ALGEBRA FORMULAS

• the process of changing an irrational number into a rational number is called rationalisation
• LAWS OF EXPONANT

  law i: aᵐxaⁿ= aᵐ⁺ⁿ

  law ii: aᵐ÷aⁿ= aᵐ⁻ⁿ

  law iii: (aᵐ)ⁿ= aᵐˣⁿ

  law iv: aᵐxbᵐ= (axb)ᵐ

  law v: aᵐ÷bᵐ= (a÷b)ᵐ
• an algebric expression if a polonomial if:

  1. the co-effecient are real numbers
  2. the power of the variable are non-negative numbers (positive)
• the highest power of the variable gives you the degree of the polynomial
• a polynomial of degree 0 i called a constant polynomials
• a polynomials of degree 1 is called a linear polynomial
• a polynomials degree 2 is called a quadratic polynomial
• a polynomial of degree 3 is called a cubic polynomial
• a polynomial of a degree 4 is called a bi-quadratic polynomial
• a polynomial having one term is called a monomial
• a polynomial having two terms is called a binomial

  a polynomial having three-term is called a trinomial
• Identity I: (a + b)2 = a2 + 2ab + b2

  
  

  Identity II: (a – b)2 = a2 – 2ab + b2

  
  

  Identity III: a2 – b2= (a + b)(a – b)

  
  

  Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab

  
  

  Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

  
  

  Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)

  
  

  Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)

  
  

  Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

  
  

  identity XI: a3 + b3 = (a + b) (a2 - xy + y2)

  
  

  identity X: a3 - b3 = (a - b) (a2 + xy + y2)
• two lines which are drawn perpendicular to each other in a coordinate plain is called coordinate axes
• the coordinate axes meet at a point called the origin. it is denoted by o
• the coordinate axes divide the plain into four parts called the quadrants
• signs of convention of quadrants are:

  I : + , +

  II : - , +

  III : - , -

  IV : + , -
• the first coordinate is called the x-coordinate or the abscissa

  the second coordinate is called the y-coordinate or ordinate
• An equation of the form ax+by=c or ax+by+c=0, where a, b, and c are real numbers, is called a linear equation in two variables.
• the value of the variables satisfying the linear equations in two variables is a solution of a linear equation in two variable
• HERON'S FORMULA

  s= semi perimeters= half, length of the boundary, sum of all sides

  s= a+b+c/2

  ar(triangle)= √s(s-a)(s-b)(s-c)
• statistics is a brach of mathematics which deals with the collection, interpretation and representation of information called data.

  data are of two types:

  1. draw data- the data collected by the investigator himself
  2. secondary data- the data collected from the investigator
• the analyzes of the collected data is called interpretation
• representation of collected data is usually done in two ways

  1. tabulation
  2. graphical form

  -bar graph

  -histogram

  -frequency polygon
• class mark: the mid value of the class intervals is called the class mark, it is given by= lower limit+upper limit/2
• adjustment factors of histogram: lower limit(2nd class) - upper limit (1st class)/2