# Class 10 Maths Formula Sheets

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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!

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## 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}

 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-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