📚 CBSE Class 9 · New NCERT Syllabus 2026–27 · 6 Units · 80 Marks

Complete Guide to
Class 9 Mathematics

All 15 chapters organised into 6 official CBSE units — visual lessons, step-by-step proofs & 750+ practice questions. Built on the brand-new 2026-27 NCERT syllabus.

6
Units
15
Chapters
80
Theory Marks
750+
Practice Qs
07MUnit I · Number System 20MUnit II · Algebra 04MUnit III · Coordinate Geometry 25MUnit IV · Geometry 14MUnit V · Mensuration 10MUnit VI · Statistics & Probability

📊 All 15 Chapters Complete

15 / 15 ✅
I

Number System

1 chapter · Rational & irrational numbers, surds, proof of irrationality

07Marks
3
∞ Number Systems
Rational & irrational numbers, density, decimal representation, proof of √2 irrational, square root spiral
Proof √2 IrrationalSurdsSquare Root Spiral50 Qs
7
marks
✓ Ready→
II

Algebra

4 chapters · Polynomials, Sequences & Progressions, Algebraic Identities, Linear Equations

20Marks
2
🔢 Introduction to Polynomials
Algebraic expressions, degree, coefficients, zeroes, linear polynomials, slope & y-intercept of y = ax+b
Degree & TermsZeroesy = ax+b50 Qs
7
marks
✓ Ready→
6
🔄 Sequences and Progressions NEW
AP (nth term, sum, graph), GP (nth term, graph), fractals, Tower of Hanoi
AP ★ from Cl.10GP ★ from Cl.11Fractals50 Qs
7
marks
✓ Ready→
9
🧮 Exploring Algebraic Identities
8 standard identities, geometric models, algebra tiles, factorisation, quadratic splitting, rational expressions
8 IdentitiesFactorisationQuadraticRational Expr.50 Qs
6
marks
✓ Ready→
12
📊 Linear Equations in Two Variables EXP
Graphical method, slope-intercept form, consistency conditions, substitution & elimination methods
Substitution ★Elimination ★Pair of Eqs ★50 Qs
7
marks
✓ Ready→
III

Coordinate Geometry

1 chapter · Cartesian plane, distance & midpoint formulas, collinearity

04Marks
1
📍 Coordinate Geometry
Cartesian plane, quadrants, plotting points, distance formula, midpoint formula, collinearity of 3 points
Distance Formula ★Midpoint Formula ★Collinearity50 Qs
4
marks
✓ Ready→
IV

Geometry

5 chapters · Euclid's Geometry, Lines & Angles, Triangles, Quadrilaterals, Circles

25Marks
4
📐 Introduction to Euclid's Geometry: Axioms & Postulates
History, Baudhayana's Sulbasutras, definitions, axioms, 5 postulates, Playfair's axiom, parallelism
5 PostulatesAxiomsPlayfair's Axiom50 Qs
5
marks
✓ Ready→
5
📏 Lines and Angles
Rays, angles, linear pair theorem, vertically opposite angles, corresponding/alternate/co-interior angles, parallel line theorems
Angle TypesLinear PairParallel Lines50 Qs
6
marks
✓ Ready→
7
△ Triangles – Congruence Theorems
Rigidity of triangles, SAS/SSS/ASA/AAS/RHS congruence, isosceles triangle theorem & converse, CPCT
SAS · SSS · ASAAAS · RHSIsoscelesCPCT50 Qs
7
marks
✓ Ready→
10
▭ 4-gons (Quadrilaterals)
Parallelogram properties & theorems, midpoint theorem, central symmetry, 5 conditions to prove a parallelogram
ParallelogramMidpoint TheoremCentral Symmetry50 Qs
5
marks
✓ Ready→
11
⭕ Circles
Chords & distances, perpendicular from centre, arc angles (central = 2×inscribed), cyclic quadrilaterals
Central Angle TheoremCyclic QuadIntersecting Chords50 Qs
6
marks
✓ Ready→
V

Mensuration

2 chapters · Area & Perimeter · Surface Area & Volume

14Marks
8
📐 Area and Perimeter EXP
All shape formulas, Heron's formula, π & irrationality, area of circles & sectors, arc length, Brahmagupta's formula
Heron's FormulaSector Area ★Brahmagupta ★50 Qs
8
marks
✓ Ready→
13
📦 Surface Area and Volume
Right circular cone (l=√r²+h²), sphere (4πr²), hemisphere (3πr²), combined shapes, melting & recasting
Cone FormulasSphere SA & V1:2:3 Ratio50 Qs
5
marks
✓ Ready→
VI

Statistics and Probability

2 chapters · Data representation · Probability concepts & experiments

10Marks
14
📈 Statistics
Bar graphs, histograms, frequency polygons, measures of central tendency — mean, median, mode, empirical formula
HistogramMean · Median · ModeEmpirical Formula50 Qs
5
marks
✓ Ready→
15
🎲 Introduction to Probability
Probability scale 0–1, randomness, empirical & theoretical probability, sample space, events, tree diagrams
P(E)=n(E)/n(S)Empirical PTree Diagrams50 Qs
5
marks
✓ Ready→
🗂️

Previous Syllabus Chapters Pre-2026 · Old NCERT

These notes follow the old CBSE Class 9 syllabus (prior to 2026-27 restructuring). Chapter numbering and content differ from the current syllabus above.

1
∞ Number Systems
Rational & irrational numbers, surds, decimal expansion, real number line
→
2
🔢 Polynomials
Definitions, zeroes, Remainder & Factor theorems, algebraic identities
→
3
📍 Coordinate Geometry
Cartesian plane, plotting points, quadrants
→
4
📊 Linear Equations in Two Variables
Equations of a line, graphical method, solutions as ordered pairs
→
5
📐 Introduction to Euclid's Geometry
Axioms, postulates, Playfair's axiom, parallel lines
→
6
📏 Lines and Angles
Angle types, linear pair, vertically opposite angles, parallel line theorems
→
7
△ Triangles
Congruence rules — SAS, SSS, ASA, AAS, RHS; isosceles triangle theorem
→
8
▭ Quadrilaterals
Parallelogram properties, midpoint theorem, angle sum property
→
9
⭕ Circles
Chords, perpendicular from centre, arc angles, cyclic quadrilaterals
→
10
📐 Heron's Formula
Area of triangles using semi-perimeter; application to quadrilaterals
→
11
📦 Surface Areas and Volumes
Cube, cuboid, cylinder, cone, sphere — surface area & volume formulas
→
12
📈 Statistics
Bar graphs, histograms, frequency polygons, mean, median, mode
→
📋 View Old Syllabus Index Page →

Unit-wise Marks Distribution

UnitUnit NameChaptersMarks
I Number System Ch.3 Number Systems 07
II Algebra Ch.2 Introduction to Polynomials
Ch.6 Sequences and Progressions
Ch.9 Exploring Algebraic Identities
Ch.12 Linear Equations in Two Variables 		20
III Coordinate Geometry Ch.1 Coordinate Geometry 04
IV Geometry Ch.4 Introduction to Euclid's Geometry
Ch.5 Lines and Angles
Ch.7 Triangles – Congruence Theorems
Ch.10 4-gons (Quadrilaterals)
Ch.11 Circles 		25
V Mensuration Ch.8 Area and Perimeter
Ch.13 Surface Area and Volume 		14
VI Statistics and Probability Ch.14 Statistics
Ch.15 Introduction to Probability 		10
Total 80

Exam Pattern 2026-27

📝 Theory Paper — 80 Marks

  • MCQ / Objective (1M) — 20 questions
  • Very Short Answer (2M) — 6 questions
  • Short Answer (3M) — 7 questions
  • Long Answer (5M) — 3 questions
  • Case-Based (4M) — 3 questions

📊 Internal Assessment — 20 Marks

  • Periodic Tests (avg of 2) — 10 marks
  • Notebook Submission — 5 marks
  • Subject Enrichment — 5 marks

⭐ Two-Level System NEW

  • Proficiency Level — mandatory for all
  • Advanced Level — optional, for JEE/competitive
  • Same 15 chapters, deeper advanced problems
Question TypeMarks eachCountTotal
MCQ / Objective12020
Very Short Answer2612
Short Answer3721
Long Answer5315
Case-Based4312
Total Theory80

What's New in 2026-27

📍

Distance & Midpoint Formula

Moved into Ch.1 from Class 10

← Cl.10
🔄

Arithmetic Progressions (AP)

Moved into Ch.6 from Class 10

← Cl.10
📈

Geometric Progressions (GP)

Brand new for Cl.9 — from Cl.11

← Cl.11
📐

Sectors & Brahmagupta

Areas related to circles — Ch.8

← Cl.10
📊

Pair of Linear Equations

Substitution & elimination — Ch.12

← Cl.10
⭐

Two-Level Maths System

Proficiency (mandatory) + Advanced (optional)

Brand New