NCERT Maths Class 10 Textbook PDF is the most trusted resource for CBSE Board exam preparation. The book explains concepts with simple language, step-by-step examples, and well-graded exercises so every student—whether beginner or advanced—can build confidence. If you master this textbook first, every other reference becomes easier.
Across chapters like Real Numbers, Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Trigonometry, Circles, Constructions, Mensuration, Statistics, and Probability, the textbook focuses on reasoning over rote. Each exercise nudges you to connect a definition with an example, a formula with its geometric meaning, and a problem with a clear method.
This page gives you a teacher-crafted roadmap to use the Class 10 Maths NCERT Book effectively. You’ll find a chapter-wise snapshot, formula triggers, difficulty mapping, and a weekly plan. Each main section includes a compact table followed by detailed guidance so you can turn bullet points into well-structured exam answers.
Table of Contents
- NCERT Maths Class 10 – Syllabus Overview
- Chapter-wise Focus & Core Skills
- Essential Formula Bank & Triggers
- Question Types & Difficulty Map
- 7-Day Study Plan using the Textbook
- Frequently Asked Questions
NCERT Maths Class 10 – Syllabus Overview
Units, Weightage, and Learning Emphasis
| Unit | Representative Chapters | Skills & Outcomes |
|---|---|---|
| Number & Algebra | Real Numbers, Polynomials, Linear & Quadratic Equations, AP | Proofs, factorisation, modelling, sequence reasoning |
| Geometry | Triangles, Circles, Constructions | Similar triangles, tangent properties, precise figures |
| Coordinate & Trigonometry | Coordinate Geometry, Trigonometric Identities & H&D | Point-distance/area, angle ratios, real-life applications |
| Mensuration | Surface Areas & Volumes | Compound solids, nets, unit discipline |
| Data & Chance | Statistics, Probability | Grouped data measures, experimental probability |
Use the overview to understand how the NCERT Maths Class 10 Textbook is organised. For example, when you move from Quadratic Equations to Arithmetic Progressions, you switch from solving \(ax^2+bx+c=0\) to reasoning about a pattern’s nth term \(a_n=a+(n-1)d\). Knowing this shift helps you choose the right approach quickly in exams. Geometry brings theorems—state them cleanly and use similarity/ratio logic before computation. Trigonometry needs identity manipulation before numbers; never skip simplification like \(\sin^2 heta+\cos^2 heta=1\).
Coordinate Geometry and Mensuration are the bridge from abstract to real. Convert a story into points, slopes, distances or into dimensions like radius/height—then apply formulas. Data chapters reward neat tables and cautious rounding. Throughout, think in the NCERT style: define → connect → apply. This gentle progression is why the textbook is ideal both for concept clarity and for exams that test application more than memory.
Chapter-wise Focus & Core Skills
What to Master in Each Chapter
| Chapter | Core Skill | Typical NCERT Angle |
|---|---|---|
| Real Numbers | Euclid’s division lemma; irrationality proofs | LCM–HCF structure; prime factor patterns |
| Polynomials | Relation between zeroes & coefficients | Constructing polynomials from given roots |
| Pair of Linear Equations | Consistency; graphical meaning | Word models; elimination/substitution |
| Quadratic Equations | Discriminant, factorisation, formula | Nature of roots; optimisation setups |
| Arithmetic Progressions | nth term & sum logic | Find missing terms; inverse problems |
| Triangles | Similarity criteria; Pythagoras | Area ratios; indirect proofs |
| Coordinate Geometry | Distance, section, area | Collinearity & locus interpretation |
| Trigonometry | Identities; Heights & Distances | Angle manipulation; diagram accuracy |
| Circles & Constructions | Tangent properties; accurate steps | Reasoning with theorems; neat figures |
| Mensuration | Surface area & volume connections | Compound solids; frustum logic |
| Statistics & Probability | Mean/Median/Mode; empirical prob. | Grouped data; simple experiments |
When you study chapter-wise, always ask: what is the trigger for this concept? In Quadratic Equations, the trigger is the discriminant \(\Delta=b^2-4ac\). The moment a word problem reduces to degree 2, first check if it factors neatly; if not, decide the case \(\Delta>0, =0, <0\) and use \(x=\frac{-bpmsqrt{\Delta}}{2a}\). In Triangles, state the similarity criterion (AAA/SSS/SAS) before writing ratios. In AP, look for equal differences; the words “every row/step/month” shout \(d\). This habit of spotting triggers converts long solutions into short, precise ones.
Coordinate problems become routine when you translate language into points. For a point dividing \(AB\) in the ratio \(m:n\), write the section formula first: \(ig( \frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}ig)\). In Trigonometry, reduce before substituting numbers using identities like \(1+ an^2 heta=\sec^2 heta\). For Mensuration, sketch the solid and label clearly; then apply the right combination, e.g., CSA of cone \(=\pi r l\) with volume \(= \frac{1}{3}\pi r^2 h\). Consistency in these small steps matches the NCERT approach and secures method marks.
Essential Formula Bank & Triggers
Memorise with Meaning
| Topic | Key Formula | Trigger Phrase |
|---|---|---|
| Quadratic | \(x=\frac{-bpmsqrt{b^2-4ac}}{2a}\) | “Product/sum of two numbers”, “area maximum” |
| AP | \(a_n=a+(n-1)d),; (S_n= \frac{n}{2}[2a+(n-1)d]\) | Equal gaps, evenly spaced items |
| Triangles | \(\frac{ ext{sides}}{ ext{ratios}}\) via similarity; Pythagoras \(a^2+b^2=c^2\) | Parallel lines, equal angles, right triangle |
| Coordinate | Distance \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\); Area of triangle | “Midpoint/ratio/area/collinear” |
| Trigonometry | \(\sin^2 heta+\cos^2 heta=1\), \(1+ an^2 heta=\sec^2 heta\) | Reduce expression before substituting |
| Mensuration | Cone CSA \(\pi r l\); Sphere \(4pi r^2\), \(\frac{4}{3}\pi r^3\) | “Paint/cover/fill”, “hollow/solid/combined” |
| Statistics | \(ar{x}= \frac{\sum f x}{sum f}\) (grouped) | Class intervals & mid-points given |
| Probability | \(P(E)= \frac{ ext{favourable}}{ ext{total}}\) | Equally likely outcomes |
Formulas become powerful only when linked to a cue. Train yourself to hear the trigger phrase inside the question. If you see “successive terms differ by a constant,” jump to AP; write \(a,d\) and pick \(a_n\) or \(S_n\) as needed. When a quadratic model appears, first attempt factorisation; if coefficients resist, quickly compute \(\Delta\). For geometry, draw before you compute—the diagram tells you which theorem applies, often cutting three steps.
In Statistics, build a neat working table: class interval, frequency, mid-point \(x\), and \(fx\). Summarise at the bottom to avoid silly slips. For Probability, define the sample space clearly and confirm “equally likely”. Rushing here causes double counting. Mensuration always needs units; keep a right-margin checklist—figure, knowns, formula, substitution, unit, final sentence. This NCERT-style discipline converts average answers into high-scoring ones.
Question Types & Difficulty Map
From Recall to HOTS
| Type | Where It Appears | How to Tackle |
|---|---|---|
| Recall/One-step | Definitions, direct formula use | Underline keywords; substitute cleanly |
| Reason/AR | Identities, similarity, properties | State theorem/identity before use |
| Case-based | Linear equations, AP, mensuration | Model the situation; label variables |
| Proof/Derivation | Triangles, circles | Plan ⇒ prove ⇒ conclude; neat figure |
| Integrated (HOTS) | Co-Geo + Algebra; Trig + Mensuration | Reduce to known forms; be modular |
Start your practice set with 5–7 recall items to warm up. Then handle one assertion–reason or identity simplification to train “why” thinking. Next, pick a case-based problem; convert words into equations or a diagram, assign symbols, and only then compute. For proofs, write a spine in the margin: “Show ∠A = ∠D ⇒ triangles similar ⇒ ratio of sides ⇒ result.” This path keeps you focused and helps the examiner follow your logic.
Integrated questions are the real test. A classic mix is Coordinate Geometry with Algebra: verify collinearity by area formula \(\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0\) and then deduce a parameter relation. Another is Trigonometry with Mensuration: express height by \(an heta\) or \(\sin heta\), then compute curved surface area. Practise writing a final sentence—“Hence, the statement is true” or “Therefore, required length is … cm”—to secure the concluding mark.
7-Day Study Plan using the Textbook
Compact Loop You Can Repeat
| Day | Focus Chapters | Targets from NCERT |
|---|---|---|
| Day 1 | Real Numbers, Polynomials | 2 examples + 15 exercise Qs; one proof of irrationality |
| Day 2 | Linear & Quadratic Equations | Graph + 10 word problems; 6 discriminant cases |
| Day 3 | AP | 15 nth/sum questions; 2 inverse problems |
| Day 4 | Triangles, Circles | 3 similarity proofs; 4 tangent properties |
| Day 5 | Coordinate + Trigonometry | 6 distance/area + 6 identity simplifications |
| Day 6 | Mensuration | 4 compound solids; 2 frustum problems |
| Day 7 | Statistics & Probability | 2 grouped-data tables; 10 probability items |
Keep each session to 60–75 minutes. Begin with a 5-minute formula warm-up: speak aloud the identities—\(\sin^2 heta+\cos^2 heta=1\), \(1+ an^2 heta=\sec^2 heta\), \(a^2-b^2=(a+b)(a-b)\). Then attack the day’s target straight from the NCERT textbook pages. After solving, mark each question E/T/R: Easy, Think again, Revise next week. On Day 7, add a 40-minute mixed mini-mock picking 2–3 questions from each earlier day—this spaced repetition locks concepts.
Write steps the NCERT way: Formula → Substitution → Simplification → Unit/Conclusion. In geometry, label diagrams and cite theorems (e.g., “Using Basic Proportionality Theorem”). In mensuration, mention which surface you’re computing—CSA/LSA/TSA—before plugging values. For data, keep working columns tidy and totals boxed. These habits are small but decisive in CBSE marking schemes.