Class 9 Maths Formula Revision Guide
Class 9 Mathematics rewards students who keep formulas alive rather than memorising them once. This guide collects the formulas and key properties of the year in one place, chapter by chapter, with the units and the quick checks that catch slips. Use it to build recall pages, to compare against the revision strategy, and as a reference when practising from the study material.
How to use this guide
Do not read the tables cold. The proven routine is recall-first: write down everything you remember for a chapter on a blank sheet, then open this guide and mark what was missing. Missing items are the day's lesson. This is the exact recall step explained in how to study Class 9 Maths effectively.
Table A: Coordinates and geometry
| Chapter | Formula / property | Notes |
|---|---|---|
| 1 – Coordinates | Distance between (x₁, y₁) and (x₂, y₂) = √((x₂ − x₁)² + (y₂ − y₁)²) | Square the differences; take one square root at the end. |
| 1 – Coordinates | Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2) | Average each coordinate separately. |
| 1 – Coordinates | Quadrant signs: I ( +, + ), II ( −, + ), III ( −, − ), IV ( +, − ) | Plot a point to confirm a sign memory. |
| 5 – Circles | Circumference = 2πr, Area = πr² | π is often taken as 22/7 in Class 9 problems. |
| 5 – Circles | Angle in a semicircle = 90° | A property to state, not guess. |
| 5 – Circles | Opposite angles of a cyclic quadrilateral add to 180° | Equal chords have equal arcs, and equal central angles. |
| 12 – Quadrilaterals | Interior angle sum of a quadrilateral = (4 − 2) × 180° = 360° | General rule for an n-gon: (n − 2) × 180°. |
| 12 – Quadrilaterals | Parallelogram: opposite sides parallel and equal; diagonals bisect each other | Rectangle, rhombus and square are special cases. |
Chapter 1 details appear in the coordinate notes, and circle properties in the circle notes.
Table B: Numbers and identities
| Chapter | Formula / property | Notes |
|---|---|---|
| 3 – Numbers | Rational iff the number can be written p/q, integers p and q, q ≠ 0 | √4 = 2 is rational; √2 is irrational. |
| 3 – Numbers | (√a − √b)(√a + √b) = a − b | The product kills both roots. |
| 4 – Identities | (a + b)² = a² + 2ab + b² | Check: (2 + 3)² = 25 = 4 + 12 + 9. |
| 4 – Identities | (a − b)² = a² − 2ab + b² | The middle sign is minus. |
| 4 – Identities | a² − b² = (a + b)(a − b) | Difference of squares; check 9 − 4 = 5 = 3 + 2. |
| 4 – Identities | (x + a)(x + b) = x² + (a + b)x + ab | Product of two simple binomials. |
| 4 – Identities | (a + b)³ = a³ + 3a²b + 3ab² + b³ | Expands into four terms. |
| 4 – Identities | a³ + b³ = (a + b)(a² − ab + b²) | Cube sum factorises. |
| 4 – Identities | a³ − b³ = (a − b)(a² + ab + b²) | Cube difference factorises. |
The identity set and its sign habits are taught in the Chapter 4 notes, and number classification in the Chapter 3 notes.
Table C: Measurement and area
| Shape | Formula | Units |
|---|---|---|
| Rectangle (length l, breadth b) | Perimeter = 2(l + b), Area = lb | m, m² |
| Square (side s) | Perimeter = 4s, Area = s² | m, m² |
| Triangle (base b, height h) | Area = ½bh | m² |
| Circle (radius r) | Circumference = 2πr, Area = πr² | m, m² |
| Any triangle (sides a, b, c) | Heron: s = (a + b + c)/2 and Area = √(s(s − a)(s − b)(s − c)) | m² |
| Cyclic quadrilateral (sides a, b, c, d) | Brahmagupta: s = (a + b + c + d)/2 and Area = √((s − a)(s − b)(s − c)(s − d)) | m² |
Heron's formula is safe by default because it needs no height. Check it on a 3-4-5 triangle: s = 6, Area = √(6 × 3 × 2 × 1) = 6, which matches ½ × 3 × 4. The full method set lives in the Chapter 6 notes.
Table D: Probability, sequences and solids
| Chapter | Formula / property | Notes |
|---|---|---|
| 7 – Probability | P(event) = favourable outcomes / total outcomes; 0 ≤ P ≤ 1 | Sum of probabilities of all outcomes = 1. Prime score on one die: P = 3/6 = 1/2. |
| 8 – Sequences | Arithmetic progression: common difference d = tₖ − t₁ is constant | 295, 340, 385, … has d = 45. |
| 8 – Sequences | Geometric progression: common ratio r = tₖ/t₁ is constant | 2, 4, 8, 16, … has r = 2. |
| 8 – Sequences | nth odd number = 2n − 1 | 137 = 2(69) − 1, so 137 is the 69th odd number. |
| 8 – Sequences | Sum of first n natural numbers = n(n + 1)/2 | Triangular numbers: 1, 3, 6, 10, 15, … |
| 14 – Solids | Cuboid: Volume = lbh, Total surface area = 2(lb + bh + hl) | cm³ and cm². |
| 14 – Solids | Cube: Volume = s³, Surface area = 6s² | All faces equal. |
| 14 – Solids | Cylinder: Volume = πr²h, Curved area = 2πrh, Total area = 2πr(r + h) | Total = curved + two circles. |
| 14 – Solids | Cone: Volume = ⅓πr²h, Curved area = πrl, Total area = πr(r + l), l = √(r² + h²) | l is the slant height. |
| 14 – Solids | Sphere: Surface area = 4πr², Volume = &frac43;πr³ | No height or base needed. |
| 14 – Solids | Hemisphere: Curved area = 2πr², Total area = 3πr², Volume = ⅔πr³ | Total = curved + flat circular base. |
The sequence checks and the solids formulas are detailed in the sequence notes and the probability chapter notes.
Units that catch marks
Half the mark loss on formula questions is a units error:
- Lengths, distances and perimeters: m, cm.
- Areas: m², cm². If the question gives lengths in metres, the area is in square metres.
- Volumes and capacities: m³, cm³.
- Probability: no unit at all – it is a ratio between 0 and 1.
- Money: rupees (₹), written with the amount.
Name the quantity before solving. A student who writes "need: area" starts with the right units and the right formula automatically. The common mistakes guide lists this habit in full.
Verification checks for every formula
Every formula above has a cheap check using small numbers. Teach the checks together with the formula:
- Identity check: (2 + 3)² = 25 against 4 + 12 + 9 = 25. Any mismatch means a wrong expansion.
- Distance check: from (1, 2) to (4, 6) gives √(9 + 16) = 5. A distance that looks much larger than the graph, or negative, is wrong.
- Area check: a 3-4-5 triangle has area 6 by both ½bh and Heron's formula – they must agree.
- Solids check: cylinder with r = 7 and h = 10 gives curved area 2 × (22/7) × 7 × 10 = 440 and volume (22/7) × 49 × 10 = 1540. Both round, both plausible.
- Probability check: any answer below 0 or above 1 is impossible, and a probability of 1 suggests the event was read as certain.
The remembering system
A guide is only useful if its contents survive the exam hall. Three habits keep the formulas usable:
- Produce, then check. Use this guide the way the revision strategy prescribes: recall pages first, guide second.
- Use the formula in a story. Formula + a lived context beats formula alone. The competency questions article builds exactly those context links.
- Stage the slips. Each wrong formula from a practice set goes into the personal slip log with the correct version beside it. A short list of personal formula slips is worth more than the full table.
Intersperse these habits with the practice sets in the weekly plan so formulas are repaired while still fresh.
Frequently asked questions
Is it enough to memorise the tables?
No. A memorised formula with no unit discipline or verification check still loses marks. The tables give the tool; the checks and units in this guide keep it correct under pressure.
How often should a student review the formulas?
Weekly while a chapter is current, then every week in the rotation review. The Sunday review in the study plan is the natural slot.
Should students write formulas on a sheet during the exam?
Only from memory, as a rough recall page in the first few minutes – exams allow no notes, so a quickly written recall page acts as the student's own reference.
Which formulas are most often forgotten?
Heron's semi-perimeter, the cone's slant height l, the difference between curved and total surface area, and the sign inside an identity such as (a − b)². These four repay extra attention.
Conclusion
This guide is the complete Class 9 Mathematics formula map: coordinates, geometry, numbers, identities, measurement, probability, sequences and solids. Use it recall-first, pair every formula with its units and its small-number check, and repair slips weekly through the revision system. Every other Class 9 Maths article and resource sits on the Class 9 Maths hub.
Keep formulas alive with practice
Vyasa Academy in Hulimavu, Bangalore, drills formula use through recall pages, weekly tests and small-number checks so nothing stays only on paper.