Polygons

Posted in Terms Defined

Polygon: A simple closed curve made up of only line segments is called a polygon.

Classification of polygons:

Number of Sides Classification
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
... ...
n n-gon

Diagonal: A diagonal is a line segment connecting two non-consecutive vertices of a polygon.

Convex polygons: Where all the interior angles are less than 180° and no part of its diagonals lie outside the polygon.

Concave polygons: Where at least one interior angle is more than 180° and some of the diagonals will lie outside the polygon.

Regular polygons: A regular polygon is both 'equiangular' and 'equilateral'. e.g. equilateral triangle.

Irregular polygons: Polygons which are not equiangular or equilateral are irregular polygons. e.g. right-angled triangle.

Angle sum property: Sum of all interior angles = \( (n - 2) \times 180° \) where n --> number of interior angles.

Algebriac Expressions

Posted in Terms Defined

Algebraic Expressions:

For e.g. 4x2+3, 7y2-2y+3, etc.

The combination of variables and constants when take part in the formation of mathematical expression, then such an expression is known as Algebraic Expression.

Terms of an expressions:

Terms are added to form expression.

Consider the first expression above, the terms are (4x2) and (3).

Now consider the send expression above, which can be written as

7y2 +(-2y) + 3

therefore, the terms of the expression are (7y2), (-2y) and (3). Note, the minus sign (-) is included in the term.

Fractions

Posted in Terms Defined

Proper Fractions: The fractions, where the numerator is less than the denominator are called proper fractions.

Improper Fractions: The fractions, where the numerator is bigger than the denominator are called improper fractions.

Mixed Fractions: A mixed fraction has a combination of a whole and a part.

Equivalent Fractions: The fractions if reduced to their simplest forms are equal than these fractions are called equivalent fractions.

Simplest form of a fraction: A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.

Like Fractions: The fractions with same denominators are called like fractions.

Unlike Fractions: The fractions with different denominators are called unlike fractions.

 

Divisibility

Posted in Terms Defined

Divisibility by 2: If a number has either 0, 2, 4, 6, or 8 in its ones place then it is divisible by 2.

Divisibility by 3: If the sum of the digits of a number is a multiple of 3, then the number is divisible by 3.

Divisibility by 4: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

Divisibility by 5: If a number has either 0 or 5 in its ones place then it is divisible by 5.

Divisibility by 6: If a number is divisible by 2 and 3 both then it is divisible by 6 also.

Divisibility by 8: A number with 4 digits or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.

Algebraic Identities

Posted in Terms Defined

An identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions. By definition, the two sides of an identity are interchangeable, so we can replace one with the other at any time.

 

( x + y )2  x2 + 2 x y + y2 
( x - y )2 =  x2 - 2 x y + y2
( x + y )3 =  x+ 3 x2 y + 3 x y2 + y3
( x - y )3 =  x3 - 3 x2 y + 3 x y2 - y3
( x + y )4 =  x4 + 4 x3 y + 6 x2 y2 + 4 x y3 + y4
( x - y )4 =  x4 - 4 x3 y + 6 x2 y2 - 4 x y3 + y4
x2 - y2 = ( x + y ) ( x - y )
x- y3 = ( x - y ) ( x2 + x y + y)
x3 + y3 = ( x + y ) ( x2 - x y + y)
x4 - y4 = ( x2 - y) ( x2 + y2 )