Mathematics By Richa: May 2020

Sunday, 31 May 2020

Definition of relation with example.

RELATIONS - A relation between two sets in a collection of ordered pair containing one object from each set, if the object x take from first set and object y take from second set then obtained ordered pair (x, y) is in relation. The sets must not be empty.
In other words, A connection between two or more sets is a relation.
NOTE - Functions are type of relation.

EXAMPLE - Given example we can see objects of first set is related to objects of second set.

Here,
R = {( -1, 1), (1, 1), (7, 49), (.5, .49)}.

Sunday, 24 May 2020

MAPPING,FUNCTION, DOMAIN, CO-DOMAIN AND RANGE DEFINITION WITH EXAMPLES

MAPPING - Each element of a given set ( the domain of the function) is associated with an element of another set (the range of the function) is called mapping. Some mappings are represent in the above structure.

Function - A function is a relation for which each value from the set the first components of the ordered pair is associated with exactly one value from the set of second components of the ordered pair.

DOMAIN - The domain of a function f(x) is the set of all values for which the function is defined.

RANGE - The range of the functions is the set of all values that f takes.

Above we have two sets A and B where
A = (-1, 1, 7, -5 ) ;

B = (1, 49, 50 ) A B
here function f : A→ B ; A is domain and
B is co-domain
we know that Range is subset of Co-Domain.
So,
f (-1) = f (1) = 1
f (7) = 49
f (50 = 25.

In this example range = co-domain.
Range = (1, 49, 25 )

In given example we can see X is domain and Y is a co-domain.

We can write, Domain = (1, 2, 3 )
Co-domain = (1, 2, 3, 4 )
Range = (1, 2, 3 ).

Saturday, 23 May 2020

CLASS 12 COURSE STRUCTURE

SYLLABUS 2020 - 2021

CLASS - 12

COURSE STRUCTURE

NUMBER UNITS Marks

Relation and function 08
Algebra 10
Calculus 35
Vector and Three - Dimensional Geometry 14
Linear Programming 05
Probability 08

Total 80

Internal Assessment 20

Thursday, 21 May 2020

RELATIONS AND FUNCTIONS

RELATION - A RELATION between two sets is a collection of ordered pairs containing one object from each sets.

If the object x from the set A and the object y from set B, then the objects are said to be related if the ordered pair (x,y) is in the relation. A function is a type of relation.

Some Examples

TWIN PRIME, PRIME TRIPLETS, CO- PRIME NUMBERS

MORE ABOUT NUMBERS:

1) TWIN PRIME - Prime numbers differing by two are called twin prime number.
example - 5 and 7; 11 and 13 etc.
Solution- 7-5=2 and 13-11=2.

2) PRIME TRIPLETS - The set of three consecutive prime numbers with a difference two is called the prime triplets.

Note: (1, 3, 5) is only prime triplet set in prime numbers.

3) CO-PRIME - The pairs of numbers, which is only divisible by one are called co- prime numbers.
example - 10 and 21 are co- prime numbers ; 16 and 25 are co- prime numbers etc.

PRIME NUMBERS AND COMPOSITE NUMBERS

PRIME NUMBER - A natural number, which is divisible by 1 and itself and always greater than 1 is called prime number.

example-2, 3, 5, 7, 11, 13......and so on.

here, 2 is only even prime number, we can say Except 2, every prime number is an odd natural number.

1) Smallest even prime number is 2.
2) Smallest odd prime number is 3.

Largest prime number we can not obtained because prime number are infinitely exist.

COMPOSITE NUMBER - A natural number, which is greater than 1 and not prime.In other words we can say natural number which is divisible by more than two number, is called composite number.

example - 4, 6, 8, 9, 10,.....etc.

composite number can be even or odd.

1)Smallest composite number is 4.

2)Largest composite number we can not obtained because composite number are infinitely exist.

note - 1 is neither prime nor composite.

Monday, 18 May 2020

NCERT MATHS SYLLABUS CLASS 1

Geometry (10 hrs.)

a) Shapes and Spatial Understanding

Develops and uses vocabulary of spatial relationship (Top, Bottom, On, Under, Inside, Outside, Above, Below, Near, Far, Before, After)

b) Solids Around Us

Collects objects from the surroundings having different sizes and shapes like pebbles, boxes, balls, cones, pipes,
etc.
Sorts, Classifies and describes the objects on the basis of shapes, and other observable properties.
Observes and describes the way shapes affect movements like rolling and sliding.
Sorts 2 – D shapes such as flat objects made of card etc.

Numbers (46 hrs.)

a) Developing a sense of Numberness, Counting and Operations of Numbers 1-9 and Zero

Observes object and makes collections of objects.
Arranges the collection of objects in order by
– Matching and
– One to one correspondence
Counts the number of objects in a collection.
Makes collection of objects corresponding to a specific number.
Recognises and speaks numbers from 1 to 9.
Uses numbers from 1 to 9 in counting and comparison. (Real objects and repeated events like clapping to be used for counting)
Reads and writes numerals from 1 to 9.
Adds and subtracts using real objects and pictures.
Adds and subtracts the numbers using symbols ‘+’ and ‘-’.
Approaches zero through the subtraction pattern (such as 3 – 1 = 2, 3 – 2 = 1, 3 – 3 = 0).

b) Numbers from (10 – 20)

Forms Number sequence from 10 to 20.
Counts objects using these numbers.
Groups objects into a group of 10s and single objects.
Develops the vocabulary of group of ‘tens’ and ‘ones’.
Shows the group of tens and ones by drawing.
Counts the number of tens and ones in a given number.
Writes the numerals for eleven to nineteen.
Writes numerals for ten and twenty.
Compares numbers upto 20.

c) Addition And Subtraction (Upto 20)

Adds and subtracts numbers upto 20.

d) Numbers from 21 – 99

Writes numerals for Twenty-one to Ninety nine. Groups objects into tens and ones.
Draws representation for groups of ten and ones.
Groups a number orally into tens and ones.

e) Mental Arithmetic

Adds two single digit numbers mentally.

Money (3 hrs.)

a) Identifies common currency notes and coins.

b) Puts together small amounts of money.

Measurement (13 hrs.)

a) Length

Distinguishes between near, far, thin, thick, longer/taller, shorter, high, low.
Seriates objects by comparing their length.
Measures short lengths in terms of non-uniform units (in the context of games e.g. ‘Gilli Danda’ and ‘marblegames’).
Estimates distance and length, and verifies using nonuniform units (e.g. hand span etc.)

b) Weight

Compares between heavy and light objects.

c) Time

Distinguishes between events occurring in time using terms -earlier and later.
Gets the qualitative feel of long & short duration, of school days v/s holidays.
Narrates the sequence of events in a day.

Data Handling (6 hrs.)

Collects, represents and interprets simple data such as measuring the arm length or circumference of the head using a paper strip.

Patterns (10 hrs.)

Describes sequences of simple patterns found in shapes in the surroundings and in numbers, e.g. stamping
activity using fingers and thumb.
Completes a given sequence of simple patterns found in shapes in the surroundings and in numbers.