NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Maths from chapters 1 to 15 are provided on this page. Answers to all exercises are provided in details. These solutions are provided by expert teachers at IndCareer. Students looking for NCERT Solutions for Maths subject of Class 10 can also download the chapter-wise PDFs.

The National Council of Educational Research and Training (NCERT) is an autonomous organisation of the Government of India which was established in 1961 as a literary, scientific and charitable Society under the Societies’ Registration Act (Act XXI of 1860). Its headquarters are located at Sri Aurbindo Marg in New Delhi.

Chapterwise NCERT Solutions for Class 10 Maths:

NCERT Class 10 Maths Chapters and Exercises

Chapter 1 – Real Numbers

Topics Covered:

Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of the irrationality of 2, 3, 5 Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

Chapter 2 – Polynomials

Topics Covered:

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithms for polynomials with real coefficients.

Chapter 3 – Pair of Linear Equations in Two Variables

Topics Covered:

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for the number of solutions. The solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

Topics Covered:

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization; and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

Chapter 5 – Arithmetic Progressions

Topics Covered:

The motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

Chapter 6 – Triangles

Topics Covered:

Definitions, examples, counter-examples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

Chapter 7 – Coordinate Geometry

Topics Covered:

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

Chapter 8 – Introduction to Trigonometry

Topics Covered:

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios. Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

Chapter 9 – Some Applications of Trigonometry

Topics Covered:

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, 60°.

Chapter 10 – Circles

Topics Covered:

Tangent to a circle at, point of contact.

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

Chapter 11 – Constructions

Topics Covered:

1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

Chapter 12 – Areas Related to Circles

Topics Covered:

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)

Chapter 13 – Surface Areas and Volumes

Topics Covered:

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids are taken).

Chapter 14 – Statistics

Topic Covered:

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

Chapter 15 – Probability

Topic Covered:

The classical definition of probability. Simple problems on finding the probability of an event.

Here we have list of common Frequently Asked Questions (FAQs) commonly asked regularly by students as well as their parents.

Why NCERT solutions for class 10 maths are important?

The Class 10 Maths NCERT Solutions are designed in an innovative way so that every student can quickly understand the concept into their minds and clarifies all their doubts within a few seconds. Also, students can assess their learning abilities with the solutions of NCERT Maths for their Class 10 board exam preparation.

The NCERT Solutions for Class 10 Maths can be found online on IndCareer’s School section. It can also be downloaded in PDF format. The detailed answers for all the questions present in the NCERT textbook of Class 10 Maths are solved by subject experts, as per the NCERT guidelines.

Which book is best for Class 10 maths?

NCERT Textbooks are the best ones available in the market for students. Also, as per the survey conducted by educational analysts, around 78% of CBSE Class 10 students prefers NCERT Textbook solutions for their maths exams.

How many chapters are present in NCERT Class 10 Maths?

A total of 15 chapters are present in the NCERT Class 10 Maths. Chapter 1- Real Numbers, Chapter 2- Polynomials, Chapter 3- Pair of Linear Equations in Two Variables, Chapter 4- Quadratic Equations, Chapter 5- Arithmetic Progressions, Chapter 6- Triangles, Chapter 7- Coordinate Geometry, Chapter 8- Introduction to Trigonometry, Chapter 9- Some Applications of Trigonometry, Chapter 10- Circles, Chapter 11- Constructions, Chapter 12- Areas Related to Circles, Chapter 13- Surface Areas and Volumes, Chapter 14- Statistics, Chapter 15- Probability are the Chapters in Class 10 Maths NCERT.

Which is the toughest chapter in class 10 maths?

chapter that most of the students find difficult in class 10 maths is trigonometry. Trigonometry is an interesting topic, you will start finding it interesting once you start understanding the basic concepts. But as we know maths can be mastered with enough practice. If you keep practicing, you will be able to solve any maths question easily.