Current Affairs 6th Class

EXPONENT AND POWERS   POWER \[\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m}}-n\] \[{{5}^{3}}\div {{5}^{2}}={{5}^{3}}-2\]   FUNDAMENTALS
  •                   Exponential form is nothing but repeated multiplication.
There are two part of an exponent. Exponent\[\to \]base, Power/ Index                                                             Example:            
  •                   Base denotes the number to be multiplied and the power denotes the number of times the base is to be multiplied.
\[a\times a\times a={{a}^{3}}\](read as 'a' cubed or 'a' raised to the power 3) \[a\times a\times a\times a\times a\times a={{a}^{6}}\](read as 'a raised to the power 6 or 6th power of a)             ................................................................................... \[a\times a\times a\].......(n factors) \[={{a}^{n}}\] (read as 'a' raise to the power n or nth power of a)
  •                    (a) When a negative number is raised to an even power the value is always positive.
e.g., \[{{\left( -5 \right)}^{6}}=\left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\times \left( -5 \right)\]\[=15625\] (b) When a negative number is raised to an odd power, the value is always negative. e.g., \[{{\left( -3 \right)}^{5}}=\left( -3 \right)\times \left( -3 \right)\times \left( -3 \right)\times \left( -3 \right)\times \left( -3 \right)=\left( -243 \right)\] Note:    (a) \[{{(-1)}^{odd\,\,number}}=-1\] (b) \[{{(-1)}^{even\,\,number}}=+1\]   more...

RATIO, PROPORTION AND UNITARY METHOD   RATIO The comparison of two quantity of same kind by division is called ratio.   Example: Ratio between Rs. 30 and Rs. 50, but there can be no ratio between Rs. 30 and 50 apples, form of ratio \[=x:y\] \[x\to \]antecedent \[y\to \]consequent                                                              
  •           B The ratio of \[x\]to \[y\]
  •           B \[x\]is to \[y\]
  •           \[x:y\]
  •           B \[x\]and \[y\] are called terms of ratio.
  Types of Ratio:
  •                Compound Ratio: Ratio is compound when antecedents are multiplied by respective antecedents and consequents are multiplied by respective consequents.
Example: \[a:b,\,\,c:d,\,\,e:f,\]then compound ratio is,\[\frac{a\times c\times e}{b\times d\times f}\]  
  •                   Duplicate Ratio: If \[x:y\] is a ratio, then\[{{x}^{2}}:{{y}^{2}}\]is duplicate ratio.
Example: Find duplicate ratio of\[5:7.\] more...

ALGEBRAIC EXPRESSIONS   ALGEBRAIC EXPRESSION
\[2x\] Expression
\[2x+y\] Binomial
\[2x=14\] Equation
 
  •                  Variable: A symbol which takes various values is known as a variable. Normally it is denoted by x, y, z etc.
  •                   Algebraic expression: A combination of constants and variables connected by some or all of the four fundamental operations \[+,\] \[-,\]\[\times \]and \[\div \] is called an algebraic expression.
e.g., \[-5x+6\]is an algebraic expression.
  •                   Here \[-5\]is the coefficient of the variable 'x' and 6 is the constant.
  Various types of algebraic expression: (a) Monomial: An algebraic expression which contains only one term, is called as monomial. Thus, \[2x,\] \[3y,\] \[5xy,\] \[6a{{b}^{2}},\] \[-11\] etc. are called monomials. more...

ALGEBRA   ALGEBRA The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.   Introduction to Algebra
  •                   Variable: A letter symbol which can take various numerical values is called variable or literal.
Example: \[x,\,\,y,\,\,z\]etc.  
  •                   Constant: A symbol which can take a fixed numerical value is called a constant.
Example: \[-1,\,\,\frac{1}{2},\,\,2,\,\,4,\,\,3,\,\,5\]etc.  
  •                   Term: Numericals or literals or their combinations by operation of multiplication are called terms.
Example: \[5{{x}^{2}},\,\,7x,\,\,\frac{x}{7},\,\,\frac{{{y}^{2}}}{9},\,\,\frac{5}{2}x\]etc.  
  •                   Constant Term:  A term of an expression having no literal is called a constant term.
Example: \[4,\,\,\frac{-1}{2},\,\,\frac{7}{4}\]etc.  
  •                Algebraic expression: A combination of constant and variable connected by mathematical operations \[(+,\,\,-,\,\,\times ,\,\,\div )\] is called an algebraic expression.
more...

FACTORS AND MULTIPLES       FACTOR:
  •             One Number is said to be a factor of another when it divides the other exactly.
  •       If a number 'x' divides another number 'y' exactly, then we say that 'x' is a factor of 'y'.
  Example:                16 = 1, 2, 4, 8, 16., so, 1, 2, 4, 8 and 16 are factors of 16. 25 = 1, 5, 25. so, 1,5 and 25 are factors of 25.   MULTIPLE:
  •            A multiple of a number is a number obtained by multiplying it by integers.
or
  •           If a number 'x' divides another number 'y' exactly, then we say that 'y' is a multiple of x.
  Example:                5=5, 10, 15, 20.........and so on \[5\times 1=5,\,\,\,5\times 2=10,5\times 3=15,5\times 4=20....................\]Thus,           5, 10, 15, 20.....................are multiple of 5.   Properties of factors and multiples
  •            Factors of a number is finite.
  •            Multiples of a number is infinite.
  • more...

FRACTIONS AND DECIMALS   FUNDAMENTALS Natural numbers: All counting numbers are called natural numbers.
  •                   It is denoted by N.
  •                  \[N=\left\{ 1,2,3,4,\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \right\}\]
Whole number: Natural numbers together with zero are called whole numbers.
  •                  It is denoted by W.
  •                  \[~W=\left\{ 0,1,2,3,\_\_\_\_\_\_\_\_\_\_ \right\}\]
  •                 Fraction: A part of whole is called fraction.
or A number written in the form \[\frac{x}{y},\] where \[x\] and \[y\] are whole numbers and \[y\ne 0\] is called fraction,
  •                  \[\frac{x\to \text{Numerator}}{y\to \text{Denominator}}\]
  Types of Fraction                                      
  •                  Decimal fraction: A fraction whose denominator is 10, 100, 1000 etc.......is called a decimal fraction.
Example: \[\frac{1}{10},\frac{2}{100},\frac{5}{1000}\]etc...
  • more...

NUMBER SYSTEM   FUNDAMENTALS                     
  •                   Digits: for representing any number we use ten symbols
0, 1, 2, 3,4,5,6,7,8,9 All the other numbers are written using 10 symbols. Example: 2, 3, 4, 5 etc.
  •                  Numeral: A group of digits representing a number is called a numeral.
Example: 243, 67842, 546380, etc. are numerals.
  •                  Notation: The system of expressing a number in figure or digits is called notation.
  •                  Numeration: The logic of representing a number in words is called numeration.
                                                 \[\Rightarrow \]    Let us see the chart of Indian system and understand about Indian system.
Periods Crores Lakhs more...
SYMMETRY   SYMMETRY Symmetry is when something is made up of two parts that are exactly the same and they are facing each other.     Line Symmetry
  •                   A line of symmetry divides a figure into two mirror - image halves.
  •                  The line of Symmetry is imaginary line where you could fold the image and have both halves match exactly.
  Example:  
  •                    Letters and line symmetry
 
  •                   There are some letters which do not have any line symmetry.
 
  •                   Rhombus:
  •                  Two lines of symmetry AC and BD
  • more...

DATA HANDLING   SYMMETRY
  •                   The word 'data' means information. Its exact dictionary meaning is given facts.
  •                   Statistical data are of two types (i) primary (ii) secondary.
  •                   The number of times an observation occurs in the given data is called the frequency of the observation.
  •                   There are two types of frequency distribution.
  •          Discrete frequency distribution.
  •          Continuous frequency distribution.
 
  •                     In a discrete frequency distribution the cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.                                             
  •               A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table.
  •            Bar graphs
  • more...

PRACTICAL GEOMETRY   FUNDAMENTALS
  •                    A ruler protractor and compass are used for constructions.
  •                 Given a line 1 and a point P not on it, a line parallel to 1 can be drawn through the point P, using the idea of 'equal alternate angles' or 'equal corresponding angles'.
  •                   The sum of lengths of any two sides of a triangle is greater than its third side.
  •                   The difference of lengths of any two sides of a triangle is lesser than its third side.
  •                   The sum of angles in a triangle is \[180{}^\circ .\]
  •                   The following cases of congruence of triangles, help us construct the triangle.
  (a) S.S.S: A triangle can be drawn given the lengths of its three sides. (b) S.A.S: A triangle can be drawn given the lengths of any two sides and the measure of the angle between them. (c) A.S.A: A triangle can be drawn given the measures of two angles and the length of the side included between them. (d) R.H.S: A right angled triangle can be drawn given the length of hypotenuse and the length of one of its legs.   more...


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