Square of Numbers
Percentage
CUBE of Numbers
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ALGEBRA
- (a – b)2 = a2 + b2 – 2ab = (a+ b)2 – 4ab
- a2 + b2 = (a – b)2 + 2ab
- (a + b)2 = a2 + b2 + 2ab = (a – b)2 + 4 ab
- a2 + b2 = (a + b)2 – 2ab
- (a + b)2 + (a – b)2 = 2(a2 + b2)
- (a + b)2 – (a – b)2 = 4ab
- a2 – b2 = (a – b)(a + b)
- (a + b + c )2 = a2 + b2 + c2 + ( 2ab + 2bc +2ca )
- (a + b)3 = a3 + b3+ 3ab(a+ b) = a3 + b3+ 3a2b + 3ab2
- a3 + b3 = (a + b)3 – 3ab (a+ b)
- (a – b)3 = a3 – b3– 3ab(a – b) = a3 – b3– 3a2b + 3ab2
- a3 – b3 = (a – b)3 + 3ab (a- b)
- (a + b)3 + (a – b)3 = 2a(a2 + 3b2)
- (a + b)3 – (a – b)3 =2b(b2 + 3a2)
- a3 – b3 = (a – b)(a2 + b2 + ab ) = (a – b)3 + 3ab(a – b)
- a3 + b3 = (a + b)(a2 + b2 – ab ) = (a + b)3 – 3ab(a + b)
- a2 + b2 + c2 – 2ab – 2bc – 2ca = 1/2[(a – b)2+(b – c)2+(c – a)2]
- a3 + b3 + c3 – 3abc =
- = (a + b + c )(a2 + b2 + c2 – ab – bc – ca )
- = 1/2(a + b + c )[ (a – b)2+ (b – c)2+ (c – a)2]
- = (a + b + c ) [ (a + b + c )2 – 3( ab + bc + ca )]
- Case -1 : if (a + b + c ) = 0,then a3 + b3 + c3 = 3abc
Mensuration 2D
Triangle (त्रिभुज )
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Equilateral ( समबाहु त्रिभुज )
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Equilateral Triangle
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Isoceles (समद्विबाहु त्रिभुज )
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Isoceles Triangle
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Scalene (बिसमबाहु त्रिभुज )
- Perimeter = a+ b+ c
- Semi Perimeter (S) = (a+ b+ c)/2
- Area = √[S (S-a ) (S-b )(S-c )]
- Right angle triangle (समकोण त्रिभुज )
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Right Isoceles triangle (त्रिभुज )
Square (वर्ग )
- Perimeter =4a
- area = a2
- Diagonal = = √2a
Rhombus (सम चतुर्भुज )
- Perimeter =4a
- area = (d1 * d2)/2
Rectangle (आयत )
- Perimeter =2 (a+ b)
- area = ab
- Diagonal = = √(a2 +b2)
Parallelogram (समान्तर चतुर्भुज )
- Perimeter =2 (a+ b)
- area = ab
Trapezium (सम्लब )
Circle
Quadrilateral (चतुर्भुज)
Cyclic Quadrilateral (चक्रीय चतुर्भुज)
Bisentric Quadrilateral (द्विबीजपत्री चतुर्भुज)
Regular Octagon
Mensuration 3D
- Lateral/curved surface area (पार्श्व/वक्र पृष्ठीय क्षेत्रफल)
- LSA/CSA = Perimeter of base * height
- Total surface area (कुल पृष्ठीय क्षेत्रफल)
- TSA= LSA + 2(Area of base)
- Volume (आयतन )
- V = Area of base * height
Cube (घन)
- Side = a
- LSA/CSA = 4a2
- TSA = 6a2
- VOLUME = a3
- Side Diagonal = √2a
- Cube Diagonal (Longest Length) = √3a
Cuboid (घनाभ)
- Side = l, b, h
- CSA /LSA = Perimeter of Base * Height
- 2 (l + b) * h
- TSA = LSA + 2 (Area of Base)
- 2(lb + bh + hl)
- Volume = Area of Base * Height
- l*b*h
- Cuboid Diagonal (Longest Length) = √(l² + b² + h²)
- if X, Y, Z are three adjacent Surface Area of Cuboid Then
- X = lb , Y = bh, Z = hl
- Volume = √(XYZ)
- (l+b+h)² = l² + b² + h² +2(lb+bh+hl)
- (Sum of Side)² = (Diagonal)² + TSA
Cylinder (बेलन )
Cone (शंकु)
Sphere (गोला )
Hemi Sphere(अर्द्धगोला )
Tetrahedron (सम चतुष्फलक )
Prism (प्रिज्म )
Pyramid (पिरामिड )
Frustum ()
Kite (पतंग)
