NCERT Solutions for Class 10 Mathematics offer detailed, step-by-step answers for the Maths textbook. The book includes 14 chapters and covers Algebra, Geometry, Trigonometry, Statistics, and Probability. Class 10 Mathematics requires regular practice, and these NCERT solutions are a useful tool for improving accuracy and speed.
Whether you want to understand basic concepts or prepare for your board exams, these NCERT Class 10 Maths Solutions help you study more effectively. All exercises and questions are covered and explained in a simple manner, making Mathematics easier to understand and solve.
NCERT Solutions for Class 10 Maths Latest Chapter wise 2026 27
| S.No. | Chapter Name & Topic |
| 1 | Chapter 1 - Real Numbers |
| 2 | Chapter 2 - Polynomials |
| 3 | Chapter 3 - Pair of Linear Equations in Two Variables |
| 4 | Chapter 4 - Quadratic Equations |
| 5 | Chapter 5 - Arithmetic Progressions |
| 6 | Chapter 6 - Triangles |
| 7 | Chapter 7 - Coordinate Geometry |
| 8 | Chapter 8 - Introduction to Trigonometry |
| 9 | Chapter 9 - Some Applications of Trigonometry |
| 10 | Chapter 10 - Circles |
| 11 | Chapter 11 - Areas Related to Circles |
| 12 | Chapter 12 - Surface Areas and Volumes |
| 13 | Chapter 13 - Statistics |
| 14 | Chapter 14 - Probability |
NCERT Solutions for Class 10 Mathematics Chapter Overview
Chapter 1 - Real Numbers
The first chapter introduces real numbers and important concepts such as Euclid’s Division Lemma and Euclid’s Division Algorithm for finding HCF, and the Fundamental Theorem of Arithmetic which states that every composite number has a unique prime factorization. It also discusses applications of prime factorization in finding HCF and LCM, the properties of rational and irrational numbers, and the conditions under which rational numbers have terminating or non-terminating repeating decimal expansions. The chapter also teaches proofs of irrationality for numbers like √2.
Chapter 2 - Polynomials
Polynomials can be classified into linear, quadratic, and cubic forms based on degree. Students study the concept of zeros (or roots) of a polynomial and understand their geometric meaning as the x-coordinates where the graph intersects the x-axis. It also teaches the relationship between zeros and coefficients of quadratic polynomials. The chapter includes the Remainder Theorem, Factor Theorem, and Polynomial Division Algorithm. These concepts help build strong algebraic reasoning and form the foundation for advanced mathematics in higher classes.
Chapter 3 - Pair of Linear Equations in Two Variables
This chapter focuses on solving pairs of linear equations in two variables using methods such as substitution, elimination, and cross-multiplication. Students learn different conditions for solutions: a unique solution when lines intersect, no solution when lines are parallel, and infinitely many solutions when lines coincide.
Chapter 4 - Quadratic Equations
This chapter introduces quadratic equations and how to solve them using methods like factorization and completing the square. Students learn that the discriminant helps determine the nature of roots as real and distinct, real and equal, or non real, and also study the relationship between roots and their sum and product with coefficients. The chapter also explains the graphical meaning of roots as x intercepts of a parabola and shows how quadratic equations are used in area, speed and motion.
Chapter 5 - Arithmetic Progressions
Chapter 5 introduces Arithmetic progressions through the concept of number sequences in which the difference between consecutive terms remains constant, called the common difference. Students learn how to identify an arithmetic progression, understand its structure, and extend patterns. It also teaches the idea of finding specific terms in a sequence and analyzing patterns logically.
Chapter 6 - Triangles
This chapter talks about the concept of similarity between triangles and the conditions required to prove two triangles similar, such as AA, SSS, and SAS criteria. One of the most important concepts of this chapter is the Basic Proportionality Theorem (Thales’ theorem), which states that a line drawn parallel to one side of a triangle divides the other two sides in the same ratio, along with its converse. Students also study important properties of similar triangles, such as proportional sides, equal corresponding angles, and the relationship between their areas.
Chapter 7 - Coordinate Geometry
Coordinate Geometry introduces the Cartesian coordinate system, where points are represented using ordered pairs (x, y) on a plane formed by two perpendicular axes (x-axis and y-axis). Students learn how to locate points in different quadrants and understand the sign conventions of coordinates. The chapter teaches important concepts such as the distance between two points, the section formula for dividing a line segment in a given ratio, and the midpoint formula. It also includes the area of a triangle using coordinates. These concepts connect algebra with geometry.
Chapter 8 - Introduction to Trigonometry
This chapter introduces the study of relationships between angles and sides in right-angled triangles. Students learn the basic trigonometric ratios such as sine, cosine, and tangent, and understand how these ratios are defined using the sides of a right triangle (opposite, adjacent, and hypotenuse). The chapter explains that these ratios depend only on the angle and remain constant for similar triangles. It also includes trigonometric ratios of complementary angles, showing various relationships. Standard values of trigonometric ratios for angles like 0°, 30°, 45°, 60°, and 90° are also discussed. This chapter acts as the foundation for advanced trigonometry in higher classes.
Chapter 9 - Some Applications of Trigonometry
The chapter Some Applications of Trigonometry applies trigonometric ratios to real-life applications related to heights and distances. Students learn how to solve real-life word problems using concepts like angle of elevation and angle of depression. The chapter explains how to calculate unknown heights of objects such as towers, trees, buildings, and how to find distances that cannot be measured directly. It talks about the idea of line of sight and horizontal reference. These methods are widely used in fields like surveying, navigation, and construction.
Chapter 10 - Circles
Chapter 10 discusses the properties of circles and the relationship between tangents, chords, and radii. Students learn about a tangent being perpendicular to the radius at the point of contact, and that tangents drawn from an external point to a circle are equal in length. The chapter also includes important theorems related to angles subtended by chords, cyclic quadrilaterals, and properties of equal chords and their distances from the centre.
Chapter 11 - Areas Related to Circles
Areas Related to Circles teaches measuring and calculating different regions of a circle, including the full circle and its parts such as sectors and segments. Students learn how a sector is formed by two radii and an arc, and how a segment is formed by a chord and an arc. The chapter discusses finding the area and perimeter of these regions and solving application-based problems. These concepts help students connect geometry with practical problems.
Chapter 12 - Surface Areas and Volumes
This chapter teaches the measurement of three-dimensional objects and their properties. Students learn how to calculate the surface area and volume of basic solids such as cubes, cuboids, cylinders, cones, and spheres. The chapter also explains curved surface area, lateral surface area, and total surface area, along with how these formulas are applied to composite or combined solids. It includes real-life applications such as calculating capacity of containers, tanks, and objects of different shapes.
Chapter 13 - Statistics
Chapter 13 discusses the collection, organisation, analysis, and interpretation of data. Students learn how to represent data using frequency distributions, class intervals, cumulative frequency tables, histograms and frequency polygons. The chapter teaches measures of central tendency including mean, median, and mode for grouped data, and introduces different methods for calculating mean such as the direct method, assumed mean method, and step-deviation method. It also explains how median and mode are calculated using grouped frequency tables and how cumulative frequency helps in interpreting data.
Chapter 14 - Probability
The last chapter discusses the concept of probability as a numerical measure of uncertainty and chance. Students learn about random experiments, outcomes, sample space, and events, and how probability is calculated for equally likely outcomes using the ratio of favourable outcomes to total outcomes. The chapter explains types of events such as certain events, impossible events, and elementary events, along with the idea of complementary events where the sum of probabilities of an event and its complement is 1. It also teaches that probability values always lie between 0 and 1. Through various questions related to coins, dice and cards, students develop an understanding of prediction in mathematical terms.
