Cbse Class 10 Ncert Solutions of Maths
Chapter 1 - Real Numbers
The first chapter in CBSE Class 10 talks about HCF and LCM. This is followed by Euclid's division lemma, rational and irrational numbers, and conversion of fractions to decimals and decimals to fractions. TopperLearning NCERT solutions have the solutions to all the questions present in all four exercises. These solutions help you to revise and practice with the easiest methods provided by our experts.
Chapter 1- Real Numbers- Ex 1.1
Practise how to apply Euclid's algorithm with our step-wise NCERT CBSE Class 10 Maths Chapter 1 Exercise 1.1 solutions. Get concept insights by experts on how to correctly apply Euclid's division lemma in a tricky Maths problem. Also, check expert tips on how to solve word problems quickly.
Chapter 1- Real Numbers- Ex 1.2
Learn to work with exponents in a Maths problem on real numbers. Understand numbers better by recognising prime numbers. In our NCERT solutions, read the concept insights to understand when to express a number as the product of prime factors.
Chapter 1- Real Numbers- Ex 1.3
Revise problems based on rational numbers and irrational numbers. Understand what are co-prime integers. Find out how to solve a problem with proof by contradiction. With the concept insights given by TopperLearning's academic experts, you will have better clarity of the CBSE Class 10 Maths NCERT solutions on real numbers.
Chapter 1- Real Numbers- Ex 1.4
You may have heard of concepts like terminating and non-terminating decimal expansions. Learn how to identify these expansions and solve problems with our CBSE Class 10 Maths NCERT solutions. Also, understand the concept of prime factorisation.
Chapter 2 - Polynomials
Chapter 2 of Class 10 CBSE is on polynomials. Our solutions tell you how to verify the relation between zeros and the coefficient. The NCERT solutions also explain the method used to find the zeros of polynomials and the solutions for quadratic polynomials.
Chapter 2- Polynomials- Ex 2.1
So, how to find the number of zeroes in a polynomial? Practise the exercise problems and solutions to grasp the techniques for finding zeroes in a polynomial.
Chapter 2- Polynomials - Ex 2.2
Learn to calculate the product of zeroes and sum of zeroes by revising the problems and solutions in this section. Understand quadratic polynomials better by revising our expert solutions for CBSE Class 10 Maths NCERT exercises.
Chapter 2- Polynomials - Ex 2.3
Revise the division algorithm and learn to use it to calculate answers in exercises on polynomials. Practise the problems and CBSE Class 10 Mathematics solutions in this section to understand concepts such as dividend, remainder, and quotient.
Chapter 2- Polynomials - Ex 2.4
Dive deeper into the concept of zero of a polynomial and revisit the division algorithm by practising related CBSE Class 10 Maths problems. Understand how to work with factors of a polynomial by reviewing the steps by experts.
Chapter 3 - Pairs of Linear Equations in Two Variables
Class 10 Maths Chapter 3 is the study of algebraic and graphical methods for solving linear equations. With our solutions, revise the elimination and cross-multiplication method that can be used in solving problems based on linear equations.
Chapter 3 - Pairs of Linear Equations in Two Variables- Ex 3.1
Learn the steps to solve algebraic equations with our chapter solutions. TopperLearning's NCERT textbook solutions will give you clarity on how to draw the correct graphs to represent the equations.
Chapter 3 - Pairs of Linear Equations in Two Variables- Ex 3.2
Revise the steps to represent values from equations in a table format with our NCERT solutions. Check the expert answers to identify the values of 'x' and 'y' co-ordinates of a point in a graph.
Chapter 3 - Pairs of Linear Equations in Two Variables- Ex 3.3
How to substitute a given value in an equation to provide proof or find an answer? Learn this and more by going through the step-wise CBSE Class 10 Maths Chapter 3 Exercise 3.3 solutions for questions from NCERT textbook.
Chapter 3 – Pairs of Linear Equations in Two Variables- Ex 3.4
Solve the exercises in your NCERT Maths textbook with help of the accurate solutions by qualified Maths teachers. Revise problem-solving methods such as elimination method and substitution method using the NCERT solutions.
Chapter 3 – Pairs of Linear Equations in Two Variables- Ex 3.5
Sometimes, the given pair of equations may have a unique solution. Knowing the cross-multiplication method will help you solve such questions. Practice related exercise questions with our CBSE Class 10 Maths NCERT textbook solutions.
Chapter 3 - Pairs of Linear Equations in Two Variables- Ex 3.6
How will you solve problems wherein two equations are not linear? Read our concept insights and practise CBSE Class 10 Maths Chapter 3 Exercise 3.6 solutions from this section to get the answers.
Chapter 3 - Pairs of Linear Equations in Two Variables- Ex 3.7
Learn to use algebraic methods to solve linear equations by practising the Maths problems and solutions from this section. Refer to the NCERT solutions, understand the application of chapter concepts to solve real problems using linear equations.
Chapter 4 - Quadratic Equations
Chapter 4 is about converting word problems to quadratic equations. By using our expert answers or solutions to your Maths-related questions as your reference, you will be able to find the roots of a quadratic equation in this chapter.
Chapter 4 - Quadratic Equations- Ex 4.1
How to prove that a given equation is a quadratic equation? You can find answers to quadratic equations concepts part of your syllabus and proofs in our CBSE Class 10 Maths Chapter 4 solutions.
Chapter 4 - Quadratic Equations- Ex 4.2
While solving quadratic equations, you may have to use various techniques such as split the middle term method, Pythagoras theorem, etc. Learn to apply these techniques by learning from TopperLearning's NCERT solutions.
Chapter 4 - Quadratic Equations- Ex 4.3
In quadratic equations, learn to apply logic such as the square of a number cannot be negative and other concepts. Our CBSE Class 10 Maths solutions equip you with concept insights to understand and apply logic while writing Maths answers.
Chapter 4 - Quadratic Equations- Ex 4.4
Solve the NCERT exercise for Chapter 4 to understand how to work with discriminants for find the roots in a given equation. With the solutions, grasp the ways to find answers to real problems such as finding the perimeter of a fence or length of a park.
Chapter 5 - Arithmetic Progressions
Chapter 5 has questions on arithmetic progressions. To help you understand the concept of arithmetic progression, our experts have shared detailed answers to the NCERT textbook questions in our NCERT Solutions for Class 10.
Chapter 5 - Arithmetic Progressions- Ex 5.1
Along with the CBSE Class 10 Maths NCERT solutions, get the best tips to present the arithmetic progression a per given data. Brush up your basics by going through the solved exercises in this section.
Chapter 5 - Arithmetic Progressions- Ex 5.2
Revisit concepts such as First Term, Common Difference, etc. by browsing through the solutions for Chapter 5 exercise questions. Learn to find the missing terms in a given sequence by studying from our CBSE Class 10 Maths Chapter 5 Exercise 5.2 solutions.
Chapter 5 - Arithmetic Progressions- Ex 5.3
Understand how to work out the sum of first n terms with the appropriate formula. Learn to find the required values in a problem by multiplying or subtracting equations. Revise the NCERT model answers for Class 10 to grasp ways to analyse the given data for finding the required answers.
Chapter 5 - Arithmetic Progressions- Ex 5.4
How to find the first negative term in an arithmetic progression? How to use the sum of n terms formula to find the value of certain objects that are placed uniformly in an AP format? To find answers to these queries, solve the Chapter 5 exercise questions and review the model answers.
Chapter 6 - Triangles
Chapter 6 includes solutions on the important topic of triangles. Understand how the shape of a triangle is formed. Solve problems related to the properties of triangles in this chapter. Study the different types of triangles such as isosceles triangle, right-angled triangle, and equilateral triangle, and learn about applications of triangles in trigonometry with Class 10 Maths NCERT book solutions.
Chapter 6 - Triangles- Ex 6.1
Learn how to construct equilateral triangles, parallelograms, squares and trapeziums. Brush up your knowledge of triangles with our NCERT solutions.
Chapter 6 - Triangles- Ex 6.2
Where and how would you use the basic proportionality theorem? Get the answers in the CBSE Class 10 Maths Exercise 6.2 solutions to exercise questions in this section.
Chapter 6 - Triangles- Ex 6.3
Learn about similarity of triangles by reviewing the expert solutions to some of the Chapter 6 exercises. Understand the Angle-Angle-Angle (AAA) rule of triangles with the help of TopperLearning's NCERT solutions.
Chapter 6 - Triangles- Ex 6.4
Discover the concepts such as vertically opposite angles and alternate interior angles to better understand the properties of a triangle. Revise the various rules of triangles such as Side-Side-Side (SSS) and more with our NCERT textbook solutions.
Chapter 6 - Triangles- Ex 6.5
Through these CBSE Class 10 Maths Chapter 6 NCERT solutions, revise the properties of a right-angled triangle. Also, practise the usage of Pythagoras theorem to write the perfect answers.
Chapter 6 - Triangles- Ex 6.6
Use the NCERT solutions for Chapter 6 to revise problems based on isosceles triangles. Revisit different types of problems wherein you understand the properties of triangles, which are part of a quadrilateral or a circle.
Chapter 7 - Coordinate Geometry
Class 10 Maths Chapter 7 improves your knowledge about concepts such as slopes, origins, axes, coordinates etc. In this chapter, you will learn how to find the coordinates as per the given data. Explore answers such as finding the distance between two points, using their coordinates, and more.
Chapter 7 - Coordinate Geometry - Ex 7.1
Practise problems on finding the distance between two points with our CBSE Class 10 Maths Chapter 5 Exercise 7.1 solutions. Revise the properties of quadrilaterals by revising chapter-specific problems.
Chapter 7 - Coordinate Geometry - Ex 7.2
Revise the accurate steps to use the section formula and find the coordinates of a given point. Use TopperLearning's NCERT solutions to understand how to find the points part of the trisection of a given line segment.
Chapter 7 - Coordinate Geometry - Ex 7.3
Learn when to consider the absolute value in a given problem by reading the concept insights in our NCERT solutions. Understand the relation between collinear points and a triangle. Also, revise the steps to use area of a triangle to calculate the area of a quadrilateral.
Chapter 7 - Coordinate Geometry - Ex 7.4
Revise the CBSE Class 10 Maths NCERT exercises and solutions in Chapter 7 to understand calculations that help in finding the centre of a circle. Learn to prove that a given figure is a rhombus. Also, revise how to use the median of a triangle to calculate coordinates in a given problem.
Chapter 8 - Introduction to Trigonometry
Take advantage of our well-written NCERT solutions for Class 10 Maths Chapter 8 to practice problems related to trigonometry. Understand how to tackle problems on trigonometric ratios of angles from NCERT Solutions.
Chapter 8 - Introduction to Trigonometry - Ex 8.1
Revise how to use the Pythagoras theorem and trigonometric ratios to calculate the answers. Utilise the NCERT solutions and learn to read the given data accurately to calculate values of sin, cot, cos, tan and so on.
Chapter 8 - Introduction to Trigonometry - Ex 8.2
Go through the Chapter 8 exercise questions and the NCERT solutions created by experienced teachers to help you prepare for your exam. Understand the various methods to quickly solve complex problems on trigonometric ratios.
Chapter 8 - Introduction to Trigonometry - Ex 8.3
With the help of our chapter solutions for NCERT textbook exercises, learn to use existing values of a triangle and provide proofs as required. Also, understand the steps to calculate the value of the angle of a triangle using the relevant trigonometric formula.
Chapter 8 - Introduction to Trigonometry - Ex 8.4
In this section, practise exercises from the NCERT textbook wherein you have to prove that the given equation in the LHS is equal to RHS. Practise the CBSE Class 10 Maths Exercise 8.4 solutions multiple times to grasp the thought process for providing such proofs.
Chapter 9 - Some Applications of Trigonometry
Get detailed answers or solutions on applications of trigonometry as per the latest CBSE Class 10 NCERT books. Learn to solve questions on finding the height and distance of various objects. Also, revise the various applications of trigonometry with our NCERT solutions for Class 10 Maths Chapter 9.
Chapter 9 - Some Applications of Trigonometry - Ex 9.1
Make use of our CBSE Class 10 Maths NCERT solutions to apply the correct steps for using trigonometry to solve real-life problems. In the exercise questions, you will get to learn how to calculate a distance travelled by a person or the height of a pole by applying the chapter concepts.
Chapter 10 - Circles
Understand concepts such as tangent, secant, and number tangents from a point to a circle and more with a proper solution. Also, learn about the relevance of the radius, diameter, and the centre while studying the topic of Circles in detail.
Chapter 10 - Circles - Ex 10.1
Revise the questions on the properties of circles through TopperLearning's solutions for CBSE Class 10 Maths NCERT textbook exercises. Revisit the construction of tangents and secants. Also, learn to provide the necessary evidence to prove that the two given lines are parallel to each other.
Chapter 10 - Circles - Ex 10.2
Use our CBSE Class 10 Maths Exercise 10.2 solutions from the textbook to revise the important properties of triangles and circles. Learn to apply the Side-Side-Side Congruence rule in a given problem. Also, revise the properties of tangents and find out how you can write answers related to a quadrilateral that is circumscribing a circle.
Chapter 11 - Constructions
Class 10 Maths Chapter solutions will help you to attempt questions that involve drawing a tangent to a circle. Also, find answers on accurately creating a division of the line segments in our textbook solutions. Additionally, you will learn how to give the mathematical justification or solution of a construction.
Chapter 11 - Constructions - Ex 11.1
Learn to construct line segments to complex figures as per given information. Benefit from the NCERT model answers by Maths experts. These CBSE Class 10 Maths NCERT solutions give you step-wise answers to textbook exercises on accurately constructing the required diagram.
Chapter 11 - Constructions - Ex 11.2
You can easily score marks in your board exam with an accurately constructed diagram. All you need is the guidance to create it step by step. In our NCERT solutions, you will get the required help to draw complex diagrams involving circles, triangles, tangents, etc.
Chapter 12 - Areas Related to Circles
There are three exercises related to the area of circles in this chapter. Solve problems related to 'Perimeter and Area of a Circle', 'Areas of Combinations of Plane Figures' and 'Areas of Sector and Segment of a Circle'. Use our NCERT solutions for Class 10 Maths Chapter 12 to revise this section thoroughly.
Chapter 12 - Areas Related to Circles - Ex 12.1
Not sure how to use the circumference of a circle formula or the radius formula? Practise the answers to a variety of NCERT textbook exercises and learn how to use the right formula to find the area of a circle. Also, revise problems on finding the area of circular objects in real life.
Chapter 12 - Areas Related to Circles - Ex 12.2
Write and practise the CBSE NCERT Class 10 Maths Chapter 12 exercises and solutions to understand how to find the area of sector of a circle. Also, revisit the problems on minor sector of a circle and major sector of a circle.
Chapter 12 - Areas Related to Circles - Ex 12.3
Practise more textbook exercises related to circles with our NCERT solutions. Learn to find the area of a shaded region in a circle. Revise the steps for calculating the area of a semi-circle and the area of a quadrant of a circle.
Chapter 13 - Surface Areas and Volumes
In CBSE Class 10, the 'Surface Areas and Volumes' chapter is a part of the mensuration unit. You can find detailed explanations of these concepts on our website. The NCERT Grade 10 Maths Chapter 13 solutions will help you to practice the problems with the help of the NCERT solutions for each question.
Chapter 13 - Surface Areas and Volumes - Ex 13.1
Practise the formula to be used for finding the surface area of a cuboid. Study with the CBSE Class 10 Maths solutions by your side to find out how to calculate the inner surface area of a cylindrical object. Also, learn to compute the total surface area of an object using chapter concepts.
Chapter 13 - Surface Areas and Volumes - Ex 13.2
Through the NCERT solutions for Chapter 13, you'll be able to find the volume of solids of various shapes. These objects can be a combination of solid shapes such as a hemisphere and a cone or a triangle and a cylinder.
Chapter 13 - Surface Areas and Volumes - Ex 13.3
In the NCERT solutions of the Chapter 13 exercise, you'll learn to find the radius of a sphere and the height of a cylinder. Based on the available data, you will be able to calculate the height of a shape in real situations such as finding the height of a well.
Chapter 13 - Surface Areas and Volumes - Ex 13.4
Revise the CBSE Class 10 Maths exercises and solutions from this chapter to calculate the capacity of objects. You can do so by calculating the volume of the shape of the solid object. Through the solutions, you'll learn to use this information to calculate the cost of covering an object with a metal sheet or wrapper.
Chapter 13 - Surface Areas and Volumes - Ex 13.5
How many rounds of wire will be needed to cover a cylinder of a given dimension? Find this answer and more in the NCERT solutions by Mathematics experts. Also, revise calculations involving the volume of a double cone, a cistern, and more.
Chapter 14 - Statistics
Study with ease the concept of grouped and ungrouped data in Statistics. Without taking any stress, you can now revise cumulative frequency curves with our expert solutions for this chapter. Learn how to find the mean, mode, or median of grouped data from our NCERT solutions. Also, learn to solve questions on Statistics by understanding the concept of cumulative frequency distribution and get a proper final solution.
Chapter 14 - Statistics - Ex 14.1
Revise Statistics lessons with TopperLearning's NCERT solutions. Can you find the mean number of plants in a house or the mean daily wages of workers in a factory? You will be able to, with the exercise solutions provided by our experts.
Chapter 14 - Statistics - Ex 14.2
In the CBSE Class 10 Maths book NCERT solutions for Chapter 14, learn how to calculate the class mark as per the given data. Learn to apply the mode formula to find the modal lifetime of objects like electrical components. Revise terms such as class size, lower limit, etc.
Chapter 14 - Statistics - Ex 14.3
Use TopperLearning's NCERT solutions to understand data analysis using statistical methods such as step deviation method. Revisit lessons on calculating the mean, mode and median of the given. Understand cumulative frequencies and class intervals while studying about data analysis.
Chapter 14 - Statistics - Ex 14.4
In the chapter exercises, you will find questions on representing data in the form of graphs. Learn to draw ogives using data from a cumulative frequency distribution table. Refer our solved CBSE Class 10 Maths NCERT textbook questions to review the correct answers during Maths practice.
Chapter 15 - Probability
NCERT Class 10 Maths Chapter 15 includes detailed answers on probability-based questions. These NCERT solutions will teach you how to solve simple problems based on the concept of theoretical probability.
Chapter 15 - Probability - Ex 15.1
Revise solutions on CBSE Class 10 Maths Probability questions from the NCERT textbook to understand events. Find out how to figure out the outcomes of an event by reviewing the answers to similar questions. Also, explore the formula to calculate the probability for a given event.
Chapter 15 - Probability - Ex 15.2
Improve your intelligence with your Maths skills by practising the exercise questions and solutions from this chapter. Think of all possible outcomes of a given event by performing precise Maths calculations. Learn the right approach to solve probability problems with NCERT solutions.
CBSE Class 10 Chapter-wise Marks Weightage
Plan your Maths revision by understanding the weightage of marks for each chapter. Allot more time to grasping concepts that have high weightage. Study each CBSE Class 10 Maths chapter with TopperLearning's NCERT solutions and other study resources to gain the skills to score top marks.
Course Structure CBSE Class 10
| Units | Unit Name | Marks |
| I | NUMBER SYSTEMS | 06 |
| II | ALGEBRA | 20 |
| III | COORDINATE GEOMETRY | 06 |
| IV | GEOMETRY | 15 |
| V | TRIGONOMETRY | 12 |
| VI | MENSURATION | 10 |
| VII | STATISTICS & PROBABILTY | 11 |
| Total | 80 |
CBSE Class 10 Mathematics – Standard and Basic Question Paper Design (2021-2022)
The CBSE Board introduces changes in the question paper pattern from time to time. Take a look at the latest question paper pattern for CBSE Class 10 Mathematics. You will feel more confident when you appear for your exam if you are aware of the paper pattern.
MATHEMATICS-STANDARD QUESTION PAPER DESIGN CBSE CLASS 10 (2021-22)
Time: 3 Hours Max. Marks: 80
| Sr No. | Typology of Questions | Total Marks | % Weightage (approx.) |
| 1 | Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas | 43 | 54 |
| 2 | Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. | 19 | 24 |
| 3 | Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions | 18 | 22 |
| Total | 80 | 100 |
| Internal Assessment | Marks 20 |
| Pen Paper Test and Multiple Assessment (5+5) | 10 Marks |
| Portfolio | 05 Marks |
| Lab Practical (Lab activities to be done from the prescribed books) | 05 Marks |
MATHEMATICS-BASIC QUESTION PAPER DESIGN CBSE CLASS 10 (2021-22)
Time: 3 Hours Max. Marks: 80
| Sr. No. | Typology of Questions | Total Marks | % Weightage (approx.) |
| 1 | Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas | 60 | 75 |
| 2 | Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. | 12 | 15 |
| 3 | Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions | 8 | 10 |
| Total | 80 | 100 |
| Internal Assessment | Marks 20 |
| Pen Paper Test and Multiple Assessment (5+5) | 10 Marks |
| Portfolio | 05 Marks |
| Lab Practical (Lab activities to be done from the prescribed books) | 05 Marks |
Cbse Class 10 Ncert Solutions of Maths
Source: https://www.topperlearning.com/ncert-solutions/cbse-class-10-mathematics
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