All class 10th maths formula

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Polynomials Formulas ( x + y ) 2 = x 2 + y 2 + 2 x y ( x − y ) 2 = x 2 + y 2 − 2 x y ( x + y ) ( x − y ) = x 2 − y 2 ( x + y ) ( x + z ) = x 2 + x ( y + z ) + y z ( x + y ) ( x − z ) = x 2 + x ( y − z ) − y z x 2 + y 2 = ( x + y ) 2 − 2 x y ( x + y ) 3 = x 3 + y 3 + 3 x y ( x + y ) ( x − y ) 3 = x 3 − y 3 − 3 x y ( x − y ) ( x + y + z ) 2 = x 2 + y 2 + z 2 + 2 x y + 2 y z + 2 z x ( x − y − z ) 2 = x 2 + y 2 + z 2 − 2 x y + 2 y z − 2 z x x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) x 3 − y 3 = ( x − y ) ( x 2 + x y + y 2 ) x 4 − y 4 = ( x 2 ) 2 − ( y 2 ) 2 = ( x 2 + y 2 ) ( x 2 − y 2 ) = ( x 2 + y 2 ) ( x + y ) ( x − y ) ( x + y + z ) 2 = x 2 + y 2 + z 2 + 2 x y + 2 y z + 2 z x ( x + y − z ) 2 = x 2 + y 2 + z 2 + 2 x y − 2 y z − 2 z x ( x − y + z ) 2 = x 2 + y 2 + z 2 − 2 x y − 2 y z + 2 z x ( x − y − z ) 2 = x 2 + y 2 + z 2 − 2 x y + 2 y z − 2 z x x 3 + y 3 + z 3 − 3 x y z = [ ( x + y + z ) ( x 2 + y 2 + z 2 − x y − y z − z x ) ] 2. Arithmetic Progression Formulas nth Term of an Arithmetic Progression a n = a + ( n − 1 ) × d Sum of 1st n Terms of an Arithmetic Progression S n = n 2 [ 2 a + ( n − 1 ) d ] 3. Coordinate Geometry Formulas Distance Formula A B = √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Section Formula ( m x 2 + n x 1 m + n , m y 2 + n y 1 m + n ) Mid-point Formula ( x 1 + x 2 2 , y 1 + y 2 2 ) Area of Triangle ar ( Δ A B C ) = 1 2 × ⎡ ⎢ ⎣ x 1 ( y 2 − y 3 ) + x 2 ( y 3 − y 1 ) + x 3 ( y 1 − y 2 ) ⎤ ⎥ ⎦ 4. Trigonometry Formulas Trigonometric Identities sin 2 A + cos 2 A = 1 tan 2 A + 1 = sec 2 A cot 2 A + 1 = c o s e c 2 A Relations between Trigonometric Identities tan A = sin A cos A cot A = cos A sin A c o s e c A = 1 sin A sec A = 1 cos A Trigonometric Ratios of Complementary Angles sin ( 90 ∘ − A ) = cos A cos ( 90 ∘ − A ) = sin A tan ( 90 ∘ − A ) = cot A cot ( 90 ∘ − A ) = tan A sec ( 90 ∘ − A ) = c o s e c A c o s e c ( 90 ∘ − A ) = sec A Values of Trigonometric Ratios of 0° and 90° ∠ A 0 ∘ 30 ∘ 45 ∘ 60 ∘ 90 ∘ sin A 0 1 2 1 √ 2 √ 3 2 1 cos A 1 √ 3 2 1 √ 2 1 2 0 tan A 0 1 √ 3 1 √ 3 Not Defined sec A 1 2 √ 3 √ 2 2 Not Defined cosec A Not Defined 2 √ 2 2 √ 3 1 cot A Not Defined √ 3 1 1 √ 3 0 5. Circles Formulas Area of circle π r 2 Diameter of circle 2 r Circumference of circle 2 π r Sector angle of circle θ = ( 180 × l ) ( π r ) Area of the sector = ( θ 2 ) × r 2 Area of the circular ring = π × ( R 2 − r 2 ) θ = Angle between two radii R = Radius of outer circle r = Radius of inner circle 6. Statistics Formulas Mean a m = a 1 + a 2 + a 3 + a 4 4 = n ∑ 0 a n Median M e d i a n = l + ( n 2 − c f f ) h Mode M o = l + ( f 1 − f 0 2 f 1 − f 0 − f 2 ) h 7. Quadratic Equations Formulas Quadratic Equations a x 2 + b x + c = 0 where a ≠ 0 Quadratic Polynomial P ( x ) = a x 2 + b x + c where a ≠ 0 Zeroes of the Polynomial P ( x ) The Roots of the Quadratic Equations are zeroes One Real Root b 2 − 4 a c = 0 Two Distinct Real Roots b 2 − 4 a c > 0 No Real Roots b 2 − 4 a c < 0 8. Triangles Formulas Six elements of triangle Three sides and three angles Angle sum property of triangle Sum of three angles: ∠ A + ∠ B + ∠ C = 180 ∘ Right angled triangle Adjacent Side Opposite Side Hypotenuse Pythagoras Theorem H 2 = A S 2 + O S 2 H = Hypotenuse A S = Adjacent Side O S = Opposite Side 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) l × b × h Lateral Surface Area of Cuboid (LSA) 2 h ( l + b ) Total Surface Area of Cuboid (TSA) 2 ( l b + b h + h l ) Cube Volume of Cube x 3 Lateral Surface Area of Cube (LSA) 4 x 2 Total Surface Area of Cube (TSA) 6 x 2 Sphere Volume of Sphere 4 3 × π r 3 Lateral Surface Area of Sphere (LSA) 4 π r 2 Total Surface Area of Sphere (TSA) 4 π r 2 Right Circular Cylinder Volume of Right Circular Cylinder π r 2 h Lateral Surface Area of Right Circular Cylinder (LSA) 2 × ( π r h ) Total Surface Area of Right Circular Cylinder (TSA) 2 π r × ( r + h ) Right Pyramid Volume of Right Pyramid 1 3 × [ Area of the Base ] × h Lateral Surface Area of Right Pyramid (LSA) 1 2 × p × L Total Surface Area of Right Pyramid (TSA) LSA + [ Area of the Base ] Right Circular Cone Volume of Right Circular Cone 1 3 × ( π r 2 h ) Lateral Surface Area of Right Circular Cone (LSA) π r l Total Surface Area of Right Circular Cone (TSA) π r × ( r + L ) Hemisphere Volume of Hemisphere 2 3 × ( π r 3 ) Lateral Surface Area of Hemisphere (LSA) 2 π r 2 Total Surface Area of Hemisphere (TSA) 3 π r 2 Prism Volume of Prism B × h Lateral Surface Area of Prism (LSA) p × h Total Surface Area of Prism (TSA) π × r × ( r + L ) l = Length, h = Height, b = Breadth r = Radius of Sphere L = Slant Height