**Maths Formulas For Class 9:** Undoubtedly, Class 9 is regarded as an important grade in a student’s life. Class 9 lays the foundation for Board Examinations. To get through this class it is important for you to stay focussed and develop an understanding of all the essential concepts in every subject. All the Maths formulas for Class 9 should be at your fingertips if you want to sequentially solve your questions and score well in the exams.

Since time immemorial, Mathematics has been a troublesome subject for most of the students. They argue about learning and implementing a lot of formulas to solve various problem based questions. However, when you start analyzing these concepts carefully, then it becomes easier to absorb all the mathematical formulas. This article will prove to be helpful for all Class 9 students who are looking for the important Mathematic formulas for 9th Class one a single article. This increases the mindset to digest all the computation required to solve mathematical problems. So, let’s look at the important maths formulas for Class 9.

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## Maths Formulas For Class 9

Mathematical formulas 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 formulas.

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

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

Let’s look at some of the important chapter-wise lists of Maths formulas for Class 9.

### Class 9 Maths Formulas For Rational Numbers

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 which 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

### Class 9 Maths Formulas For Polynomials

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 root 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 Formulas 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.

### 9th Class Formulas For Algebraic Identities

Given below are the algebraic identities 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}]

### Class 9 Maths Formulas 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 And Triangles

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

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

### Class 9 Maths Formulas 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 centre).

- 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 Formulas For Surface Areas And Volumes

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

Name of the Solid Figure | Formulas |

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 formulas to interpret the ungrouped data:

Category | Mathematical Formulas |

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 Formulas 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.

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

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### Important FAQs Related To Maths Formulas For Class 9

Important FAQs related to Class 9 Maths formulaes are given below:

*Q: How can I learn these math formulas?*

**A:** Mathematics is a subject of logic. Therefore, it should be interpreted in the same way. You can learn these formulas by understanding them logically. Then, you can try solving the questions by implementing these formulas.

*Q: Are these Class 9 Maths formulas based on NCERT?*

**A: **We have written these Class 9 Maths formulas so that students can understand them. These formulas are based on NCERT, ICSE, and all the other respective boards.

*Q: Where can I practice for more Class 9 questions?*

**A: **You can practice for Class 9 questions at Embibe. Embibe offers you topic-wise questions and is available for free.

**SOLVE CLASS 9 MATHS QUESTIONS FOR FREE**

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

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