Mathematics – Helpful Formulas

 

Basic Algebra

(a + b)2= a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
a2 – b2 = (a + b)(a – b)
a2 + b2 = (a + b)2 – 2ab  or  (a – b)2 + 2ab
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc +ac)  or  a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2(ab – bc +ac)  or  a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + b3 + 3ab(a + b)  or  a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – b3 – 3ab(a – b)  or  a3 – 3a2b + 3ab2 – b3
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
a4 – b4 = (a2 – b2)(a2 + b2)  or  (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
an + bn = (a + b)(an-1 – an-2b + an-3b2 … – abn-2 + bn-1)

Indices

pn = p.p.p…….n times
pn⋅ pm = pm+n
pn ⋅ qn = (p ⋅ q)n
pm/ pn = xm-n
pn / qn = (p / q)n
(pn)m = pn⋅m
pnm = p(nm)
p-n = 1 / pn
a0 = 1 where a ∈ R , a!=0

 

Mathematical Properties

 

Commutative Property of Addition : a + b = b + a
Commutative Property of Multiplication : a x b = b x a
Associative Property of Addition : a + (b + c) = (a + b) + c
Associative Property of Multiplication : a x (b x c) = (a x b) x c
Additive Identity Property : a + 0 = a
Multiplicative Identity Property :  a x 1 = a
Additive Inverse Property : a + ( – a ) = 0
Multiplicative Inverse Property : a ( 1/a ) = 1
Zero Property of Multiplication  : a x 0 = 0

 

Mensuration

Perimeter
  • Square = 4a
  • Rectangle = 2a +2b
  • Triangle = a + b + c
Circumference
  • Circle = 2 (pi) r = (pi) x diameter
Area
  • Square = a2
  • Rectangle = a x b
  • Parallelogram = b x h
  • Triangle= ½ (base x height)
  • Trapezoid = h/2 (b1 + b2)
  • Circle = pi x r 2
  • Equilateral Triangle = ½(ah) = [ sqrt(3) / 4 ] x a2
  • Triangle with given a,b,c = sqrt [ s(s-a)(s-b)(s-c) ] when s = (a+b+c)/2 (Heron’s Formula)
  • Sphere = 4 (pi) r2
Surface Area
  • Cube= 6a2
  • Cylinder = 2 . pi . r . h
  • Sphere = 4 x pi x r 2
Volume
  • Cylinder = bh
  • Cone = bh/3
  • Sphere = 4 x pi x r3 / 3
Pythagoras Theorem
  • a2 + b2 = c2
Distance Formula
  • d = sqrt[(x2 – x1)2 +(y2 – y1)2]
Slope of a line
  • m = y2 – y1 / x2 -x1
Mid- Point Formula
  • M = (x1 + x2 )/ 2 , (y1 + y2 )/ 2
Slope-intercept form of the equation of a line
  • y = mx + c
Quadratic formula
  • X = [-b ± sqrt(b2 – 4ac)] /2a
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This Post Has 26 Comments

  1. NAEEM June 1, 2020 Reply

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  2. ACX July 22, 2020 Reply

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    1. Daniyal March 10, 2021 Reply

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  7. adil September 24, 2020 Reply

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    Good work Thanks For This Help

  10. Muhammad Zia November 22, 2020 Reply

    اللہ تعالی عزوجل یہ علمی ویب سائیٹ بنانے والے انکے والدین بیوی بچوں کے علم عُمر عمل میں بے حساب اضافہ فرمائیں اور ان سب کا خاتمہ ایمان پر فرمائیں آمین ثم آمین یارب العالمین بجاہ النبی الامین صلی اللہ تعالی علیہ والہ واصحابہ وبارک وسلم

    1. Author November 22, 2020 Reply

      Ameen. Thank You. Muhammad Zia

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    1. Author December 3, 2020 Reply

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  13. SUHAIL Abbas Buller February 22, 2021 Reply

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  14. A.H June 4, 2021 Reply

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  17. name November 2, 2021 Reply

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  18. Umer Naveed December 4, 2021 Reply

    Jazak Allah

  19. Umer Naveed December 4, 2021 Reply

    Allah aap say razi ho….

  20. ahmed January 9, 2022 Reply

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  21. Abbas January 29, 2022 Reply

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