Mathematics – Helpful Formulas

Mathematics – Helpful Formulas

Share


 

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
*More Formulas will be added very soon…
*Bookmark this page, so you can access it easily.
*Google Chrome Mobile Users can add it to home screen.
Report any mistake in the comment section.

Share

This Post Has 15 Comments

  1. NAEEM

    THANKS!!! THIS HELPED ALOT

  2. ACX

    thanks

  3. ali

    Plzz make one for Physics

  4. Nasir

    Plz make one for Physics

    1. SIKANDAR JAMIL

      Amazing!

  5. Muhammad Waleem

    great work thanks

  6. adil

    best website in the world

  7. adil

    plz make for physics

  8. Aayan Zaidi

    Nice

  9. kashan

    Good work Thanks For This Help

  10. Muhammad Zia

    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

      Ameen. Thank You. Muhammad Zia

  11. Emily

    Thank you so much Sir
    Your this effort had lighten a number of bright future…
    May God always be with u and give all happiness u desire…
    I am really very glad of ur effort
    👏

    1. Author

      Welcome.

  12. Sohail Abbas

    Great Work!
    Appreciated and Recommended to others.
    Its a great effort. May Allah success you in every field of life. You provided students and teachers a helpful platform. Kindly keep it up.

Leave a Reply