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By Karan Singh Bisht
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Updated on 8 Jul 2026, 16:50 IST
Maths formulas for Class 9 are provided here to help students who find Mathematics difficult or confusing. Many students feel nervous about Maths because of formulas, calculations, and problem-solving steps. However, with the right guidance and regular practice, the subject becomes easier to understand.
To support students, we have compiled all the important Class 9 Maths formulas in a simple and easy-to-remember format. These formulas are based on the latest syllabus and cover key topics from the class 9 Ganita Manjari Maths book, including Algebra, Geometry, Polynomials, Coordinate Geometry, and other important chapters.
Students can use these formulas for quick revision, homework, assignments, and exam preparation. This formula collection helps build conceptual clarity and makes Mathematics more approachable for Class 9 learners.
Mathematics is a subject that may seem challenging to many students, but with clear concepts, regular practice, and a strong understanding of formulas, it becomes much easier to score well in exams. To support Class 9 students in their preparation, Infinity Learn provides a well-organized collection of important Class 9 Maths formulas in one place.
These formulas are prepared by Infinity Learn expert teachers according to the latest Class 9 Maths syllabus and CBSE guidelines. Students can refer to these formulas while completing assignments, solving homework questions, revising chapters, or preparing for exams.
Along with Maths formulas, students can also access NCERT Solutions for Class 9 Maths on Infinity Learn to revise the complete syllabus and strengthen their understanding of each chapter. Infinity Learn also provides helpful study resources such as NCERT Solutions for Class 9 for other subjects, helping students learn better and perform confidently in their academic journey.
| Chapter No. | Download Maths formulas for Class 9 All Chapters PDF |
| Chapter 1 | Orienting Yourself: The Use of Coordinates |
| Chapter 2 | Introduction to Linear Polynomials |
| Chapter 3 | The World of Numbers |
| Chapter 4 | Exploring Algebraic Identities |
| Chapter 5 | I’m Up and Down, and Round and Round |
| Chapter 6 | Measuring Space: Perimeter and Area |
| Chapter 7 | The Mathematics of Maybe: Introduction to Probability |
| Chapter 8 | Predicting What Comes Next?: Exploring Sequences and Progressions |
When students understand the logic behind each formula, solving different types of Maths problems becomes much easier. A clear understanding of formulas helps students apply them correctly instead of simply memorizing them. The chapter-wise Class 9 Maths all formulas listed below are designed to support quick revision and strong exam preparation. By practicing maths formulas for class 9 regularly and understanding their applications, students can improve accuracy, build confidence, and aim for higher marks in the final examination.
The point where the x-axis and y-axis intersect is called the origin.
Origin = O(0, 0)
Any point in the Cartesian plane is written as: P(x, y)
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The x-coordinate shows the distance from the y-axis, and the y-coordinate shows the distance from the x-axis.
If a point lies on the x-axis, its y-coordinate is zero.
P(x, 0)
If a point lies on the y-axis, its x-coordinate is zero.
P(0, y)
For example:
B(4.5, 0) lies on the x-axis.
H(0, 4) lies on the y-axis.
| Quadrant | Sign of x-coordinate | Sign of y-coordinate | General Form |
| Quadrant I | Positive | Positive | (+, +) |
| Quadrant II | Negative | Positive | (−, +) |
| Quadrant III | Negative | Negative | (−, −) |
| Quadrant IV | Positive | Negative | (+, −) |
If two points are: A(x₁, y₁) and B(x₂, y₂)
then the distance between them is:
AB = √[(x₂ − x₁)² + (y₂ − y₁)²]
This formula is based on the Baudhāyana–Pythagoras Theorem and is used to find the distance between any two points in the coordinate plane.
If two points have the same y-coordinate:
A(x₁, y) and B(x₂, y)
then the distance is:
AB = |x₂ − x₁|
If two points have the same x-coordinate:
A(x, y₁) and B(x, y₂)
then the distance is:
AB = |y₂ − y₁|
If M is the midpoint of the line segment joining:
A(x₁, y₁) and B(x₂, y₂)
then:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The end-of-chapter exercises ask students to identify the midpoint using coordinate relationships.
If M(x, y) is the midpoint of A(x₁, y₁) and B(x₂, y₂), then:
x = (x₁ + x₂)/2
y = (y₁ + y₂)/2
This can be rearranged to find the unknown endpoint:
x₂ = 2x − x₁
y₂ = 2y − y₁
If points P and Q trisect the line segment joining:
A(x₁, y₁) and B(x₂, y₂)
where P is closer to A and Q is closer to B, then:
P = ((2x₁ + x₂)/3, (2y₁ + y₂)/3)
Q = ((x₁ + 2x₂)/3, (y₁ + 2y₂)/3)
The PDF includes a question based on finding the coordinates of trisection points.
If a circle has centre O(0, 0) and radius r, then a point P(x, y) lies on the circle if:
x² + y² = r²
A point lies:
The end-of-chapter exercises include questions based on checking whether points lie on, inside, or outside a circle with centre at the origin.
If the scale is given as:
1 cm = 1 unit
or
1 cm = 1 foot
then distances measured on the graph can be converted into real distances using the given scale.
| Concept | Formula / Rule | Use |
| Algebraic expression | Term + Term + Constant | Used to form expressions from word problems. |
| Coefficient | In ax, coefficient = a | The numerical factor multiplied by a variable. |
| Constant term | In ax + b, constant = b | The fixed number that does not contain a variable. |
| Degree of polynomial | Highest power of the variable | Used to identify whether a polynomial is linear, quadratic, or cubic. |
| Linear polynomial | ax + b, where a ≠ 0 | A polynomial of degree 1. |
| Linear equation | ax + b = c | Formed when a linear polynomial is equated to a constant. |
| Value of a polynomial | p(x) = ax + b | Substitute the given value of x to find the value of the polynomial. |
| General linear relationship | y = ax + b | Shows the relation between two variables x and y. |
| Slope / rate of change | a = (y₂ − y₁) / (x₂ − x₁) | Finds the fixed increase or decrease per unit change in x. |
| Constant term / y-intercept | b = y − ax | Used to find b after finding a. |
| Linear growth | y = a + bx | Used when a quantity increases by a fixed amount. |
| Linear decay | y = a − bx | Used when a quantity decreases by a fixed amount. |
| nth term of a linear pattern | Tₙ = a + (n − 1)d | Used when consecutive terms have a constant difference d. |
| Difference in a linear pattern | d = T₂ − T₁ | Used to check whether a pattern is linear. |
| Graph of a linear relationship | y = ax + b | The graph is always a straight line. |
| Parallel lines | y = ax + b₁ and y = ax + b₂ | Lines are parallel when their slopes are equal. |
| Line passing through origin | y = ax | When b = 0, the graph passes through the origin. |
| Concept | Description | Formula / Example |
| Zero (Addition) | When zero is added to a number, the number remains unchanged. [cite: 1] | a + 0 = a [cite: 1] |
| Zero (Subtraction) | When zero is subtracted from a number, the number remains unchanged. [cite: 1] | a - 0 = a [cite: 1] |
| Zero (Multiplication) | When any number is multiplied by zero, the result is zero. [cite: 1] | a × 0 = 0 [cite: 1] |
| Integers (Mixed Signs) | The product of a debt (negative) and a fortune (positive) is a debt. [cite: 1] | (-3) × 4 = -12 [cite: 1] |
| Integers (Same Signs) | The product of two debts (negatives) is a fortune (positive). [cite: 1] | (-3) × (-4) = 12 [cite: 1] |
| Concept | Description | Formula / Equation |
| Definition | A number expressed as a ratio of two integers. [cite: 1] | p/q, where q ≠ 0 [cite: 1] |
| Equality | The condition for two rational numbers to be equal. [cite: 1] | a/b = c/d if ad = bc [cite: 1] |
| Addition | Adding fractions with the same denominator. [cite: 1] | a/b + c/b = (a + c)/b [cite: 1] |
| Subtraction | Subtracting fractions with the same denominator. [cite: 1] | a/b - c/b = (a - c)/b [cite: 1] |
| Multiplication | Multiplying two rational numbers. [cite: 1] | (a/b) × (c/d) = ac/bd (where b ≠ 0, d ≠ 0) [cite: 1] |
| Division | Dividing two rational numbers. [cite: 1] | (a/b) ÷ (c/d) = ad/bc (where b ≠ 0, c ≠ 0, d ≠ 0) [cite: 1] |
| Commutative (Addition) | The order of addition does not change the result. [cite: 1] | a/b + c/d = c/d + a/b [cite: 1] |
| Commutative (Multiplication) | The order of multiplication does not change the result. [cite: 1] | (a/b) × (c/d) = (c/d) × (a/b) [cite: 1] |
| Distributive Law | Multiplication distributes over addition for rational numbers. [cite: 1] | p(q + r) = pq + pr [cite: 1] |
| Absolute Value | The non-negative distance of a rational number from 0. [cite: 1] | |x| ≥ 0 [cite: 1] |
| Distance | The distance between two rational numbers a and b on the number line. [cite: 1] | |a - b| [cite: 1] |
| Density (Average) | Finding a rational number exactly halfway between a and b. [cite: 1] | (a + b) / 2 [cite: 1] |
| Concept | Description | Formula / Equation |
| Baudhāyana-Pythagoras | Calculating the diagonal (d) of a square where each side is 1 unit long. [cite: 1] | 12 + 12 = d2 ⇒ d = √2 [cite: 1] |
| Mādhava's Infinite Series | The infinite sum used to express the exact value of π. [cite: 1] | π = 4 × (1 - 1/3 + 1/5 - 1/7 + ...) [cite: 1] |
| Algebraic Identities | Formula |
| Square of a binomial sum | (x + y)2 = x2 + 2xy + y2 |
| Square of a binomial difference | (x - y)2 = x2 - 2xy + y2 |
| Square of a trinomial | (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx |
| Difference of squares | (x + y)(x - y) = x2 - y2 |
| Product of binomials (common term) | (x + a)(x + b) = x2 + (a + b)x + ab |
| Product of binomials (general) | (ax + b)(cx + d) = acx2 + (ad + bc)x + bd |
| Difference of cubes | x3 - y3 = (x - y)(x2 + xy + y2) |
| Sum of cubes | x3 + y3 = (x + y)(x2 - xy + y2) |
| Cube of a binomial sum | (x + y)3 = x3 + 3x2y + 3xy2 + y3 |
| Cube of a binomial difference | (x - y)3 = x3 - 3x2y + 3xy2 - y3 |
| Extended three-variable identity | x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - xz - yz) |
| Concept | Mathematical Rule / Formula |
| Chords and Angles at the Centre | AB = DE ⇔ ∠ACB = ∠DCE |
| Perpendicular from Centre to Chord | CM ⊥ AB ⇔ AM = BM |
| Distance of Chords from Centre | AB = FG ⇔ CE = CH |
| Comparing Chord Distances | AB > DE ⇒ CF < CG |
| Length of a Chord | L = 2√(r2 - d2) |
| Arcs and Angles at the Centre | ∠AOB = 2∠APB |
| Angle in a Semicircle | ∠ADB = 90° |
| Angles in the Same Segment | ∠ADB = ∠AEB |
| Condition for Concyclic Points | ∠ACB = ∠ADB ⇒ A, B, C, D are concyclic |
| Cyclic Quadrilaterals | ∠A + ∠C = 180° ∠B + ∠D = 180° |
Infinity Learn Class 9 Maths Formula PDF is a useful revision resource for students who want to learn and revise important Maths formulas quickly. It brings all key formulas together in a simple, chapter-wise format, making it easier for students to prepare for exams, complete homework, and solve practice questions confidently.
Prepared by Infinity Learn expert teachers, the formula PDF follows the latest Class 9 Maths syllabus and covers important topics from the Ganita Manjari book. Each formula is presented clearly so students can understand its meaning, application, and use in problem-solving.
Using the Infinity Learn Class 9 Maths Formula PDF helps students save revision time, strengthen concepts, avoid formula confusion, and improve accuracy in exams. It is especially helpful for last-minute revision and regular practice throughout the academic year.
Maths formulas for class 9 PDF can be a powerful revision tool when used regularly and correctly. Students should not only memorize the formulas but also understand where and how each formula is applied.
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Students can download the Maths formulas for class 9 pdf from Infinity Learn. The PDF includes important formulas in a simple, chapter-wise format for quick revision and exam preparation.
Yes, Infinity Learn provides Maths formulas for Class 9 all chapters pdf, covering key topics such as Algebra, Geometry, Polynomials, Coordinate Geometry, Mensuration, and other important chapters.
The Class 9 Maths formula PDF helps students revise formulas quickly, understand their applications, and solve questions more accurately. It is useful for homework, assignments, class tests, and final exam preparation.
Yes, the formulas available on Infinity Learn are prepared by experienced subject experts to ensure accuracy, clarity, and alignment with the latest Class 9 Maths syllabus.
Yes, the Maths formulas for Class 9 all chapters pdf is very useful for last-minute revision. It helps students quickly recall important formulas before exams and improves confidence while solving problems.
Students should choose Infinity Learn because it provides well-organised, easy-to-understand, and expert-prepared Maths formula PDFs that support better learning, quick revision, and strong exam preparation.
You can learn Class 9 Maths formulas by revising them chapter-wise and understanding the logic behind each formula instead of only memorising them. After learning a formula, practise related questions from the Ganita Manjari textbook and compare your answers with Infinity Learn expert solutions. Regular revision, writing formulas in a notebook, and solving sample questions will help you remember them better.
Yes, the Class 9 Maths formulas are based on the latest CBSE curriculum and follow the topics covered in the Ganita Manjari Maths book. Infinity Learn provides these formulas in a simple, chapter-wise format to help students revise important concepts and prepare effectively for exams.