How will Class 10 Maths NCERT Solutions help CBSE students?

Study concepts, doubts, practice, and revisions of each concept regularly with the help of NCERT Solutions in order to prepare properly for these exams.

Must I Practice all the Questions given in NCERT Solutions Class 10 Maths?

Though practicing all questions is too good, make sure to practice the most important topics and question types.

How do the NCERT Solutions Class 10 Maths develop problem-solving skills in a student?

The NCERT Solutions give problems step by step to the students, and this helps the student to know how a problem is solved and then apply it himself.

Should I make notes while studying through NCERT Solutions for Class 10 Maths?

This will help in making quick revisions and the student can remember the concepts and problem-solving tactics more easily.

State some of the favored ways of learning the concepts involved in the NCERT Solutions Class 10 Maths?

The more you practice the problems, go through the review solutions, and try to apply concepts to different types of problems, the better grasp you will get.

What are the key topics of Class 10 Maths NCERT Solutions?

Following are the key topics of NCERT Solutions for Class 10 Maths Solutions: Real Numbers, Polynomials, Quadratic Equations, Arithmetic Progressions, and Trigonometry.

Can we solve problems other than the methods mentioned in CBSE Solutions Class 10 Maths?

Yes, sometimes finding alternative methods to solve a problem improves understanding and also offers different perspectives on problem-solving.

How many chapters are there in NCERT Class 10 Maths Solutions?

There are 15 chapters in total in the NCERT Class 10 Maths textbook.

What are the benefits of Class 10 Maths NCERT Solutions for the CBSE students?

Explanation, practice for exams, and laying a solid foundation for future mathematical concepts.

What are the Salient Features of formulas in NCERT Solutions for Class 10 Maths?

Some of the Salient formulas lie in Quadratic Equations, Trigonometric Identities, and Surface Areas and Volumes.

Why should I do CBSE Solutions for Class 10 Maths regularly?

Doing practice regularly strengthens your concepts, problem-solving skills, and preparation for an exam.

NCERT Solutions for Class 10 Maths (Updated for 2026-27)

List of Chapters	Notes
Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progressions
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 9: Some Applications of Trigonometry
Chapter 10: Circles
Chapter 11: Areas Related to Circles
Chapter 12: Surface Areas and Volumes
Chapter 13: Statistics
Chapter 14: Probability

Important Topics

Learning Outcomes

Theorems

Formulas

Prime Number
Composite Number
Rational Number
Irrational Number
Real Number

The properties of real numbers.
Euclid's Division Lemma and its applications.
The Fundamental Theorem of Arithmetic.
Prime factorisation techniques.
The relationship between HCF and LCM.

Euclid's Division Lemma
Fundamental Theorem of Arithmetic

HCF × LCM = Product of Two Numbers (for two positive integers)

Topic	Key Point
Euclid's Division Lemma	Used to find HCF
HCF & LCM	HCF × LCM = Product of Two Numbers
Fundamental Theorem	Every composite number has a unique prime factorisation
Decimal Expansion	Rational numbers have terminating or recurring decimals

Exercise 2.1

Exercise 2.2

Exercise 2.3

Important Topics

Learning Outcomes

Theorems

Formulas

Polynomial
Monomial
Binomial
Trinomial
Degree of a Polynomial
Zero of a Polynomial

Polynomial expressions and their degrees.
Zeros of a polynomial.
Relationship between zeros and coefficients.
Graphical representation of polynomials.

Relationship between zeros and coefficients of a polynomial

For a quadratic polynomial ( $a x^{2} + b x + c$ ):

Sum of zeros = (-b/a)
Product of zeros = (c/a)

Topic	Formula / Concept
Sum of Zeros	−b/a
Product of Zeros	c/a
Degree	Highest power of the variable
Graph	X-intercepts represent zeros

Important Topics

Learning Outcomes

Formulas

Graphical interpretation
Unique solution
Infinite solutions
No solution

Solving linear equations graphically.
Solving equations algebraically.
Substitution method.
Elimination method.
Cross-multiplication method.
Applications in real-life situations.

General form:

( $a_{1} x + b_{1} y + c_{1} = 0$ )

( $a_{2} x + b_{2} y + c_{2} = 0$ )

Method	Best Used For
Graphical	Visual understanding
Substitution	Simple equations
Elimination	Eliminating one variable
Cross Multiplication	Direct algebraic solution

Exercise 4.1

Exercise 4.2

Exercise 4.3

Important Topics

Learning Outcomes

Formulas

Word problems
Nature of roots
Algebraic solutions

Standard form of quadratic equations.
Solving by factorisation.
Completing the square.
Quadratic formula.
Nature of roots.

Standard Form: $(a x^{2} + b x + c = 0,; a \neq = 0)$

Quadratic Formula:
$[x = \frac{- b \pm b ^{2} - 4 a c}{2 a}]$

Discriminant:
$[D = b^{2} - 4 a c]$

Nature of Roots:

(D>0): Two distinct real roots
(D=0): Two equal real roots
(D<0): No real roots (complex roots)

Sum and Product of Roots:
$[α + β = - \frac{b}{a}]$
$[α β = \frac{c}{a}]$

Completing the Square Identity:
$[x^{2} + b x = (x + \frac{b}{2})^{2} - (\frac{b}{2})^{2}]$

Topic	Formula
Quadratic Formula	x = (−b ± √(b² − 4ac))/2a
Discriminant	D = b² − 4ac
D > 0	Two distinct real roots
D = 0	Equal roots
D < 0	No real roots

Important Topics

Learning Outcomes

Formulas

Sequence patterns
Sum calculations
Practical applications

Arithmetic sequences.
Common difference.
Finding the nth term.
Sum of the first n terms.
Real-life applications of arithmetic progressions.

$(a_{n} = a + (n - 1) d)$
$(S_{n} = \frac{n}{2} [2 a + (n - 1) d])$

Formula	Purpose
an = a + (n−1)d	nth term
Sn = n/2 [2a+(n−1)d]	Sum of n terms

Important Topics

Learning Outcomes

Formulas

Similarity
Ratio and proportion
Geometrical proofs

Important Theorems

Basic Proportionality Theorem
Pythagoras Theorem
Converse of Pythagoras Theorem

Similar triangles.
Criteria for similarity.
Basic Proportionality Theorem.
Pythagoras Theorem.
Applications of similar triangles.

Similarity Ratio: $[\frac{A B}{D E} = \frac{BC}{EF} = \frac{A C}{D F}]$

Basic Proportionality Theorem (BPT):
If (DE \parallel BC), then
$[\frac{A D}{D B} = \frac{A E}{EC}]$

Pythagoras Theorem:
$[c^{2} = a^{2} + b^{2}]$
(where (c) is the hypotenuse)

Converse of Pythagoras Theorem:
If
$[c^{2} = a^{2} + b^{2},]$
then the triangle is right-angled.

Area of Similar Triangles:
$[\frac{Area _{1}}{Area _{2}} = (\frac{Corresponding Side _{1}}{Corresponding Side _{2}})^{2}]$

Perimeter of Similar Triangles:
$[\frac{P _{1}}{P _{2}} = \frac{Corresponding Side _{1}}{Corresponding Side _{2}}]$

Concept	Key Point
Similarity	Corresponding angles equal
BPT	Parallel line divides sides proportionally
Pythagoras	Hypotenuse² = Base² + Perpendicular²

Exercise 7.1

Exercise 7.2

Exercise 7.3

Important Topics

Learning Outcomes

Formulas

Coordinate plotting
Distance calculation
Midpoint concepts

Cartesian coordinate system.
Distance formula.
Section formula.
Internal division of a line segment.

Distance Formula:
$[d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}]$

Midpoint Formula:
$[M (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})]$

Section Formula (Internal Division):
If point (P) divides (AB) in the ratio (m:n),
$[P (\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})]$

Origin:
$[O = (0, 0)]$

Quadrants:
$[I : (+, +), II : (-, +), III : (-, -), IV : (+, -)]$

Formula	Use
Distance Formula	=Find distance between two points
Section Formula	Divide a line segment internally

Important Topics

Learning Outcomes

Formulas

Right-angled triangles
Angle measurement
Ratio relationships

Trigonometric ratios.
Standard angle values.
Trigonometric identities.
Complementary angle relationships.

sin²θ + cos²θ = 1
sec²θ = 1 + tan²θ
cosec²θ = 1 + cot²θ

Formula	Importance
sin²θ + cos²θ = 1	Fundamental identity
sec²θ = 1 + tan²θ	Identity
cosec²θ = 1 + cot²θ	Identity

Exercise 9.1

Important Topics

Learning Outcomes

Formulas

Real-life measurement problems
Surveying
Navigation

Heights and distances.
Angle of elevation.
Angle of depression.
Practical applications of trigonometry.

Trigonometric Ratios (SOH–CAH–TOA):
$[sin θ = \frac{Perpendicular}{Hypotenuse}, cos θ = \frac{Base}{Hypotenuse}, tan θ = \frac{Perpendicular}{Base}]$

Reciprocal Ratios:
$[cosec θ = \frac{1}{s i n θ}, sec θ = \frac{1}{c o s θ}, cot θ = \frac{1}{t a n θ}]$

Pythagorean Identity:
$[sin^{2} θ + cos^{2} θ = 1]$

Height Formula:
$[Height = Distance \times tan θ]$

Distance Formula:
$[Distance = \frac{Height}{t a n θ}]$

Concept	Application
Angle of Elevation	Looking upward
Angle of Depression	Looking downward
Heights & Distances	Practical measurements

Exercise 10.1

Exercise 10.2

Important Topics

Learning Outcomes

Formulas

Circle
Radius
Tangent
Point of Contact

Theorems

Tangent is perpendicular to the radius at the point of contact.
Tangents drawn from an external point are equal.

Tangents to a circle.
Properties of tangents.
Relationship between radius and tangent.

Radius ⟂ Tangent:
$[OT ⊥ PT]$
(Radius (OT) is perpendicular to tangent (PT) at the point of contact (T).)

Equal Tangents from an External Point:
[PA = PB]

Right Triangle Relation (using Pythagoras):
$[O P^{2} = O T^{2} + P T^{2}]$
where (OT=r) (radius).

Length of Tangent from an External Point:
$[PT = O P^{2} - r^{2}]$

Property	Key Point
Radius ⟂ Tangent	At point of contact
External Point	Tangents drawn are equal

Exercise 11.1

Exercise 11.2

Exercise 11.3

Important Topics

Learning Outcomes

Formulas

Area of sectors.
Area of segments.
Circumference.
Applications of circle geometry.

Circumference = 2πr
Area = πr²
Area of Sector = (θ/360) × πr²

Formula	Purpose
Circumference = 2πr	Boundary length
Area = πr²	Circle area
Sector Area	(θ/360) × πr²

Exercise 12.1

Exercise 12.2

Exercise 12.3

Important Topics

Learning Outcomes

Formulas

Cube
Cuboid
Cone
Cylinder
Sphere
Hemisphere
Frustum

Surface area calculations.
Volume calculations.
Combination of solids.
Practical mensuration problems.

Cube:
$[LSA = 4 a^{2}, TSA = 6 a^{2}, V = a^{3}]$

Cuboid:
$[LSA = 2 h (l + b), TSA = 2 (l b + bh + h l), V = l bh]$

Cylinder:
$[CSA = 2 π r h, TSA = 2 π r (r + h), V = π r^{2} h]$

Cone:
$[l = r^{2} + h^{2}, CSA = π r l, TSA = π r (l + r), V = \frac{1}{3} π r^{2} h]$

Sphere:
$[Surface Area = 4 π r^{2}, V = \frac{4}{3} π r^{3}]$

Hemisphere:
$[CSA = 2 π r^{2}, TSA = 3 π r^{2}, V = \frac{2}{3} π r^{3}]$

Frustum of a Cone:

$[l = h^{2} + (R - r)^{2}] [CSA = π (R + r) l] [TSA = π (R + r) l + π (R^{2} + r^{2})] [V = \frac{1}{3} πh (R^{2} + R r + r^{2})]$

Solid	Remember
Cube	TSA & Volume
Cuboid	TSA & Volume
Cylinder	CSA, TSA & Volume
Cone	Slant Height
Sphere	Surface Area & Volume

Important Topics

Learning Outcomes

Formulas

Data collection
Data analysis
Interpretation of grouped data

Mean
Median
Mode
Cumulative frequency
Graphical representation of data

Mean (Ungrouped Data):
$[\overset{x}{ˉ} = \frac{\sum x}{n}]$

Mean (Grouped Data):
$[\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}]$

Median (Grouped Data):
$[Median = l + (\frac{\frac{N}{2} - c f}{f}) h]$

Mode (Grouped Data):
$[Mode = l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) h]$

Cumulative Frequency:
$[CF = \sum f]$

Measure	Meaning
Mean	Average
Median	Middle value
Mode	Most frequent value

Exercise 14.1

Important Topics

Learning Outcomes

Formulas

Event
Experiment
Sample Space
Outcome

Probability of an event.
Sample space.
Experimental probability.
Classical probability.

Probability of an Event:
$[P (E) = \frac{Number of favourable outcomes}{Total number of possible outcomes}]$

Complementary Event:
$[P (E^{'}) = 1 - P (E)]$

Experimental Probability:
$[P (E) = \frac{Number of times the event occurs}{Total number of trials}]$

Sample Space:
$[n (S) = Total number of possible outcomes]$

Probability Range:
$[0 \leq P (E) \leq 1]$

Formula	Meaning
P(E) = Favourable Outcomes / Total Outcomes	Classical Probability

Unit	Topics Covered
Number Systems	Real Numbers
Algebra	Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions
Coordinate Geometry	Coordinate Geometry
Geometry	Triangles, Circles
Trigonometry	Introduction to Trigonometry, Applications of Trigonometry
Mensuration	Areas Related to Circles, Surface Areas and Volumes
Statistics & Probability	Statistics, Probability

Chapter	Common Mistakes	How to Avoid Them
Real Numbers	Incorrect prime factorisation or HCF–LCM calculations	Verify factorisation step by step and use the HCF × LCM relation carefully.
Polynomials	Errors in finding zeros or relating them to coefficients	Write the polynomial in standard form before applying formulas.
Pair of Linear Equations	Arithmetic mistakes during elimination or substitution	Simplify each step and check the solution by substitution.
Quadratic Equations	Wrong use of the quadratic formula or sign errors	Substitute values carefully and calculate the discriminant first.
Arithmetic Progressions	Using the wrong formula for the nth term or sum	Identify whether the question asks for a term or the total sum.
Triangles	Applying similarity criteria incorrectly	Match corresponding sides and angles before solving.
Coordinate Geometry	Errors in coordinates or formula substitution	Label points correctly and use brackets while substituting values.
Introduction to Trigonometry	Confusing trigonometric ratios and identities	Memorise standard values and revise identities regularly.
Applications of Trigonometry	Choosing the wrong angle or ratio	Draw a neat diagram and identify the angle of elevation or depression first.
Circles	Forgetting tangent properties	Remember that the radius is perpendicular to the tangent at the point of contact.
Areas Related to Circles	Mixing up sector and segment formulas	Read the figure carefully before selecting the formula.
Surface Areas and Volumes	Using the wrong surface area or volume formula	Identify the solid correctly and note whether TSA, CSA, or volume is required.
Statistics	Incorrect cumulative frequency calculations	Prepare the frequency table carefully before solving.
Probability	Wrong sample space or favourable outcomes	List all possible outcomes before calculating probability.

Chapter	JEE Foundation	Physics & Physical Chemistry Support	Why It Matters
Real Numbers	★★★★☆	★★★☆☆	Strengthens numerical calculations, ratios, and scientific computations.
Polynomials	★★★★★	★★★☆☆	Builds algebraic skills used in Physics equations and Physical Chemistry calculations.
Pair of Linear Equations in Two Variables	★★★★★	★★★★☆	Helps solve simultaneous equations used in Physics and Chemistry numericals.
Quadratic Equations	★★★★★	★★★★★	Frequently used in projectile motion, optics, and higher Physics calculations.
Arithmetic Progressions	★★★★☆	★★☆☆☆	Develops logical reasoning and sequence-based mathematical thinking.
Triangles	★★★★★	★★★★☆	Forms the foundation of trigonometry used extensively in Physics.
Coordinate Geometry	★★★★★	★★★★☆	Useful for graph interpretation, vectors, and Mechanics.
Introduction to Trigonometry	★★★★★	★★★★★	Essential for Mechanics, Waves, Optics, and rotational motion in Physics.
Some Applications of Trigonometry	★★★★★	★★★★★	Applied in height-distance problems, Mechanics, and geometrical Physics.
Circles	★★★★☆	★★★☆☆	Supports coordinate geometry and circular motion concepts.
Areas Related to Circles	★★★☆☆	★★★☆☆	Useful in geometry, measurement, and practical Physics applications.
Surface Areas and Volumes	★★★★☆	★★★★★	Important for density, pressure, volume, and measurement-based Physics and Physical Chemistry problems.
Statistics	★★★☆☆	★★★☆☆	Helps analyse experimental data, graphs, and observations.
Probability	★★★★☆	★★☆☆☆	Develops analytical reasoning and statistical thinking.

CBSE Notes for Class 10 Maths Chapter 1 Real Numbers

CBSE Notes for Class 10 Maths Chapter 2 Polynomials

CBSE Notes for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

CBSE Notes for Class 10 Maths Chapter 4 Quadratic Equation

CBSE Notes for Class 10 Maths Chapter 5 Arithmetic Progressions

CBSE Notes for Class 10 Maths Chapter 6 - Triangles

CBSE Notes for Class 10 Maths Chapter 7 Coordinate Geometry

CBSE Notes for Class 10 Maths Chapter 8 Introduction to Trigonometry

CBSE Notes for Class 10 Maths Chapter 9 Some Applications of Trigonometry

CBSE Notes for Class 10 Maths Chapter 10 Circles

CBSE Notes for Class 10 Maths Chapter 11 Areas Related to Circles

CBSE Notes for Class 10 Maths Chapter 12 Surface Areas and Volumes

CBSE Notes for Class 10 Maths Chapter 13 Statistics

CBSE Notes for Class 10 Maths Chapter 14 Probability

Frequently Asked Questions

How will Class 10 Maths NCERT Solutions help CBSE students?

Must I Practice all the Questions given in NCERT Solutions Class 10 Maths?

How do the NCERT Solutions Class 10 Maths develop problem-solving skills in a student?

Should I make notes while studying through NCERT Solutions for Class 10 Maths?

State some of the favored ways of learning the concepts involved in the NCERT Solutions Class 10 Maths?

What are the key topics of Class 10 Maths NCERT Solutions?

Can we solve problems other than the methods mentioned in CBSE Solutions Class 10 Maths?

How many chapters are there in NCERT Class 10 Maths Solutions?

What are the benefits of Class 10 Maths NCERT Solutions for the CBSE students?

What are the Salient Features of formulas in NCERT Solutions for Class 10 Maths?

Why should I do CBSE Solutions for Class 10 Maths regularly?

Join ALLEN!

Related Articles:-

NCERT Solutions Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions Class 10 Maths Chapter 3 Linear Equations in Two Variables

NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry

NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry

NCERT Solutions Class 10 Maths Chapter 6 Triangles

NCERT Solutions Class 10 Maths Chapter 10 Circles

NCERT Solutions Class 10 Maths

1.0NCERT Solutions Class 10 Maths Chapters: Download PDF

2.0Important Topics covered under CBSE NCERT Class 10 Maths

3.0NCERT Solutions Class 10 Maths Chapter-wise Details

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Class 10 Maths Chapter 1 Exercises: -

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

Class 10 Maths Chapter 2 Exercises:-

Quick Revision Table

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

Class 10 Maths Chapter 3 Exercises:-

Quick Revision Table

NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations

Class 10 Maths Chapter 4 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

Class 10 Maths Chapter 5 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Class 10 Maths Chapter 6 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

Class 10 Maths Chapter 7 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

Class 10 Maths Chapter 8 Exercises:-

Quick Revision Table

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

Class 10 Maths Chapter 9 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 10 Circles

Class 10 Maths Chapter 10 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 11 Areas Related to Circles

Class 10 Maths Chapter 11 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes

Class 10 Maths Chapter 12 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 13 Statistics

Class 10 Maths Chapter 13 Exercises:-

Quick Revision Table

NCERT Solutions for Class 10 Maths Chapter 14 Probability

Class 10 Maths Chapter 14 Exercises:-

Quick Revision Table

4.0Chapterwise Distribution of CBSE Class 10 Maths:

5.0Latest NCERT Class 10 Maths Syllabus (2026–27)

Unit-wise Syllabus Overview

Why Students Should Know the Syllabus

6.0 Common Mistakes Students Make in Class 10 Maths and How to Avoid Them

7.0The Importance of Class 10 Maths NCERT Solutions Beyond Class 10

JEE/NEET Foundation: Importance of Each Chapter in Class 10 Maths

8.0Other Important Study Material for Class 10 Students

9.0 Class 10 Maths Exam Preparation Strategy

Build Strong Conceptual Understanding

Complete NCERT Before Using Other Books

Practice Maths Every Day

Create a Formula and Theorem Revision Notebook

Focus on Competency-Based Questions