Welcome to your structured hub for NCERT Solutions for Class 9 Maths, crafted to align tightly with the latest CBSE syllabus and the official NCERT textbooks. Each chapter below provides crisp, step-by-step methods, examiner-friendly presentation, and signposted practice so you can revise efficiently for school tests and board exams in Class 10. Pair these solutions with school worksheets, sample papers, and topic-wise practice to build accuracy and speed.
Use this page as your day-to-day companion during exam preparation. Where helpful, we reference typical short answer patterns, common pitfalls, and links (anchors) to each exercise. If you need the base text, you can download NCERT book for class 9 Mathematics from trusted portals and cross-verify question numbering. As you move chapter by chapter, cultivate clean work, correct units, and clear justifications—habits that also strengthen performance across science and maths. For additional challenge, consult NCERT exemplar solutions and attempt higher order thinking skill (HOTS) questions.
Why these NCERT solutions matter
- Aligned to NCERT & CBSE: Step-wise logic mirrors NCERT textbooks and the CBSE syllabus.
- Exam-ready layout: Each answer is presented in the format preferred in board exams and periodic tests.
- Smart practice: Linked exercises (anchors) let you jump directly to a topic; pair with sample papers and NCERT exemplar solutions for mastery.
- Skill building: Emphasis on reasoning and higher order thinking skill (HOTS) to boost confidence for future competitive paths.
Class 9 Maths — Unit-wise Weightage (Indicative)
| Unit No. | Unit Name | Marks (Theory) |
|---|---|---|
| I | Number Systems | 8 |
| II | Algebra | 17 |
| III | Coordinate Geometry | 4 |
| IV | Geometry | 28 |
| V | Mensuration | 13 |
| VI | Statistics & Probability | 10 |
| Total | 80 | |
Note: Use your school’s latest blueprint and CBSE circulars for the current session.
Class 9 Maths — Chapter Index
| S.No. | Chapter | Go to |
|---|---|---|
| 1 | Number Systems | # |
| 2 | Polynomials | # |
| 3 | Coordinate Geometry | # |
| 4 | Linear Equations in Two Variables | # |
| 5 | Introduction to Euclid’s Geometry | # |
| 6 | Lines and Angles | # |
| 7 | Triangles | # |
| 8 | Quadrilaterals | # |
| 9 | Areas of Parallelograms and Triangles | # |
| 10 | Circles | # |
| 11 | Constructions | # |
| 12 | Heron’s Formula | # |
| 13 | Surface Areas and Volumes | # |
| 14 | Statistics | # |
| 15 | Probability | # |
Chapter 1: Number Systems
Master the extended number line (integers, rationals, irrationals, reals), decimal expansions, and laws of rational exponents. Typical NCERT textbooks problems include locating surds (e.g., √2, √3) on the number line and classifying decimals as terminating or non-terminating repeating—key skills for exam preparation. Keep definitions tight and justify each step; examiners reward clarity in board exams.
Exercises
- Exercise 1.1 — Real numbers overview; decimal types.
- Exercise 1.2 — Rational/irrational checks; proofs with contradiction.
- Exercise 1.3 — Laws of exponents; converting forms.
- Exercise 1.4 — Representing decimals on the line.
- Exercise 1.5 — More on surds and rationalisation.
- Exercise 1.6 — Applications and mixed practice.
Chapter 2: Polynomials
Learn degree, coefficients, zeros, identity checks, factorisation, and the Remainder/Factor Theorems. For higher order thinking skill (HOTS), connect zeros and graph intercepts. Present solutions step-wise and substitute to verify results—habits that align with CBSE syllabus marking. Pair practice with sample papers for speed.
Exercises
- Exercise 2.1 — Types and degrees.
- Exercise 2.2 — Zeros and identities.
- Exercise 2.3 — Division algorithm applications.
- Exercise 2.4 — Factor theorem; factorisation.
- Exercise 2.5 — Mixed practice.
Chapter 3: Coordinate Geometry
Grasp Cartesian plane basics: axes, quadrants, and plotting points. Many errors in tests come from sign mistakes—write the ordered pair (x, y) clearly and mark quadrants. These fundamentals bridge to distance/slope in later classes; mastering them now strengthens science and maths reasoning for future board exams.
Exercises
- Exercise 3.1 — Basics and plotting.
- Exercise 3.2 — Quadrant identification.
- Exercise 3.3 — Applications and puzzles.
Chapter 4: Linear Equations in Two Variables
Work with equations of the form ax + by + c = 0; plot lines, find intercepts, and interpret solutions. Draw neat graphs with scaled axes and label intercepts—presentation matters in board exams. Link to word problems and tables of values for solid conceptual grip.
Exercises
- Exercise 4.1 — Infinite solutions idea.
- Exercise 4.2 — Graphing from tables.
- Exercise 4.3 — Intercepts and forms.
- Exercise 4.4 — Applications/word problems.
Chapter 5: Introduction to Euclid’s Geometry
Understand Euclid’s postulates, axioms, and the structure of proofs. Keep statements precise and draw minimal clean diagrams. This chapter builds the language of geometry—essential for later theorems in triangles, circles, and quadrilaterals as per NCERT textbooks.
Exercises
- Exercise 5.1 — Axioms & postulates.
- Exercise 5.2 — Logical deductions.
Chapter 6: Lines and Angles
Master vertical opposite angles, linear pair, alternate interior/corresponding angles, and triangle angle sum. State the theorem, apply it, and close with a sentence that links steps—this simple habit matches exam preparation best practices across CBSE.
Exercises
Chapter 7: Triangles
Congruence (SSS, SAS, ASA, RHS), inequalities, and basic properties are core. Write clear reasons next to each step. Triangle questions often carry method marks—so even partial progress helps in board exams.
Exercises
Chapter 8: Quadrilaterals
Focus on parallelogram properties, conditions for a quadrilateral to be a parallelogram, and mid-point theorems. Draw to scale when possible; mark knowns and unknowns. This clarity mirrors the CBSE syllabus emphasis on logical presentation.
Exercises
Chapter 9: Areas of Parallelograms and Triangles
Learn area relations by converting shapes and using base-height logic carefully. Show which base/height pair you’ve used—this small line often secures a mark in board exams.
Exercises
Chapter 10: Circles
Theorems on equal chords, perpendicular distances from centre, angles subtended by an arc, and cyclic quadrilaterals. State theorem → apply → conclude; keep diagrams neat and labelled—examiner-friendly, NCERT textbooks style.
Exercises
Chapter 11: Constructions
Precisely construct triangles (given conditions), angle bisectors, and specific angles. Write steps adjacent to the figure. Accuracy plus steps = full marks in most board exams style questions.
Exercises
Chapter 12: Heron’s Formula
Apply Heron’s formula for triangle areas and extend to composite shapes. Show semi-perimeter, substitution, and simplification neatly. Link back to sample papers for variety in mixed figures.
Exercises
Chapter 13: Surface Areas and Volumes
Compute curved/total surface areas and volumes of cubes, cuboids, cylinders, cones, spheres, and combinations. Write formulas first, substitute values with units, and present final answers rounded as per question. Dimensional consistency is a common slip—double-check!
Exercises
- Exercise 13.1
- Exercise 13.2
- Exercise 13.3
- Exercise 13.4
- Exercise 13.5
- Exercise 13.6
- Exercise 13.7
- Exercise 13.8
- Exercise 13.9
Chapter 14: Statistics
Learn to collect, tabulate, and represent data (bar graph, histogram, frequency polygon), and compute mean/median/mode. Always state class intervals clearly and check inclusive/exclusive conventions. This chapter regularly appears in periodic tests; practise with sample papers to improve time management during exam preparation.
Exercises
Chapter 15: Probability
Foundation of empirical probability using simple experiments: coins, dice, cards. Write sample space cleanly and reduce fractions. Many questions are short and scoring—good for maintaining momentum in board exams and developing higher order thinking skill around fairness and randomness.
Exercises
Download & Practice
- NCERT Solutions for Class 9 Maths — PDF (All Chapters)
- Chapter-wise Important Questions (VSA/SA/LA) & Worksheets
- NCERT Exemplar Solutions (Selected Topics)
- Sample Papers & Previous Year Question Papers
Exam Tips & Strategy
- Concept first, speed next: Build fundamentals from the NCERT textbooks, then time yourself with sample papers.
- Show steps: Even partial progress earns method marks—critical in board exams.
- Formula diary: Maintain and revise daily; annotate with units and conditions.
- Balance practice: Mix arithmetic, algebra, geometry, and data handling to mirror the CBSE syllabus spread.
- Reflect: After each test, note 3 errors and fix them—this builds real exam preparation momentum.