Current Affairs 6th Class

                                                                                      Mensuration     Learning Objectives
  • Mensuration
  • Perimeter of Geometrical Shapes
  • Area of Geometrical Shapes
  Mensuration Mensuration is the branch of mathematics which deals with the measurement of lengths, area and volume of the plane and solid figures.   Perimeter of a plane figure: The distance all round a plane figure is called perimeter of the figure or the lengths of boundary of a plane figure is known as its perimeter                         \ Perimeter of the quadrilateral \[ABCD=AB+BC+CD+DA\]                                                 \[=40\text{ }cm+10\text{ }cm+40\text{ }cm+10\text{ }cm\]                                                 \[=100\text{ }cm\] Perimeter of the hexagon \[ABCDEF=AB+BC+CD+DE+EF+FA\]                                                 \[=100\text{ }m+120\text{ }m+90\text{ }m+45\text{ }m+60\text{ }m+80\text{ }m\]                                                 \[=495\text{ }m\]   Perimeter of a scalene triangle = Sum of all the three sides of the triangle. Example: Find the perimeter of the triangle ABC. Perimeter of the triangle \[ABC=AB+BC+CA\]                                     \[=4\text{ }cm+12\text{ }cm+8\text{ }cm\]                                     \[=24cm\]   Perimeter of a rectangle \[=2\times \left( length+breadth \right).\] Example: Find the perimeter of the following rectangle ABCD. Perimeter of rectangle \[ABCD=2\times \left( AB+BC \right)\]                                     \[=2\times \left( 15cm+9cm \right)\]                                     \[=48\text{ }cm\]   Perimeter of regular shapes Perimeter of an equilateral triangle \[\text{=3 }\!\!\times\!\!\text{ length of one side}\]. Example: Find the perimeter of the given triangle. Perimeter of the triangle \[=3\times 4\text{ }cm\]                                     \[=12\text{ }cm\]               Perimeter of a square: \[\text{4 }\!\!\times\!\!\text{ length of one side}\text{.}\] Example: Find the perimeter of the given square. Perimeter of the square \[=4\times 1\text{ }m\]                                     \[=4\text{ }m\]   Perimeter of regular pentagon \[=5\text{ }\times \text{ }length\text{ }of\text{ }one\text{ }side.\] Example: Find the perimeter of the given pentagon. Perimeter of the pentagon \[=5\times 4\text{ }cm\]                                     \[=20\text{ }cm\]   Perimeter of the regular hexagon \[=6\times length\text{ }of\text{ }one\text{ }side.\] Perimeter of the hexagon \[=6\times 5\text{ }cm\]                                     \[=30\text{ }cm.\]   Area of a plane figure: The measurement of the region enclosed by a plane figure is called area of the figure or area is the amount of surface covered by the shape. Area of triangle \[=\frac{1}{2}\times base\times height.\] Example: Find the area of the given triangle. Area of the triangle \[=\frac{1}{2}\times 4cm\times 6cm=12c{{m}^{2}}\]                         Area of rectangle: \[length\times breadth.\] Example: Find the area of the given rectangle. Area of the rectangle \[=8\text{ }cm\times 6\text{ }cm=48\text{ }c{{m}^{2}}\] more...

                                                                                      Data Handling   Learning Objectives
  • Data
  • Statistics
  Data A collection of information in the form of numerical figures is called data. Raw data: Data obtained in the original form is called raw data. Tabulation of data: Arranging the data in a systematic form in the form of a table is known as tabulation of data.   Statistics The branch of mathematics which deals with the collection, presentation, analysis and interpretation of numerical data is called statistics.   Example A dice was thrown 30 times and the following outcomes were noted: 4, 3, 3, 2, 5, 4, 4, 6, 1, 2, 2, 3, 4, 6, 2, 3, 3, 4, 1, 2, 3, 3, 4, 5, 6, 3, 2, 1, 3, 4. Represent the above data in the form of frequency distribution. Explanation: We may present the data as shown below:  
Outcome Tally marks No. of outcomes
1 3
2 6
3 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...
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 called a decimal fraction.
Example: \[\frac{1}{10},\frac{2}{100},\frac{5}{1000}\]etc...
  • 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.

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...

GEOMETRY   GEOMETRY Geometry is derived from two greek words "Geo" means "Earth" metron means "Measurement". That means measurement of Earth is called geometry.               Basics terms of geometry
  •                  There are three basics undefined terms of geometry.
(i) Point       (ii) Line       (iii) Plane   Point: Point is a mark of position, it is made by sharp tip of pen, pencil and nail.
  •           It is denoted by capital letter.
  •           It is represented by
  •           A point has no length, no breadth and no thickness.
  •                   Line segment: The distance between two points in a same plane is called a line segment.
  •           It is denoted by\[\overline{AB}\]. It is measured in 'cm' or 'inch'.
  •           more...

  •                    The branch of geometry that deals with the measurement of length, area, or volume.
  •                   The length of the sides enclosing the figure is called its perimeter.
  •                   The amount of space in the boundary of plane figure.
  •                    Unit of area is square unit.
  Some important formula of Mensuration SQUARE:-                        
  •                     Perimeter of square\[=4\times side=4a\]
  •                    Area of square\[={{(side)}^{2}}={{(a)}^{2}}\]
  •                    Diagonal of square \[=\sqrt{2}\times \] side
  RECTANGLE                         more...

MENTAL ABILITY   FUNDAMENTALS Mental Ability: The power to learn or retain knowledge, in law, the ability to understand the fact and significance of your behavior.
  •                      Mental ability develop logical thinking among students.
  •                      Mental ability is based on some concepts.
  Series completion                                        
  •                      Number series
  •                     Alphabet series
  •                Number Series: The three or more numbers having a sequence of pattern is given. The numbers follow a certain rule which relates the consecutive terms. Students should be able to recognize the rule or pattern. This will be help them to find the next term or number.
  Look at the example given below 1.            Series of odd number 1, 3, 5, 7, 9, ___________ Ans.:    Next number is 11.   2.            Series of even number. 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.
  •                    Letters and line symmetry
  •                   There are some letters which do not have any line symmetry.
  •                   Rhombus:
  •                  Two lines of symmetry AC and BD
  • more...

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