### Geometry

Geometry Shapes Formulas for Class 9 | ||
---|---|---|

Geometric Figure |
Area |
Perimeter |

Rectangle | A= l × w | P = 2 × (l+w ) |

Triangle | A = (1⁄2) × b × h | P = a + b + c |

Trapezoid | A = (1⁄2) × h × (b_{1}+ b_{2}) |
P = a + b + c + d |

Parallelogram | A = b × h | P = 2 (a+b) |

Circle | A = π r^{2} |
C = 2 π r |

### Algebra

Algebraic Identities 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}=^{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 =^{1}/_{2}[(x – y)^{2}+ (y – z)^{2}+ (z – x)^{2}]

**Algebra Identities**

(x + β)² = x² + β² + 2 x β |

(x – β)² = x² + β² – 2 x β |

(x + θ) (x – θ) = x² – θ² |

(x + α)(x + θ) = x² + (α + θ)x + αθ |

(x + α)(x – θ) = x² + (α – θ)x – αθ |

(x – α)(x + θ) = x² + (θ – α)x – xθ |

(x – α)(x – θ) = x² – (α + θ)x + αq |

(α + θ)³ = α³ + θ³ + 3αθ(α + θ) |

(α – θ)³ = α³ + θ³ – 3αθ(α – θ) |

(α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ |

(α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ |

(α – β + θ)² = α² + β² + θ²- 2αβ – 2βθ + 2αθ |

(α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ |

(x)³ + (β)³ = ( x + β) (x² – xβ + β) |

(x)³ – (β)³ = ( x + β) (x² – xβ + β) |

### Surface Area and Volumes

Shape |
Surface Area |
Volume |

Cuboid | 2(lb + bh +lh)
l= length, b=breadth, h=height |
lbh |

Cube | 6a^{2} |
a^{3} |

Cylinder | 2πr(h+r)
r = radius of circular bases h = height of cylinder |
πr^{2}h |

Cone | πr(l+r)
r=radius of base l=slant height Also, l |
(1/3)πr^{2}h |

Sphere | 4πr^{2} |
(4/3)πr^{3} |

**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.

### Polynomial

**Statistics (Measure of Central Tendency)**

### Statistics

Measure of Central Tendency | |

Mean | Sum of Observation/Total number of observation = ∑ x/n |

Median | [(n+1)/2]th term [For odd number of observation]
Mean of (n/2)th term and (n/2+1)th term [For even number of observation] |

Mode | Value which is repeated maximum time in a data set |

### 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.

Empirical Probability = Number of trials with expected outcome/Total number of Trials |

### 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:

## Class 9 Maths Formulas Examples

**Example 1:** Simplify the following expression: (3 + √7)(3 – √7)

**Solution: **Using the formula, (a + b)(a – b) = a^{2} – b^{2}

We can solve it as (3 + √7)(3 – √7) = 9 – 7 = 2

**Example 2 :** A school building is to be supported using cylindrical pillars. If the height of the pillars = 10 m and radius of the pillar = 20 cm, how much concrete is needed to make 7 cylindrical pillars?

**Solution:** To know how much concrete is needed we need to find the volume of a cylinder and then multiply it with the number of cylinders needed.

We know that the volume of cylinder = πr^{2}h

so, substituting the value of radius = 0.2 m and height = 10 m we get,

= 22/7 × 0.2 × 0.2 × 10

= 8.8 / 7 = 1.257 m^{3}

Since 7 pillars are needed, the net concrete needed is,

8.8/7× 7 = 8.8 m^{3}

### FAQs (Frequently Asked Questions)

Q1. What are the Formulas of Maths Class 9?

Ans. Maths formulas Class 9 are rules written with Mathematics symbols. It usually joins two or more quantities with an equal symbol. When you know the value of one quantity, you can easily derive the value of another quantity using Maths formulas. For example, the formula of a right-angled triangle = ½ × Base × Height.

**Q2. How to Remember All formulas of Maths Class 9 NCERT?**

Ans. The simplest way is to create a story to remember everything you are trying to learn. Similarly, the Maths formulas and equations can be learned in the form of the story. This sequence of stories enables you to memorize the formulas in a particular order. Also, make sure to understand how the equations are derived rather than mugging up as this will help you to remember all formulas of Maths Class 9 for a long time.

*Q1: Is it necessary to understand the derivation of the Maths formulas?***A:** It is a good practice to understand the derivation of the Maths formulas. That way, you can arrive at the formulas yourself even if you forget them in the exam.

*Q2: 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.

*Q3: Are these Class 9 Maths formulas based on NCERT?***A: **We have compiled these Class 9 Maths formulas so that students can understand them. These formulas are based on NCERT, ICSE, and all the other respective boards.

*Q4: Where can I practice for more Class 9 Maths questions?***A: **You can practice for Class 9 Maths questions at Embibe. Embibe offers you topic-wise questions which are available for free.

*Q5: Is NCERT Maths enough for Class 9?***A:** 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.

### What are the Important Formulas for Class 9 Maths?

Class 9 math includes topics of Number System, Polynomials in algebra, Solid Geometry, Statistics and Probability. Some of the important formulas from these topics can be seen below:

- (a + b) (a – b) = a
^{2}– b^{2} - (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{3}= a^{3}– b^{3}– 3ab(a – b) - Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl, ‘l’ = √(r
^{2}+ h^{2}) - Volume of a Cone = (1 / 3 )πr
^{2}h - Volume of a Sphere = (4/3) πr
^{3} - Volume of a Hemisphere = (2/3) πr
^{3} - Mean = Sum of the observations / Total number of observations
- Experimental Probability Formula: The trial counts in which the event (E) has occurred / The sum of trials

### 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:

- 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.

### What are the Basic Formulas in Class 9 Maths?

The basic formulas in class 9 maths are from the topics of number system, algebra, geometry, statistics and probability. Remembering the basic entities from the Number System will help the students understand the rational and irrational numbers better. The expansion formulas of polynomials are helpful in finding the roots of equations. In geometry, it is important that the students remember the basic formulas of finding area and volume of different shapes and objects.

### What are the important formulas covered in class 9 Algebra?

The important formulas covered in class 9 algebra help in demonstrating the difference between linear, quadratic, and cubic polynomials. Apart from the basic factorization formulas of polynomials as mentioned below, the students are advised to revise the important concepts of the Remainder theorem and the Factor theorem, that help identify the factors of a polynomial.

- (a + b) (a – b) = a
^{2}– b^{2} - (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{3}= a^{3}– b^{3}– 3ab(a – b)

### 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.

### How many formulas are there in Class 9 Maths?

There are around 30 important class 9 maths formulas which, if learned well, can help the students in solving a lot of problems because usually most of the other formulas are derived from these basic ones. If we see how many formulas are there in each of the topics in class 9 maths then it would be as follows:

- The number system has 5 basic entities which helps students understand the relationship of rational and irrational numbers.
- In algebra, the major 5 significant formulas explain the concept of factorization, which is helpful throughout the study of algebra to facilitate finding the roots of equations.
- The surface area and volume segment has around 15 formulas covering the dimensions of cuboid, sphere, cylinder and cones.
- Statistics and probability has 5 simple formulas that help in statistical analysis and predictability of events in probability.

### How can I Memorize Class 9 Maths formulas?

The best way to remember the class 9 maths formulas is to practice the problems based on them. This not only helps in understanding the usage and the appropriate relevance of all the formulas but also helps avoiding the unnecessary burden of mugging them up.

The students can also take the help of digital notes available online. They can save the formula sheet as their mobile screensaver or desktop wallpaper. This will ensure that everytime they use their mobile or laptop, the formula wallpaper will remind them to have a quick revision throughout the day.

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