NCERT Solutions Class 10 Maths

Mathematics is the NCERT textbook for Class X, built around algebra, geometry, trigonometry, mensuration, statistics and probability. NCERT Solutions Class 10 Maths provide chapter-wise answers with formulas, constructions, proofs, graphs and step-by-step methods.

NCERT Solutions Class 10 Maths are based on the NCERT Mathematics Textbook for Class X, reprinted for the 2026-27 academic year. The book covers 14 chapters, from Real Numbers to Probability, along with two optional appendices on Proofs in Mathematics and Mathematical Modelling. It follows a reasoning-based approach where students learn formulas, theorems, graphs, constructions, identities and numerical methods through examples and exercises. 

Key Takeaways

• Book Name: Mathematics is the NCERT textbook for Class X in 2026-27.
• Total Chapters: The textbook has 14 chapters from Real Numbers to Probability.
• Main Areas: The book covers algebra, geometry, trigonometry, mensuration, statistics and probability.
• Practice Note: Appendices on Proofs in Mathematics and Mathematical Modelling are optional reading.

NCERT Solutions Class 10 Maths Structure 2026-27

Overview of the NCERT Class 10 Maths Book 2026-27

The NCERT Class 10 Maths book builds mathematical reasoning through definitions, examples, theorems, constructions, exercises and summaries. It moves from number theory and algebra into geometry, trigonometry, mensuration, statistics and probability.

The official book title is Mathematics: Textbook for Class X. The 2026-27 reprint follows the rationalised structure and contains 14 chapters. The book also includes answers and hints after the appendices.

The ncert class 10 maths solutions page reflects how this textbook works. The book uses different learning elements across chapters:

• Worked examples
• Exercises
• Optional exercises
• Theorems and proofs
• Constructions and analysis
• Chapter summaries
• Answers and hints
• Optional appendices

NCERT Class 10 Maths Chapter List 2026-27

The NCERT Class 10 Maths chapter list has 14 chapters. The sequence moves from real numbers, polynomials and equations into geometry, trigonometry, mensuration, statistics and probability.

Chapter Wise Guide to NCERT Solutions Class 10 Maths

Class 10 maths chapter wise solutions move from formula use to proof, graph reading, construction logic and data interpretation. Each chapter needs written steps because final answers alone do not show the method.

Chapter 1: Real Numbers

Chapter 1 introduces Euclid’s division lemma and the Fundamental Theorem of Arithmetic. Students use prime factorisation to find HCF and LCM.

The chapter also revisits irrational numbers. It explains why numbers such as √2 and √3 cannot be written as p/q.

NCERT solutions class 10 maths answers for this chapter show division steps, prime factors and proof logic. A complete answer must state the theorem or property used.

Important formulas:

HCF × LCM = Product of two numbers

Dividend = Divisor × Quotient + Remainder

Chapter 2: Polynomials

Chapter 2 explains the geometrical meaning of zeroes of a polynomial. Students learn how graph intersections with the x-axis show zeroes.

The chapter also covers the relationship between zeroes and coefficients of a polynomial. This is important for finding zeroes without drawing a graph.

Class 10 maths ncert solutions for this chapter include graph interpretation and algebraic verification. Students should write the polynomial form clearly before substituting values.

Important formulas for quadratic polynomial ax² + bx + c:

Sum of zeroes = -b/a

Product of zeroes = c/a

Chapter 3: Pair of Linear Equations in Two Variables

Chapter 3 covers graphical and algebraic methods for solving two linear equations. Students learn substitution and elimination methods.

The chapter also explains when two lines intersect, remain parallel or coincide. This decides whether the pair has one solution, no solution or infinitely many solutions.

NCERT class 10 maths chapter wise solutions for this chapter show each equation transformation. Graphical answers should mention the point of intersection.

Important forms:

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

For one solution:

a₁/a₂ ≠ b₁/b₂

For no solution:

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

For infinitely many solutions:

a₁/a₂ = b₁/b₂ = c₁/c₂

Chapter 4: Quadratic Equations

Chapter 4 introduces quadratic equations and their solutions by factorisation. Students also learn how to identify the nature of roots.

The chapter is important because many questions require forming an equation from a word problem. Students must define the variable before writing the equation.

NCERT Solutions Class 10 Maths answers for this chapter include factorisation steps and root verification. Nature of roots questions use the discriminant.

Important formulas:

Quadratic equation: ax² + bx + c = 0

Discriminant: D = b² - 4ac

If D > 0, roots are real and distinct.

If D = 0, roots are real and equal.

If D < 0, roots are not real.

Chapter 5: Arithmetic Progressions

Chapter 5 explains arithmetic progressions, nth term and sum of first n terms. Students identify common difference and use it to find missing terms.

The chapter includes word problems based on sequences. Students must separate first term, common difference and number of terms before substituting.

Class 10 maths solutions 2026-27 for AP questions show formula choice clearly. The same problem may need both nth term and sum formula.

Important formulas:

an = a + (n - 1)d

Sn = n/2 [2a + (n - 1)d]

Sn = n/2 (a + l)

Chapter 6: Triangles

Chapter 6 covers similar figures, similarity of triangles and criteria for similarity. It includes AA, SAS and SSS similarity criteria.

The chapter also uses proportionality in triangles. Diagram reading is essential because many answers depend on matching corresponding sides.

NCERT maths class 10 solutions for this chapter explain the theorem used before writing ratios. Geometry answers should not jump directly to the final value.

Important ideas:

AA similarity: Two corresponding angles are equal.

SAS similarity: One angle is equal and including sides are proportional.

SSS similarity: Corresponding sides are proportional.

Chapter 7: Coordinate Geometry

Chapter 7 introduces distance formula and section formula. Students use coordinates to calculate lengths and internal division points.

The chapter connects algebra with geometry. Points on the Cartesian plane become measurable through formulas.

Class 10 mathematics ncert solutions for this chapter show substitution carefully. Sign errors are common when points contain negative coordinates.

Important formulas:

Distance between (x₁, y₁) and (x₂, y₂):

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Section formula for point dividing in ratio m:n:

x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Chapter 8: Introduction to Trigonometry

Chapter 8 introduces trigonometric ratios, specific angles and trigonometric identities. Students learn sine, cosine, tangent, cosecant, secant and cotangent.

The chapter uses right triangles. Students must identify perpendicular, base and hypotenuse correctly.

NCERT class 10 maths solutions for this chapter explain ratio selection and identity use. Proving identity questions need one side to be simplified into the other.

Important ratios:

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Important identities:

sin² θ + cos² θ = 1

1 + tan² θ = sec² θ

1 + cot² θ = cosec² θ

Chapter 9: Some Applications of Trigonometry

Chapter 9 applies trigonometry to heights and distances. Students solve questions involving angle of elevation and angle of depression.

The chapter usually uses right-triangle diagrams. A correct diagram can decide the entire solution.

NCERT Solutions for Class 10 Maths answers for this chapter show diagram setup, ratio selection and final height or distance. Units must be written at the end.

Common ratio used:

tan θ = Height/Distance

Chapter 10: Circles

Chapter 10 explains tangents to a circle and the number of tangents from a point. Students learn that a tangent touches a circle at exactly one point.

The chapter also explains that the radius through the point of contact is perpendicular to the tangent. This property is used in many proof questions.

Class 10 maths textbook solutions for this chapter state the tangent theorem clearly. Proof answers should mention equal tangents from an external point where needed.

Important facts:

Radius ⟂ Tangent at point of contact

Tangents from an external point are equal in length

Chapter 11: Areas Related to Circles

Chapter 11 covers areas of sectors and segments of a circle. Students use angle, radius and circle formulas together.

The chapter often combines geometry with mensuration. Students may need to subtract triangle area from sector area to find segment area.

NCERT Solutions Class 10 Maths answers for this chapter show the exact part of the circle being calculated. This avoids confusion between sector and segment.

Important formulas:

Area of circle = πr²

Circumference of circle = 2πr

Area of sector = θ/360 × πr²

Length of arc = θ/360 × 2πr

Chapter 12: Surface Areas and Volumes

Chapter 12 explains surface area and volume of combinations of solids. Students solve questions involving cylinders, cones, spheres and hemispheres.

The chapter tests visualisation. Students must identify which surfaces are exposed and which parts are joined.

NCERT class 10 maths solutions for this chapter separate curved surface area, total surface area and volume. A good answer names the solid before applying the formula.

Important formulas:

CSA of cylinder = 2πrh

Volume of cylinder = πr²h

CSA of cone = πrl

Volume of cone = 1/3πr²h

Surface area of sphere = 4πr²

Volume of sphere = 4/3πr³

Surface area of hemisphere = 3πr²

Volume of hemisphere = 2/3πr³

Chapter 13: Statistics

Chapter 13 explains mean, mode and median of grouped data. Students learn direct, assumed mean and step-deviation methods for mean.

The chapter uses frequency tables. Students must copy class intervals and frequencies accurately.

NCERT solutions class 10 maths for Statistics show table columns clearly. Errors in midpoint, cumulative frequency or class interval can change the final answer.

Important formulas:

Mean = Σfixi/Σfi

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h

Median = l + [(n/2 - cf)/f] × h

Chapter 14: Probability

Chapter 14 introduces theoretical probability. Students calculate probability using favourable outcomes and total possible outcomes.

The chapter includes examples based on coins, dice, cards and everyday events. Students must list outcomes correctly before writing probability.

NCERT Solutions Class 10 Maths answers for this chapter show the sample space and favourable cases. Probability values must lie between 0 and 1.

Important formula:

P(E) = Number of favourable outcomes / Total number of outcomes

For any event E:

0 ≤ P(E) ≤ 1