NCERT Exemplar Class 10 Maths is designed to stretch your thinking beyond routine textbook questions. It introduces higher order thinking skills through HOTS, case-based, and application questions that match the latest CBSE focus on competency-based assessment. If you aim to score 90+ and also prepare for JEE/NTSE foundations, the Exemplar is your best daily practice companion.
Unlike the main textbook, the Exemplar book groups problems to reveal patterns: how a single concept can appear as MCQ, assertion–reason, short answer, or a multi-step proof. When you train with these variations, your speed and accuracy improve, and you learn to choose the shortest valid method for each problem type.
This page gives you an exam-focused plan: a quick chapter snapshot, difficulty mapping, must-know formulas, and a practical weekly schedule. Each section contains a compact table followed by teacher-style explanations so you can convert bullet points into full, well-structured answers in the board exam.
Table of Contents
- What Is NCERT Exemplar Class 10 Maths?
- Chapter-wise Topics & Core Skills
- Problem Types vs Difficulty (HOTS Map)
- Essential Formulas & Quick Checks
- 7-Day Prep Plan & Daily Targets
- Frequently Asked Questions
What Is NCERT Exemplar Class 10 Maths?
Purpose, pattern, and how to use it
| 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 |
The Exemplar is not a second textbook; it is a question bank that teaches you to think. Begin with a chapter’s definitions and examples from the main NCERT, then open the Exemplar. Solve a small set (20–30 mins) daily, not a weekend marathon. For every problem, note the trigger—the exact clue that tells you which theorem or identity to use. This habit develops pattern recognition, which is crucial for boards and Olympiad-style problems.
Treat solutions as a learning tool, not a shortcut. After each attempt, compare your approach to the ideal solution. Ask: “Could I justify each transformation?” For algebraic steps, show key transitions neatly—e.g., state \((a+b)^2 = a^2 + 2ab + b^2\) before expanding. For geometry, write the theorem name in brackets—(Thales, Pythagoras, Similar Triangles). Clean reasoning earns method marks even if arithmetic slips.
Chapter-wise Topics & Core Skills
What to master in each chapter
| 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 |
Use this chapter map to plan focused practice. For example, when you study Quadratic Equations, revise the identity \((x – \alpha)(x – \eta) = x^2 – (alpha + eta)x + alphaeta\) and the discriminant \(\Delta = b^2 – 4ac\). Exemplar questions often hide the discriminant in word problems—like checking if a given scenario yields real or equal roots—so train yourself to scan for the coefficients quickly and decide the case: \(\Delta > 0, = 0, < 0\). Similarly, in Triangles, Exemplar tasks love ratio arguments; always state the similarity criterion (e.g., AAA) before applying proportionality.
In Coordinate Geometry, practise converting language to coordinates. If a point divides \(AB\) in the ratio \(m:n\), immediately write the section formula and only then substitute: \(\left(\frac{mx_2 + nx_1}{m+n},; \frac{my_2 + ny_1}{m+n}
ight)\). For Trigonometry, reserve daily 10 minutes to manipulate identities like \(\sin^2 heta + \cos^2 heta = 1\) and \(1 + an^2 heta = \sec^2 heta\); Exemplar questions frequently require a clean reduction before numbers appear.
Problem Types vs Difficulty (HOTS Map)
Where to spend your effort
| 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) |
Use the HOTS map to allocate time wisely. Start sessions with 5–7 MCQs to warm up, then take one AR or case problem that forces you to explain why a statement is true. For proof-based items, sketch the figure first and mark given/equal/required clearly. Write a backbone plan in the margin: “Show ∠A = ∠D ⇒ triangles similar ⇒ ratio of sides ⇒ result.” This outline prevents you from wandering and helps examiners follow your thought process.
Multi-chapter questions are common in Exemplar. A classic blend is Coordinate Geometry with Algebra: verify collinearity by checking area of triangle using \(\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)| = 0\), then deduce a relation among parameters. Another is Trigonometry with Mensuration, where you must express heights or radii using \(an, \sin, \cos\) before computing curved surface area or volume. Practise writing units and final statements—”Hence, the statement is true/false”—to secure the last method mark.
Essential Formulas & Quick Checks
Memorise, but also understand triggers
| 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 |
Formulas are memory anchors, but the Exemplar tests whether you know when to use them. For instance, the quadratic formula is powerful, but factoring is faster when coefficients suggest tidy factors. Train a two-step scan: (1) try factorisation; (2) if not clean, use discriminant/ formula. For AP, look for the phrase “every… increases by …” or “seats in each row,” which screams \(a, d\). In trigonometry, never plug values before reducing; identities can cut a 7-line mess to 2 lines.
For coordinate geometry, convert stories to points and ratios first; the algebra then becomes routine. Always carry a tiny checklist on the margin: diagram, known, required, formula, substitution, unit. In probability, define the sample space explicitly before counting favourable outcomes—this prevents double-counting and earns precision credit. With this disciplined approach, Exemplar questions become predictable rather than scary.
7-Day Prep Plan & Daily Targets
Compact weekly loop you can repeat
| 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 |
This 7-day loop balances concepts and variety. Keep each session to 60–75 minutes. Begin with a 5-minute formula warm-up (speak them aloud), then attack the day’s set. After solving, mark each question as Easy/Think again/Revise. On Day 7, include a 40-minute mixed mini-mock (15 questions) pulling 2–3 problems from each day. This spaced repetition consolidates learning and reveals weak links before they hurt your board score.
While practising, write units and reasons explicitly. For example, in mensuration, state “Using CSA of a cone \(= \pi r l\)” before substituting. In trigonometry, if you use \(an heta = \frac{ ext{opp}}{ ext{\adj}}\) in heights & distances, label the triangle and angle first. Small habits like these convert partial understanding into full marks, and they mirror the expectations behind Exemplar’s stepwise solutions.