NCERT Solutions for Class 10 Maths – Free Download

NCERT Solutions for Class 10 Maths Updated for 2022-23 Session – Free PDF Download

NCERT solutions for class 10 maths provides students with the necessary tools to approach and solve mathematical problems in an effective and efficient manner. The solutions are designed to help students understand the concepts and principles underlying the various mathematical operations and to develop the skills required to perform these operations fluently. In addition, the solutions also provide students with practice in using the various methods and techniques for solving mathematical problems.

NCERT solutions class 10 maths is a great resource for students who want to ace their board exams. The solutions are easy to follow and are written in a step-by-step manner. Additionally, the solutions are available for free online. Hence, students can save a lot of time and money by opting for this resource.

NCERT Solutions for Class 10 Maths are available at Infinity Learn for all tasks from Chapters 1 to 15. Our professional faculty has curated these NCERT Solutions to aid students in their term-by-term exam preparation. Students looking for NCERT Solutions for Class 10 Maths can download complete chapter-by-chapter PDFs to help them solve questions more effectively.

The answers to the questions in NCERT books are, without a doubt, the best study material available to students.

Students can assess their degree of preparation and subject comprehension by practising textbook questions. The answers to these questions in the books can assist students in quickly resolving their difficulties.

Class 10 Math Chapters:

• 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

NCERT Solutions for Class 10 Maths Free PDF Download

Students can use NCERT Solutions for Class 10 as references and study aids. Students would benefit from practising the NCERT textbook exercise solutions in preparation for tests.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers – Term I

Students will investigate real and irrational numbers in Chapter 1 of Class 10. The chapter begins with Euclid’s Division Lemma, which claims that “there exist unique integers q and r satisfying

a=bq+r,0≤r<ba=bq+r,0≤r<b

Using the Fundamental Theorem of Arithmetic, we can calculate the LCM and HCF of two positive integers.

Topics discussed in this chapter:

After reviewing previous work and showing and inspiring through examples, the Fundamental Theorem of Arithmetic is stated. The decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

Steps to Take –

Follow the methods below to find the HCF of two positive integers, say c and d, with c > d:

• Step 1: To c and d, use Euclid’s division lemma. As a result, we need to find two whole numbers, q and r, such that c=dq+r,0≤r<d.c=dq+r,0≤r<d.
• Step 2: If r = 0 and c and d have the same HCF, then d is the HCF of c and d. If r≠0,r≠0, 4 divided and r using the division lemma.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials – Term I

The chapter on polynomials begins with the definitions of degree, linear polynomial, quadratic polynomial, and cubic polynomial. There are four exercises in this chapter, one of which is optional. Questions about finding the number of zeroes using a graph are included in Exercise 2.1. It necessitates an understanding of the Geometrical Meaning of a Polynomial’s Zeroes. Students must discover the zeros of a quadratic polynomial and the quadratic polynomial in some of the questions in Exercise 2.2, based on the Relationship between Zeroes and Coefficients of a Polynomial. The concept of the division algorithm is defined in Exercise 2.3, and students will find questions connected to it. The optional exercise 2.4 has questions from all of Chapter 2’s ideas.

The following are the topics covered in this chapter:

A polynomial’s zeros. Only the zeroes and coefficients of quadratic polynomials have a relationship.

Here again, we see that Dividend = Divisor × Quotient + Remainder. We’re using a method comparable to Euclid’s division algorithm, which you learned about in Chapter 1.

If p(x) and g(x) are any two polynomials with g(x)≠0,g(x)≠0,

we can find polynomials q(x) and r(x) such that p(x)=g(x)×q(x)+r(x),p(x)=g(x)×q(x)+r(x),

where r(x) = 0 or degree of r(x) < degree of g(x).

The Division Algorithm for Polynomials is the name given to this result.

The Exercises discussed in this chapter are:

NCERT Solutions of Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables – Term I

The concept of a Pair of Linear Equations in Two Variables is explained in this chapter. This chapter has seven tasks, each describing a different approach to solving the pair of linear equations. Exercise 3.1 shows how to algebraically and graphically depict a scenario. Exercise 3.2 illustrates how to use the Graphical Method to solve a pair of linear equations. The Algebraic, Elimination, Cross-Multiplication, and Substitution Method are described in Exercises 3.3, 3.4, 3.5, and 3.6. Exercise 3.7 is a free-form exercise with a variety of questions. To grasp solving linear equations, students must practice these activities.

Consistency/inconsistency of a pair of linear equations in two variables and the graphical method of solving them. The number of solutions to algebraic conditions By substitution and elimination, a pair of linear equations in two variables can be solved algebraically. Situational issues are easy to solve. Simple equations that can be reduced to linear equations.

Important formula:

A pair of linear equations in two variables, x, and y, has a universal form.

a1x+b1y+c1=0 and a2x+b2y+c2=0,a1x+b1y+c1=0 and a2x+b2y+c2=0,

where

a1,b1,c1,a2,b2,c2a1,b1,c1,a2,b2,c2 are all real values and a12+b12≠0 and a22+b22≠0a12+b12≠0 and a22+b22≠0 are both true.

NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations – Term II

Students will learn how to write a quadratic equation in its standard form in this chapter. The chapter covers the factorization approach and the completing square method for solving quadratic equations. The chapter concludes with the topic of identifying the nature of roots, which asserts that a quadratic equation

ax2+bx+c=0ax2+bx+c=0 has a

• Two distinct real roots, If b2−4ac>0b2−4ac>0
• Two equal roots, If b2−4ac=0b2−4ac=0
• No actual roots, If b2−4ac<0b2−4ac<0

A quadratic equation in standard form is [Equation]Factorization, and the quadratic formula is used to solve quadratic equations with only real roots. The discriminant and the nature of the roots have a relationship. Situational situations involving quadratic equations that are relevant to day-to-day operations (problems on equations reducible to quadratic equations are excluded)

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions – Term II

This chapter introduces students to a new Arithmetic Progression (A.P.) concept. There are four exercises in this chapter. Students will find questions relating to describing a scenario in the form of A.P., determining the first term and difference of an A.P., and determining whether or not a series is A.P. in Exercise 5.1.

In Exercise 5.2, you’ll discover questions about calculating an A.P.’s nth term using the formula below.

an=a+(n−1)dan=a+(n−1)d

Higher-level questions based on A.P. are included in the final exercise to help students improve their analytical and problem-solving skills.

Studying Arithmetic Progression is motivated by a variety of factors. The nth term and the sum of the first n terms of A.P. are deduced and used to solve everyday problems.

(Applications based on an A.P.’s sum to n terms are not accepted.)

NCERT Solutions for Class 10 Maths Chapter 6 Triangles – Term I

The concept of a similar and congruent figure is introduced in the first chapter of Triangles. It describes the criteria for the similarity of two triangles and theorems about triangle similarity. The Pythagoras Theorem and the converse of Pythagoras’ Theorem are discussed at the end of this chapter.

The topics covered in this chapter are as follows:

Similar triangle definitions, examples, and counterexamples.

1. (Motivate) A line is parallel to the third side of a triangle if it divides two sides of the triangle in the same ratio.
2. (Motivate) If the corresponding angles in two triangles are equal, their corresponding sides are proportionate, and the triangles are similar, the triangles are similar.
3. (Motivate) Two triangles are comparable if their corresponding sides are proportionate, their complementary angles are equal, and their corresponding angles are equal.
4. (Motivate) Two triangles are comparable if one of their angles is equal and the sides that include these angles are proportionate.
5. (Motivate) The ratio of the squares of two comparable triangles’ corresponding sides equals the ratio of their areas.
6. (Prove) The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
7. (Motivate) In a triangle, the angle opposite the first side is right if the square on one side equals the sum of the squares on the other two sides.

The exercises that are included in this chapter are as follows:

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry – Term I

In this chapter, students will learn how to calculate the distance between two locations whose coordinates are supplied and the area of a triangle formed by three specified points. This chapter of Coordinate Geometry will expose students to the Distance Formula, Section Formula, and Area of a Triangle.

Topics covered in this chapter are:

• List of lines (In two dimensions)
• Concepts of coordinate geometry and graphs of linear equations are reviewed.
• The formula for calculating distance.
• The formula for the section (internal division)

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry – Term I

Students will learn about trigonometry in this chapter. They’ll look at trigonometric ratios of the angles, which are the ratios of a right triangle with respect to its sharp angles. The trigonometric ratios for angles of [Equation]are also defined in this chapter.

• Trigonometric ratios of a right-angled triangle’s acute angle. Their existence has been proven (well-defined).
• The trigonometric ratios of [Equation]have different values: the ratios and their relationships.
• Trigonometric Identities
• The identity [Equation]sin2A + cos2A = 1 is proved and applied. Only simple identifiers will be provided.

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry – Term II

The students will learn the applications of trigonometry in this chapter, which is a continuation of the previous chapter. It’s used in geography, navigation, mapmaking, and figuring out where an island is about longitudes and latitudes. In this chapter, students will learn how to use trigonometry to calculate the heights and distances of various objects without measuring them. They’ll learn about the line of sight, angle of elevation, and angle of depression.

Important topics:

Heights And Distances —Angle of Elevation and Angle of Depression

Simple height and distance problems. Only 30°, 45°, and 60° of elevation/depression should be used.

Important concepts:

• The line of sight is drawn from an observer’s eye to a point in the observed thing.

Exercises covered in this chapter:

☞9.1 class 10 – 16 Questions (16 Long Answers)

NCERT Solutions for Class 10 Maths Chapter 10 Circles – Term II

Important topics covered in this chapter:

At the point of contact, tangent to a circle

1. (Prove) The tangent of a circle at any point is perpendicular to the radius through the point of contact.
2. (Demonstrate) that tangents drawn from an exterior point to a circle have the same length.

Important theorems:

The tangent at any point on a circle is perpendicular to the radius through the point of contact, according to Theorem 10.1.

The lengths of tangents taken from an external point to a circle are equal, according to Theorem 10.2.

Exercises covered in this chapter:

NCERT Solutions for Class 10 Maths Chapter 11 Constructions – Term II

There are a total of two exercises in this chapter. Everything students have learned about construction in previous sessions will come in handy. Students will learn how to divide a line segment in Exercise 11.1. They will learn how to construct tangents to a circle in Exercise 11.2. The methods and stages for construction are described, and some examples are to help the students understand.

Topics covered in this chapter:

1. A ratio-based division of a line segment (internally).
2. A tangent to a circle is a line drawn from a point outside.

Important concepts:

• 11.1: To divide a line segment in a specified ratio.
• 11.2: Construct a triangle similar to a given triangle using the supplied scale factor.
• 11.3: Construct the tangents into a circle from a location outside it.

Exercises covered in this chapter:

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles – Term I

The perimeter and area of a circle are introduced in this chapter. Using this notion, the chapter describes how to calculate the area of a circular region’s sector and segment.

Important topics:

Encourage students to think about the area of a circle and the area of its sectors and segments. Areas, perimeters, and circumferences of the above-mentioned planar figures are used to solve problems. (Problems with estimating the area of a circle segment should be limited to central angles of 60° and 90° only.) Triangles, simple quadrilaterals, and circles should be drawn on the plane.)

Important formulas:

• circumference [Equation]
• area of the circle = [Equation]
• Area of the sector of angle [Equation][Equation]
• Length of an arc of a sector of angle[Equation][Equation]where r is the radius of the circle

Exercises covered in his chapter:

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes – Term II

There are a total of 5 exercises in Chapter 13. Exercise 13.2 shows the volume of objects generated by joining any two of a cuboid, cone, cylinder, sphere, and hemisphere. The volume, curved surface area, and total surface area of a frustum of a cone are all determined in Exercise 13.4. The final exercise is optional and contains high-level questions based on the chapter’s subjects.

Important topics:

1. Surface areas and volumes of cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones are made of any two.

Important formulas:

TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemispheres

• Diameter of the sphere [Equation]
• The surface area of the sphere [Equation]
• The volume of Sphere [Equation]
• The curved surface area of the Cylinder [Equation]
• Area of two circular bases [Equation]
• The total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder [Equation]
• The volume of the Cylinder[Equation]
• The slant height of the cone [Equation]
• The curved surface area of the cone[Equation]
• The total surface area of the cone [Equation]
• The volume of the cone[Equation]
• The perimeter of cuboid [Equation]
• Length of the longest diagonal of a cuboid [Equation]

Total surface area of cuboid = 2(l×b + b×h + l×h)

Volume of Cuboid = l × b × h

Exercises covered in this chapter:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics – Term II

Students will learn how to convert ungrouped data to grouped data and calculate the Mean, Mode, and Median.

Topics covered in this chapter:

The mode, mean, and median of grouped data (bimodal situation to be avoided). Only the Direct and the Assumed Mean methods are used to calculate the mean.

Exercises covered in this chapter:

NCERT Solutions for Class 10 Maths Chapter 15 Probability – Term I

Probability is the subject of the final chapter. The chapter begins with a discussion of probability theory. There are several instances presented to describe it effectively.

Important topics:

Probability is defined traditionally. Finding the likelihood of an event is a simple problem.

Exercises covered:

Chapter-wise Marks Weightage of Class 10 Maths for CBSE First Term

Chapter-wise Marks Weightage for CBSE Class 10 Maths Second Term

Key Features:

• Assist students in addressing difficulties using concepts.
• Encourages children to come up with a variety of problem-solving solutions.
• For some questions that are difficult to answer, hints are provided.
• Aids pupils in determining whether or not the answers they provided for the questions are correct.

How are NCERT Solutions for CBSE Class 10 Maths Useful for Term Exams?

Math is an important subject in CBSE Class 10 for students. We have provided total aid to students in preparation for this exam. Class 10 is the first benchmark reflected in the future academic records for any kid. For term-by-term test preparation, CBSE always recommends NCERT books.

Exam preparation is a time-consuming procedure requiring a thorough comprehension of each chapter. This procedure necessitates diligent study and a methodical approach to solving the problems. NCERT 10 Class Maths Solutions are crucial to preparing students for competitive entrance exams. NCERT books are known for their clarity and understanding of concepts. The NCERT Class 10 Mathematics Books are prepared transparently and clearly, facilitating the effective breakdown of complex subjects.

Continue to visit this page for comprehensive chapter-by-chapter NCERT Solutions for Class 10 Maths PDF free download for all courses. Students can use the Maths Solver App to receive a more tailored learning experience and better prepare for exams.

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