In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

Class 10 Maths Formula Sheets

Go back to  'Class 10'

Do you dislike Math formulas and equations because they seem complicated or difficult to grasp? What if we told you that they can help increase your exam scores? Or that you no longer need to mug up all Maths formulas of Class 10? 

Our team of Math experts have created a list of Class 10 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!

Have a doubt that you want to clear? Get them clarified with simple solutions from our Math Experts at Cuemath Online Classes. Book a FREE trial today!

Important Maths Formulas for Class 10

1. Polynomials Formulas

\(\begin{align}( {x + y})^2  = x^2  + y^2  + 2xy\end{align}\)

\(\begin{align}( {x - y})^2  = x^2  + y^2 - 2xy\end{align}\)

\(\begin{align}( {x + y} )( {x - y} ) = x^2  - y^2 \end{align}\)

\(\begin{align}(x + y)(x + z) = x^2  + x\,(y + z) + yz \end{align}\)

\(\begin{align}(x + y)(x - z) = x^2  + x\,(y - z) - yz \end{align}\)

\(\begin{align}x^2  + y^2  = \left( {x + y} \right)^2  - 2xy \end{align}\)

\(\begin{align} ( {x + y} )^3  = x^3  + y^3  + 3xy ( {x + y} ) \end{align}\)

\(\begin{align} \left( {x - y} \right)^3  = x^3  - y^3  - 3xy\left( {x - y} \right)  \end{align}\)

\(\begin{align} \left( {x + y + z} \right)^2  = x^2  + y^2  + z^2  + 2xy + 2yz + 2zx  \end{align}\)

\(\begin{align} \left( {x - y - z} \right)^2  = x^2  + y^2  + z^2  - 2xy + 2yz - 2zx \end{align}\)

\(\begin{align} {x^3  + y^3  = \left( {x + y} \right)\left( {x^2  - xy + y^2 } \right)}  \end{align}\)

\(\begin{align}  {x^3  - y^3  = \left( {x - y} \right)\left( {x^2  + xy + y^2 } \right)} \end{align}\)

\(\begin{align} x^4 - y^4 &= \left( {x^2 } \right)^2 - \left( {y^2 } \right)^2 \\ &= \left( {x^2 + y^2 } \right)\left( {x^2 - y^2 } \right) \\&= \left( {x^2 + y^2 } \right)\left( {x + y} \right)\left( {x - y} \right) \end{align}\)

\(\begin{align} \left( {x + y + z} \right)^2  = x^2  + y^2  + z^2  + 2xy + 2yz + 2zx \end{align}\)

\(\begin{align} \left( {x + y - z} \right)^2  = x^2  + y^2  + z^2  + 2xy - 2yz - 2zx  \end{align}\)

\(\begin{align} \left( {x - y + z} \right)^2  = x^2  + y^2  + z^2  - 2xy - 2yz + 2zx  \end{align}\)

\(\begin{align} \left( {x - y - z} \right)^2  = x^2  + y^2  + z^2  - 2xy + 2yz - 2zx  \end{align}\)

\(\begin{align} x^3 &+ y^3 + z^3 - 3xyz \\&= \begin{bmatrix}\left( {x + y + z} \right) \\ \left( {x^2 + y^2 + z^2 - xy - yz - zx} \right) \end{bmatrix} \end{align}\)

2. Arithmetic Progression Formulas

nth Term of an Arithmetic Progression

\(\begin{align} {a_n  = a + (n - 1) \times d} \end{align}\)

Sum of 1st n Terms of an Arithmetic Progression

\(\begin{align} {S_n  = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]}  \end{align}\)

3. Coordinate Geometry Formulas

Distance Formula \(\begin{align} {AB = \sqrt {\left( {x_2  - x_1 } \right)^2  + \left( {y_2  - y_1 } \right)^2 } }  \end{align}\)
Section Formula \(\begin{align} {\left( {\frac{{mx_2  + nx_1 }}{{m + n}},\frac{{my_2  + ny_1 }}{{m + n}}} \right)}  \end{align}\)
Mid-point Formula \(\begin{align}  {\left( {\frac{{x_1  + x_2 }}{2},\;\frac{{y_1  + y_2 }}{2}} \right)}  \end{align}\)
Area of Triangle \(\begin{align} \text{ar}(\Delta A B C)=\frac{1}{2} \times \begin{bmatrix}x_{1}(y_{2}-y_{3})+\\x_{2}(y_{3}-y_{1})+\\x_{3}(y_{1}-y_{2})\end{bmatrix} \end{align}\)

4. Trigonometry Formulas

Trigonometric Identities \(\begin{align}  \sin ^2 A + \cos ^2 A = 1  \end{align}\)
\(\begin{align}  \tan ^2 A + 1 = \sec ^2 A  \end{align}\)
\(\begin{align}  \cot ^2 A + 1 = {\rm{cosec}}^2 A \end{align}\)
Relations between Trigonometric Identities \(\begin{align}  \tan A = \frac{{\sin A}}{{\cos A}}   \end{align}\)
\(\begin{align}  \cot A = \frac{{\cos A}}{{\sin A}}   \end{align}\)
\(\begin{align}  {\rm{cosec}}\,A = \frac{1}{{\sin A}}   \end{align}\)
\(\begin{align}  \sec A = \frac{1}{{\cos A}}   \end{align}\)
Trigonometric Ratios of Complementary Angles \(\begin{align} \sin \left( {90^\circ   - A} \right) = \cos A   \end{align}\)
\(\begin{align} \cos \left( {90^\circ   - A} \right) = \sin A   \end{align}\)
\(\begin{align} \tan \left( {90^\circ   - A} \right) = \cot A   \end{align}\)
\(\begin{align} \cot \left( {90^\circ   - A} \right) = \tan A   \end{align}\)
\(\begin{align} \sec \left( {90^\circ   - A} \right) = {\rm{cosec}}\,A   \end{align}\)
\(\begin{align} {\rm{cosec}}\left( {90^\circ   - A} \right) = \sec A   \end{align}\)
 

 

Values of Trigonometric Ratios of 0° and 90°
\(\angle A\) \(0^\circ \) \(30^\circ \) \(45^\circ \) \(60^\circ \) \(90^\circ \)
\(\sin A\) \(0\) \(\begin{align} \frac{1}{2}   \end{align}\) \(\begin{align} \frac{1}{{\sqrt 2 }} \end{align}\) \(\begin{align} \frac{{\sqrt 3 }}{2}   \end{align}\) \(1\)
\(\cos A\) \(1\) \(\begin{align} \frac{{\sqrt 3 }}{2}   \end{align}\) \(\begin{align} \frac{1}{{\sqrt 2 }} \end{align}\) \(\begin{align} \frac{1}{2}   \end{align}\) \(0\)
\(\tan A\) \(0\) \(\begin{align} \frac{1}{{\sqrt 3 }}  \end{align}\) \(1\) \(\begin{align} \sqrt 3   \end{align}\) Not Defined
\(\sec A\) \(1\) \(\begin{align} \frac{2}{{\sqrt 3 }}  \end{align}\) \(\begin{align} \sqrt 2   \end{align}\) \(2\) Not Defined
\(\text{cosec } A \) Not Defined \(2\) \(\begin{align} \sqrt 2   \end{align}\) \(\begin{align} \frac{2}{{\sqrt 3 }}  \end{align}\) 1
\(\cot A\) Not Defined \(\begin{align} \sqrt 3   \end{align}\) \(1\) \(\begin{align} \frac{1}{{\sqrt 3 }}  \end{align}\) 0

5. Circles Formulas

Area of circle \(\begin{align}  \pi r^2   \end{align}\)
Diameter of circle \(\begin{align}  2r  \end{align}\)
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

\(\begin{align}  = \pi  \times \left( {R^2  - r^2 } \right) \end{align}\)

\(\begin{align}\theta &= \text{Angle between two radii}\\R &= \text{Radius of outer circle}\\r &= \text{Radius of inner circle}\end{align}\)

6. Statistics Formulas

Mean \(\begin{align}  {a_m  = \frac{{a_1  + a_2  + a_3  + a_4 }}{4} = \frac{{\sum\limits_0^n a }}{n}}  \end{align}\)
Median \(\begin{align} {{\rm{Median}} = l + \left( {\frac{{\frac{n}{2} - cf}}{f}} \right)h}  \end{align}\)
Mode \(\begin{align} {M_o  = l + \left( {\frac{{f_1  - f_0 }}{{2f_1  - f_0  - f_2 }}} \right)h}  \end{align}\)

7. Quadratic Equations Formulas

Quadratic Equations \(\begin{align} &ax^2 + bx + c = 0\\ &\text{where }a \ne 0 \end{align}\)
Quadratic Polynomial \(\begin{align} &P(x) = ax^2 + bx + c \\& \text{ where }a \ne 0 \end{align}\)
Zeroes of the Polynomial  \(P(x) \) The Roots of the Quadratic Equations are zeroes
One Real Root \(\begin{align}  b^2  - 4ac = 0 \end{align}\)
Two Distinct Real Roots \(\begin{align}   {b^2  - 4ac > 0}   \end{align}\)
No Real Roots \(\begin{align}   {b^2  - 4ac < 0}  \end{align}\)

8. Triangles Formulas

Six elements of triangle Three sides and three angles
Angle sum property of triangle Sum of three angles: 
\(\begin{align}   \angle {\rm{A}} + \angle {\rm{B}} + \angle {\rm{C}} = 180^\circ  \end{align}\)
Right angled triangle Adjacent Side
Opposite Side
Hypotenuse
Pythagoras Theorem \(\begin{align}  H^2 = AS^2 + OS^2 \end{align}\)
\(\begin{align}H&= \text{Hypotenuse}\\AS&=\text{Adjacent Side}\\OS&=\text{Opposite Side}\end{align}\)
Equilateral Triangles All sides are equal
Isosceles Triangle Two sides are equal

 

Congruent Triangles Their corresponding parts are equal
SSS Congruence of two triangles Three corresponding sides are equal
SAS Congruence of two triangles Two corresponding sides and an angle are equal
ASA Congruence of two triangles Two corresponding angles and a side are equal

9. 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) \(\begin{align}  \pi  \times r \times \left( {r + L} \right)    \end{align}\)
\(\begin{align} l &= \text{Length, } \\ h &= \text{Height,} \\ b &= \text{Breadth}  \\  r &= \text{Radius of Sphere}  \\  L &= \text{Slant Height}  \end{align}\)

 

Our FREE CBSE Class 10 chapter-wise formulas PDF covers the following chapters:

  • Chapter-1   Real Numbers
  • Chapter-2   Polynomials
  • Chapter-3   Pair of Linear Equations in Two Variables
  • Chapter-4   Quadratic Equations
  • Chapter-5   Arithmetic Progressions
  • Chapter-6   Triangles
  • Chapter-7   Coordinate Geometry
  • Chapter-8   Introduction to Trigonometry
  • Chapter-9   Some Applications of Trigonometry
  • Chapter-10 Circles
  • Chapter-11 Constructions
  • Chapter-12 Areas Related to Circles
  • Chapter-13 Surface Areas and Volumes
  • Chapter-14 Statistics
  • Chapter-15 Probability
Download FREE PDF of Formula Sheets for Class 10
CBSE Class 10 Formulas Sheet
  
Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school