Maths Formulae

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Square of Numbers

SQURAE OF Numbers
SQURAE OF Numbers

 

Percentage 

Percentage 
Percentage

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CUBE of Numbers

  • 1 = 1
  • 2 = 8
  • 3 = 27
  • 4 = 64
  • 5 = 125
  • 6 = 216
  • 7 = 343
  • 8 = 512
  • 9 = 729
  • 10 = 1000
  • 11 = 1331
  • 12 = 1728
  • 13 = 2197
  • 14 = 2744
  • 15 = 3375
  • 16 = 4096
  • 17 = 4913
  • 18 = 5832
  • 19 =6859
  •  20 = 8000
  • 21 = 9261
  • 22 = 10648
  • 23 =12167
  • 24 =13824
  • 25 = 15625

 

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 

ice screenshot 20231117 204614

Mensuration  2D

Triangle (त्रिभुज )

  • Equilateral ( समबाहु त्रिभुज )

    • Equilateral Triangle
      Equilateral Triangle

  • Isoceles (समद्विबाहु त्रिभुज )

    • Isoceles Triangle
      Isoceles Triangle

  • 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 )
  • Right Isoceles triangle (त्रिभुज )

    • Right Isoceles Triangle

Square (वर्ग )

  • Perimeter  =4a
  • area = a
  • Diagonal = = √2a

 

Rhombus (सम चतुर्भुज )

  • Perimeter  =4a
  • area = (d1 * d2)/2
Rhombus
Rhombus

Rectangle (आयत )

  • Perimeter  =2 (a+ b)
  • area = ab 
  • Diagonal = = √(a2 +b2)

Parallelogram (समान्तर चतुर्भुज )

  • Perimeter  =2 (a+ b)
  • area = ab 

Trapezium (सम्लब )

Trapezium
Trapezium

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)

Cuboid
Cuboid

 

  • 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 )

Cylinder
Cylinder

Cone (शंकु)

Cone

Sphere (गोला )

Sphere
Sphere

Hemi Sphere(अर्द्धगोला )

Hemisphere
Hemisphere

Tetrahedron (सम चतुष्फलक )

Tetrahedron

Prism (प्रिज्म )

Pyramid (पिरामिड )

Frustum ()

Kite (पतंग)