| Non-Rationalised NCERT Books Solution | ||||||
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Class 10 Mathematics NCERT Solutions (Non-Rationalised)
Chapter 1 Real Numbers
Explore the world of real numbers—including rational and irrational numbers—and learn how to use the Euclidean Division Algorithm to find the HCF and LCM of numbers. This chapter builds on the fundamental theorem of arithmetic and primes, using examples like $2^3 \times 3^2 = 72$. Strengthen your understanding of number properties essential for higher classes.
Chapter 2 Polynomials
Dive into polynomials—expressions containing variables and coefficients. Learn about zeros of a polynomial and how they relate to its coefficients through the identity $ax^2 + bx + c = 0$. Master factorization techniques and the Remainder Theorem to solve complex algebraic problems with ease.
Chapter 3 Pair of Linear Equations in Two Variables
Understand how to solve pairs of linear equations in two variables using the graphical, substitution, and elimination methods. Learn how two lines can intersect, be parallel, or coincide, and interpret real-world situations algebraically as $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$.
Chapter 4 Quadratic Equations
Master quadratic equations of the form $ax^2 + bx + c = 0$. Learn various solving methods—factorization, completing the square, and quadratic formula. Understand how the discriminant ($b^2 - 4ac$) determines the nature of roots and explore applications in daily life and geometry.
Chapter 5 Arithmetic Progressions
Understand sequences and series where each term increases by a constant difference $d$. Learn formulas like $a_n = a + (n-1)d$ and $S_n = \frac{n}{2}[2a + (n-1)d]$. Apply A.P. concepts to practical problems like savings and distance calculations.
Chapter 6 Triangles
Learn the similarity and congruence of triangles with important theorems like AA, SAS, and SSS. Apply the Pythagoras Theorem $a^2 + b^2 = c^2$ and its converse to prove relationships between sides and angles. Strengthen reasoning and geometric visualization skills.
Chapter 7 Coordinate Geometry
Study the Cartesian plane and learn how to find the distance between two points using $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, the midpoint formula, and the section formula. Apply these tools to find areas of triangles and locate geometric figures in real-life contexts.
Chapter 8 Introduction to Trigonometry
Discover trigonometric ratios—sine, cosine, tangent, and their reciprocals. Understand relationships like $\sin^2 \theta + \cos^2 \theta = 1$ and values of trigonometric ratios for standard angles. This chapter lays the foundation for advanced trigonometric applications.
Chapter 9 Some Applications of Trigonometry
Apply trigonometric ratios to solve height and distance problems in real life. Learn how angles of elevation and depression help calculate building heights, mountain distances, and more—making math practical and visual.
Chapter 10 Circles
Explore the geometry of circles—including tangents, chords, and angles subtended. Learn that a tangent to a circle is perpendicular to the radius at the point of contact, and understand the relationships between tangents drawn from an external point.
Chapter 11 Constructions
Practice constructing triangles, bisectors, tangents, and circles using a compass and straightedge. Strengthen your geometric accuracy and logical understanding through practical design-based constructions.
Chapter 12 Areas Related to Circles
Learn to calculate areas of sectors and segments using formulas like $\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2$. Apply these to real-world problems involving circular tracks, wheels, and design patterns.
Chapter 13 Surface Areas and Volumes
Calculate the surface area and volume of 3D solids like cylinders, cones, and spheres using formulas such as $V = \frac{4}{3}\pi r^3$. Develop spatial reasoning through combined solid shapes and real-life examples.
Chapter 14 Statistics
Organize and analyze data using frequency tables, bar graphs, and cumulative frequency curves. Learn measures of central tendency—mean, median, and mode—and apply them in interpreting real-life data distributions.
Chapter 15 Probability
Understand the concept of probability as a measure of uncertainty. Learn how to compute the probability of events using $\text{P(E)} = \frac{\text{Number of favourable outcomes}}{\text{Total outcomes}}$, and apply it to real-life random experiments like tossing coins or rolling dice.