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Class 9 Mathematics NCERT Solutions (Non-Rationalised)
Chapter 1 Number Systems
Master the concept of Number Systems with detailed Class 9 NCERT Solutions. This chapter covers rational and irrational numbers, real numbers, and their precise representation on the number line. Learn to simplify expressions like $\sqrt{5}$ and $\frac{3}{4}$ and understand the concept of real number operations following CBSE guidelines.
Chapter 2 Polynomials
Dive into polynomials, their types, degrees, and zeroes with examples from the Non-Rationalised NCERT Class 9 Maths Book. Understand the Remainder Theorem and Factor Theorem, and learn how to verify relationships between coefficients and zeroes for polynomials like $x^2 - 3x + 2 = 0$.
Chapter 3 Coordinate Geometry
Explore Coordinate Geometry and learn to plot points on the Cartesian plane. Practice finding the distance between two points using the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ and midpoints of line segments. This chapter builds a bridge between algebraic and geometric concepts.
Chapter 4 Linear Equations in Two Variables
Learn to express real-life problems as linear equations in two variables of the form $ax + by + c = 0$. Use graphical and algebraic methods to solve equations and understand how each equation represents a straight line on the coordinate plane.
Chapter 5 Introduction to Euclid’s Geometry
Understand the foundation of geometry through Euclid’s postulates and axioms. This chapter emphasizes logical reasoning and definitions, helping students appreciate how geometric principles are derived systematically from axioms.
Chapter 6 Lines and Angles
Study angles formed by intersecting lines, such as complementary, supplementary, and vertically opposite angles. Learn key theorems like “If two lines are parallel, alternate angles are equal”, and solve geometry problems step by step.
Chapter 7 Triangles
Deepen your understanding of triangles — their congruence criteria (SSS, SAS, ASA, RHS), and properties like the inequality of sides and angles. Each example is supported with logical reasoning and visual proofs for conceptual clarity.
Chapter 8 Quadrilaterals
Explore the properties of quadrilaterals such as parallelograms, rectangles, and rhombuses. Learn and prove theorems like “the diagonals of a rectangle are equal” and apply them to solve geometry problems efficiently.
Chapter 9 Areas of Parallelograms and Triangles
Calculate areas of parallelograms and triangles using algebraic and geometric methods. Understand that triangles on the same base and between the same parallels are equal in area — a key CBSE concept reinforced through examples.
Chapter 10 Circles
Learn about chords, tangents, and angles subtended by arcs. Practice proving that “the perpendicular from the center of a circle to a chord bisects the chord.” Real-world examples illustrate how circles appear in geometry and design.
Chapter 11 Constructions
Gain practical skills by constructing triangles and bisectors using a compass and ruler. Step-by-step methods are provided for bisecting angles, constructing perpendiculars, and dividing line segments in a given ratio like $2:3$.
Chapter 12 Heron’s Formula
Learn to find the area of a triangle using Heron’s Formula, $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter. This powerful method applies even when the height is not known, reinforcing practical problem-solving.
Chapter 13 Surface Areas and Volumes
Strengthen your geometry foundation by calculating surface areas and volumes of solids like spheres, cylinders, and cones. Use formulas such as $V = \pi r^2h$ and $A = 2\pi rh + 2\pi r^2$ for practical applications in daily life.
Chapter 14 Statistics
Develop analytical skills by learning how to collect, organize, and interpret data. Understand mean, median, and mode, and represent data graphically through bar graphs and histograms following the CBSE syllabus.
Chapter 15 Probability
Build an intuitive understanding of probability through real-life situations involving random experiments. Learn to calculate simple probabilities like $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$ using logical reasoning.