Algebra formulas

Formulas for powers or indices

  • a^0 = 1 \mbox{, for all a }
  •  a^m \times a^n = a^{m+n}
  • a^m / a^n = a^{m-n}
  • a^{-m} = \frac {1} {a^m}
  • a^{b^c} = a^{bc}

 

Simple Interest

The formula to calculate simple interest is:

 

\mbox{p }\times \mbox{t }\times \mbox{r }

where,

p = principal
r = interest rate
t = time

 

Compound interest

Formula to Final amount to calculate compound interest is :

 

\mbox{A }= \mbox{p }(1+\frac{\mbox{r}}{\mbox{n}})^{\mbox{nt}}

where,
A = final amount
p = principal
r = interest rate
t = time in years
n = number of times per year, interest is compounded

 

Formula for finding nth term in an AP is :

a + (n-1) d

 

Formula for finding sum of n terms in an AP is :

S = \frac {n} {2} [\mbox{first term} + \mbox{last term}]

or,

S = \frac {n} {2} [2a + (n-1)d]

 

Formula for nth term in geometric progression is :

ar^{n-1}

 

Formula for sum of terms in geometric progression is :

if r >1, then

S = \frac {a(r^n - 1)} {r - 1}

if r <1, then

S = \frac {a(1 - r^n)} {1 - r}

 

Logarithms

log_a (mn) = log_a m + log_a n

log_a (m/n) = log_a m - log_a n

log_a (m^n) = n log_a m

log_n (m) = log_a m / log_a n

log_n (m) = 1/log_m n

 

Square Formulas

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

a^2 - b^2 = (a - b)(a + b)

(a + b)^2 + (a - b)^2 = 2(a^2 + b^2)

(a + b)^2 - (a - b)^2 = 4ab

 

Cube Formulas

(a + b)^3 = a^3+ 3a^2b + 3ab^2+ b^3

(a - b)^3 = a^3- 3a^2b + 3ab^2- b^3

 

Special number zero

0/a = 0, where a is not equal to 0.

a^0 = 1

0^a = 0

a \times 0 = 0

a/0 is undefined

 

 

You may also like the following post for Geometry formulas .

Click on the following link for Geometry formulas.

Geometry Math Formulas

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