In short: This is a complete, chapter-wise list of every important formula from the new CBSE Class 9 Maths textbook Ganita Manjari Part I (2026-27). Each formula includes what every variable means, a worked example, and a quick memory tip. Use this as your revision sheet before exams — and learn which formulas carry the highest marks weightage so you can prioritize smartly.
The new Ganita Manjari Part I textbook has 8 chapters, and the theory paper is worth 80 marks (plus 20 for internal assessment). If you are still searching for formulas based on the old 15-chapter NCERT book, those lists are outdated. Everything below is organized to match the 2026-27 syllabus exactly.
For a full chapter-wise strategy, scoring plan, and common mistakes to avoid, check out our Class 9 Maths Complete Guide.
Chapter 1: Orienting Yourself — The Use of Coordinates
Coordinate Geometry carries 4 marks in the annual exam — a small but guaranteed scoring area.
Distance Formula
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
- d = distance between two points
- (x₁, y₁) and (x₂, y₂) = coordinates of the two points
Example: Find the distance between A(3, 4) and B(7, 1).
d = √[(7−3)² + (1−4)²] = √[16 + 9] = √25 = 5 units
Tip: Always square the differences first, then add — never add first then square.
Section Formula (Internal Division)
If point P divides the line segment joining A(x₁, y₁) and B(x₂, y₂) in the ratio m:n, then:
$$P = \left(\frac{mx_2 + nx_1}{m+n},\ \frac{my_2 + ny_1}{m+n}\right)$$
Example: Find the point dividing A(2, 3) and B(8, 9) in ratio 1:2.
P = ((1×8 + 2×2)/(1+2), (1×9 + 2×3)/(1+2)) = (12/3, 15/3) = (4, 5)
Tip: The ratio "m" always multiplies the other point's coordinates (B, not A). Think "cross multiply."
Midpoint Formula
$$M = \left(\frac{x_1 + x_2}{2},\ \frac{y_1 + y_2}{2}\right)$$
This is just the section formula with m:n = 1:1.
Example: Midpoint of (4, 6) and (10, 2) = ((4+10)/2, (6+2)/2) = (7, 4)
Tip: Midpoint = average of x-values, average of y-values.
Chapter 2: Linear Polynomials
Algebra carries 20 marks total (Chapters 2 and 4 combined) — the second-highest weightage unit.
Zero of a Linear Polynomial: If p(x) = ax + b (a ≠ 0), the zero is x = −b/a.
Example: p(x) = 3x + 6 → zero is x = −6/3 = −2
Tip: Zero means "the value of x that makes the polynomial equal to zero." Set p(x) = 0 and solve.
Remainder Theorem
When a polynomial p(x) is divided by (x − a), the remainder is p(a).
Example: Find the remainder when p(x) = x³ + 2x − 5 is divided by (x − 1).
Remainder = p(1) = 1 + 2 − 5 = −2
Tip: The divisor is (x − a), so substitute x = a. If the divisor is (x + 3), substitute x = −3.
Factor Theorem
(x − a) is a factor of p(x) if and only if p(a) = 0.
Example: Is (x − 2) a factor of x² − 5x + 6? Check p(2) = 4 − 10 + 6 = 0. Yes, it is a factor.
Tip: Factor theorem is just the remainder theorem with remainder = 0. If the remainder is zero, the divisor is a factor.
Chapter 3: The World of Numbers
The Number System carries 7 marks.
Types of Numbers
- Natural Numbers (N): 1, 2, 3, …
- Whole Numbers (W): 0, 1, 2, 3, …
- Integers (Z): …, −2, −1, 0, 1, 2, …
- Rational Numbers (Q): numbers of the form p/q where p and q are integers, q ≠ 0
- Irrational Numbers: numbers that cannot be expressed as p/q (e.g., √2, √3, π)
- Real Numbers (R): all rational and irrational numbers together
Rationalizing the Denominator
$$\frac{1}{\sqrt{a}} = \frac{1}{\sqrt{a}} \times \frac{\sqrt{a}}{\sqrt{a}} = \frac{\sqrt{a}}{a}$$
$$\frac{1}{a + \sqrt{b}} = \frac{a - \sqrt{b}}{a^2 - b}$$
Example: Rationalize 1/(3 + √2) → Multiply by (3 − √2)/(3 − √2) = (3 − √2)/(9 − 2) = (3 − √2)/7
Tip: Multiply top and bottom by the conjugate — just flip the sign in the middle.
Laws of Exponents for Real Numbers
| Law | Formula |
|---|---|
| Product of powers | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Quotient of powers | aᵐ ÷ aⁿ = aᵐ⁻ⁿ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ |
| Zero exponent | a⁰ = 1 (a ≠ 0) |
| Negative exponent | a⁻ⁿ = 1/aⁿ |
| Fractional exponent | a^(1/n) = ⁿ√a |
Tip: "Same base? Add powers for multiplication, subtract for division." Repeat this until it becomes automatic.
Chapter 4: Algebraic Identities
This chapter pairs with Chapter 2 for the Algebra unit (20 marks total). Identity-based questions appear every single year.
Standard Algebraic Identities
| Identity | Expanded Form |
|---|---|
| (a + b)² | a² + 2ab + b² |
| (a − b)² | a² − 2ab + b² |
| a² − b² | (a + b)(a − b) |
| (a + b)³ | a³ + 3a²b + 3ab² + b³ = a³ + b³ + 3ab(a + b) |
| (a − b)³ | a³ − 3a²b + 3ab² − b³ = a³ − b³ − 3ab(a − b) |
| a³ + b³ | (a + b)(a² − ab + b²) |
| a³ − b³ | (a − b)(a² + ab + b²) |
| (a + b + c)² | a² + b² + c² + 2ab + 2bc + 2ca |
Example: Expand (2x + 3)² = (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9
Example: Factorize 8x³ − 27 = (2x)³ − 3³ = (2x − 3)(4x² + 6x + 9)
Tip: The cube identities look complicated, but notice the pattern — the second factor always has three terms with alternating signs. Practice 5 problems of each identity and the pattern sticks.
Practice any chapter on Padhaao
AI tutor for CBSE, ICSE & 15 state boards · 10 learning modes · 3 free chapters daily
Chapter 5: Circles, Lines, Angles, Triangles, and Quadrilaterals
Geometry is the highest-scoring unit at 25 marks. This chapter is large and covers multiple topics.
Lines and Angles
- Vertically opposite angles are equal.
- The sum of angles on a straight line = 180° (linear pair).
- If a transversal crosses two parallel lines:
- Alternate interior angles are equal.
- Co-interior (same-side interior) angles are supplementary (sum = 180°).
- Corresponding angles are equal.
Triangle Properties
- Angle sum property: Sum of all angles in a triangle = 180°
- Exterior angle theorem: Exterior angle = sum of the two non-adjacent interior angles
- Pythagoras Theorem: In a right triangle, hypotenuse² = base² + perpendicular² (or a² + b² = c²)
- Area of a triangle = ½ × base × height
- Heron's Formula: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2
Example (Heron's): Triangle with sides 5, 6, 7. s = (5+6+7)/2 = 9. Area = √[9 × 4 × 3 × 2] = √216 = 6√6 ≈ 14.7 sq. units
Tip: Always calculate s first and write it down. The most common error is computing s wrong.
Quadrilateral Properties
- Sum of all angles of a quadrilateral = 360°
- Parallelogram: Opposite sides equal, opposite angles equal, diagonals bisect each other
- Rectangle: All angles 90°, diagonals equal and bisect each other
- Rhombus: All sides equal, diagonals bisect each other at right angles
- Square: All sides equal, all angles 90°, diagonals equal and bisect at right angles
Circle Theorems
- Equal chords are equidistant from the center.
- The perpendicular from the center to a chord bisects the chord.
- Angle in a semicircle is 90°.
- Angles subtended by the same arc are equal.
- The angle subtended by an arc at the center is double the angle at any point on the remaining part of the circle.
Tip: Draw diagrams for every circle theorem problem. Without a diagram, you will misidentify arcs and angles.
Chapter 6: Perimeter and Area
Mensuration carries 12 marks.
| Shape | Perimeter | Area |
|---|---|---|
| Square (side a) | 4a | a² |
| Rectangle (l × b) | 2(l + b) | l × b |
| Triangle (sides a, b, c) | a + b + c | ½ × base × height |
| Circle (radius r) | 2πr | πr² |
| Semicircle (radius r) | πr + 2r | ½πr² |
| Parallelogram (base b, height h) | 2(a + b) | b × h |
| Trapezium (parallel sides a, b; height h) | a + b + c + d | ½(a + b) × h |
| Rhombus (diagonals d₁, d₂) | 4 × side | ½ × d₁ × d₂ |
Surface Area and Volume
| Solid | Surface Area | Volume |
|---|---|---|
| Cube (side a) | 6a² | a³ |
| Cuboid (l, b, h) | 2(lb + bh + hl) | l × b × h |
| Cylinder (r, h) | 2πr(r + h) | πr²h |
| Cone (r, h, slant l) | πr(r + l) | ⅓πr²h |
| Sphere (r) | 4πr² | ⁴⁄₃πr³ |
| Hemisphere (r) | 3πr² | ⅔πr³ |
Tip: Always write the formula first, then substitute values. Examiners give step marks for writing the correct formula even if your calculation has an error.
Chapter 7: Probability
Probability is part of the Statistics & Probability unit (12 marks combined).
Basic Probability Formula
$$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$
- 0 ≤ P(E) ≤ 1
- P(sure event) = 1
- P(impossible event) = 0
- P(E) + P(not E) = 1, so P(not E) = 1 − P(E)
Example: A bag has 3 red and 5 blue balls. Probability of picking a red ball = 3/(3+5) = 3/8
Tip: Always count the total outcomes carefully. The most common error is forgetting to include all possibilities in the denominator.
Chapter 8: Sequences and Progressions
Arithmetic Progression (AP)
| Formula | Meaning |
|---|---|
| aₙ = a + (n−1)d | nth term of AP |
| Sₙ = n/2 [2a + (n−1)d] | Sum of first n terms |
| Sₙ = n/2 (a + l) | Sum when last term l is known |
| d = a₂ − a₁ | Common difference |
- a = first term, d = common difference, n = number of terms, l = last term
Example: Find the 10th term of AP: 2, 5, 8, 11, …
a = 2, d = 3, n = 10 → a₁₀ = 2 + (10−1)(3) = 2 + 27 = 29
Geometric Progression (GP)
| Formula | Meaning |
|---|---|
| aₙ = arⁿ⁻¹ | nth term of GP |
| Sₙ = a(rⁿ − 1)/(r − 1) | Sum of n terms when r > 1 |
| Sₙ = a(1 − rⁿ)/(1 − r) | Sum of n terms when r < 1 |
| r = a₂/a₁ | Common ratio |
- a = first term, r = common ratio
Example: Find the 5th term of GP: 3, 6, 12, 24, …
a = 3, r = 2, n = 5 → a₅ = 3 × 2⁴ = 3 × 16 = 48
Tip: AP means the difference between consecutive terms is constant. GP means the ratio between consecutive terms is constant. If you are confused about which one a problem is, check: subtract or divide consecutive terms.
How to Memorize Class 9 Maths Formulas Effectively
Knowing formulas exist and actually remembering them during an exam are two different things. Here is what works:
1. Write, do not just read. Write each formula by hand at least 5 times on separate days. Motor memory from writing is stronger than visual memory from reading.
2. Understand the derivation. You do not need to memorize derivations for the exam, but understanding why a formula works makes it stick. For example, the midpoint formula is the section formula with m:n = 1:1.
3. Group related formulas. (a+b)² and (a−b)² differ by one sign. a³+b³ and a³−b³ differ by one sign in each factor. Practice them in pairs.
4. Use flashcards. Formula name on one side, formula on the other. Test yourself daily for 2 weeks. For more, read our guide on why flashcards work.
5. Solve problems, not just recite. Applying a formula cements it far better than repeating it 50 times. Solve at least 3 problems per formula.
Formulas Most Likely Asked in Exams — Priority Table
Not all formulas are equally likely to appear. Based on marks weightage and past question patterns, here is your priority list:
| Priority | Formula/Topic | Why It Matters |
|---|---|---|
| 🔴 High | Algebraic Identities (all 8) | Part of the 20-mark Algebra unit, at least one question guaranteed |
| 🔴 High | Heron's Formula | Frequently asked 3-5 mark question in Geometry/Mensuration |
| 🔴 High | AP nth term and sum formulas | New chapter — expect fresh questions in 2027 exams |
| 🔴 High | Circle theorems (angle at center, semicircle) | Part of the 25-mark Geometry unit |
| 🟡 Medium | Surface area and volume (cylinder, cone, sphere) | 12-mark Mensuration unit, numerical-based |
| 🟡 Medium | Factor and Remainder Theorem | Standard 3-mark question type |
| 🟡 Medium | Laws of Exponents | Appears in simplification problems |
| 🟢 Lower | Distance and Section Formula | Only 4 marks for Coordinate Geometry, but easy full marks |
| 🟢 Lower | Probability formula | Simple application, usually 2-3 marks |
The high-priority formulas should be rock solid before you move to anything else. If you are short on time, master the red rows first, then yellow, then green.
Frequently Asked Questions
How many formulas are there in Class 9 Maths for 2026-27?
There are approximately 40-50 key formulas across all 8 chapters of Ganita Manjari Part I. The exact count depends on whether you count each algebraic identity and each mensuration shape separately. This page covers all the essential ones. You do not need to memorize anything beyond what is listed here for the annual exam.
Are the Class 9 Maths formulas different for 2026-27 compared to previous years?
Yes. The new Ganita Manjari Part I reorganizes content. Sequences and Progressions (AP/GP) is now in Class 9, and Coordinate Geometry includes the section formula. Always use formula lists that reference the new textbook.
Which chapter has the most formulas in Class 9 Maths?
Chapter 6 (Mensuration) has the most individual formulas covering perimeter, area, surface area, and volume for multiple shapes. Chapter 4 (Algebraic Identities) comes second with 8 standard identities.
Can I score 90+ in Class 9 Maths by just memorizing formulas?
No. Formulas are necessary but not sufficient. About 60-70% of the exam tests your ability to apply formulas in problems. Memorizing the formula is step one. Solving 10-15 problems with it is step two.
How should I revise formulas before the exam?
Create a 2-3 page formula sheet grouped by chapter. Revise daily for the last two weeks. In the exam hall, do a "brain dump" — write down key formulas on the rough sheet before starting any question.
Are GP formulas important for Class 9 exams?
Yes. Ganita Manjari Part I includes Sequences and Progressions as Chapter 8, so both AP and GP are examinable. AP gets more questions, but know GP nth term and sum formulas too.
Start Practicing These Formulas with Padhaao
Reading formulas is step one. Applying them is where real learning happens. Padhaao gives you chapter-wise practice problems aligned to Ganita Manjari Part I, with step-by-step AI explanations when you get stuck. No more staring at a formula wondering how to use it.
Want the full chapter with solved examples?
10 learning modes. Board-specific content. 3 free chapters every day.
Try it free