Mathematics – Helpful Formulas

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Mathematics – Helpful Formulas

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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 25 Comments

  1. NAEEM 1 Jun 2020 Reply

    THANKS!!! THIS HELPED ALOT

  2. ACX 22 Jul 2020 Reply

    thanks

  3. ali 25 Aug 2020 Reply

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  4. Nasir 31 Aug 2020 Reply

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    1. SIKANDAR JAMIL 9 Sep 2020 Reply

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  5. Muhammad Waleem 4 Sep 2020 Reply

    great work thanks

  6. adil 20 Sep 2020 Reply

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    1. Daniyal 10 Mar 2021 Reply

      Indeed

      1. Usman 25 Mar 2021 Reply

        Sir 11th class ky liye koi material nahi ha magr you are doing well and Very well job

  7. adil 24 Sep 2020 Reply

    plz make for physics

  8. Aayan Zaidi 5 Nov 2020 Reply

    Nice

  9. kashan 5 Nov 2020 Reply

    Good work Thanks For This Help

  10. Muhammad Zia 22 Nov 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 22 Nov 2020 Reply

      Ameen. Thank You. Muhammad Zia

  11. Emily 29 Nov 2020 Reply

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    1. Author 3 Dec 2020 Reply

      Welcome.

  12. Sohail Abbas 6 Dec 2020 Reply

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  13. SUHAIL Abbas Buller 22 Feb 2021 Reply

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  14. A.H 4 Jun 2021 Reply

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  15. javeria 19 Aug 2021 Reply

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  16. Epic Mateen 17 Sep 2021 Reply

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  17. name 2 Nov 2021 Reply

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  18. Umer Naveed 4 Dec 2021 Reply

    Jazak Allah

  19. Umer Naveed 4 Dec 2021 Reply

    Allah aap say razi ho….

  20. ahmed 9 Jan 2022 Reply

    mashaAllah great work , helped a lot

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