ALGEBRA
Factorising rule: Perfect square trinomials: Logarithms
► Square of a sum:
Square of a difference: Then log base a of N equal to x)
Difference of squares: ▪ a: base
►
▪ x: index (power)
▪ N: Number
►
Factor trick:
► Ex:
Rule:
► ►
► ►
►
►
Differentiation by first principal ►
►
A rule for differentiating powers of x
Laws for logarithms
1.
Ex: 2.
3.
Differentiating powers with negative indices
4.
5.
Ex:
6.
7.
Differentiating powers with fractional indices Equations involving logarithms and
Ex: indices
'The log of the number over the log of the base'
Ex: Solve
The chain rule
Solving exponential and logarithmic
Ex: equations
Change of base
Exponential rates using base e
▪ k: the growth/ decay constant
The product rule
▪
Ex:
▪
▪ t: time
Algebra Page 1
Factorising rule: Perfect square trinomials: Logarithms
► Square of a sum:
Square of a difference: Then log base a of N equal to x)
Difference of squares: ▪ a: base
►
▪ x: index (power)
▪ N: Number
►
Factor trick:
► Ex:
Rule:
► ►
► ►
►
►
Differentiation by first principal ►
►
A rule for differentiating powers of x
Laws for logarithms
1.
Ex: 2.
3.
Differentiating powers with negative indices
4.
5.
Ex:
6.
7.
Differentiating powers with fractional indices Equations involving logarithms and
Ex: indices
'The log of the number over the log of the base'
Ex: Solve
The chain rule
Solving exponential and logarithmic
Ex: equations
Change of base
Exponential rates using base e
▪ k: the growth/ decay constant
The product rule
▪
Ex:
▪
▪ t: time
Algebra Page 1
