NCERT Exemplar Class 10 Maths is the definitive resource for students aiming to master higher-order thinking skills and secure 90+ marks in their CBSE board examinations for the 2025-26 academic session.
Every year, thousands of Class 10 students discover that completing the regular NCERT textbook exercises is not enough to tackle the trickier questions that appear in board exams. The NCERT Exemplar Class 10 Maths bridges this gap by presenting problems that require deeper reasoning, multi-concept application, and real-world mathematical thinking. Published by the National Council of Educational Research and Training, this supplementary resource transforms average scorers into confident problem-solvers.
Whether you are preparing for CBSE boards, laying your foundation for JEE Main, or targeting scholarships through NTSE and Olympiad examinations, the Exemplar provides the structured challenge you need. This comprehensive guide walks you through chapter-wise breakdowns, difficulty mapping, essential formulas, and a practical preparation schedule that fits into your daily routine. For students seeking immediate access to study materials, you can explore the NCERT Exemplar Class 10 Maths PDF for quick reference.
Understanding NCERT Exemplar Class 10 Maths: Purpose and Structure
The NCERT Exemplar Class 10 Maths is fundamentally different from your regular mathematics textbook. While the standard NCERT book introduces concepts through explanations and practice exercises, the Exemplar assumes you already understand the basics and challenges you to apply them in unfamiliar situations. This distinction is crucial for board exam success, where 20-25% of questions now test competency-based learning.
Why This Matters: CBSE’s shift towards competency-based assessment means that rote learning and formula memorisation alone cannot guarantee high scores. The Exemplar trains you to think like a mathematician—identifying patterns, choosing optimal solution strategies, and justifying every step of your reasoning.
The Exemplar book organises each chapter into distinct question categories: Multiple Choice Questions (MCQs), Very Short Answer questions, Short Answer questions, and Long Answer questions. Additionally, you will encounter Assertion-Reason questions and case-based problems that integrate real-life scenarios with mathematical concepts. This variety mirrors the exact pattern you will face in your board examination.
| Feature | What it means for you | How To practise |
|---|---|---|
| HOTS & application | Real-life and multi-step reasoning | Attempt after revising examples; write reasons for each step |
| Mixed item types | MCQ, very short, case/AR, long | Group by concept first, then by type for speed |
| Concept integration | Links Algebra–Geometry–Trigonometry | Keep a “concept map” to track cross-links |
When approaching the Exemplar, adopt a systematic method rather than random problem-solving. Begin each chapter by revising the corresponding NCERT textbook section—review definitions, theorems, and solved examples thoroughly. Then, open the Exemplar and attempt questions in order of difficulty: start with MCQs to build confidence, progress to short answers for concept reinforcement, and finally tackle HOTS questions to push your boundaries.
Key Insight: The Exemplar is not meant to replace your textbook—it is designed to supplement it. Think of the NCERT textbook as learning to walk, and the Exemplar as learning to run. Attempting Exemplar problems without mastering basics is counterproductive and leads to frustration.
One powerful technique is maintaining an error log. For every Exemplar question you solve incorrectly, note down: the question type, the concept tested, your mistake, and the correct approach. Review this log weekly. Within two months, you will notice patterns in your errors—perhaps you consistently forget to consider negative roots in quadratic equations, or you miss cases in absolute value problems. This self-awareness transforms your preparation quality.
Chapter-wise Analysis and Difficulty Mapping
The NCERT Exemplar Class 10 Maths covers all fifteen chapters prescribed in the CBSE syllabus, but not all chapters demand equal attention. Understanding the weightage distribution and difficulty level of each chapter helps you allocate study time intelligently. Based on previous years’ board exam patterns and CBSE marking schemes, we have categorised chapters into high-priority, moderate-priority, and foundation categories.
| Chapter | Core Skill / Theorem | Typical Exemplar Focus |
|---|---|---|
| Real Numbers | Euclid’s division lemma, irrationality proofs | Prime factor patterns, LCM–HCF structure |
| Polynomials | Zeroes–coefficients relation | Constructing polynomials from given roots |
| Pair of Linear Equations | Consistency & geometry of lines | Word problems, parametric cases |
| Quadratic Equations | Discriminant & nature of roots | Minimum/maximum value, root relations |
| Arithmetic Progressions | nth term & sum | Inverse problems (find \(n\) or \(d\)) |
| Triangles | Similarity criteria, Pythagoras | Area ratios, indirect proofs |
| Coordinate Geometry | Distance, section, area of triangle | Locus and condition-based questions |
| Trigonometry | Identities, heights & distances | Multi-step angle manipulation |
| Circles & Constructions | Tangent properties, division/ tangents | Proof + neat figure accuracy |
| Mensuration | Surface area & volume connections | Compound solids, frustum |
| Statistics & Probability | Mean/Median/Mode, empirical prob. | Grouped data reasoning, experiments |
High-Priority Chapters include Coordinate Geometry, Introduction to Trigonometry, Applications of Trigonometry, and Circles. These chapters collectively contribute 35-40 marks in the board examination and feature prominently in competitive exams. The Exemplar problems in these chapters test your ability to visualise geometric relationships, apply multiple trigonometric identities in sequence, and prove geometric propositions rigorously.
For Quadratic Equations, the Exemplar presents problems that go beyond simple factorisation. You will encounter questions requiring you to form quadratic equations from given conditions, analyse the nature of roots using discriminant, and solve word problems involving profit-loss, speed-distance, and work-time scenarios. The chapter on Arithmetic Progressions similarly escalates difficulty by combining AP concepts with algebraic manipulation and geometric reasoning.
Important: Students often underestimate the Surface Areas and Volumes chapter. While basic formulas are straightforward, Exemplar problems involve composite figures (hemisphere attached to cone, frustum calculations, conversion between shapes). Dedicate extra practice time to visualising three-dimensional figures.
The Real Numbers and Polynomials chapters, while carrying lower marks individually, are foundational for algebraic manipulation throughout the paper. The Exemplar’s treatment of Euclid’s division lemma, HCF-LCM relationship, and polynomial division prepares you for proof-based questions that appear unexpectedly in other chapters.
| Problem Type | Typical Chapters | Difficulty Trend |
|---|---|---|
| MCQ / One-step | Real Numbers, Polynomials | Easy–Moderate (concept recall) |
| Assertion–Reason (AR) | Trigonometry, Statistics | Moderate (logic of why/why not) |
| Case/Competency | Linear Equations, AP, Mensuration | Moderate–Hard (model a situation) |
| Proof/Derivation | Triangles, Circles | Hard (sequence of theorems) |
| Multi-chapter | Co-Geo + Algebra; Trig + Mensuration | Hard (integration of ideas) |
For students planning to continue with mathematics in Class 11, mastering the Exemplar problems in Trigonometry and Coordinate Geometry is particularly valuable. These chapters directly connect to Class 11 topics like Trigonometric Functions and Straight Lines. The analytical skills developed here provide a significant advantage when you encounter the NCERT Exemplar Class 11 Maths Chapter materials next year.
Essential Formulas and Quick Reference Guide
Success in NCERT Exemplar Class 10 Maths requires more than knowing formulas—you must recognise which formula applies to each problem type and execute calculations efficiently. This section compiles the most frequently tested formulas organised by chapter, along with common mistakes to avoid and quick verification techniques.
Quadratic Equations form the backbone of Class 10 algebra. The standard form ax² + bx + c = 0 yields solutions through the quadratic formula: x = (-b ± √(b²-4ac))/2a. The discriminant D = b²-4ac determines root nature: D > 0 gives two distinct real roots, D = 0 gives two equal roots, and D < 0 indicates no real roots. In Exemplar problems, you frequently need to find conditions on coefficients for specific root relationships.
Formula Alert: For sum and product of roots: if α and β are roots, then α + β = -b/a and αβ = c/a. These relationships are tested extensively in HOTS questions where you must form new equations from given root conditions.
Coordinate Geometry formulas appear in approximately 12-15% of board questions. The distance formula √[(x₂-x₁)² + (y₂-y₁)²] and section formula {(m₁x₂ + m₂x₁)/(m₁+m₂), (m₁y₂ + m₂y₁)/(m₁+m₂)} must be automatic. The area of triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) equals ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|. Exemplar problems often require proving collinearity (area = 0) or finding unknown vertices given area constraints.
| Topic | Key Formula | When to trigger |
|---|---|---|
| Quadratic | \(x=\frac{-bpmsqrt{b^2-4ac}}{2a}\) | Word problems leading to degree-2 equations |
| AP | \(a_n=a+(n-1)d),; (S_n= \frac{n}{2}[2a+(n-1)d]\) | Equal gaps, “every month/row/step” patterns |
| Trig Identities | \(\sin^2 heta+\cos^2 heta=1),; (1+ an^2 heta=\sec^2 heta\) | Reduce expressions before substituting numbers |
| Coordinate | \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\), area formula | Distance/collinearity/triangle tests |
| Probability | \(P(E)= \frac{ ext{favourable}}{ ext{total}}\) | Equally likely outcomes, simple experiments |
Trigonometric identities require flawless recall. The fundamental identity sin²θ + cos²θ = 1 generates two variations: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ. Exemplar problems frequently require transforming complex expressions using these identities. A common HOTS pattern involves proving LHS = RHS by strategically converting all terms to sine and cosine.
For Circles, memorise the tangent properties: a tangent is perpendicular to the radius at the point of contact, and tangent lengths from an external point are equal. These properties, combined with the Pythagoras theorem, solve most Exemplar problems in this chapter. The alternate segment theorem (angle between tangent and chord equals angle in the alternate segment) appears in advanced questions.
Surface Areas and Volumes require you to remember formulas for six basic shapes—cube, cuboid, cylinder, cone, sphere, and hemisphere—plus their combinations. The frustum of a cone (curved surface area = π(r₁+r₂)l where l = √[h² + (r₁-r₂)²]) is particularly important for application problems. When shapes are combined, the key principle is: Total surface area = Sum of exposed surfaces (subtract overlapping areas).
Important: In mensuration problems, always verify unit consistency before calculations. Converting all measurements to centimetres or metres at the start prevents costly errors. Additionally, remember that volume conversions involve cubing: 1 m³ = 1,000,000 cm³ and 1 litre = 1000 cm³.
7-Day Preparation Strategy and Daily Targets
Effective preparation for NCERT Exemplar Class 10 Maths requires a structured approach that balances new problem-solving with revision of previously covered material. This seven-day cycle, designed for students approximately three months before board exams, can be repeated throughout your preparation period with increasing difficulty levels.
Day 1-2: Algebra Block — Focus on Real Numbers, Polynomials, and Quadratic Equations. Solve 15 MCQs and 10 short-answer questions from the Exemplar. Pay special attention to questions involving the relationship between zeroes and coefficients of polynomials. Target completion time: 90 minutes daily.
| Day | Focus | Target Tasks |
|---|---|---|
| Day 1 | Algebra (Poly/Quadratic) | 20 MCQ + 5 AR + 3 long; formula recap |
| Day 2 | Linear Eqns & AP | 10 word probs + 10 AP nth/sum + 2 case |
| Day 3 | Triangles & Circles | 4 proofs + 6 ratio Qs + 2 construction |
| Day 4 | Coordinate Geometry | 6 distance/section + 4 area + 2 locus |
| Day 5 | Trigonometry | 12 identity simplifications + 4 H&D |
| Day 6 | Mensuration | 6 compound solids + 4 frustum |
| Day 7 | Statistics & Probability | 3 grouped data + 8 probability + 1 mini-mock |
Day 3-4: Geometry Block — Cover Triangles, Circles, and Coordinate Geometry. These chapters require diagram-based thinking. For every geometry problem, draw an accurate figure before attempting the solution. Practise 10 proof-based questions daily—these develop the logical reasoning that CBSE rewards with full marks. Students comfortable with coordinate geometry can also preview related concepts in the NCERT Exemplar Class 11 Maths Chapter resources.
Day 5: Trigonometry Focus — Dedicate an entire day to trigonometric identities and applications. Solve 20 mixed problems from Introduction to Trigonometry and 10 application problems involving heights and distances. Time each problem—identity proofs should take 3-4 minutes maximum, while application problems may need 6-8 minutes.
Why This Matters: Trigonometry problems appear across multiple question types in board exams—MCQs, short answers, and