**Maths Formulae For Class 9:** Class 9 is one of the most important grades in a student’s life. It lays the foundation of the Board exams. To get through this grade the candidates need to stay focused and develop an understanding of all the necessary concepts in each subject. Mathematics is a feared subject among many students. It is tricky but it is not difficult but many students are not able to get it. This causes them to avoid this subject and focus on other subjects. This reluctance causes them to lose marks in the overall scenario, thought may be doing quite well in the other subjects.

Many a time students do not understand the chapter, which causes them to lose interest from studying this subject. To address this problem and reduce their anxiety on the subject, we have accumulated all the important for 9th standard Maths subject. If the students have all the formulae at one place, they will be able to learn these and understand their applications to solve the problems. This will make them successful in solving the problems and regain their interest in the subject thus improving their grades in the subject and overall marksheet as well. Through this article, the candidates can check all formulas of polynomials class 9 and formulae for all identities of Maths Class 9. With the help of the formula, the candidates can easily solve the questions and also it will improve their efficiency and speed. They can directly apply the formula to the questions. So let’s take a look at the important formula for Class 9.

**Latest Update:**

👉 The CBSE results for Class 10 and Class 12 Term 1 will be released soon.

*Please Note: If you are having difficulties accessing the formulae on your mobile, try opening the desktop site on your mobile from your mobile’s browser settings.*

*Practice Embibe’s**Exclusive CBSE Term 1 Sample Papers Based on New Guidelines:*

Here at Embibe, you can get the Free CBSE Revised MCQ Mock Test 2021 for all topics. The MCQ Test offered by Embibe is curated based on revised CBSE Class Books, paper patterns and syllabus for the year 2021. This mock test series has a comprehensive selection of relevant questions and their solutions. Candidates in CBSE Board can take these free mock tests to practise and find areas where they need to improve for their board exams.

Table of Contents

## Maths Formulas for Class 9

Mathematical formulae are not just to close your eyes and learn. You got to focus on understanding the formula, implement and analyze. This will make it easier for you to solve maths problems. You can logically learn such formulae.

Before getting into the list of the formulae, let’s check out the major chapters of Class 9 Maths for which formulae are needed:

**Numbers****Polynomials****Coordinate Geometry****Algebra****Triangles****Areas of Parallelograms and Triangles****Circles****Heron’s Formula****Surface Areas and Volumes****Statistics****Probability**

**Download** – **Algebra Formulae for Class 9**

Let’s look at some of the important chapter-wise lists of formulae for all Class 9 polynomials identities and all other Class 9 identities in Mathematics.

### Class 9 Maths All Formulas PDF

Any number that can be written in the form of p ⁄ q where p and q are integers and q ≠ 0 are rational numbers. Irrational numbers cannot be written in the p ⁄ q form.

- There is a unique real number that can be represented on a number line.
- If r is one such rational number and s is an irrational number, then (r + s), (r – s), (r × s) and (r ⁄ s) are irrational.
- For positive real numbers, the corresponding identities hold together:
- \(\sqrt{ab}\) = \(\sqrt{a} × \sqrt{b}\)
- \(\sqrt{\tfrac{a}{b}}\) = \(\frac{\sqrt{a}}{\sqrt{b}}\)
- \((\sqrt{a}+\sqrt{b})\times(\sqrt{a}-\sqrt{b})=a-b\)
- \((a+\sqrt{b})\times(a-\sqrt{b})=a^2-b\)
- \((\sqrt{a}+\sqrt{b})^2=a^2+2\sqrt{ab}+b\)

- If you want to rationalize the denominator of 1 ⁄ √ (a + b), then we have to multiply it by √(a – b) ⁄ √(a – b), where a and b are both the integers.
- Suppose a is a real number (greater than 0) and p and q are the rational numbers.
- a
^{p}x b^{q }= (ab)^{p+q} - (a
^{p})^{q}= a^{pq} - a
^{p}/ a^{q }= (a)^{p-q} - a
^{p}/ b^{p}= (ab)^{p}

- a

*Download also,*

### Polynomial Formula Class 9

A polynomial p(x) denoted for one variable ‘x’ comprises an algebraic expression in the form:

**p(x) = a**_{n}**x**^{n}** + a**_{n-1}**x**^{n-1}** + ….. + a**_{2}**x**^{2}** + a**_{1}**x + a**_{0} ; where a_{0}, a_{1}, a_{2}, …. a_{n} are constants where a_{n} ≠ 0

- Any real number; let’s say ‘a’ is considered to be the zero of a polynomial ‘p(x)’ if p(a) = 0. In this case, a is said to be the mysqladmin of the equation p(x) = 0.
- Every one variable linear polynomial will contain a unique zero, a real number which is a zero of the zero polynomial and non-zero constant polynomial which does not have any zeros.
**Remainder Theorem:**If p(x) has the degree greater than or equal to 1 and p(x) when divided by the linear polynomial x – a will give the remainder as p(a).**Factor Theorem:**x – a will be the factor of the polynomial p(x), whenever p(a) = 0. The vice-versa also holds true every time.

### Class 9 Maths Formulae for Coordinate Geometry

Whenever you have to locate an object on a plane, you need two divide the plane into two perpendicular lines, thereby, making it a Cartesian Plane.

- The horizontal line is known as the x-axis and the vertical line is called the y-axis.
- The coordinates of a point are in the form of (+, +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant; where + and – denotes the positive and the negative real number respectively.
- The coordinates of the origin are (0, 0) and thereby it gets up to move in the positive and negative number.

### Class 9 Algebraic Identities

Once the students have a hold over **all Algebraic identities class 9**, they will be able to solve all the Algebra related problems in their exams. Given below are **Algebraic identities for class 9** which are considered very important **Maths formulas for Class 9**:

- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}-b^{2} - (x + a) (x + b) = x
^{2}+ (a + b) x + ab - (x + a) (x – b) = x
^{2}+ (a – b) x – ab - (x – a) (x + b) = x
^{2}+ (b – a) x – ab - (x – a) (x – b) = x
^{2}– (a + b) x + ab - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab (a + b) - (a – b)
^{3}= a^{3}– b^{3}– 3ab (a – b) - (x + y + z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy +2yz + 2xz - (x + y – z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy – 2yz – 2xz - (x – y + z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy – 2yz + 2xz - (x – y – z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy + 2yz – 2xz - x
^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z) (x^{2}+ y^{2}+ z^{2}– xy – yz -xz) - x
^{2 }+ y^{2}= \(\frac{1}{2}\) [(x + y)^{2}+ (x – y)^{2}] - (x + a) (x + b) (x + c) = x
^{3 }+ (a + b + c)x^{2}+ (ab + bc + ca)x + abc - x
^{3}+ y^{3}= (x + y) (x^{2 }– xy + y^{2}) - x
^{3}– y^{3}= (x – y) (x^{2 }+ xy + y^{2}) - x
^{2}+ y^{2}+ z^{2}– xy – yz – zx = \(\frac{1}{2}\) [(x – y)^{2}+ (y – z)^{2}+ (z – x)^{2}]

**Practice 9th CBSE Exam Questions**

### Class 9 Maths Formulae for Triangles

A triangle is a closed geometrical figure formed by three sides and three angles.

- Two figures are congruent if they have the same shape and same size.
- If the two triangles ABC and DEF are congruent under the correspondence that A ↔ D, B ↔ E and C ↔ F, then symbolically, these can be expressed as ∆ ABC ≅ ∆ DEF.

**Right Angled Triangle: Pythagoras Theorem**

Suppose ∆ ABC is a right-angled triangle with AB as the perpendicular, BC as the base and AC as the hypotenuse; then Pythagoras Theorem will be expressed as:

**(Hypotenuse)**^{2}** = (Perpendicular)**^{2}** + (Base)**^{2}

i.e. **(AC)**^{2}** = (AB)**^{2}** + (BC)**^{2}

### Class 9 Maths Formulas for Areas of Parallelograms & Triangles

A parallelogram is a type of quadrilateral that contains parallel opposite sides.

- Area of parallelogram = Base × Height
- Area of Triangle = \(\frac{1}{2}\) × Base × Height

### Class 9 Maths Formulae for Circle

A circle is a closed geometrical figure. All points on the boundary of a circle are equidistance from a fixed point inside the circle (called the center).

- Area of a circle (of radius r) = π × r
^{2} - The diameter of the circle, d = 2 × r
- Circumference of the circle = 2 × π × r
- Sector angle of the circle, θ = (180 × l ) / (π × r )
- Area of the sector = (θ/2) × r
^{2}; where θ is the angle between the two radii - Area of the circular ring = π × (R
^{2}– r^{2}); where R – radius of the outer circle and r – radius of the inner circle

### Class 9 Maths Heron’s Formula

Heron’s Formula is used to calculate the area of a triangle whose all three sides are known. Let’s suppose the length of three sides are a, b and c.

**Step 1 –**Calculate the semi-perimeter, \(s=\frac{a+b+c}{2}\)**Step 2 –**Area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)

### Class 9 Maths Formulae for Surface Areas & Volumes

**Here, LSA stands for Lateral/Curved Surface Area** and **TSA stands for Total Surface Area**.

Name of the Solid Figure | Formulae |

Cuboid | LSA: 2h(l + b)TSA: 2(lb + bh + hl)Volume: l × b × hl = length, b = breadth, h = height |

Cube | LSA: 4a^{2}TSA: 6a^{2}Volume: a^{3}a = sides of a cube |

Right Circular Cylinder | LSA: 2(π × r × h)TSA: 2πr (r + h)Volume: π × r^{2} × hr = radius, h = height |

Right Pyramid | LSA: ½ × p × lTSA: LSA + Area of the baseVolume: ⅓ × Area of the base × hp = perimeter of the base, l = slant height, h = height |

Prism | LSA: p × hTSA: LSA × 2BVolume: B × hp = perimeter of the base, B = area of base, h = height |

Right Circular Cone | LSA: πrlTSA: π × r × (r + l)Volume: ⅓ × (πr^{2}h)r = radius, l = slant height, h = height |

Hemisphere | LSA: 2 × π × r^{2}TSA: 3 × π × r^{2}Volume: ⅔ × (πr^{3})r = radius |

Sphere | LSA: 4 × π × r^{2}TSA: 4 × π × r^{2}Volume: 4/3 × (πr^{3})r = radius |

### Class 9 Maths Formulas for Statistics

Certain facts or figures which can be collected or transformed into some useful purpose are known as data. These data can be graphically represented to increase readability for people.

Three measures of formulae to interpret the ungrouped data:

Category | Mathematical Formulae |

Mean, \(\bar{x}\) | \(\frac{\sum x}{n}\) x = Sum of the values; N = Number of values |

Standard Deviation, \(\sigma\) | \(\sigma= \sqrt{\frac{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}}{N-1}}\) x _{i} = Terms Given in the Data, x̄ = Mean, N = Total number of Terms |

Range, R | R = Largest data value – Smallest data value |

Variance, \(\sigma^2\) | \(\sigma^2\ = \frac{\sum x_{i}-\bar{x}}{N}\) x = Item given in the data, x̅ = Mean of the data, n = Total number of items |

### Class 9 Maths Formulae for Probability

Probability is the possibility of any event likely to happen. The probability of any event can only be from 0 to 1 with 0 being no chances and 1 being the possibility of that event to happen.

\(Probability=\frac{Number\: of\: favourable\: outcomes}{Total\: Number\: of\: outcomes}\)

**Attempt 9th CBSE Exam Mock Tests**

These are some of the important math formula Class 9 which will be helpful to you in making your preparation journey a rather easy one. Take free **Class 9 Maths Mock Tests** of Embibe. Refer to the formulae whenever required. Make the best use of all the available resources. Securing a high score in Maths will be a cakewalk for you.

Maths Formula For Class 8 | Maths Formula For Class 10 |

Trigonometry Table | Trigonometric Ratios |

Mensuration Formula | – |

### Frequently Asked Questions

**Q. Where can I practice for more Class 9 Maths questions?****Ans: **You can practice for Class 9 Maths questions at Embibe. Embibe offers you topic-wise questions which are available for free.

**Q. Is NCERT Maths enough for Class 9?****Ans:** Yes, for Class 9. NCERT Maths book is enough. Just make sure you understand all the concepts and solve all the questions diligently. Note that regular practice is a must.

**Q. How can I learn these Math formulae?****Ans:** Mathematics is a subject of logic. Therefore, it should be interpreted in the same way. You can learn these formulae by understanding them logically. Then, you can try solving the questions by implementing these formulae.

**Q. Are the Class 9 Maths formulae based on NCERT?****Ans: **We have compiled these Class 9 Maths formulae so that students can understand them. These formulae are based on NCERT, ICSE, and all the other respective boards.

**Q. How can you learn all the formulae of Class 9 Maths NCERT?Ans: **You can try to remember all that you are trying to learn in the form of a story. Sequencing will help you to memorize the formulae in a particular order. Also, make sure to understand the derivations of the formulae rather than rote learning. This way, you will be able to remember all formulae of Maths Class 9 for a long time.

*Pro Tip: Embibe offers interactive learning videos and topic-wise practice questions for the CBSE Class 9 exams. Through the world’s most intelligent AI-based educational platform we offer calibrated feedback based on your performance and guarantees improvement in days. Take our free mock test today.*

*Now that we got a detailed article on Class 9 Maths Formulas, if you have any queries, feel free to ask in the comments section below. We will get back to you at the earliest. *Stay tuned to **Embibe** for latest news and updates on NCERT Class 9 Mathematics formulae.

*Embibe wishes you all the best!*