Maths Formulas for Class 9: Get Important Formulas - Embibe
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  • Written By Akash_Anand
  • Last Modified 25-06-2022
  • Written By Akash_Anand
  • Last Modified 25-06-2022

Maths Formulas For Class 9: Check Details On Chapter-wise Formulas & Examples

Maths Formulas for Class 9: One of the most essential grades in a student’s life is Class 9. It lays the groundwork for the Board examinations. Mathematics is a topic that many students despise, owing to the mathematical formulas. Although it is challenging but not impossible, many pupils are unable to grasp it. This causes people to avoid the topic and concentrate on other things.

Because of their reluctance, they lose marks in the overall scenario, while doing well in other courses. It would be fantastic if students could find formulae for polynomials in Class 9 and other topics all in one place. They will be more successful at solving difficulties as a result, and their grades will improve. Candidates can get formulas for all Mathematics chapters in Class 9 in this article. Continue reading to know more.

Maths Formulas for Class 9

Mathematical formulae are not just to close your eyes and learn. You got to focus on understanding all the formulas of maths, implement them and analyze. All maths formulas 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:

  1. Numbers
  2. Polynomials
  3. Coordinate Geometry
  4. Algebra
  5. Triangles
  6. Areas of Parallelograms and Triangles
  7. Circles
  8. Heron’s Formula
  9. Surface Areas and Volumes
  10. Statistics
  11. Probability

DownloadAlgebra 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.

Learn 9th CBSE Exam Concepts

Topic-wise Maths Formulas for Class 9

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.

  1. There is a unique real number that can be represented on a number line.
  2. 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.
  3. For positive real numbers, the corresponding identities hold together:
    1. \(\sqrt{ab}\) = \(\sqrt{a} × \sqrt{b}\)
    2. \(\sqrt{\tfrac{a}{b}}\) = \(\frac{\sqrt{a}}{\sqrt{b}}\)
    3. \((\sqrt{a}+\sqrt{b})\times(\sqrt{a}-\sqrt{b})=a-b\)
    4. \((a+\sqrt{b})\times(a-\sqrt{b})=a^2-b\)
    5. \((\sqrt{a}+\sqrt{b})^2=a^2+2\sqrt{ab}+b\)
  4. 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.
  5. Suppose a is a real number (greater than 0) and p and q are the rational numbers.
    1. ap x b= (ab)p+q
    2. (ap)q = apq
    3. ap / a= (a)p-q
    4. ap / bp = (ab)p

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Algebra Formulae For Class 9

Polynomial Class 9 Formula

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

p(x) = anxn + an-1xn-1 + ….. + a2x2 + a1x + a0 ; where a0, a1, a2, …. an are constants where an ≠ 0

  1. 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.
  2. Every one variable linear polynomial will contain a unique zero, a real number which is a zero of the zero polynomial and a non-zero constant polynomial which does not have any zeros.
  3. 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).
  4. 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.

Maths Formulas for Class 9 – 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.

  1. The horizontal line is known as the x-axis and the vertical line is called the y-axis.
  2. 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.
  3. The coordinates of the origin are (0, 0) and thereby it gets up to move in the positive and negative numbers.

Practice 9th CBSE Exam Questions

Maths Formulas for 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:

  1. (a + b)2 = a2 + 2ab + b2
  2. (a – b)2 = a2 – 2ab + b2
  3. (a + b) (a – b) = a2 -b2
  4. (x + a) (x + b) = x2 + (a + b) x + ab
  5. (x + a) (x – b) = x2 + (a – b) x – ab
  6. (x – a) (x + b) = x2 + (b – a) x – ab
  7. (x – a) (x – b) = x2 – (a + b) x + ab
  8. (a + b)3 = a3 + b3 + 3ab (a + b)
  9. (a – b)3 = a3 – b3 – 3ab (a – b)
  10. (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
  11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  14. x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
  15. x+ y2 =  \(\frac{1}{2}\) [(x + y)2 + (x – y)2]
  16. (x + a) (x + b) (x + c) = x+ (a + b + c)x2 + (ab + bc + ca)x + abc
  17. x3 + y3 = (x + y) (x– xy + y2)
  18. x3 – y3 = (x – y) (x+ xy + y2)
  19. x2 + y2 + z2 – xy – yz – zx = \(\frac{1}{2}\) [(x – y)2 + (y – z)2 + (z – x)2]

Maths Formulas for Class 9 – Triangles

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

  1. Two figures are congruent if they have the same shape and same size.
  2. 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

Maths Formulas for Class 9 for Areas of Parallelograms & Triangles

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

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

Maths Formulas for Class 9 for Circle

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

  1. Area of a circle (of radius r) = π × r2
  2. The diameter of the circle, d = 2 × r
  3. Circumference of the circle = 2 × π × r
  4. Sector angle of the circle, θ = (180 × l ) / (π × r )
  5. Area of the sector = (θ/2) × r2; where θ is the angle between the two radii
  6. Area of the circular ring = π × (R2 – r2); where R – radius of the outer circle and r – radius of the inner circle

Maths Formulas for Class 9 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 the three sides is a, b and c.

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

Maths Formulas for Class 9 for Surface Areas & Volumes

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

Name of the Solid FigureFormulae
CuboidLSA: 2h(l + b)
TSA: 2(lb + bh + hl)
Volume: l × b × h

l = length,
b = breadth,
h = height
CubeLSA: 4a2
TSA: 6a2
Volume: a3

a = sides of a cube
Right Circular CylinderLSA: 2(π × r × h)
TSA: 2πr (r + h)
Volume: π × r2 × h

r = radius,
h = height
Right PyramidLSA: ½ × p × l
TSA: LSA + Area of the base
Volume: ⅓ × Area of the base × h

p = perimeter of the base,
l = slant height, h = height
PrismLSA: p × h
TSA: LSA × 2B
Volume: B × h

p = perimeter of the base,
B = area of base, h = height
Right Circular ConeLSA: πrl
TSA: π × r × (r + l)
Volume: ⅓ × (πr2h)

r = radius,
l = slant height,
h = height
HemisphereLSA: 2 × π × r2
TSA: 3 × π × r2
Volume: ⅔ × (πr3)

r = radius
SphereLSA: 4 × π × r2
TSA: 4 × π × r2
Volume: 4/3 × (πr3)

r = radius

Maths Formulas for Class 9 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:

CategoryMathematical Formulae
Mean, \(\bar{x}\)\(\frac{\sum x}{n}\)
x = Sum of the values; N = Number of values
Standard Deviation, \(\sigma\)\(\sigma= \sqrt{\frac{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}}{N-1}}\)

xi = Terms Given in the Data, x̄ = Mean, N = Total number of Terms
Range, RR = 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

Maths Formulas for Class 9 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 happening.

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

Attempt 9th CBSE Exam Mock Tests

These are some of the important maths formulas in 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 8Maths Formula For Class 10
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Mensuration Formula –

Below are the frequently asked questions with solutions about CBSE Class 9 formulas

Q.2: 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.3: 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.4: 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.5: How can you learn all the polynomial Class 9 formulas for 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 guarantee 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.

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