NCERT Solutions for Class 10 Maths 2025-26 (Free PDF)

NCERT Solutions for Class 10 Maths are the most trusted way to prepare for CBSE board exams because the majority of board-level questions are based on NCERT concepts, examples, and exercises. On this page, you will get Class 10 Maths NCERT Solutions (2025-26) for all 14 chapters with clear, step-by-step explanations that match the CBSE marking scheme. Whether your goal is to strengthen basics, avoid common mistakes, or improve speed and accuracy, these solutions are designed to help you score higher with consistent practice.

Each chapter is organized exercise-wise so you can quickly find the exact question you are practicing. You can also access free PDF downloads chapter-wise for offline revision, last-minute practice, and exam-day confidence. If you follow the study method shared below and revise key formulas regularly, these NCERT Maths Solutions Class 10 can be your single most effective resource for board exam success in the 2025-26 session.

Key Highlights of Class 10 Maths NCERT Solutions

• Complete Coverage: All 14 chapters with exercise-wise solutions
• Step-by-Step Solutions: Detailed explanations for every problem
• Board Exam Focus: Answers formatted per CBSE marking scheme
• Free PDF Download: Access solutions offline anytime
• Updated for 2025-26: Aligned with latest NCERT syllabus
• Expert Verified: Prepared by experienced mathematics teachers

Why NCERT Solutions for Class 10 Maths Are Essential

NCERT Solutions for Class 10 Maths matter because NCERT is the foundation of the CBSE Maths syllabus. When you learn concepts through NCERT and practice questions using step-based solutions, you build the exact skills required for board exams: concept clarity, correct method, and proper presentation. This is important because CBSE awards marks step-wise. Even if your final answer is wrong due to a small mistake, correct steps can still help you score partial marks.

NCERT solutions also help you understand how formulas and theorems are applied. Many students lose marks not because they do not know the concept, but because they skip steps, use wrong identities, or write incomplete reasoning. With Class 10 Maths NCERT Solutions, you learn the right approach for each question type—algebraic simplification, proof-based geometry, trigonometric identities, and data-based statistics.

Another advantage is competitive readiness. Strong NCERT-level preparation supports exams like NTSE and builds basics for future entrance exams such as JEE. If your NCERT base is strong, advanced problems become easier because you can identify patterns quickly and apply concepts confidently.

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Chapter-Wise NCERT Solutions for Class 10 Maths

Below is the complete list of NCERT Maths Solutions Class 10 for all chapters. Use the “View Solutions” link to open the chapter page, practice exercise-wise, and download chapter PDFs for offline revision. These solutions are aligned to the CBSE Class 10 Maths Solutions 2025-26 preparation needs and focus on correct steps, reasoning, and accuracy.

Ch. No	Chapter Name	Exercises	Key Topics	Solutions
1	Real Numbers	Ex 1.1 – 1.4	Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, Irrational Numbers	View Solutions
2	Polynomials	Ex 2.1 – 2.4	Zeroes of Polynomial, Division Algorithm, Relationship between Zeroes and Coefficients	View Solutions
3	Pair of Linear Equations in Two Variables	Ex 3.1 – 3.7	Graphical Method, Substitution, Elimination, Cross-Multiplication	View Solutions
4	Quadratic Equations	Ex 4.1 – 4.4	Factorization, Completing Square, Quadratic Formula, Nature of Roots	View Solutions
5	Arithmetic Progressions	Ex 5.1 – 5.4	nth Term, Sum of n Terms, AP Applications	View Solutions
6	Triangles	Ex 6.1 – 6.6	Similarity Criteria, BPT, Pythagoras Theorem	View Solutions
7	Coordinate Geometry	Ex 7.1 – 7.4	Distance Formula, Section Formula, Area of Triangle	View Solutions
8	Introduction to Trigonometry	Ex 8.1 – 8.4	Trigonometric Ratios, Ratios of Complementary Angles, Identities	View Solutions
9	Some Applications of Trigonometry	Ex 9.1	Heights and Distances, Angle of Elevation/Depression	View Solutions
10	Circles	Ex 10.1 – 10.2	Tangent Properties, Number of Tangents from External Point	View Solutions
11	Areas Related to Circles	Ex 11.1 – 11.3	Area of Sector, Segment, Combination of Figures	View Solutions
12	Surface Areas and Volumes	Ex 12.1 – 12.3	Combination of Solids, Conversion of Solids, Frustum	View Solutions
13	Statistics	Ex 13.1 – 13.3	Mean, Median, Mode of Grouped Data	View Solutions
14	Probability	Ex 14.1 – 14.2	Classical Probability, Complementary Events	View Solutions

Algebra Chapters (1-5)

Algebra is the highest scoring unit for many students because it is logic-based and follows fixed methods. Chapters like Polynomials, Linear Equations, Quadratic Equations, and Arithmetic Progressions frequently appear in board exams. The most common mistakes here include sign errors, skipping steps, and incorrect factorization. Use the solutions to learn the exact CBSE-friendly presentation and practice until you can solve standard question types confidently.

• Real Numbers: HCF/LCM using prime factorization, Euclid’s algorithm-based questions
• Polynomials: Finding zeroes, verifying relationships, division algorithm
• Linear Equations: Consistency conditions, word problems, elimination/substitution methods
• Quadratic Equations: Nature of roots, quadratic formula, real-life application problems
• Arithmetic Progressions: nth term and sum-based word problems

Geometry Chapters (6-7, 10-11)

Geometry requires concept clarity and clean reasoning. Chapters like Triangles and Circles often include proof-based questions, which are easy to score if your steps are correct and structured. Coordinate geometry is formula-based and becomes very scoring once you learn the standard formats. Focus on writing correct statements, matching reasons, and drawing neat diagrams where required.

• Triangles: Similarity criteria, Basic Proportionality Theorem (BPT), Pythagoras theorem
• Coordinate Geometry: Distance formula, section formula, area of triangle via coordinates
• Circles: Tangent properties, number of tangents from an external point
• Areas Related to Circles: Sector/segment area problems and mixed figures

Trigonometry Chapters (8-9)

Trigonometry becomes simple when your basics are strong. First, memorize ratios for standard angles and key identities. Next, practice simplifying expressions step-by-step. In heights and distances, always draw a diagram first and label angles and sides clearly. The solutions on this page show the correct method, which helps you avoid common mistakes like wrong identity selection or incorrect angle interpretation.

• Introduction to Trigonometry: Ratios, complementary angles, identities
• Applications: Angle of elevation/depression, height-distance questions

Statistics & Probability (13-14)

Statistics and Probability are formula-based and can be high scoring with practice. In statistics, accuracy in table creation and calculations is important. In probability, understand the definition, total outcomes, favorable outcomes, and complementary events. Practice a variety of sums to improve speed and reduce calculation errors.

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Unit-Wise Marks Distribution & Weightage

Use this unit-wise distribution as a guide for planning your revision. Give more time to high-weightage units like Algebra, Geometry, and Trigonometry, while ensuring you do not ignore smaller units because they can add easy marks.

Unit	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 & Probability	11
Total		80

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Important Formulas for Class 10 Maths

Keep a separate formula notebook and revise it weekly. Below is a chapter-wise formula checklist to support your Class 10 Maths Solutions PDF practice and quick revision before exams.

Algebra (Ch 1-5) Formula Checklist

• Euclid’s Division Algorithm: a = bq + r, where 0 ≤ r < b
• Quadratic Formula: x = [−b ± √(b² − 4ac)] / (2a)
• Nature of Roots: D = b² − 4ac (D > 0, D = 0, D < 0)
• AP nth Term: a_n = a + (n−1)d
• Sum of n Terms of AP: S_n = n/2 [2a + (n−1)d]

Geometry & Coordinate Geometry (Ch 6-7, 10-11)

• Distance Formula: √[(x₂−x₁)² + (y₂−y₁)²]
• Section Formula (Internal): ( (mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n) )
• Area of Triangle: 1/2 |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
• Circle Tangent: Tangent at any point of a circle is perpendicular to the radius through the point of contact
• Area of Sector: (θ/360) × πr²
• Length of Arc: (θ/360) × 2πr

Trigonometry (Ch 8-9)

• sin θ = Perpendicular / Hypotenuse
• cos θ = Base / Hypotenuse
• tan θ = Perpendicular / Base
• Identity: sin²θ + cos²θ = 1
• Identity: 1 + tan²θ = sec²θ
• Identity: 1 + cot²θ = cosec²θ

Mensuration (Ch 12) Quick Revision

• CSA of Cylinder: 2πrh
• TSA of Cylinder: 2πr(h + r)
• Volume of Cylinder: πr²h
• Volume of Cone: (1/3)πr²h
• Volume of Sphere: (4/3)πr³
• CSA of Frustum: π(r₁ + r₂)l

Statistics & Probability (Ch 13-14)

• Mean of Grouped Data: x̄ = Σ(f_ix_i) / Σf_i
• Median (Grouped Data): l + [ ( (n/2) − cf ) / f ] × h
• Mode (Grouped Data): l + [ (f₁ − f₀) / (2f₁ − f₀ − f₂) ] × h
• Probability: P(E) = (Number of favorable outcomes) / (Total outcomes)
• Complementary Event: P(not E) = 1 − P(E)

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How to Use These Solutions for Board Exam Success

To get maximum benefit from NCERT Solutions for Class 10 Maths, follow a step-by-step study method. This improves understanding, speed, and exam presentation.

• Step 1: Read the chapter concept and solved examples from the NCERT textbook first.
• Step 2: Attempt each exercise question on your own before checking the solution.
• Step 3: Compare your method with the solution and correct your steps, not just the final answer.
• Step 4: Maintain an error notebook for repeated mistakes (sign errors, wrong identities, calculation slips).
• Step 5: Revise formulas weekly and re-solve incorrect questions after 3-4 days.
• Step 6: After completing a unit, solve a sample paper or previous year paper for time practice.

Time management tip: divide practice into short sessions. For example, practice 20-30 questions daily instead of long sessions once a week. Regular practice improves retention and confidence.

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Tips to Score 100/100 in Class 10 Maths

If your goal is a perfect score, focus on accuracy, presentation, and revision. These practical tips are based on common CBSE marking patterns and student mistakes.

• Solve NCERT completely: Do every example and every exercise question without skipping.
• Master Algebra first: Algebra gives consistent scoring opportunities with practice.
• Write full steps: Never jump steps in board exams; step marks matter.
• Revise formulas daily: Keep a formula sheet and revise for 10 minutes daily.
• Practice proofs separately: Write Triangle and Circle proofs 2-3 times to improve flow.
• Improve calculation speed: Practice mental math for squares, cubes, and common fractions.
• Solve timed papers: Attempt at least 10 sample/previous papers with a stopwatch.
• Check units and signs: Most mistakes happen due to sign errors and wrong substitutions.
• Draw clean diagrams: Use a sharp pencil and label points clearly in geometry questions.
• Revise weak chapters first: Fix weak areas early to avoid last-minute panic.

Exam-day strategy: start with the section you find easiest to build confidence and secure quick marks. Keep the last 10-15 minutes for re-checking calculations and final answers.

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CBSE Class 10 Maths Exam Pattern 2025-26

The CBSE Class 10 Maths paper typically evaluates conceptual understanding, application, and reasoning. To perform well, practice a balanced set of question types: direct formula-based, application-based, case-study style, and reasoning/proof questions. Use the marking scheme mindset: clear steps, correct formula, and neat presentation.

• Focus on step marking: even partial correct work can earn marks.
• Balance your practice: include easy, moderate, and challenging questions from each unit.
• Time allocation: avoid spending too long on one question; move ahead and return later.

Best practice: after finishing each unit, solve one unit-based test. In the last month, shift to full-length timed papers to build speed and confidence.

Frequently Asked Questions (FAQs)

Additional Resources

To strengthen your preparation beyond NCERT Solutions for Class 10 Maths, use these resources for practice, revision, and exam-level confidence:

• NCERT Solutions for Class 10 (All subjects)
• NCERT Exemplar Class 10 Maths (HOTS practice)
• CBSE Sample Papers Class 10 Maths (Timed practice)
• NCERT Books for Class 10 (Textbook PDFs)
• Class 10 Maths Formulas (Quick revision)

For best results, complete NCERT first, then practice Exemplar, and finally solve sample papers and previous year papers under exam-like timing.

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NCERT Solutions for Class 10 Maths can help you build strong fundamentals, improve problem-solving speed, and write answers in the correct CBSE format. When you practice chapter-wise, revise formulas regularly, and solve a few timed papers, scoring high becomes achievable. Bookmark this page for quick access to all chapter links and use the solutions as your daily practice guide for the 2025-26 session.

Stay consistent, focus on your weak areas early, and practice with full steps. Explore the chapter-wise links above, download PDFs for offline study, and if you have doubts, use the comment section to ask your questions.