मंथिकाManthika
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Mathematics · Class 10

CBSE 2026–27 · 14 chapters

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Chapters

Ch 1–5Ch 6–8Ch 9Ch 10Ch 11–12Ch 13–14
Ideas map for Chapter 1, Real Numbers: how the chapter's ideas build on one another

1. Real Numbers

Fundamental Theorem of Arithmetic (statement, after reviewing earlier work, motivated through examples). Proofs of irrationality of √2 · √3 · √5. Competency: "prove algebraically the irrationality of numbers like √2, √3, √5, 3 + 2√5"

Read freeIdeas map for Chapter 2, Polynomials: how the chapter's ideas build on one another

2. Polynomials

zeros of a polynomial · relationship between zeros and coefficients of quadratic polynomials · find zeros graphically and algebraically

Read freeIdeas map for Chapter 3, Linear Equations: how the chapter's ideas build on one another

3. Linear Equations

graphical method · consistency/inconsistency · algebraic conditions for number of solutions · solution by substitution and by elimination · simple situational problems

Ideas map for Chapter 4, Quadratic Equations: how the chapter's ideas build on one another

4. Quadratic Equations

standard form ax² + bx + c = 0 · solutions (only real roots) by factorisation and by the quadratic formula · discriminant and nature of roots · situational problems from day-to-day activities

Ideas map for Chapter 5, Arithmetic Progressions: how the chapter's ideas build on one another

5. Arithmetic Progressions

motivation · derivation of the nth term and the sum of the first n terms · daily-life applications

Ideas map for Chapter 6, Triangles: how the chapter's ideas build on one another

6. Triangles

definitions · examples · counter-examples of similar triangles. (Prove) Basic Proportionality Theorem. State without proof: its converse · AA · SSS · SAS similarity criteria. Competency: differentiate congruent from similar figures

Ideas map for Chapter 7, Coordinate Geometry: how the chapter's ideas build on one another

7. Coordinate Geometry

review of concepts · distance formula · section formula (internal division only)

Ideas map for Chapter 8, Intro to Trigonometry: how the chapter's ideas build on one another

8. Intro to Trigonometry

ratios of an acute angle of a right triangle · proof of their existence (well-defined) · motivate the ratios defined at 0° and 90° · values at 30° · 45° · 60° · relationships between the ratios · proof and applications of sin²A + cos²A = 1 · only simple identities · (topics combined from freeze items 9 (Introduction to Trigonometry), 10 (Trigonometric Identities) -- this book folds them into one chapter)

Ideas map for Chapter 9, Applications of Trigonometry: how the chapter's ideas build on one another

9. Applications of Trigonometry

angle of elevation · angle of depression · simple problems · at most two right triangles · angles only 30° · 45° · 60°

Ideas map for Chapter 10, Circles: how the chapter's ideas build on one another

10. Circles

tangent at the point of contact. (Prove) the tangent is perpendicular to the radius through the point of contact. (Prove) the lengths of tangents from an external point are equal

Ideas map for Chapter 11, Areas Related to Circles: how the chapter's ideas build on one another

11. Areas Related to Circles

area of sectors and segments · problems on areas and perimeter or circumference of these figures · segment problems restricted to central angles 60° · 90° · 120°

Ideas map for Chapter 12, Surface Areas & Volumes: how the chapter's ideas build on one another

12. Surface Areas & Volumes

surface areas and volumes of combinations of any two of cubes · cuboids · spheres · hemispheres · right circular cylinders and cones

Ideas map for Chapter 13, Statistics: how the chapter's ideas build on one another

13. Statistics

mean · median and mode of grouped data (bimodal situations avoided) · mean by direct · assumed-mean and step-deviation methods · median and mode by the algebraic method

Ideas map for Chapter 14, Probability: how the chapter's ideas build on one another

14. Probability

classical definition · simple problems on the probability of an event

About this book

A Class 9 or 10 student with no tutor can learn every syllabus topic from this book alone, practise it to board-paper standard, and check every answer on the page.

More about this book

That means nothing is left for a teacher to fill in. Each chapter starts where you are, builds the idea step by step, and shows worked examples before it sets you a problem. Where a chapter needs something from last year, it teaches that too instead of assuming it. The first problem of every exercise is solved in full on the page, with the reason beside each step; the rest are answered under the set, with every full solution online, free.

Mathematics, Class 10, on the 2026–27 CBSE syllabus — the board year.

It follows the CBSE Mathematics syllabus for 2026–27 chapter by chapter, in NCERT's order. Each chapter teaches its idea from the beginning, shows worked examples before it sets a problem, and names the mistakes students actually make. Where a chapter needs something from the previous class, the book teaches that too rather than assume the reader has it. The first problem of every exercise is solved in full on the page, with the reason beside each step; the rest are answered under the set, with every full solution online, free. The back matter carries the solutions, a formula sheet, a mistakes index and a glossary.

What it is not: an NCERT solutions book — it solves its own problems only; a sample-paper or previous-year-paper bank; a coaching module or test series; a CBSE or NCERT publication; the school — no lab work, projects or internal-assessment help. It is one book for both Class 10 maths papers, Basic and Standard, with no Basic-only shortcut.

What a page looks like

The first page of Chapter 1, Real Numbers: the chapter's contents and a picture of two learners packing mangoes into trays
A story page: Kabir and Priya's heap of 60 mangoes, with a drawing of five trays of twelve and four trays of fifteen
An ideas page: every composite number factors into primes, with a diagram of the orders the same primes can come out in

Pages from the Math 10 book.

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