NCERT Solutions For Class 10 Maths 2023 For Term 1 & Term 2: NCERT Solutions for Class 10 Maths are available here for all exercises from Chapters 1 to 15. Our expert faculty has prepared these NCERT Solutions to assist students in their Class 10 Board Exam preparations. Students looking for NCERT Solutions for Class 10 Maths can download complete chapter-wise PDFs from this article to help them solve problems more effectively.
Download Chapter-Wise NCERT Solutions for Class 10 Maths 2023 For Term 1 & Term 2
To practice the NCERT Class 10 Maths Solution for each chapter, simply click on the specific chapter links provided below.
- Class 10 Maths NCERT Solutions Chapter 1 Real Numbers
- Class 10 Maths NCERT Solutions Chapter 2 Polynomials
- Class 10 Maths NCERT Solutions Chapter 3 Pair of Linear Equations in Two Variables
- Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations
- Class 10 Maths NCERT Solutions Chapter 5 Arithmetic Progressions
- Class 10 Maths NCERT Solutions Chapter 6 Triangles
- Class 10 Maths NCERT Solutions Chapter 7 Coordinate Geometry
- Class 10 Maths NCERT Solutions Chapter 8 Introduction to Trigonometry
- Class 10 Maths NCERT Solutions Chapter 9 Some Applications of Trigonometry
- Class 10 Maths NCERT Solutions Chapter 10 Circles
- Class 10 Maths NCERT Solutions Chapter 11 Constructions
- Class 10 Maths NCERT Solutions Chapter 12 Areas Related to Circles
- Class 10 Maths NCERT Solutions Chapter 13 Surface Areas and Volumes
- Class 10 Maths NCERT Solutions Chapter 14 Statistics
- Class 10 Maths NCERT Solutions Chapter 15 Probability
These NCERT Solutions for Class 10 Maths 2023 will also assist students in gaining a better understanding of the concepts covered in the Textbook for Class 10 Maths.
NCERT Solutions For Class 10 Maths: Chapter-Wise Descriptions
Let us have a look at what each of the chapters in the NCERT Syllabus of Class 10 Maths deals with:
NCERT Solutions For Class 10 Maths Chapter 1: Real Numbers- Term 1
Here you will see four exercises based on the different topics of the chapter related to,
- Euclid’s Division Lemma,
- The Fundamental Theorem of Arithmetic,
- Revisiting Irrational Numbers,
- Revisiting Rational Numbers and Their Decimal Expansions.
Topics Covered in Class 10 Maths Chapter 1 Real Numbers for Term I:
- Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples.
- The decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.
NCERT Solutions For Class 10 Maths Chapter 2: Polynomials-Term 1
You will get four exercises with the last exercise as an optional one in this chapter. You have already learned the basics of polynomials in Class 9. This is the continuation of that topic.
In Class 9, you have already studied the introduction of the chapter briefs polynomials with one variable and their degrees.
Here you will learn more about,
- Linear polynomials,
- Quadratic polynomials,
- Cubic polynomial,
- Geometrical meaning of the zeroes of a polynomial,
- The relationship between zeroes and coefficients of a polynomial,
- Division algorithm for polynomials.
Topics Covered in Class 10 Maths Chapter 2 Polynomials for Term I:
- Zeroes of a polynomial.
- Relationship between zeroes and coefficients of quadratic polynomials only.
NCERT Solutions For Class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables- Term 1
In Maths Chapter 3, you will see seven exercises with the last exercise being optional.
Topics Covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables for Term I:
- Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.
- Algebraic conditions for a number of solutions.
- Solution of a pair of linear equations in two variables algebraically – by substitution and by elimination.
- Simple situational problems.
- Simple problems on equations are reducible to linear equations.
You will know to solve the pair of linear equations by graphical method (which will be solved on graph sheets) and algebraic methods (using the three methods mentioned above).
You have to solve the equations which are reducible to a pair of linear equations. You will get plenty of examples and exercise questions.
NCERT Solutions For Class 10 Maths Chapter 4: Quadratic Equations- Term 2
Quadratic Equation is one of the essential chapters in the syllabus of the CBSE Class 10 syllabus for Maths. It has four exercises. Here, you can build a depth concept on the standard form of the quadratic equation with the help of examples.
Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations for Term II:
- The 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 (problems on equations reducible to quadratic equations are excluded)
NCERT Solutions For Class 10 Maths Chapter 5: Arithmetic Progressions- Term 2
An Arithmetic Progression (AP) is a sequence of numbers, and each term is obtained by adding a fixed number to the preceding term except the first term.
Here In this chapter, you will come to know,
- Basics of AP,
- Common difference,
- Finite and infinite AP,
- the nth term of an AP,
- The sum of the first n terms of an AP, etc.
The chapter has four exercises with an optional last exercise. Also, you will see a number of examples of problems with detailed solutions to clear your concepts in this chapter.
Topics Covered in Class 10 Maths Chapter 5 Arithmetic Progressions for Term II:
- 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 (Applications based on a sum to n terms of an A.P. are excluded)
NCERT Solutions For Class 10 Maths Chapter 6: Triangles- Term 1
You will see six exercises with one being optional. You have already studied the congruence of triangles that were discussed in Class 9. Here you will know about similar triangles with several theorems, proofs, and problems.
Topics Covered in Class 10 Maths Chapter 6 Triangles for Term I:
Definitions, examples, and counterexamples 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. (Motivate) 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. (Motivate) 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.
NCERT Solutions For Class 10 Maths Chapter 7: Coordinate Geometry- Term 1
You will find four exercises in Coordinate Geometry Chapter. In this chapter, you will know
- How to find the distance between two points whose coordinates are given,
- How to find the area of the triangle formed by three given points.
Topics Covered in Class 10 Maths Chapter 7 Coordinate Geometry for Term I:
- LINES (In two dimensions)
- Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division)
NCERT Solutions For Class 10 Maths Chapter 8: Introduction To Trigonometry- Term 1
Trigonometry is a very important chapter. If you clear your concept in this chapter, it will be very helpful for future higher grades.
- The chapter has a total of 4 exercises and example problems. The discussion starts with trigonometric ratios where you study sine, cosine, tangent, cosecant, secant, and cotangent.
- You will also learn the trigonometric ratios of complementary angles and trigonometric identities. You need to solve plenty of problems to build a better understanding of the chapter.
Topics Covered in Class 10 Maths Chapter 8 Introduction to Trigonometry for Term I:
- Trigonometric ratios of an acute angle of a right-angled triangle.
- Proof of their existence (well defined). Values of the trigonometric ratios of 300, 450, and 600.
- Relationships between the ratios.
NCERT Solutions For Class 10 Maths Chapter 9: Some Applications Of Trigonometry- Term 2
In this chapter, you will learn about some applications of trigonometry. You will learn to implement trigonometry and solve real-life problems.
You will see that the chapter has only one exercise. All the questions are based on real-life applications of trigonometry.
Topics Covered in Class 10 Maths Chapter 9 Some Applications of Trigonometry for Term II:
- HEIGHTS AND DISTANCES-Angle of elevation, Angle of Depression.
- Simple problems with heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, and 60°
NCERT Solutions For Class 10 Maths Chapter 10: Circles- Term 2
You have already studied the basic definition and other fundamentals of circles in the previous class. The chapter has two theorems and two exercises. Here you will learn mainly about the tangent to a circle and the number of tangents from a point on a circle.
Topics Covered in Class 10 Maths Chapter 10 Circles for Term II:
Tangent to a circle at, the 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.
NCERT Solutions For Class 10 Maths Chapter 11: Constructions- Term 2
In this chapter, you will learn a few more constructions using your past knowledge of the basic constructions.
Topics Covered in Class 10 Maths Chapter 11 Constructions for Term II:
1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
You will have a better knowledge of using geometrical instruments.
NCERT Solutions For Class 10 Maths Chapter 12: Areas Related To Circles- Term 1
Maths Chapter 12 Area Related to Circles is about finding the areas of the sector, a segment of a circle, and areas of a combination of plane figures.
Topics Covered in Class 10 Maths Chapter 12 Areas Related to Circles for Term I:
- Motivate the area of a circle; the area of sectors and segments of a circle.
- Problems based on areas and perimeter/circumference of the plane figures. (In calculating the area of a segment of a circle, problems should be restricted to a central angle of 60° and 90° only. Plane figures involving triangles, simple quadrilaterals, and circles should be taken.)
NCERT Solutions For Class 10 Maths Chapter 13: Surface Areas And Volumes- Term 2
In this chapter, you will study surface areas and volumes of combinations of solids. It is a continuation of the discussion in Class 9 on cuboids, cones, cylinders, and spheres.
Topics Covered in Class 10 Maths Chapter 13 Surface Areas and Volumes for Term II:
1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.
2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with a combination of not more than two different solids be taken).
You will learn the concept of Frustum of a cone is discussed. A total of five exercises are there in this chapter, where the last one is optional.
NCERT Solutions For Class 10 Maths Chapter 14: Statistics- Term 2
In this chapter, you will see four exercises with more arithmetic calculations.
Topics Covered in Class 10 Maths Chapter 14 Statistics for Term II:
- Mean, median, and mode of grouped data (bimodal situation to be avoided).
- Mean by Direct Method and Assumed Mean Method only.
NCERT Solutions For Class 10 Maths Chapter 15: Probability- Term 1
Here you will know the study and calculation of the probability of occurrence of an event very common in our daily life.
Topics Covered in Class 10 Maths Chapter 15 Probability for Term I:
- The classical definition of probability.
- Simple problems in finding the probability of an event.
By studying this chapter, you will know the mathematical approach to understanding probability related to real life.
Why Choose Kopykitab Class 10 Maths NCERT Solutions?
By choosing the NCERT Class 10 Maths Solution from Kopykitab, you will get tremendous benefits. Some of the benefits are as given below:
- This page contains a free PDF of NCERT Solutions for Class 10 Maths.
- The solutions provided here are very simple and easy to understand.
- The NCERT (CBSE) Syllabus and Books are used to solve the questions. As a result, knowing these answers will undoubtedly support students in achieving good exam results.
- Time and money-saving
- Get a thorough concept in every solution
We have covered a detailed guide on NCERT Solutions for CBSE Class 10 Maths. Feel free to ask any questions in the comment section below.
Frequently Asked Questions on NCERT Solutions for Class 10 Maths 2023 For Term 1 & Term 2
Will the NCERT Class 10 Maths Solutions help me to solve problems easily?
The Class 10 exam is one of the most important stages in a student’s life. Mathematics is a topic that focuses on numerical and conceptual comprehension, which aids in the achievement of higher grades. For better performance, students should first comprehend the academic year’s syllabus and then learn the topics based on it. Students’ logical thinking and analytical skills will develop as they solve textbook problems using the solutions PDF.
Where will I get the NCERT Maths Class 10 Solutions PDF?
You can get the NCERT Maths Class 10 Solutions PDF from the above article.
How do I solve Class 10 Mathematics problems easily?
You can solve any type of problem in the final board examination if you prepare the latest CBSE Class 10 Maths Syllabus with the help of NCERT Solutions Pdf for Maths.