Mathematics – Helpful Formulas

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 8 Comments

  1. NAEEM 1 Jun 2020 Reply

    THANKS!!! THIS HELPED ALOT

  2. ACX 22 Jul 2020 Reply

    thanks

  3. ali 25 Aug 2020 Reply

    Plzz make one for Physics

  4. Nasir 31 Aug 2020 Reply

    Plz make one for Physics

    1. SIKANDAR JAMIL 9 Sep 2020 Reply

      Amazing!

  5. Muhammad Waleem 4 Sep 2020 Reply

    great work thanks

  6. adil 20 Sep 2020 Reply

    best website in the world

  7. adil 24 Sep 2020 Reply

    plz make for physics

Leave a Reply