problem-solving. It lays a foundation for advanced algebra topics in higher classes.
Chapter 10 Visualising Solid Shapes
Learn how to visualize 3D objects such as cubes, cuboids, and cylinders. Understand nets of solids and orthographic views to connect 2D representations with real 3D structures. This topic improves spatial visualization and geometric understanding.
Chapter 11 Mensuration
Study surface area and volume of solids like cubes, cuboids, and cylinders. Use formulas such as $V = l \times b \times h$ and $A = 2(lw + lh + wh)$. Learn practical applications of mensuration in construction, packaging, and real-world measurements.
Chapter 12 Exponents and Powers
Understand laws of exponents such as $a^m \times a^n = a^{m+n}$ and express numbers in standard form like $5.6 \times 10^7$. Learn to handle very large and very small numbers efficiently using scientific notation.
Chapter 13 Direct and Inverse Proportions
This chapter deals with direct and inverse variation concepts. In direct proportion, when one quantity increases, the other increases ($x_1/y_1 = x_2/y_2$); whereas in inverse proportion, when one increases, the other decreases ($x_1y_1 = x_2y_2$). Real-life problems like speed and time are included for better understanding.
Chapter 14 Factorisation
Learn different methods of factorising algebraic expressions—by taking out common factors, using identities, and regrouping terms. For example, factorise $a^2 - b^2 = (a - b)(a + b)$. These techniques improve problem-solving efficiency in algebraic simplification.
Chapter 15 Introduction to Graphs
Get introduced to graphs and the Cartesian plane. Learn how to plot points $(x, y)$ and interpret data using bar graphs, line graphs, and linear equations. Real-life data representation like temperature charts is also included for visualization skills.
Chapter 16 Playing with Numbers
This chapter develops logical reasoning through number patterns, divisibility rules, and puzzles. Explore tricks for identifying divisibility by numbers like $2$, $3$, $5$, and $9$. Strengthen problem-solving and mental math skills with engaging examples.