## Math Formula for Class IX

For most of the students, class 9^{th} Maths is the nightmare and the formulas are very difficult to learn. If you will not show a positive attitude towards learning mathematics then there are chances that may lose your interest from learning.

Sometimes, students feel nervous just before the exams and develop a feeling of insecurity. To handle all these problems wisely, the best idea is to download the complete list of maths formulas for class 9 in PDF format and take with you wherever you go.

#### Class 9 Polynomials Formulas

- Monomial = \( {\rm{3}},2x,\frac{2}{3}y{\rm{etc}}{\rm{.}} \)
- Binomial = \( (2x + 3y),(3x – 2y){\rm{etc}}{\rm{.}} \)
- Trinomial = \( x^2 + 4x + 5{\rm{etc}}{\rm{.}} \)
- Linear Polynomial = \( x + 2,3x + 5{\rm{etc}}{\rm{.}} \)
- Quadratic Polynomial = \( ax^2 + bx + c{\rm{etc}}{\rm{.}} \)
- Cubic Polynomial = \( x^3 + 4x^2 + 5{\rm{etc}}{\rm{.}} \)
- Biquadratic Polynomial = \( x^4 + 5x^3 + 2x^2 + 3 \)

#### Class 9 Coordinate Geometry Formulas

- Equation of a line = \( ax + by + c = 0 \)
- Equation of a circle = \( x^2 + y^2 = r^2 \)

Here ‘r’ is the radius of the circle - Equation of a parabola = \( y^2 = 4ax \)
- Equation of an ellipse = \( \frac{{x^2 }}{{a^2 }} + \frac{{y^2 }}{{b^2 }} = 1 \)
- Equation of hyperbola = \( \frac{{x^2 }}{{a^2 }} – \frac{{y^2 }}{{b^2 }} = 1 \)
- Distance formula D = \( \sqrt {\begin{bmatrix}{\left( {x_2 – x_1 } \right)^2 } +\\ {\left( {y_2 – y_1 } \right)^2 }\end{bmatrix}} \)
- Angle between two lines = \( \tan ^{ – 1} \left( {\frac{{m_2 – m_1 }}{{1 + m_1 m_2 }}} \right) \)

#### Class 9 Triangles Formulas

- Area of Isoscele Triangle = \( \frac{1}{2}bh\)
- Altitude of an Isosceles Triangle= \( \sqrt{a^{2}-\frac{b^{2}}{4}}\)
- Perimeter of Isosceles Triangle = \( 2\,a+b\)<br/ >Where, b = Base , h = Height, a = length of the two equal sides
- Area of an Right Triangle = \( \frac{\sqrt{1}}{2}bh\)
- Perimeter of an Right Triangle = \( a+b+c\)
- semi Perimeter of an Right Triangle = \( \frac{a+b+c}{2}\)

where:; b:Base, h:Hypotenuse a: Hight - Area of Scalene Triangle = \( \sqrt{s(s-a)(s-b)(s-c)} \)
- Perimeter of Scalene Triangle = \( a+b+c \)

Where: a, b, c are Side of Scalene Triangle - Area of an Equilateral Triangle = \( \frac{\sqrt{3}}{4}a^{2}\)
- Perimeter of an Equilateral Triangle = \( 3a\)
- Semi Perimeter of an Equilateral Triangle = \( \frac{3a}{2}\)
- Height of an Equilateral Triangle = \( \frac{\sqrt{3}}{2}a\)

Where, a:side, h: altitude

#### Class 9 Quadrilaterals Formulas

- Area of a Square = \( side^{2}\)
- Area of a Kite = \( \frac {1}{2} \times Diagonal_{1} \times Diagonal_{2} \)
- Perimeter of Kite= \( 2(a+b)\)
- Area of a Parallelogram = \( Base \times height \)
- Perimeter of Parallelogram= \( 2(Base + height)\)
- Area of a Rectangle = \( Length \times Breadth \)
- Perimeter of Rectangle= \( 2(Length + Breadth)\)
- Area of a Trapezoid = \( \frac {Base_{1} + Base_{2}}{2} \times hiehgt \)
- Perimeter of Trapezoid= \( Side_{1} + Side_{2} + Side_{3} + Side_{4}\)

#### Class 9 Areas of Parallelograms and Triangles Formulas

- Area of a Parallelogram = \( b\times h\)
- Perimeter of Parallelogram = \( 2\left(b+h\right)\)
- Height of Parallelogram = \( \frac{Area}{Base}\)

Where: b is the length of any base and h is the corresponding altitude or height. - \( p^{2}+q^{2}=2(a^{2}+b^{2})\)

Where: p,q are the diagonals, a,b are the parallel sides - Area of a Triangle = \( \frac{1}{2}ah \)

Where: a is the base of the triangle. h is the height of the triangle. - Perimeter of a Triangle = \( a+b+c\) < br />Where: a, b, and c are three different sides of a Triangle.

#### Class 9 Circles Formulas

- Area of a circle =\( \pi r^{2}=\frac{{\pi}d^{2}}{4}=\frac{{C} \times {r}}{2}\)
- Perimeter of Circle = \( 2 \pi r \)
- Area of a half circle = \( \frac{{\pi}r^{2}}{2}\)
- Area of a Quarter circle = \( \frac{{\pi}r^{2}}{4}\)
- Area of Sector of a circle = \( \frac{θ}{360}\pi r^{2}\)
- Length of an arc of a sector = \( \frac{θ}{360}{2 \pi r}\)
- Sector angle of circle = \( \frac{180 \times l}{\pi r}\)
- Area of the sector = \( \frac{θ}{2} \times r^{2}\)
- Area of the circular ring = \( \pi \times (R^{2} – r^{2})\)

Where,**r**is the radius of the circle.**d**is the diameter of the circle.**C**is the circumference of the circle.**θ**is the Angle between two radius.**R**is the Radius of Outer Circle.

#### Class 9 Heron’s Formula

- Area of Triangle = \( \sqrt{s(s-a)(s-b)(s-c)} \)
- Perimeter of Triangle =\( a+b+c \)
- Semi perimeter of Triangle =\( \frac{a+b+c}{2} \)

Where,**a**,**b**,**c**are Side of Triangle

#### Class 9 Surface Areas and Volumes Formulas

- Surface area of Cube = \( 6a^{2}\)
- Volume of a cube = \( a^{3}\)

Where, a is the side length of the cube. - Surface area of Cuboid = \( 2(lb + bh + hl)\)
- Volume of a Cuboid = \( h \times l \times w\)

Where, l: Height, h: Legth, w: Depth - Diameter of a sphere = \( 2r\)
- Circumference of a sphere = \( 2\pi r\)
- Surface area of a sphere = \( 4\pi r^{2}\)
- Volume of a sphere = \( \frac{4}{3}\: \pi r^{3}\)
- Curved Surface area of a Hemisphere = \( 4\pi r^{2}\)
- Total Surface area of a Hemisphere = \( 3\pi r^{2}\)
- Volume of a Hemisphere = \( \frac{2}{3}\: \pi r^{3}\)

Where, r: Radius - Curved Surface area of a Cylinder = \( 2\pi rh\)
- Total Surface area of a Cylinder = \( 2\pi r(r+h)\)
- Volume of a Cylinder = \( \pi r^{2} h\)Where, r: Radius, h: Height
- Total Surface Area of cone = \( \pi r \left (s+r \right )\)
- Vomule of cone = \( \frac {1}{3}\pi r^{2}h\)
- Curved Surface Area of cone = \( \pi rs\)

Where,**r**: radius of cone.**h**:height of cone.**s**: slant height of the cone.

#### Class 9 Statistics Formulas

- \(\ Mean\; \bar{x} = \frac{\sum x}{n}\)

Where,**x**= Items given,**n**= Total number of items - \(\ Range = Largest\; Value – Smallest\; Value \)
- If n is odd, \(\ Median = (\frac{n+1}{2})^{th}term\)
- If n is even, \(\ Median = \frac{(\frac{n}{2})^{th}term+(\frac{n}{2}+1)^{th}term}{2}\)

where,**n**= Total number of items - \(\ Variance = \sigma ^{2} = \frac{\sum (x- \bar{x})^{2}}{n}\)

Where,**x**= Items given,**x¯**= Mean,**n**= Total number of items - Standard Deviation \(\ \sigma = \sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}\)

Where,**x**= Items given,**x¯**= Mean,**n**= Total number of items

#### Class 9 Probability Formulas

- Probability = \(\ \frac{No. \;of\; Favorable \;outcome}{No.\; of\; all\; possible\; outcome} \)

#### Algebra Formulas For Class 9 Maths

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

Once you are sure of the topics and the logic behind then it is always easy for you to learn the formulas and solve the most difficult problems too. In the next sections, we will discuss the chapter-wise marking scheme and the total number of chapters for study in class 9.

## CBSE Class 9 Mathematics Unit-Wise Weightage

Moreover, once you learn Math Formulas, they are important for other subjects too like Physics, Economics, Chemistry etc. Learning online is the smartest way today with handy learning aid for students. When you learn online, the PDF formulas file is prepared carefully after deep research and observation.

At the same time, you will get hands-on practice material for exam preparation and complete their syllabus faster. For students, basic Mathematics formulas are the foundation for other subjects in class 9. Not only for students, but an online PDF guide and formulas are good for teachers as well and they can use it as a reference and brush up their mathematical skills in minutes.

Units | Unit Name | Marks |

I | NUMBER SYSTEMS | 8 |

II | ALGEBRA | 17 |

III | COORDINATE GEOMETRY | 4 |

IV | GEOMETRY | 28 |

V | MENSURATION | 13 |

VI | STATISTICS & PROBABILTY | 10 |

Total |
80 |

## NCERT Solutions For Class 9 Maths by Chapters

Recently, a new assessment scheme has been introduced for the class 9^{th} CBSE. Students will be assessed on the basis of final exams for each subject carrying 100 marks. It constitutes 80 marks for final exams and 20 marks for internal assessments. Students should know this assessment before they start preparing for the final exams for the current session. Also, students must-have a depth understanding of the basic concepts of each chapter and their respective formulas.

- Chapter 1 – Number Systems
- Chapter 2 – Polynomials
- Chapter 3 – Coordinate Geometry
- Chapter 4 – Linear Equations in Two Variables
- Chapter 5 – Introduction to Euclids Geometry
- Chapter 6 – Lines and Angles
- Chapter 7 – Triangles
- Chapter 8 – Quadrilaterals
- Chapter 9 – Areas of Parallelograms and Triangles
- Chapter 10 – Circles
- Chapter 11 – Constructions
- Chapter 12 – Heron’s Formula
- Chapter 13 – Surface Areas and Volumes
- Chapter 14 – Statistics
- Chapter 15 – Probability

### Class 9 Maths Formulas By Chapters

In the previous section, we have already given chapters for class 9^{th} and their marking schemes. You should have a complete idea of each chapter before you start preparing for the final exams. These are the number system, Algebra, Geometry, Coordinate Geometry, Mensuration, Statistics, and Probability. These topics are common when you prepare for competitive exams too and they had plenty of real-life applications too. So, start your foundation today and be a front-runner in your future.

- Chapter 2 – Polynomials
- Chapter 3 – Coordinate Geometry
- Chapter 7 – Triangles
- Chapter 8 – Quadrilaterals
- Chapter 9 – Areas of Parallelograms and Triangles
- Chapter 10 – Circles
- Chapter 12 – Heron’s Formula
- Chapter 13 – Surface Areas and Volumes
- Chapter 14 – Statistics
- Chapter 15 – Probability

### Summary

Here, are the benefits you should understand while studying important math formulas chapter-wise for class 9.

- You can score good marks in your final exams.
- You can complete the syllabus on time with confidence.
- You can revise the concepts and formulas quickly.
- This is easy to memorize formulas when they are available altogether.
- You would know your strengths and weakness. It would be great for spending more time in managing your weaknesses.
- Also, you will get a route to prepare for the competitive exams.