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NCERT Solutions For Class 10 Maths

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Last updated date: 19th Mar 2024
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MVSAT 2024

NCERT Solutions for Class 10 Maths Chapter-Wise PDF Free Download

NCERT Solutions for 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 PDF, offering clear explanations and step-by-step solutions to problems. The aim is to make mathematical concepts more accessible and understandable for students. The 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.

The Math syllabus for Class 10 is made to give you a solid understanding of important math topics. It teaches you the basics, helps you grasp concepts and theories, and tests your knowledge through practice problems and examples in your textbook.


The exercises in the NCERT textbook are meant to help you use what you've learned about each topic as much as possible. Before you start each exercise, there are examples you can look at to help you understand the questions better. These examples have step-by-step explanations that make it easier to learn.


Chapter-Specific NCERT Solutions for Class 10 Maths

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.


Note: The chapters on constructions have been excluded from the Class 10 Maths textbook for the 2023-24 academic year


Get ready for a smooth learning journey with our NCERT Solutions! Our expert teachers, with years of experience, have crafted step-by-step explanations for all chapters and exercises. You can easily download the PDF format, making your learning experience hassle-free. 


The Class 10 Maths NCERT Solutions PDFs cover all the Exercises from Chapters 1 - 15 present in the NCERT books. These NCERT Maths Class 10 solutions are written according to the CBSE exam guidelines to increase the students understanding of the subject and help them to score well. The PDF 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 Solutions

Other Materials

  • Important Questions

  • Revision Notes


Get an idea about “How will the paper of NCERT class 10 maths be conducted?


NCERT Solutions for Class 10 Maths All Chapters

Competitive Exams after 12th Science

NCERT Solutions for Class 10 Maths Chapter Details, Formulas and Exercises PDF

Chapter 1 - Real Numbers

In Chapter 1 - Real Numbers, there are 4 Exercises, This chapter focuses on real numbers and irrational numbers. It also covers 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.

Topics Covered in Class 10 Real Numbers

  • Real Numbers

  • Euclid’s Division Lemma

  • Fundamental Theorem of Arithmetic

  • Irrational Numbers

  • Rational Numbers

Chapter 1 - Real Numbers Exercises in PDF Format

Class 10 Real Numbers Exercise 1.1 - 5 Questions (4 Long Answers, 1 Short Answer)

Class 10 Real Numbers Exercise 1.2 - 7 Questions (4 Long Answers, 3 Short Answers)

Class 10 Real Numbers Exercise 1.3 - 3 Questions (3 Short Answers)

Class 10 Real Numbers Exercise 1.4 - 3 Questions (3 Short Answers)



Students can access extra study materials for Real Numbers on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 2 - Polynomials

There are a total of 4 Exercises including an optional Exercise in Chapter 2 Polynomials. 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 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.

Topics Covered in Class 10 Polynomials

  • Zeros of a polynomial. 

  • Relationship between zeroes 

  • Coefficients of quadratic polynomials only.


Chapter 2 - Polynomials Exercises in PDF Format

Class 10 Polynomials Exercise 2.1 - 1 Question (1 Short Answer)

Class 10 Polynomials Exercise 2.2 - 2 Questions (2 Short Answers)

Class 10 Polynomials Exercise 2.3 - 5 Questions (2 Short Answers, 3 Long Answers)

Class 10 Polynomials Exercise 2.4 - 5 Questions (2 Short Answers, 3 Long Answers)


Students can access extra study materials for Polynomials on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 3 - Pair of Linear Equations in Two Variables

Chapter 3 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.


Topics Covered in Class 10 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.

Chapter 3 - Pair of Linear Equations in Two Variables Exercises in PDF Format

Class 10 Pair of Linear Equations in Two Variables Exercise 3.1 - 3 Questions (2 Short Answers, 1 Long Answer)

Class 10 Pair of Linear Equations in Two Variables Exercise 3.2 - 7 Questions (5 Short Answers, 2 Long Answers)

Class 10 Pair of Linear Equations in Two Variables Exercise 3.3 - 3 Questions (2 Short Answers, 1 Long Answer)

Class 10 Pair of Linear Equations in Two Variables Exercise 3.4 - 2 Questions (2 Long Answers)

Class 10 Pair of Linear Equations in Two Variables Exercise 3.5 - 4 Questions (4 Short Answers)

Class 10 Pair of Linear Equations in Two Variables Exercise 3.6 - 2 Questions (2 Long Answers)

Class 10 Pair of Linear Equations in Two Variables Exercise 3.7 - 8 Questions (1 Short Answer, 7 Long Answers)


Students can access extra study materials for Pair of Linear Equations in Two Variables on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 4 - Quadratic Equations

Chapter 4 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.


Topics Covered in Class 10 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.

Chapter 4 - Quadratic Equations Exercises in PDF Format

Class 10 Quadratic Equations Exercise 4.1 - 2 Questions (1 Short Answer, 1 Long Answer)

Class 10 Quadratic Equations Exercise 4.2 - 6 Questions (6 Short Answers)

Class 10 Quadratic Equations Exercise 4.3 - 11 Questions (8 Short Answers, 3 Long Answers)

Class 10 Quadratic Equations Exercise 4.4 - 5 Questions (2 Short Answers, 3 Long Answer)

Students can access extra study materials for Quadratic Equations on Vedantu. These resources are available for download, offering additional support for your studies.



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.

Topics Covered in Class 10 Arithmetic Progressions

  • 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 5 - Arithmetic Progressions Exercises in PDF Format

Class 10 Arithmetic Progressions Exercise 5.1 - 4 Questions (1 Short Answer, 3 Long Answers)

Class 10 Arithmetic Progressions Exercise 5.2 - 20 Questions (10 Short Answers, 10 Long Answers)

Class 10 Arithmetic Progressions Exercise 5.3 - 20 Questions (7 Short Answer, 13 Long Answers)

Class 10 Arithmetic Progressions Exercise 5.4 - 5 Questions (5 Long Answers)


Students can access extra study materials for Arithmetic Progressions on Vedantu. These resources are available for download, offering additional support for your studies.



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.

Topics Covered in Class 10 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

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.

Chapter 6 - Triangles Exercises in PDF Format

Class 10 Triangles Exercise 6.1 - 3 Questions (3 Short Answers)

Class 10 Triangles Exercise 6.2 - 10 Questions (9 Short Answers, 1 Long Answer)

Class 10 Triangles Exercise 6.3 - 16 Questions (12 Short Answer, 4 Long Answer)

Class 10 Triangles Exercise 6.4 - 9 Questions (7 Short Answers, 2 Long Answers)

Class 10 Triangles Exercise 6.5 - 17 Questions (15 Short Answer, 2 Long Answer)

Class 10 Triangles Exercise 6.6 - 10 Questions (5 Short Answers, 5 Long Answers)


Students can access extra study materials for Triangles on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 7 - Coordinate Geometry

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.


Topics Covered in Class 10 Coordinate Geometry

  • Concepts of coordinate geometry

  • Graphs of linear equations

  • Distance formula 

  • Section formula

Chapter 7 - Coordinate Geometry Exercises in PDF Format

Class 10 Coordinate Geometry Exercise 7.1 - 10 Questions (3 Short Answers, 7 Long Answer)

Class 10 Coordinate Geometry Exercise 7.2 - 10 Questions (2 Short Answers, 8 Long Answer)

Class 10 Coordinate Geometry Exercise 7.3 - 5 Questions (2 Short Answers, 3 Long Answer)

Class 10 Coordinate Geometry Exercise 7.4 - 8 Questions (3 Short Answers, 5 Long Answer)


Students can access extra study materials for Coordinate Geometry on Vedantu. These resources are available for download, offering additional support for your studies.



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.


Topics Covered in Class 10 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.


Chapter 8 - Introduction to Trigonometry Exercises in PDF Format

Class 10 Introduction to Trigonometry Exercise 8.1 - 11 Questions (8 Short Answers, 3 Long Answers)

Class 10 Introduction to Trigonometry Exercise 8.2 - 4 Questions (2 Short Answers, 2 Long Answers)

Class 10 Introduction to Trigonometry Exercise 8.3 - 7 Questions (5 Short Answers, 2 Long Answers)

Class 10 Introduction to Trigonometry Exercise 8.4 - 5 Questions (3 Short Answers, 2 Long Answers)


Students can access extra study materials for Introduction to Trigonometry on Vedantu. These resources are available for download, offering additional support for your studies.



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 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.

Chapter 9 - Some Applications of Trigonometry Exercises in PDF Format

Class 10 Some Applications of Trigonometry Exercise 9.1 - 16 Questions (16 Long Answers)


Students can access extra study materials for Some Applications of Trigonometry on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 10 - Circles

You have learned about circles and related terms like chords, segments, and arcs previously. Now, we are going to learn situations where a circle and a line are on the same plane. This chapter focuses on understanding Tangents to a Circle and the Number of Tangents from a Point on a Circle.


Theorems

Tangent to a circle at the point of contact


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

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

  3. Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

  4. Theorem 10.2: The lengths of tangents drawn from an external point to a circle are equal.


Case-based Theorem

Number of Tangents from a Point on a Circle


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

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

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


Topics Covered in Class 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.

Chapter 10 - Circles Exercises in PDF Format

Class 10 Circles Exercise 10.1 - 4 Questions (2 Short Answer, 2 Long Answers)

Class 10 Circles Exercise 10.2 - 13 Questions (2 Short Answers, 14 Long Answers)


Students can access extra study materials for Circles on Vedantu. These resources are available for download, offering additional support for your studies.



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.


Topics Covered in Class 10 Constructions

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.

Chapter 11 - Constructions Exercises in PDF Format

Class 10 Constructions Exercise 11.1 - 7 Questions (7 Long Answers)

Class 10 Constructions Exercise 11.2 - 7 Questions (7 Long Answers)


Students can access extra study materials for Constructions on Vedantu. These resources are available for download, offering additional support for your studies.



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.


Topics Covered in Class 10 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.

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

Chapter 12 - Areas Related to Circles Exercises in PDF Format

Class 10 Areas Related to Circles Exercise 12.1 - 5 Questions (5 Short Answers)

Class 10 Areas Related to Circles Exercise 12.2 - 14 Questions (9 Short Answers, 5 Long Answers)

Class 10 Areas Related to Circles Exercise 12.3 - 16 Questions (9 Short Answers, 7 Long Answers)


Students can access extra study materials for Area Related to Circles on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 13 - Surface Areas and Volumes

Chapter 13 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.


Topics Covered in Class 10 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.

  • 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


Chapter 13 - Surface Areas and Volumes Exercises in PDF Format

Class 10 Surface Areas and Volumes Exercise 13.1 - 9 Questions (2 Short Answers, 7 Long Answers)

Class 10 Surface Areas and Volumes Exercise 13.2 - 8 Questions (1 Short Answer, 7 Long Answers)

Class 10 NCERT Solutions Surface Areas and Volumes Exercise 13.3 - 9 Questions (9 Long Answers)

Class 10 Surface Areas and Volumes Exercise 13.4 - 5 Questions (5 Long Answers)

Class 10 Surface Areas and Volumes Exercise 13.5 - 7 Questions (7 Long Answers)


Students can access extra study materials for Surface Areas and Volume on Vedantu. These resources are available for download, offering additional support for your studies.



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.


Topics Covered in Class 10 Statistics

  • Mean, median and mode of grouped data. 

  • Mean by Direct Method and Assumed Mean Method only.


Chapter 14 - Statistics Exercises in PDF Format

Class 10 Statistics Exercise 14.1 - 9 Questions (9 Long Answers) 

Class 10 Statistics Exercise 14.2 - 6 Questions (6 Long Answers)

Class 10 Statistics Exercise 14.3 - 7 Questions (7 Long Answers)

Class 10 Statistics Exercise 14.4 - 3 Questions (3 Long Answers)


Students can access extra study materials for Statistics on Vedantu. These resources are available for download, offering additional support for your studies.



Chapter 15 - Probability

Chapter 15 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.


Topics Covered in Class 10 Probability

  • Classical definition of probability. 

  • Simple problems on finding the probability of an event.

Chapter 15 - Probability Exercises in PDF Format

Class 10 Probability Exercise 15.1 - 25 Questions (22 Short Answers, 3 Long Answers)

Class 10 Probability Exercise 15.2 - 5 Questions (5 Short Answers)


Students can access extra study materials for Probability on Vedantu. These resources are available for download, offering additional support for your studies.



CBSE Class 10 Maths Exam Pattern for 2023-24

The CBSE Class 10 Maths Exam Pattern for 2023-24 consists of two parts:

  • Internal Assessment: This is conducted by the school throughout the year and carries 20 marks. It typically includes periodic tests, project work, and other activities.

  • Board Exam: This is a 3-hour pen-and-paper exam conducted by the CBSE and carries 80 marks. The exam pattern is as follows:

Section

Question Type

Number of Questions

Marks

A

Very Short Answer

5

20

B

Short Answer

11

30

C

Long Answer and Case-based

7

30


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 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.


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 or 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


Conclusion 

Vedantu's NCERT Solutions for Class 10 Maths by Vedantu provide clear and concise explanations, making complex mathematical concepts easy to grasp. The solutions cover essential topics like algebra, geometry, trigonometry, and statistics, preparing students for future studies. It's crucial to focus on problem-solving techniques and real-life applications to enhance practical skills. Vedantu's approach encourages self-learning and critical thinking, fostering a deeper understanding of mathematical principles. Regular practice with these class 10 NCERT Maths solutions is key to mastering the board exam, and ensuring students are well-prepared for exams.

FAQs on NCERT Solutions For Class 10 Maths

1. What are the topics covered in Class 10 chapters of Mathematics?

The topics covered in Class 10 chapters of Mathematics are:


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.

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

To cover the whole Maths syllabus of class 10 on time, you can refer to NCERT Solutions for class 10 provided by 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 PDF 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 Maths concept or numerical problem of Class 10, will NCERT Solutions help me?

Yes, definitely. NCERT Solutions 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. 

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 Class 10 NCERT Solutions for Maths PDF?

Solutions for Class 10 Mathematics 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 in PDF format. You can use these as a guide for finishing the NCERT exercises.

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 do the concepts explained in the NCERT Class 10 Maths Textbook?

The Vedantu’s solutions of Class 10 NCERT 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. 

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.