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NCERT Solutions for Class 10 Maths (2023-24)

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Last updated date: 26th Feb 2024
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IVSAT 2024

NCERT Solutions for Class 10 Maths - Free PDF Download All Chapters

NCERT Solutions for Class 10 Maths serve as a valuable resource for students navigating the complexities of mathematics at the 10th-grade level. These solutions are specifically designed to complement the NCERT class 10 Maths book, offering clear explanations and step-by-step solutions to problems. The aim is to make mathematical concepts more accessible and understandable for students. The Class 10 Maths NCERT solutions cover a wide range of topics, including algebra, geometry, trigonometry, statistics, and more. Students can rely on these solutions to reinforce their understanding of fundamental mathematical principles and enhance problem-solving skills. One notable advantage of NCERT Solutions Class 10 Maths is their alignment with the curriculum prescribed by the Central Board of Secondary Education (CBSE). This ensures that students are well-prepared for their board exams, as the solutions closely follow the CBSE class 10th maths guidelines and exam patterns.


NCERT Solutions for Class 10 Maths - Chapter 1 to 15 with Exercises image


Class 10 Maths syllabus aims at helping the students build a strong base of these topics by giving them the basic knowledge about them, making them understand theorems and concepts and testing them enough in the form of exercise and examples in the textbook. The exercises in the NCERT textbook are designed for the students to use their skills and learnings of each topic to the maximum. Before each exercise, the students are also given enough examples to refer to and understand the questions with the help of the step by step explanations provided in the textbooks.


👉 Please check here for  Crash Course for Class 10 CBSE

NCERT Solutions for Class 10 Maths | Chapter-Wise List

Given below are the chapter-wise NCERT Solutions for Class 10 Maths. These solutions are provided by the Maths experts at Vedantu in a detailed manner. You can use it as your 10th maths guide. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.




NCERT Solutions for Class 10 Maths provided here covers all the chapters and Exercises of Class 10 Maths. These solutions are prepared by expert teachers who are having years of experience in teaching Maths for Class 10 students. Class 10 Maths NCERT Solutions are explained in step by step manner and available in PDF format. Students can now download the class 10 Maths NCERT solutions PDFs for an uninterrupted learning experience.

 

The Class 10 Maths NCERT Solution PDFs cover all the Exercises from Chapters 1 - 15 present in the NCERT books. These Class 10 Maths solutions are written according to the CBSE exam guidelines to increase the students understanding of the subject and help them to score well. The NCERT solutions for class 10 Mathematics PDFs will not only prepare the students for final exams but will also help to understand the concept better as a 10th Maths guide. Science and Maths are two important subjects of class 10 and if you are looking for reliable and accurate NCERT Solutions for Class 10 Science you will find that on Vedantu.


Detailed Overview of Class 10 Maths NCERT Solutions

Class:

NCERT Solutions for Class 10

Subject:

Class 10 Maths

Number of Chapters:

15

Content Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

Chapter Wise

Other Materials

  • Important Questions

  • Revision Notes


Competitive Exams after 12th Science

NCERT Solutions for Class 10 Maths PDF Updated for 2023-24 Session

NCERT Maths solution pdfs for Class 10 is a very reliable and accurate source of information. The study material contains an exhaustive explanation to all the questions. These answers are written clearly and step by step to maximise retention. While going through these solutions, students will find themselves understanding the concept better. Practising regularly is a prerequisite if students want to score well in mathematics. NCERT solutions Class 10th act as a perfect guide for you. You can consult the class 10th maths guide to brush up on your memory or help you if you get stuck somewhere.

 

The solutions provided by Vedantu are formulated and designed by professionals who have years of experience in the field of teaching. The answers are given in simple language for the students to understand the concept better. Vedantu aims at providing solutions for each question which is easy for students of different calibre to understand. All the syllabus and solutions are updated in accordance with the changes to the NCERT textbook or the syllabus guidelines given by the CBSE. Vedantu is the leading online platform providing answers for all the solutions for each and every subject and class. Helping students understand a subject and enjoy learning new things is what Vedantu strives for. Hence, the comfort and ease of the students are foremost when developing solutions for the questions. The solutions come in handy if the students get stuck or need to understand what they are doing wrong. It is a good way for the students to analyse their answers and performance and also get more practice by referring to the extra questions in the solutions pdf. 

 

NCERT Solutions for Class 10 Maths Chapter 1 - Real Numbers

There are 4 Exercises present in this chapter. Students will learn about real numbers and irrational numbers in the 1st chapter of Class 10 Maths. CBSE Class 10 Maths Chapter 1 explains Euclid’s Division Lemma, HCF, LCM, Divisibility of integers, rational number, irrational number and decimal expansion of rational numbers with the help of theorem.

 

Euclid’s Division Lemma states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤r <b”. This gives the base for the division algorithm which is used to take out the HCF for two positive integers. The Fundamental Theorem of Arithmetic is also explained in this chapter. It explains how the LCM and HCF for two positive integers can be derived.

 


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 10 Maths Solutions –


NCERT Solution for Class 10 Mathematics Chapter 2 - Polynomials

There are a total of 4 Exercises including an optional Exercise in the 2nd chapter of class 10 Maths. The first Exercise is about finding zeros of polynomials p(x). In the second Exercise, the students need to find a quadratic polynomial. The second Exercise is based on the relationship between 0’s and coefficients of a polynomial. The third Exercise has questions on the division of polynomials. The last Exercise covers questions from all the concepts of Class 10 Maths Chapter 2.

 

The students should also know the steps to derive the Division Algorithm for polynomials. It can be asked in the exam as it is an important concept in the chapter that has been explained.

 


 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

The third chapter of class 10 maths is about the linear equations in two variables. It describes what a linear equation in two variables is and how to solve the problems of linear equations in two variables. In the first Exercise (Ex 3.1), representing a problem or situation algebraically and graphically is taught. The second Exercise, i.e, Ex 3.2, depicts the methods of solving linear equations by graphical method. The next four Exercises, Ex 3.3, 3.4, 3.5 and 3.6 explain the different types of methods of solving the pairs of linear equations. The methods explained here are algebraic method, cross-multiplication method, elimination method and substitution method. Exercise 3.7 is a mixed bag. It contains questions from all the Exercises.


Important Formulas:

The general form for a pair of linear equations in two variables, x and y, is

$a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$

Where,
$a_1, b_1, c_1, a_2, b_2, c_2$ - real numbers 

Here $a_1^2 + b_1^2 \neq 0$ and $a_2^2 + b_2^2 \neq 0$ 



Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Maths Chapter 4 - Quadratic Equations

Chapter 4 of Class 10 Maths NCERT book PDF solution is all about quadratic equations. This chapter explains what a quadratic equation is and the methods of solving quadratic equations. It also explains the factorization method of solving quadratic equations and the square method. The chapter gives the details of relationships between discriminants and the nature of roots. Also, the problems of real-life have been solved as examples in this chapter.

 

Important formulas for the students to keep in mind:

If b2 - 4ac > 0, then the answer obtained should be two distinct real roots. 

If b2 - 4ac = 0, then the roots of the equation ax2 + bx + c = 0 should be -b/2a

It can be said in this case then that the equation ax2 + bx + c = 0 has two equal roots.

If b2 – 4ac < 0, then there is no real number whose square is b2 – 4ac. Hence, there are no real roots for the given quadratic equation in this case.

b2 – 4ac is called the discriminant of this quadratic equation since, b2 – 4ac determines whether the quadratic equation ax2 + bx + c = 0 has real roots or not



 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 10 Maths Solutions –

NCERT Solutions for Class 10 Mathematics Chapter 5 - Arithmetic Progressions

This chapter introduces a new topic to the students - Arithmetic Progression, commonly called AP. Students will learn what is AP, the derivation of the nth term, finding the sum of first n terms of the AP and solving the real-life problems using AP in this chapter. The first Exercise of the chapter teaches how to represent a problem or situation in the form of AP, how to find the first term and difference of the AP and to find whether the given series is AP or not. The next Exercise, Ex 5.2 explains how to find the nth term of the AP using the formula. The third Exercise describes how to find the sum of the first n terms of AP and contains questions related to the topic. The last and fourth exercises have questions related to the topics taught in the chapter.

 

Important formulas that come in handy while solving questions from the exercises in the textbook are:

  1. Finding the nth term of a progression-
    nth term = a + (n-1) d

  1. 2. Sum of the first n terms in sequence-
    Sn = n/2 [2a + (n-1)d]

 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 10 Maths Solutions –

NCERT Solutions for Class 10 Maths Chapter 6 - Triangles

Chapter 6 of class 10 gives details about the triangles. The chapter gives details about the figures with the same shape but different sizes. It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles. Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of Pythagoras theorem is explained.

 

Important theorems that students should know thoroughly while preparing for the exam include:

 

Theorem 1: 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.

 

Theorem 2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

 

Theorem 3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

 

Theorem 4: If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

 

Theorem 5: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

 

Theorem 6: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

 

Theorem 7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

 

Theorem 8: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

 

Theorem 9: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

 

All the exercises throughout the chapter test how well the students have understood these theorems and if they are able to apply them and get answers to the questions. If the students have enough practice of the questions from the exercise, then understanding the theorems will be relatively easy for them as well.



 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry

Class 10 Maths Chapter 7 explains coordinate geometry, the maths of locating a given point with the help of an ordered pair of numbers. The coordinate or cartesian geometry helps to find the distance between two points whose coordinates are given. The concept of finding the area of a triangle formed by three given points. Also, the ways of finding the coordinates of the point which divides a line segment joining two given points in a given ratio are explained in the chapter. The students will learn distance formula, section formula and area of triangles in this chapter of NCERT Solutions.

 

Important Formulas:

1. Distance Formula - $P Q=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

2. Section Formula - $m_1: m_2=\left(\dfrac{m_1 x_2+m_2 x_1}{m_1+m_2}, \dfrac{m_1 y_2+m_2 y_1}{m_1+m_2}\right)$

2. Area of Triangle $ = \dfrac{1}{2}\left[x_1\left(y_2 - y_3\right) + x_2\left(y_3 - y_1\right) + x_3\left(y_1 - y_2\right)\right]$




Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 10 Maths Solutions –

 

NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry

Chapter 8 of NCERT Solutions introduces trigonometry to the students. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of the angles. Also, the trigonometric ratios for angles 0∘ and 90∘. Students will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities.

 

The chapter gives a basic introduction to trigonometry that comes in handy for the students in Class 11 and 12 as well. They are taught the introductory formulas of trigonometry so that they have a strong grip over the basics that will help them in higher classes and the future. In addition to the formulas, the relationship between the ratios and angles is also explained in the chapter. 


Important Formulas:

1. $\sin \theta = \dfrac{\text{Side opposite to angle}}{\text{Hypotenuse}} = \dfrac{\text { Perpendicular }}{\text { Hypotenuse }} = P/H$

2. $\cos \theta = \dfrac{\text { Adjacent side to angle } \theta}{\text { Hypotenuse }} = \dfrac{\text { Base }}{\text { Hypotenuse }} = B/H$

3. $\tan \theta = \dfrac{\text {Side opposite to angle }\theta}{\text {Adjacent side to angle }\theta} = P/B$

4. $\sec \theta = \dfrac{1}{\cos \theta}$

5. $\cot \theta = \dfrac{1}{\tan \theta}$

6. $\text{cosec} \theta = \dfrac{1}{\sin \theta}$

7. $\tan \theta = \dfrac{{Sin} \theta}{{Cos} \theta}$


Angle

30°

45°

60°

90°

Sinθ

0

1/2

1/√2

√3/2

1

Cosθ

1

√3/2

1/√2

½

0

Tanθ

0

1/√3

1

√3

Undefined

Cotθ

Undefined

√3

1

1/√3

0

Secθ

1

2/√3

√2

2

Undefined

Cosecθ

Undefined

2

√2

2/√3

1


Trigonometric ratios that are important for complementary angles are:

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,

cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A

sin2 A + cos2 A = 1,

sec2 A – tan2 A = 1 for 0° ≤ A < 90°,

cosec2 A = 1 + cot2 A for 0° < A ≤ 90°



 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry

Chapter 9 is the continuation of chapter 8 where the students will learn about the application of trigonometry which they learnt in the previous chapter. This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects. They will also learn how trigonometry is applied and used in navigation, construction and determining the position of any piece of land based on the total latitude and longitudes.

 

Topics Covered in Class 10 Maths Chapter 9 - Some Applications of Trigonometry:

In Class 10 Maths Chapter 9, we delve into "Some Applications of Trigonometry" with a focus on "Heights and Distances." This involves exploring angles of elevation and depression, specifically at 30°, 45°, and 60°.


Let's understand a few key points:


  • Line of Sight: This is the line drawn from your eye to the point you're looking at.

  • Angle of Elevation: When the point you're viewing is above your eye level, like when you tilt your head up.

  • Angle of Depression: When the point you're viewing is below your eye level, like when you lower your head.


To apply these concepts practically to solve problems related to heights and distances, consider three key factors:


  1. The distance from the observer (DE) to the base of the object (minar).

  2. The angle of elevation (∠BAC) from the observer to the top of the object.

  3. The height of the observer (AE).


Assuming you know these three conditions, you can determine the height of the object (minar). In the figure, we observe that CD equals CB plus BD. Here, BD is equivalent to AE, which represents the height of the observer.


To find BC, we utilize trigonometric ratios involving ∠BAC or ∠A in triangle ABC. Since BC is the opposite side concerning the known ∠A, our options are narrowed down to using either tan A or cot A, as these ratios involve AB and BC.


Therefore, we can use tan A = BC/AB or cot A = AB/BC to find BC. Adding AE to BC yields the height of the minar.



 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 9 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Mathematics Chapter 10 - Circles

Chapter 10 for class 10 maths, NCERT Solutions continues the details of Circles studies in previous classes. In this chapter, students will be introduced to the concept of tangents and the number of tangents from a point on a circle. 

 

Important Theorems –

Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 2: The lengths of tangents drawn from an external point to a circle are equal.


Tangents to a circle from a certain point have three situations:


1. There is no tangent to a circle passing through a point lying inside the circle.

2. There is one and only one tangent to a circle passing through a point lying on the circle.

3. There are exactly two tangents to a circle through a point lying outside the circle.




Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Mathematics Chapter 11 - Constructions

Chapter 11 is one of the interesting chapters. This chapter is all about constructing various geometric figures. The students will learn to divide a line segment, and how to draw tangents to a circle. The methods of construction are well explained in the chapter to clear the concepts.

 

Methods and steps for the construction of the tangents to the circle are explained in the chapter with enough examples before each exercise. Examples before each exercise are given so that understanding the methods and theorems becomes easier for the students.


In Class 10 Maths Chapter 11 on Constructions, We Learn about Three Main Topics:

1. Division of a Line Segment: This is about splitting a line into two parts, but not just any parts. We learn to do this in a specific ratio. Imagine you have a line, and you want to divide it in a certain way. This is what we're talking about here.


2. Tangent to a Circle: Ever wondered how to draw a line that just touches a circle from the outside? That's what we dive into here. It's like drawing a line that gently rests against the circle from a point outside it.


3. Constructing a Similar Triangle: Here, we explore how to create a triangle that looks just like another triangle but maybe in a different size. We use something called a scale factor to guide us in making the new triangle the right size compared to the original one.


Important Points:

Construction 11.1: To divide a line segment in a given ratio.

This is about splitting a line in a specific ratio. Think of it as cutting a line into pieces, but we're being very precise about how long each piece is.


Construction 11.2: To construct a triangle similar to a given triangle as per the given scale factor.

Imagine you have a triangle, and you want to make another one that looks just like it but maybe bigger or smaller. That's what we're learning to do in this construction, using something called a scale factor.


Construction 11.3: To construct the tangents to a circle from a point outside it.

Drawing a line that gently touches a circle from the outside might sound tricky, but with this construction, we figure out just how to do that. It's like drawing the perfect tangent line to the circle.




Along with this, students can also download additional study materials provided by Vedantu, for Chapter 11 of CBSE Class 10 Maths Solutions –


NCERT Solutions Class 10 Maths Chapter 12 - Areas Related to Circles

As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle are clarified here. This chapter further explains how to find the area of the figures that contains a circle or part of a circle.

 

Important formulas from within the chapter for the students to practice–

Circumference = 2πr

Area of the circle = πr2

Area of the sector of angle θ = (θ/360) × πr2

Length of an arc of a sector of angle θ = (θ/360) × 2 π r where r is the radius of the circle




 Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Maths Chapter 13 - Surface Areas and Volumes

Chapter 13 of Class 10 Maths NCERT book PDF solution is about the surface areas and volumes of different objects and shapes. In the five Exercises of this chapter, find the surface area of any object which is made up of two or more different solid shapes. The solid shapes include cuboid, cone, sphere, hemisphere and cylinder. Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions that ask about the conversion from one shape to another. This chapter further explains how to find the volume, curved surface area and total surface area of a frustum of a cone.

 

Important formulas used for calculating surface areas and volumes of different objects

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

Diameter of sphere = 2r

The surface area of sphere = 4 π r2

The volume of Sphere = 4/3 π r3

The curved surface area of Cylinder = 2 πrh

Area of two circular bases = 2 πr2

The total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2

Volume of Cylinder = π r2 h

Slant height of cone = l = √(r2 + h2)

Curved surface area of cone = πrl

Total surface area of cone = πr (l + r)

Volume of cone = ⅓ π r2 h

Perimeter of cuboid = 4(l + b +h)

Length of the longest diagonal of a cuboid = √(l2 + b2 + h2)

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

Volume of Cuboid = l × b × h




Along with this, students can also download additional study materials provided by Vedantu, for Chapter 13 of CBSE Class 10 Maths Solutions –

 

NCERT Solutions for Class 10 Maths Chapter 14 - Statistics

This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped. They further learn about finding the mean, median and mode of the given data. In the next exercise, they will learn about the cumulative frequency distribution and draw cumulative frequency curves.


Important Formulas:

The mean of the grouped data can be found by 3 methods.


1. Direct Method: $\overline{{x}}=\dfrac{\sum_{i=1}^n f_i x_i}{\sum_{i=1}^n f_i}$, where $\sum f_i x_i$ is the sum of observations from value $i=1$ to $n$ And $\sum f_i$ is the number of observations from value $i=1$ to $n$

2. Assumed mean method: $\overline{{x}}=a+\dfrac{\sum_{i=1}^n f_i d_i}{\sum_{i=1}^n f_i}$

3. Step deviation method $: \overline{{x}}=a+\dfrac{\sum_{i=1}^n f_i u_i}{\sum_{i=1}^n f_i} \times h$

4. Mode: $=l+\dfrac{f_1-f_0}{2 f_1-f_0-f_2} \times h$

5. Median: $=l+\dfrac{\dfrac{n}{2}-c f}{f} \times h$



 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 14 of CBSE Class 10 Maths Solutions –


NCERT Solutions for Class 10 Maths Chapter 15 - Probability

Chapter 15 or the last chapter of NCERT Solutions for Class 10 Maths teaches probability. It elaborates and explains the difference between experimental probability and theoretical probability.  The chapter is full of examples to clarify the concept of probability to the learners.

 

Probability is also an extremely important chapter for the students to focus on as this chapter is further discussed and new topics are introduced in the classes ahead. It is important that the students get a strong grip on the basics of the chapter in class 10 so that keeping up with the formulas and new topics introduced in higher classes is easier. If the students understand well and practice enough it is also an easy chapter to score good marks in.

 

Important Formulas:

  1. The chance of something happening, let's call it event E, is called its probability, written as P(E). 

\[ P(A) = \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

We figure this out by assuming that all the possible outcomes are equally likely.

  1. If an event is guaranteed to happen, we say it has a probability of 1. If it's impossible, then its probability is 0.

  2. The probability of any event E is a number between 0 and 1. If it's a sure thing, it's close to 1; if it's impossible, it's close to 0.

  3. When an event has only one possible outcome, it's called an elementary event. When we add up the probabilities of all the elementary events in an experiment, the total is always 1.


 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 15 of CBSE Class 10 Maths Solutions –


Finding accurate answers online is a difficult task but Vedantu’s NCERT class 10 Maths SolutionsPDF is a reliable source. Students can download the PDF easily and start going through the chapters. You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score well.

 

CBSE Class 10 Maths Exam Pattern for 2023-24

The Central Board of Secondary Education conducts CBSE Class 10 Board exams every year. The exam is of 100 marks where 80 marks are for theory whereas 20 marks are given for internal assessment. To understand the marking scheme in a better way, you should understand the exam pattern clearly. To score well in the exam, you should know how much mark is awarded for each question and each step of the question. Every year, just before the board exams, the board releases sample papers and marking schemes so that all the doubts of the students are cleared. According to the revised pattern of CBSE, 25% of the theory questions are going to be objective. The number of questions is increased and the marks per question are reduced. This marking scheme will be helpful to the students as the maximum number of questions will become objective or very short answer type as the marks per question has been reduced.

 

CBSE focuses on the all-around development of Class 10 students to prepare them for their further education. To perform well in Class 10 then becomes fairly important. So students are advised to go through the NCERT solution for Class 10 PDF regularly. CBSE marking scheme is stepwise so you have scored accordingly. Therefore students should write each step clearly and give a proper conclusion at the end of the answer. The unit wise marks weightage of the mathematics paper is as follows:

 

The paper has four sections. There are a total of 30 questions for 80 marks.

 



CBSE Class 10 Maths Chapter-Wise Marks Weightage 

Sr.no

Chapter Name

Marks

1

Number System

6

2

Algebra

20

3

Coordinate Geometry

6

4

Geometry

15

5

Trigonometry

12

6

Mensuration

10

7

Statistics and Probability

11


Total

80


Internal Assessment

20


Total

100

 

Internal Assessment for CBSE Class 10 Maths

Internal Assessment

Pen Paper Test and Multiple Assessment

10 Marks

Portfolio 

5 Marks

Lab Practical

5 Marks

Total

20 Marks


CBSE Class 10 Maths Question Paper Design 2023-24

Sr. No

Type of Questions

Total Marks

Weightage

1

Memory: Terms, answers, basic concepts and recalling of facts.

Understanding: Compare, organize, interpret, translate, describe and stating main ideas.

43

54

2

Apply: Solving problems by applying the knowledge, facts, theorems and rules in different ways.

19

24

3

Analyse: Analyse the information provided and make inferences. 

Evaluate: Opine about the validity of quality of work and validity of ideas.

Create:  Creating alternative solutions to the given problem and grouping the elements.

18

22

Total

 

80

100

 

CBSE Class 10th New Plan 2023

The following are some major changes that are planned to be introduced in the new CBSE Exam Pattern:

  • Question papers will be designed to assess students' problem-solving and analytical skills.

  • The paper design will be revised to include more short answer-type questions, like those ranging from 1 to 5 points.

  • Some vocational course exams might be held in February, and final board exams will be completed in March within 15 days.

  • Following the early completion of boards, the results are likely to be announced earlier than the existing structure's schedule.


Topics Covered in Class 10 Chapter Wise

1. Real Numbers 

  • Real Numbers

  • Euclid’s Division Lemma

  • Fundamental Theorem of Arithmetic

  • Irrational Numbers

  • Rational Numbers


2. Polynomials 

  • Zeros of a polynomial. 

  • Relationship between zeroes 

  • Coefficients of quadratic polynomials only.


3. Pair of Linear Equations in Two Variables

  • Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. 

  • Algebraic conditions for 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 reducible to linear equations.


4. Quadratic Equations

  • 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 formulas. 

  • Relationship between discriminant and nature of roots. 

  • Situational problems based on quadratic equations.


5. Arithmetic Progression

  • 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.


6. Triangles 

  • Concept of a similar and congruent figure

  • Theorems related to the similarity of triangles

  • Areas of similar triangles

  • Pythagoras Theorem and converse of Pythagoras Theorem


7. Coordinate Geometry

  • Concepts of coordinate geometry.

  • Graphs of linear equations. 

  • Distance formula. 

  • Section formula.


8. Introduction to Trigonometry

  • Trigonometric ratios of an acute angle of a right-angled triangle. 

  • Proof of their existence. 

  • Values of the trigonometric ratios. 

  • Relationships between the ratios.


9. Some Applications of Trigonometry

  • Angle of elevation. 

  • Angle of Depression.

  • Simple problems on heights and distances.


10. Circles

  • Various terms related to a circle such as a chord, segment.

  • Important Theorems

  • Tangent to a Circle.

  • Number of Tangents from a Point on a Circle.


11. Constructions

  • Dividing a line segment.

  • Construction of tangents to a circle.


12. Areas Related to Circles

  • Calculate the area of a circle

  • Area of sectors and segments of a circle. 

  • Problems based on areas and perimeter.

  • Circumference of the above plane figures.


13. Surface Areas and Volumes

  • Surface areas and volumes of combinations of any two figures like cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

  • Problems that involve converting one type of metallic solid into another and other mixed problems. 


14. Statistics

  • Mean, median and mode of grouped data. 

  • Mean by Direct Method and Assumed Mean Method only.


15. Probability

  • Classical definition of probability. 

  • Simple problems on finding the probability of an event.


Benefits of NCERT Solution for Class 10 Maths: Your 10th Maths Guide

NCERT 10 Maths solutions PDF created at Vedantu is one of the most sought after study materials online. Vedantu’s online learning ecosystem has everything the students need. Students go through the PDF and gain an in-depth understanding of the topics which prepares them for their final exams and also for their further studies. Some key features of the Class 10 NCERT Maths solution PDF are:

  • Step by step calculation of every question to improve understanding of the topic.

  • An exhaustive explanation of the problems to encourage concept-based learning.

  • Up to date with the improvements made in the syllabus.

  • Categorised chapter wise to improve ease of use.

  • Great for revision and brushing up before examinations.

  • Additional questions to help you track your progress.

  • Follow an exam pattern to help you score well in the examinations.

  • Great for revision as the whole syllabus is consolidated in one solution PDF that makes it easier for the students to refer to before the exam.

  • Solutions are provided in a simple easy to understand language. 

  • Extra solved questions are also provided so that students can refer to them while practising extra questions

  • Modified to any changes made in the syllabus or exam pattern by the CBSE board.

  • They are available to download for free on the Vedantu website. The students can download them at any point they feel necessary and start focussing on their preparation with the help of the solutions pdf.

How will CBSE Class 10 Maths Solutions Help You To Score High Marks in Board Exams?

Maths is an important as well as difficult subject to crack. To score high marks in maths board exams, you need to have a clear picture of the concepts taught in grade 10. If you can grasp the concepts and topics of class 10 maths, you can definitely score very high marks in the board exams. But this is not easy. You need to do constant practise along with understanding the topics and the concepts behind them. To make the work smarter for you, NCERT Solutions are provided. Here, a detailed description of all the topics is provided by the highly qualified experts of Vedantu. They put all their experience in the pdf of NCERT Solutions for Class 10 Maths. So, if you want to score high marks in board exams do refer to our pdfs which will make your scoring high.

 

The solutions PDF can help you at any point for wherever you are getting stuck in the syllabus. It has extra practice questions for you to assess your performance once you have understood the concepts clearly. The concepts are explained in such an easy manner that the students can understand them quickly. Maths is a subject that requires thorough practice besides the understanding of the concept. The PDF gives easy to understand explanations and enough practise questions for the students to follow. It is their complete guide for how to prepare for exams well and score good marks in the board exams. The solutions pdf have enough extra questions for you to understand the kinds of questions to expect in the exam as well. The sample papers provided online can also be practised. This 10th Maths Guide will give you a chance to assess your knowledge of all the topics and also how you would attempt the actual exam.

 

Why Refer NCERT Maths Class 10 Solutions PDF for Board Exams?

The Class 10 NCERT Maths solutions PDF for boad exam have several benefits, such as: 


  • NCERT Maths Class 10 PDF is a free PDF available online, providing students with easy access to study materials.

  • The exam pattern emphasizes application-based learning, testing concepts taught in textbooks.

  • Students need to be well-versed in formulas, theorems, identities, and diagrams for exams, making preparation seem challenging.

  • Vedantu’s NCERT solution for Class 10, assisting students in their exam preparations. 

  • The PDF is organized into chapters, facilitating efficient use as a reference study material.

  • NCERT Solutions for Class 10 PDF helps manage time during exam preparations by providing quick access to specific chapters for problem-solving.

  • Chapters are focused on based on their marks weightage, and solutions are presented in an easy-to-understand language.

  • The solutions PDF becomes a go-to book for revision, allowing students to practice and score well in exams.

  • Solutions are designed by experienced teachers who understand exam expectations, providing insights into correct answer formulation.

  • The NCERT textbook is the main resource recommended by the CBSE for Class 10 Maths exam preparation.

  • Students are advised to thoroughly practice each question and example from the textbook for exam readiness along with 10th Maths Guide. 

  • Board exam question papers are usually formed from the NCERT textbooks, establishing the textbook's importance.

  • Vedantu’s solutions PDF aligns with the NCERT book, ensuring accuracy and relevance.

  • The solutions PDF is updated in accordance with changes in the textbook or CBSE requirements.

  • After studying from NCERT textbooks, students can refer to the solutions PDF for extra help and practice.

  • The solutions PDF provides answers to exercise questions, aiding students when they face challenges.

  • The NCERT textbook serves as the primary resource for students to commence their exam preparation.

  • Examples in the textbook offer insights into question paper expectations, guiding students on answer formulation.


Vedantu’s NCERT Solutions for Class 10 Maths, aligned with the NCERT textbook, stand as a valuable and accessible tool for students to ace their exams with a clear understanding of concepts and effective problem-solving skills.

  

Important Tips for Scoring Well in the Board Exams

Class 10 is an important class in most students’ school lives and is the first class where the students have to appear for a board exam. The class may seem daunting but if the students have been thorough with their studies for the whole academic year then it will not be difficult for them to score good marks at all. To achieve a good score it is necessary that the students keep the following tips and suggestions in mind for the whole year and especially while preparing for the exams.


1. Regular Revision is Key:

  • Consistency in revising and practicing daily lessons is crucial.

  • Regular practice ensures a better understanding and prevents topics from becoming overwhelming during exams.


2. Practice Extensively:

  • Practice all examples and exercises in the NCERT book.

  • Utilize solutions PDF for self-assessment and focus on areas with incorrect answers.

  • Refer to Vedantu's solutions for additional practice and clarity.


3. Concept Clarity Matters:

  • Seek teacher assistance for any doubts promptly.

  • Utilize Vedantu's Solutions PDF for easy-to-understand explanations.

  • Ensure a clear understanding of all concepts well in advance of exams.


4. Understand Syllabus and Paper Pattern:

  • Familiarize yourself with the syllabus, topic weights, and exam pattern.

  • This knowledge aids in efficient exam preparation.


5. Effective Time Management:

  • Create a timetable considering topic weights and personal strengths/weaknesses.

  • Set daily and weekly goals for focused and motivated study sessions.

  • Include breaks for effective learning and retention.


6. Identify Strengths and Weaknesses:

  • Allocate equal time to all topics; practice weaker areas more.

  • Ensure confidence in every topic by thorough practice.


7. Note-taking for Consolidation:

  • Write down theorems and formulas for consolidation and quick revision.

  • Notes act as a reference point and aid in better memorization.


8. Class 10 Maths Resources:

  • Master with our detailed class 10th Maths Guide.

  • Practice sample papers and previous years' question papers.

  • Understand the question patterns to prepare effectively.

  • Vedantu's website offers sample papers for practice.


9. Prioritize Rest and Preparation:

  • Ensure a good night's sleep and a healthy meal before the exam.

  • Gather necessary materials the night before to avoid last-minute stress.


10. Exam Simulation for Time Management:

  • Practice answering sample papers under timed conditions.

  • Assess and improve time management skills to attempt all questions.


11. Presenting Answers Effectively:

  • Answer questions in the order presented in the paper.

  • Highlight final answers and relevant formulas for clarity.

  • Avoid leaving any questions unattempted; partial answers can secure marks.


Following the above-mentioned tips and being sincere in your preparation will help you score good marks in the exams. Having a strong base in Maths in Class 10 is definitely beneficial for classes ahead and in the future. This will help you have an edge over others even in competitive exams. Most competitive exams have maths sections and the questions generally asked pertain to what you may have learnt in school. Having a good grip over the formulas and the topics will definitely help you perform well in these exams as well.


CBSE Class 10 Maths Study Materials

CBSE Class 10 Maths Revision Notes

CBSE Class 10 Maths Important Questions

CBSE Class 10 Maths Formulas

CBSE Class 10 Maths RD Sharma Solutions

CBSE Class 10 Maths RS Aggarwal Solutions

CBSE Class 10 Maths Sample Papers

CBSE Class 10 Maths NCERT Exemplar Solutions

CBSE Class 10 Maths Previous Year Question Papers


Conclusion 

Vedantu's NCERT Solutions for Class 10 Mathematics offer a comprehensive and user-friendly resource for students. The solutions align seamlessly with the Class 10 Maths book PDF in an accessible format, enhancing understanding and aiding effective exam preparation. The structured approach ensures clarity on complex topics, making it an invaluable tool for students seeking mastery in mathematics. The availability of the NCERT Class 10 Maths book PDF further facilitates easy access and study. With the convenience of a FREE downloadable PDF, it caters to diverse learning styles. Vedantu's Class 10 NCERT Maths Solutions helps students navigate the challenges of their mathematics curriculum.

FAQs on NCERT Solutions for Class 10 Maths (2023-24)

1. How will NCERT Solutions for Class 10 Maths help me in learning?

NCERT Solutions for class 10 Maths is prepared for overall learning of a student. It explains all the concepts of class 10 CBSE. It also provides the solutions of all the NCERT textbook questions. Also, it has questions for practice. So, you can learn the concepts, solve NCERT textbook questions and also practice extra questions provided hence learning the all of maths class 10 CBSE.

2. How can I cover the whole syllabus of Class 10 Maths on time?

To cover the whole syllabus of class 10 Maths on time, you can refer to NCERT Solutions for class 10 from Vedantu. Compiled by a group of experts, these solutions will prove a true guide to you. Whether it's about covering the syllabus or scoring high marks, Vedantu’s NCERT Solutions always comes handy. So, download the solutions today and enjoy studying!

3. Can I get NCERT Solutions for Class 10 Maths for free?

Yes, you can download NCERT Solutions for class 10 Maths for completely free of cost from Vedantu’s official website. The solutions are prepared by the experts of Vedantu after a lot of research and these are as per the latest guidelines of CBSE. You can download it hassle free from the official website of Vedantu at free of cost.

4. If I am stuck on any concept or numerical problem, will NCERT Solutions for Class 10 Maths help me?

Yes, definitely. NCERT Solutions for class 10 Maths are designed in such a way that it will help you in concept clearance and then practice. In Mathematics, concept clearance is very much required as the questions will be based on concepts only and you have to solve it logically. So, refer to NCERT Solutions for class 10 Maths and enjoy learning.

5. Is NCERT Solutions for Class 10 Maths enough for scoring high in exams?

Scoring high in exams depends on how well you are aware of the concepts and how well you can imply that on numerical and logical problems. NCERT Solutions will help you in clearing your concepts well and building a strong foundation. So, if your concepts are clear, and you practice well, NCERT Solutions are enough to score high marks in the exam.

6. Where will I get the NCERT Solutions for Class 10 Maths PDF?

Solutions for Class 10 Maths is one of the best ways for you to prepare for your board exam. The solutions are present on Vedantu’s website (vedantu.com) free of cost. Vedantu’s NCERT solutions are available in PDF format so that you can download them and use them to study online. Students can download these from Vedantu mobile app as well. All the solutions are explained in an easy format along with the concepts. With these solutions in your hand, you won’t have to worry about finishing your NCERT syllabus.

7. How to master in Class 10 Maths CBSE?

In order to master your Class 10 CBSE, you need to focus on finishing your NCERT syllabus. This involves solving all the questions and the examples. To help you with this, Vedantu offers NCERT Solutions for Class 10 Maths in PDF format. You can use these as a guide for finishing the NCERT exercises. All the solutions are provided in a step-by-step format for your benefit. It is the easiest way for you to score well in your exams.

8. Where can I download CBSE Class 10 NCERT Mathematics PDF Solutions?

CBSE Class 10 NCERT Mathematics PDF solutions are nothing short of a blessing for the students. Vedantu offers PDFs of thoroughly written solutions where all the questions from NCERT exercises are explained in detail. Follow these steps to download them:

  • Visit the page of ‘NCERT Solutions for Class 10 Maths’ on the official website of Vedantu (vedantu.com).

  • Find the exercise for which you want a solution and click on the ‘Download PDF’ link.

  • The solutions will be downloaded into your system. You’ll also receive a message/ mail with a direct download button of your preferred solution.

9. What are the concepts explained in the solutions of NCERT Class 10 Maths Textbook?

The Vedantu’s solutions of NCERT Class 10 Maths textbook can help all the students of Class 10th with helpful tips and tricks for solving math problems. These tricks are provided at the end of all chapters. There are 15 chapters in total that students have to study for the Class 10 exam. All the chapters are explained in a detailed manner by the subject matter experts. You can download the NCERT Class 10 Maths PDF solutions from Vedantu (vedantu.com) and learn all the chapters from the syllabus.

10. How can I save these Class 10 NCERT Maths Solutions for reference?

Vedantu’s Class 10 NCERT Maths Solutions is the easiest way for you to prepare for your Class 10 exams. These solutions PDF cover the concepts as well as solutions to exercises. If you want to save them for reference, you will have to download their PDF files. There is a separate PDF file for each exercise that you can save on your mobile phone or computer for future reference. If you want, you can print these files for easy access.