NCERT Solutions for Class 10th Mathematics

NCERT Solutions for Class 10 Maths from chapters 1 to 15 are provided on this page. Answers to all exercises are provided in detail. These solutions are provided by expert teachers at IndCareer.

Mathematics is a crucial subject for students in Class 10, as it lays the foundation for their future academic and professional pursuits. 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.

NCERT Class 10 Maths Chapters and Exercises

Chapterwise NCERT Solutions for Class 10 Maths:

• NCERT Solutions for Chapter 1 – Real Numbers
• NCERT Solutions for Chapter 2 – Polynomials
• NCERT Solutions for Chapter 3 – Pair of Linear Equations in Two Variables
• NCERT Solutions for Chapter 4 – Quadratic Equations
• NCERT Solutions for Chapter 5 – Arithmetic Progressions
• NCERT Solutions for Chapter 6 – Triangles
• NCERT Solutions for Chapter 7 – Coordinate Geometry
• NCERT Solutions for Chapter 8 – Introduction to Trigonometry
• NCERT Solutions for Chapter 9 – Some Applications of Trigonometry
• NCERT Solutions for Chapter 10 – Circles
• NCERT Solutions for Chapter 11 – Constructions
• NCERT Solutions for Chapter 12 – Areas Related to Circles
• NCERT Solutions for Chapter 13 – Surface Areas and Volumes
• NCERT Solutions for Chapter 14 – Statistics
• NCERT Solutions for Chapter 15 – Probability

NCERT Class 10 Maths Chapters

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. 

Chapter 4 – Quadratic 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: 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 0^o and 90^o. 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

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

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

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

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

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

Chapter 15 – Probability

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

Tips for Effective Use of NCERT Solutions

Utilizing NCERT Solutions effectively can significantly enhance a student’s understanding of Mathematics and improve their performance in exams. Here are some practical tips to make the most out of these resources:

Integrating Solutions into Study Routine

1. Daily Practice: Incorporate NCERT Solutions into your daily study schedule. Dedicate specific time slots for practicing problems from each chapter to reinforce learning.
2. Chapter-wise Approach: Focus on one chapter at a time. Read the corresponding NCERT textbook chapter, then attempt the exercises before referring to the solutions for any doubts.
3. Set Goals: Establish clear study goals for each session, such as completing a certain number of problems or mastering a specific concept. This structured approach helps maintain focus and motivation.

Practicing Beyond Solutions

1. Attempt Without Looking: Try solving problems without immediately referring to the solutions. This practice enhances problem-solving skills and builds confidence.
2. Use Varied Resources: While NCERT Solutions are comprehensive, supplement your practice with additional problems from reference books or online resources to gain exposure to different question types.
3. Mock Tests: Regularly take mock tests using NCERT-style questions to simulate exam conditions. This helps in time management and familiarizes you with the exam format.

Utilizing Solutions for Revision

1. Identify Weak Areas: Use NCERT Solutions to pinpoint concepts you struggle with. Focus your revision on these areas to ensure a well-rounded understanding.
2. Summarize Key Concepts: After solving problems, summarize the key formulas and concepts in a separate notebook. This will serve as a quick reference during revision.
3. Group Study: Engage in group study sessions where you can discuss solutions and clarify doubts with peers. Teaching others is an effective way to reinforce your understanding.
4. Regular Revision: Schedule regular revision sessions using NCERT Solutions before exams. This will help consolidate your knowledge and improve retention.

By effectively integrating NCERT Solutions into your study routine, practising beyond the provided solutions, and utilizing them for revision, you can enhance your understanding of Mathematics and perform better in examinations.

Frequently Asked Questions (FAQs)

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

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