Maths Formulas for Class 9: Class 9 is one of the most important phase in a student’s life. Here lies the foundation of board exams. Board exams are a challenge in themselves. Mathematics is a difficult and intimidating subject because of its mathematical formulas. It is a bit difficult but not too difficult yet many students could not achieve it.
Due to the mathematical formula, they avoid this subject and focus on other subjects. This reluctance causes them to lose marks in the overall scenario, although may perform quite well in other subjects.
Mathematics often intimidates students because it comes with the complexity of learning the formulas. A glimpse of the formulas can raise the anxiety of the students and this is the reason why many of them are hesitant to study the subject.
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But we are here with one such solution locker of formulas that to help calm the anxiety of the students and have an easy approach to learn the formulas of class 9 maths, this article is a summary list of all the important formulas and how to remember them. Provides some useful tips and tricks for
It would be great if students had the formulas for class 9 polynomials and other such topics in Ashan language and in one place. This will enable them to solve problems and thus improve their grades. In this article, candidates can get the formulas for all the chapters of Maths in Class 9. Read chapter-wise important formulas for class 9.
Maths Formulas for Class 9
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Mathematical formulas are not just meant to be learned blindly. You have to focus on understanding, applying and analyzing all the formulas of mathematics. All Maths Formulas make it easy for you to solve maths questions. You can learn such formulas logically.
Before getting into the list of formulas, let us examine the major chapters in class 9 maths that require formulas.
List of Important Class 9 Math Formulas
- 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 us look at some important chapter-wise lists of formulas for all Polynomial Identities for Class 9 and All other Identities of Class 9 in Mathematics.
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Class 9 Maths Topic Wise All Formulas
Any number that can be written as p / q where p and q are integers and q ≠ 0 are rational numbers. Irrational numbers cannot be written in the form p / q.
- There is a unique real number that can be represented on a number line.
- If r is such a 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:
- ab−−√ab = a−−√×b√a×b
- ab−−√ab = a√b√ab
- (a−−√+b√)×(a−−√−b√)=a−b(a+b)×(a−b)=a−b
- (a+b√)×(a−b√)=a2−b(a+b)×(a−b)=a2−b
- (a−−√+b√)2=a2+2ab−−√+b(a+b)2=a2+2ab+b
- If you want to rationalize the denominator of 1 ⁄ √ (a + b), we need to multiply it by √ (a – b)/√ (a – b), where a and b are both integers.
- Let a be a real number (greater than 0) and p and q be rational numbers.
- ap x bq = (ab)p+q
- (ap)q = apq
- ap / aq = (a)p-q
- ap / bp = (ab)p
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Polynomial Formula Class 9
The polynomial p(x) for a variable ‘x’ has an algebraic expression:
p(x) = anxn + an-1xn-1 + ….. + a2x2 + a1x + a0 ; where a0, a1, a2, …. an are constants where an ≠ 0
- Any real number; Let ‘a’ be considered the zero of the polynomial ‘P(x)’ if P(a) = 0. In this case, a is said to be the of the equation P(x) = 0.
- Each one-variable linear polynomial will have a unique zero, a real number that is the zero of the zero polynomial and a non-zero constant polynomial with no zeros.
- Remainder Theorem: If the power of p(x) is greater than or equal to 1 and dividing p(x) by the linear polynomial x – a will give the remainder in the form p(a).
- Factoring Theorem: x – a will be a factor of the polynomial p(x) whenever p(a) = 0. The opposite is also true every time.
Class 9 Maths Formulae for Coordinate Geometry
Whenever you have to trace an object on a plane, you need to divide the plane into two perpendicular lines, making it a Cartesian plane.
- The horizontal line is called the x-axis and the vertical line is called the y-axis.
- The coordinates of a point are in the first quadrant as (+, +), in the second quadrant as (-, +), in the third quadrant as (-, -) and in the fourth quadrant as (+, -) ; where + and – denote positive and negative real numbers respectively.
- The coordinates of the origin are (0, 0) and thus it moves up to move in positive and negative numbers.
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Class 9 Algebraic Identities
Once the students get hold of all the Algebraic Identities of Class 9, they will be able to solve all the algebra related problems in their exam. Given below are the algebraic identities for class 9 which are considered to be very important maths formulas for class 9:
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (a + b) (a – b) = a2 -b2
- (x + a) (x + b) = x2 + (a + b) x + ab
- (x + a) (x – b) = x2 + (a – b) x – ab
- (x – a) (x + b) = x2 + (b – a) x – ab
- (x – a) (x – b) = x2 – (a + b) x + ab
- (a + b)3 = a3 + b3 + 3ab (a + b)
- (a – b)3 = a3 – b3 – 3ab (a – b)
- (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
- (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
- (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
- (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
- x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
- x2 + y2 = 1212 [(x + y)2 + (x – y)2]
- (x + a) (x + b) (x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
- x3 + y3 = (x + y) (x2 – xy + y2)
- x3 – y3 = (x – y) (x2 + xy + y2)
- x2 + y2 + z2 – xy – yz – zx = 1212 [(x – y)2 + (y – z)2 + (z – x)2]
Maths formulas for class 9 for Triangles
A triangle is a closed geometric figure made up of three sides and three angles.
- Two figures are congruent if they have the same shape and size.
- If two triangles ABC and DEF are congruent under the correspondence that A ↔ D, B ↔ E and C ↔ F, then symbolically, they can be expressed as ∆ ABC ≅ ∆ DEF.
Right Angled Triangle: Pythagoras Theorem
Let ∆ ABC be a right angled triangle in which AB is perpendi ∆ ABC ≅ ∆ DEF.cular, BC is base and AC is hypotenuse; Then the Pythagorean theorem would 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 = 1212 × Base × Height
Class 9 Maths Formulae for Circle
A circle is a closed geometric figure. All points on the boundary of a circle are equidistant from a fixed point inside the circle (called the center).
- Area of a circle (of radius r) = π × r2
- 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) × r2; where θ is the angle between the two radii
- Area of the circular ring = π × (R2 – r2); 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 three sides are known. Let the lengths of three sides be a, b and c.
- Step 1 – Calculate the semi-perimeter, s=a+b+c2s=a+b+c2
- Step 2 – Area of the triangle = s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√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: 4a2 TSA: 6a2 Volume: a3a = sides of a cube |
| Right Circular Cylinder | LSA: 2(π × r × h) TSA: 2πr (r + h) Volume: π × r2 × hr = radius, h = height |
| Right Pyramid | LSA: ½ × p × l TSA: LSA + Area of the base Volume: ⅓ × Area of the base × hp = perimeter of the base, l = slant height, h = height |
| Prism | LSA: p × h TSA: LSA × 2B Volume: B × hp = perimeter of the base, B = area of base, h = height |
| Right Circular Cone | LSA: πrl TSA: π × r × (r + l) Volume: ⅓ × (πr2h)r = radius, l = slant height, h = height |
| Hemisphere | LSA: 2 × π × r2 TSA: 3 × π × r2 Volume: ⅔ × (πr3)r = radius |
| Sphere | LSA: 4 × π × r2 TSA: 4 × π × r2 Volume: 4/3 × (πr3)r = radius |
Class 9 Maths Formulas for Statistics
Some facts or figures which can be collected or converted into some useful purpose are known as data. These figures can be represented graphically to increase readability for people.
Three measures of formulas for the interpretation of unclassified data:
| Category | Mathematical Formulae |
| Mean, x¯x¯ | ∑xn∑xn x = Sum of the values; N = Number of values |
| Standard Deviation, σσ | σ=∑ni=1(xi−x¯¯¯)2N−1−−−−−−−−−√σ=∑i=1n(xi−x¯)2N−1
xi = Terms Given in the Data, x̄ = Mean, N = Total number of Terms |
| Range, R | R = Largest data value – Smallest data value |
| Variance, σ2σ2 | σ2 =∑xi−x¯Nσ2 =∑xi−x¯N
x = Item given in the data, x̅ = Mean of the data, |
Class 9 Maths Formula for Probability
Probability is the probability that any event will occur. The probability of any event can only range from 0 to 1, with 0 being no probability and 1 being the probability of that event occurring.
Probability=NumberoffavourableoutcomesTotalNumberofoutcomesProbability=NumberoffavourableoutcomesTotalNumberofoutcomes
These are some of the important maths formulas for class 9 which will help you in making your preparation journey easier. Take Embibe’s Class 9 Maths mock tests for free. Refer to sources whenever required. Make the best use of all available resources. It will be easy for you to get high marks in maths.
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FAQ
Q.1: Where can I practice for more Class 9 Maths questions?
Answer: You can practice on Embibe for class 9 maths questions. NRACETJOB provides you topic wise questions which are available free of cost.
Question 2: Is NCERT Maths enough for class 9?
Answer: 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 exercise is a must.
Q.3: How can I learn these math formulas?
Answer: Mathematics is a matter of reasoning. Therefore it should be interpreted in the same way. You can learn these formulas by understanding them logically. Then, you can try to solve the questions by applying these formulas.
Q.4: Are the maths formulas for class 9 based on NCERT?
Answer: We have compiled these formulas for class 9 maths so that students can understand them. These formulas are based on NCERT, ICSE and all other related boards.
Q.5: How can you learn Maths NCERT All Polynomial Class 9 Formulas?
Answer: You can try to remember everything you are trying to learn in story form. Sequencing will help you memorize formulas in a specific order. Also, be sure to understand the etymologies of formulas rather than cramming them. In this way you will be able to remember all the formulas of class 9 maths for a long time.