Class 9 Maths Formula Sheets

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Do you dislike Math formulas and equations because they seem complicated or difficult? What if we told you that you no longer need to mug up all Math formulas of Class 9?

Our team of Math experts have created a list of Class 9 Maths formulas for you with logical explanations as well as the method of how and where to use them. Success is said to be the sum of small efforts that are repeated daily and by using this list of important formulas in your exam preparations, you will be able to understand their logic, solve complex problems faster, score higher marks in your school exams and crack various competitive exams!

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Important Maths Formulas for Class 9

1. Polynomial Expresssions Formulas

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

2. Coordinate Geometry Formulas

Equation of a line \(\begin{align}  ax + by + c = 0   \end{align}\)
Equation of a circle \(\begin{align}  x^2  + y^2  = r^2    \end{align}\)
Here ‘\(r \)’ is the radius of the circle
Equation of a parabola \(\begin{align}  y^2  = 4ax    \end{align}\)
Equation of an ellipse \(\begin{align}  \frac{{x^2 }}{{a^2 }} + \frac{{y^2 }}{{b^2 }} = 1   \end{align}\)
Equation of hyperbola \(\begin{align}  \frac{{x^2 }}{{a^2 }} - \frac{{y^2 }}{{b^2 }} = 1   \end{align}\)
Distance formula \(\begin{align} D = \sqrt {\begin{bmatrix}{\left( {x_2 - x_1 } \right)^2 } +\\ {\left( {y_2 - y_1 } \right)^2 }\end{bmatrix}}   \end{align}\)
Angle between two lines \(\begin{align}  \theta  = \tan ^{ - 1} \left( {\frac{{m_2  - m_1 }}{{1 + m_1 m_2 }}} \right)    \end{align}\)

3. Circles Formulas

Area of circle  \(\begin{align}   \pi r^2     \end{align}\)
Diameter of circle  \( 2r \)
Circumference of circle  \(\begin{align}    2\pi r     \end{align}\)
Sector angle of circle  \(\begin{align}    \theta  = \frac{{\left( {180 \times l} \right)}}{{\left( {\pi r} \right)}}     \end{align}\)
Area of the sector \(\begin{align}     \left( {\frac{\theta }{2}} \right) \times r^2      \end{align}\)
Area of the circular ring \(\begin{align}   = \pi  \times \left( {R^2  - r^2 } \right)   \end{align}\)
\(\begin{align}\theta &= \text{Angle between two radii}\\R &= \text{Radius of outer circle}\\r &= \text{Radius of inner circle}\end{align}\)

4. Surface Area and Volume Formulas

Cuboid
Volume of Cuboid (LSA) \(\begin{align} l \times b \times h \end{align}\)
Lateral Surface Area of Cuboid (LSA) \(\begin{align}  2h\left( {l + b} \right)    \end{align}\)
Total Surface Area of Cuboid (TSA) \(\begin{align}  2\left( {lb + bh + hl} \right)   \end{align}\)
Cube
Volume of Cube \(\begin{align} x^3   \end{align}\)
Lateral Surface Area of Cube (LSA) \(\begin{align}   4x^2    \end{align}\)
Total Surface Area of Cube (TSA) \(\begin{align}   6x^2     \end{align}\)
Sphere
Volume of Sphere \(\begin{align}   \frac{4}{3} \times \pi r^3      \end{align}\)
Lateral Surface Area of Sphere (LSA) \(\begin{align}    4\pi r^2       \end{align}\)
Total Surface Area of Sphere (TSA) \(\begin{align}  4\pi r^2        \end{align}\)
Right Circular Cylinder
Volume of Right Circular Cylinder \(\begin{align}   \pi r^2 h     \end{align}\)
Lateral Surface Area of Right Circular Cylinder (LSA) \(\begin{align}   2 \times \left( {\pi rh} \right)     \end{align}\)
Total Surface Area of Right Circular Cylinder (TSA) \(\begin{align}   2\pi r \times \left( {r + h} \right)     \end{align}\)
Right Pyramid
Volume of Right Pyramid \(\begin{align}   \frac{1}{3} \times \begin{bmatrix}\text{Area of }\\\text{the Base}\end{bmatrix} \times h  \end{align}\)
Lateral Surface Area of Right Pyramid (LSA) \(\begin{align}   \frac{1}{2} \times p \times L   \end{align}\)
Total Surface Area of Right Pyramid (TSA) \(\begin{align}   {\text{LSA}} + \begin{bmatrix}\text{Area of }\\\text{the Base}\end{bmatrix} \end{align}\)
Right Circular Cone
Volume of Right Circular Cone \(\begin{align}   \frac{1}{3} \times \left( {\pi r^2 h} \right) \end{align}\)
Lateral Surface Area of Right Circular Cone (LSA) \(\begin{align}   \pi rl \end{align}\)
Total Surface Area of Right Circular Cone (TSA) \(\begin{align}   \pi r \times \left( {r + L} \right)    \end{align}\)
Hemisphere
Volume of Hemisphere \(\begin{align}  \frac{2}{3} \times \left( {\pi r^3 } \right)   \end{align}\)
Lateral Surface Area of Hemisphere (LSA) \(\begin{align}  2\pi r^2    \end{align}\)
Total Surface Area of Hemisphere (TSA) \(\begin{align}  3\pi r^2     \end{align}\)
Prism
Volume of Prism \(\begin{align}  B \times h     \end{align}\)
Lateral Surface Area of Prism (LSA) \(\begin{align}  p \times h     \end{align}\)
Total Surface Area of Prism (TSA) \(\begin{align}  \pi  \times r \times \left( {r + L} \right)    \end{align}\)
\(\begin{align} l &= \text{Length, } \\ h &= \text{Height,} \\ b &= \text{Breadth}  \\  r &= \text{Radius of Sphere}  \\  L &= \text{Slant Height}  \end{align}\)

5. Statistics Formulas

Mean \(\begin{align}   \overline x   \end{align}\) \(\begin{align}   \frac{{\sum x }}{n}   \end{align}\)
\(\begin{align}  x &= {\text{Sum of the Values}} \\ n &= {\text{Number of Values}}  \end{align}\)
Standard Deviation, \(\begin{align}   \sigma    \end{align}\) \(\begin{align}   \sigma  = \sqrt {\frac{{\sum\nolimits_{i = 1}^n {} \left( {x_i  - \overline x } \right)^2 }}{{N - 1}}}     \end{align}\)
\(\begin{align}    x_i  &= {\text{Terms Given in the Data}}, \\ \overline x  &= {\text{Mean}}, \\ 
 N &= {\text{Total Number of Terms}}     \end{align}\)
Range \( R \) \(\begin{align} R = \begin{bmatrix}\text{Largest}\\\text{value}\end{bmatrix} -\begin{bmatrix}\text{Smallest} \\ \text{value}\end{bmatrix} \end{align}\)
Variance, \(\begin{align}   \sigma    \end{align}\) \(\begin{align} \sigma ^2  = \frac{{\sum {x_i  - \overline x } }}{N}  \end{align}\)
\(\begin{align}   x &= {\text{Item given in the data}}, \\ \overline x  &= {\text{Mean of the data}},\\  N &= {\text{Total number of terms}}   \end{align}\)

6. Heron's Formula 

Perimeter
Right-angle triangle \(\begin{align}  P = b + h + d  \end{align}\)
\(\begin{align}   &{\text{Height}} = h,\\ & {\text{Base}} = b, \\ & {\text{Hypotenuse}} = d,  \end{align}\)
Isosceles right-angle triangle \(\begin{align} p &= 2a + a\sqrt 2  \\ a &= \text{Equal Sides}   \end{align}\)
Triangle with different sides \( a,\;b,\;c \) \(\begin{align} P = a + b + c  \end{align}\)
Square with side \(a\) \(\begin{align}  P = 4a   \end{align}\)
Rectangle \(\begin{align}  &P = 2L + 2B \\ &{\text{Length}} = L, \\&{\text{Breadth}} = B   \end{align}\)
Parallelogram with
two sides \(a\) and \(b\) 
\(\begin{align}  P = 2a + 2b   \end{align}\)
Rhombus with diagonals
\(\begin{align}  d_1  \end{align}\) and \(\begin{align}  d_2  \end{align}\)
\(\begin{align}  P = 2\sqrt {d_1^2  + d_2^2 }  \end{align}\)

 

Area
Right-angle triangle \(\begin{align}   {A = \frac{1}{2} \times b \times h}  \end{align}\)
Isosceles right-angle triangle \(\begin{align} {A = \frac{1}{2} \times a^2 }   \end{align}\)
Triangle with different sides \( a,\;b,\;c \) \(\begin{align}  {A = 2\sqrt {s(s - a)(s - b)(s - c)} }  \end{align}\)
Here,  \(\begin{align}   s = \frac{{a + b + c}}{2}   \end{align}\)
Square with side \(a\) \(\begin{align}  A = a^2    \end{align}\)
Rectangle \(\begin{align}  A = L \times B   \end{align}\)
Parallelogram with two sides \(a\) and \(b\)  \(\begin{align}  A = {\text{Base}} \times {\text{Height}}   \end{align}\)
Rhombus with diagonals \(\begin{align}  d_1  \end{align}\) and \(\begin{align}  d_2  \end{align}\) \(\begin{align}   {A = \frac{1}{2}d_1 d_2 }  \end{align}\)

7. Probability Formulas

\(\begin{align} \text{Probability}  \end{align}\) \(\begin{align} = \frac{\text{No. of Favourable Outcomes}}{\text{Total No. of Outcomes}} \end{align}\)

 

Our FREE CBSE Class 9 chapter-wise formulas PDF covers the following chapters:

  • 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
Download FREE PDF of Formula Sheets for Class 9
CBSE Class 9 Formulas Sheet