CBSE Class 9 Maths (2026) has 12 chapters, and around 45 formulas cover the whole 80-mark paper — that's it. The heaviest blocks are Algebra (20 marks), Geometry (27 marks) and Mensuration (13). Class 9 is the year where the formulas you learn become the tools for Class 10 boards, so learning them properly now saves you twice.
- Unit weightage 2026
- 1. Number Systems · 2. Polynomials · 3. Coordinate Geometry · 4. Linear Equations in Two Variables
- 5. Euclid's Geometry · 6. Lines & Angles · 7. Triangles · 8. Quadrilaterals · 9. Circles
- 10. Heron's Formula · 11. Surface Areas & Volumes · 12. Statistics
- Tricks to remember them · FAQs
Where the 80 marks come from
| Unit (chapters) | Marks |
|---|---|
| Geometry (Ch 5–9) | 27 |
| Algebra (Ch 2, 4) | 20 |
| Mensuration (Ch 10–11) | 13 |
| Number Systems (Ch 1) | 10 |
| Statistics (Ch 12) | 6 |
| Coordinate Geometry (Ch 3) | 4 |
Theory 80 + internal assessment 20 = 100. Geometry is the biggest block — and most of it is proofs and properties, not formulas.
Ch 1 — Number Systems 10 marks
| Formula | Used for |
|---|---|
| am × an = am+n; am ÷ an = am−n | Laws of exponents for real numbers |
| (am)n = amn; a0 = 1 | |
| √a × √b = √(ab); √a/√b = √(a/b) | Operations on surds |
| Rationalise 1/(a + √b) by multiplying with (a − √b) | Rationalising the denominator — the chapter's standard question |
| a1/n = n√a | Fractional exponents |
Ch 2 — Polynomials 20-mark unit
| Identity | Used for |
|---|---|
| (a + b)² = a² + 2ab + b² | The first two identities — used everywhere, including Class 10 |
| (a − b)² = a² − 2ab + b² | |
| a² − b² = (a + b)(a − b) | Difference of squares |
| (x + a)(x + b) = x² + (a + b)x + ab | Factorising quadratics |
| (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Three-term square |
| (a + b)³ = a³ + b³ + 3ab(a + b) | Cube identities |
| (a − b)³ = a³ − b³ − 3ab(a − b) | |
| a³ + b³ = (a + b)(a² − ab + b²) | Sum and difference of cubes |
| a³ − b³ = (a − b)(a² + ab + b²) | |
| a³ + b³ + c³ − 3abc = (a+b+c)(a²+b²+c²−ab−bc−ca) | If a + b + c = 0, then a³ + b³ + c³ = 3abc — a favourite question |
| Remainder Theorem: remainder of p(x) ÷ (x − a) is p(a) | Finding remainders without dividing |
| Factor Theorem: (x − a) is a factor ⇔ p(a) = 0 | Testing factors |
Ch 3 — Coordinate Geometry 4 marks
| Concept | Used for |
|---|---|
| Point (x, y): x = abscissa, y = ordinate | Plotting points on the Cartesian plane |
| Quadrant signs: I (+,+), II (−,+), III (−,−), IV (+,−) | Identifying quadrants — a common 1-marker |
Ch 4 — Linear Equations in Two Variables 20-mark unit
| Formula | Used for |
|---|---|
| ax + by + c = 0, where a, b are not both zero | Standard form of a linear equation |
| Every solution is a point on the line; a line has infinitely many solutions | Graph questions — plot two points and join them |
Ch 5 — Introduction to Euclid's Geometry 27-mark unit
| Concept | Used for |
|---|---|
| Axioms and postulates (things equal to the same thing are equal, etc.) | Reasoning questions — no formulas, only logic |
Ch 6 — Lines & Angles 27-mark unit
| Property | Used for |
|---|---|
| Linear pair adds to 180°; vertically opposite angles are equal | Basic angle chasing |
| Parallel lines: corresponding = equal, alternate = equal, co-interior add to 180° | The transversal questions — the chapter's core |
| Angle sum of a triangle = 180°; exterior angle = sum of two opposite interior angles | Triangle angle problems |
Ch 7 — Triangles 27-mark unit
| Criterion | Used for |
|---|---|
| SSS, SAS, ASA, AAS, RHS | Proving two triangles congruent (note: SSA is not valid) |
| Angles opposite equal sides are equal (and its converse) | Isosceles triangle proofs |
Ch 8 — Quadrilaterals 27-mark unit
| Property | Used for |
|---|---|
| Angle sum of a quadrilateral = 360° | Angle questions |
| Parallelogram: opposite sides and angles equal; diagonals bisect each other | The most-used property set |
| Mid-point theorem: the line joining midpoints of two sides is parallel to the third and half of it | The chapter's flagship proof |
Ch 9 — Circles 27-mark unit
| Theorem | Used for |
|---|---|
| Equal chords subtend equal angles at the centre | Chord questions |
| Perpendicular from the centre bisects the chord | Very common proof |
| Angle at centre = 2 × angle at any point on the remaining circle | The most-asked circle theorem |
| Angles in the same segment are equal; angle in a semicircle = 90° | Standard results |
| Cyclic quadrilateral: opposite angles add to 180° | Cyclic quadrilateral proofs |
Ch 10 — Heron's Formula 13-mark unit
| Formula | Used for |
|---|---|
| s = (a + b + c)/2 | Semi-perimeter — always compute this first |
| Area = √(s(s − a)(s − b)(s − c)) | Area of any triangle from its three sides — no height needed |
| Area = ½ × base × height | When the height is given, use this instead — much faster |
| Equilateral triangle: Area = (√3/4)a² | Shortcut worth memorising |
Ch 11 — Surface Areas & Volumes 13-mark unit
| Solid | Formulas |
|---|---|
| Cube | V = a³; TSA = 6a²; LSA = 4a² |
| Cuboid | V = lbh; TSA = 2(lb + bh + hl); LSA = 2h(l + b) |
| Cylinder | V = πr²h; CSA = 2πrh; TSA = 2πr(r + h) |
| Cone | V = ⅓πr²h; CSA = πrl; TSA = πr(l + r); l = √(r² + h²) |
| Sphere | V = (4/3)πr³; SA = 4πr² |
| Hemisphere | V = (2/3)πr³; CSA = 2πr²; TSA = 3πr² |
Ch 12 — Statistics 6 marks
| Formula | Used for |
|---|---|
| Mean = Σxi/n | Ungrouped data |
| Mean = Σfixi/Σfi | Grouped data |
| Median: middle value; if n is even, average the two middle values | Arrange in order first — always |
| Mode = the most frequently occurring observation | Simple frequency questions |
Note: probability is not part of the current rationalized Class 9 syllabus — it begins in Class 10.
Tricks to remember them
Learn the identities as a family. (a + b)² and (a − b)² differ by one sign. a³ + b³ and a³ − b³ differ by two signs. Learn the "+" version properly, then flip the middle signs for the "−" version — that's 6 identities from 3.
Heron's formula: find s first, always. Every mistake in this chapter comes from rushing into the square root before computing the semi-perimeter. Write s = (a+b+c)/2 as your first line, every single time.
Cone, cylinder, sphere are one family. Learn the cylinder (πr²h). A cone is exactly ⅓ of it. A sphere is (4/3)πr³, and a hemisphere is half of that. Four formulas from one.
The slant height trap. In a cone, l = √(r² + h²) — the slant height is NOT the height. Curved surface area uses l, volume uses h. This single confusion costs more marks than any other in Class 9 mensuration.
Write, don't read. Once a week, write each chapter's formulas on a blank page from memory, check against this chart, and rewrite only what you missed. Three weeks and it's all in your head — because in the exam your hand writes, your eyes don't read.
The complete handwritten Class 9 Maths formula chart
This page is your online quick-check. The handwritten chart is what goes on your study wall:
- Full 2026-27 syllabus — all 12 chapters, compact and exam-focused
- Colour-coded formula boxes with diagrams for fast recall
- Real handwritten notes by toppers — IITians, NITians and district toppers
- Instant PDF or printed book (COD available, all-India delivery)
- Available in English and Hindi medium
FAQs
How many formulas are there in Class 9 Maths?
Around 45 core formulas across the 12 chapters. Polynomials (the algebraic identities) and Surface Areas & Volumes contribute the largest share; much of Geometry is properties and proofs rather than formulas.
Which chapter has the highest weightage in Class 9 Maths?
Geometry (Euclid's Geometry, Lines & Angles, Triangles, Quadrilaterals, Circles) carries 27 of the 80 marks, followed by Algebra at 20 and Mensuration at 13.
How do I print this Class 9 formula chart?
Use the print button at the top of this page, or press Ctrl+P (Cmd+P on Mac). The page automatically strips the background and extras, printing only the formula tables as a clean chart.
What are the most important identities in Class 9 Maths?
(a ± b)², a² − b², the cube identities (a ± b)³ and a³ ± b³, and a³ + b³ + c³ − 3abc — this last one gives 3abc whenever a + b + c = 0, a repeated exam question.
When do I use Heron's formula instead of ½ × base × height?
Use Heron's when you know all three sides but no height. If a height is given, ½ × base × height is much faster.
Is probability in the Class 9 syllabus?
No. Probability is not part of the current rationalized Class 9 Maths syllabus — it starts in Class 10.
Do Class 9 formulas come in Class 10 boards?
Yes, constantly. The algebraic identities power Class 10 Polynomials and Quadratic Equations, the circle theorems return in Class 10 Circles, and mensuration repeats almost unchanged.
Is there a Class 9 Maths formula chart in Hindi?
Yes — the handwritten notes linked above are available in both English and Hindi medium versions, with the same formulas and diagrams.