ICSE Class 6 Maths Syllabus

 ICSE Class 6 Maths Syllabus

1. Number System:
   1. Numbers:
      1. Consolidating the sense of numbers up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc.
      2. Place Value
      3. Indian Number System and International Number System. Comparison of the International number system and Indian Number System.
   2. Natural numbers and Whole numbers:
      1. Properties of numbers (Associative, commutative, distributive, multiplicative identity, additive identity)
      2. Number Line.
   3. Negative Numbers and Integers:
      1. Use of negative numbers.
      2. Connection of negative numbers in daily life.
      3. Representation of negative numbers in the number line.
      4. Ordering of negative numbers.
      5. Addition and subtraction of integers.
      6. Identification of integers on the number line.
   4. Sets
      1. Idea of sets
      2. Representation of sets
      3. The cardinality of sets.
   5. Fractions
      1. Representation of fractions.
      2. Fraction as a division.
      3. Proper, improper and mixed fractions.
      4. Equivalent Fractions.
      5. Operations on fractions.
      1. Word problems involving addition and subtraction of decimals.
   6. Playing with numbers
      1. Simplification of brackets
      2. HCF and LCM, prime factorization and division method for LCM and HCF, the property LCM * HCF = product of two numbers.
2. Ratio and Proportion
   1. Difference between Ratio and Fraction.
   2. Concept of Ratio.
   3. Unitary method.
   4. Word problems based on proportions and ratio.
   5. Introduction to speed and problems based on speed, time and distance.
3. Algebra
   1. Introduction to constants, variable and unknown through patterns through appropriate word problems and generalisations
   2. Introduction to algebraic terms like expressions, literal numbers, coefficient, factors, polynomials degree, like and unlike terms.
   3. Framing algebraic expressions.
   4. Evaluation of algebraic expressions by substituting a value for the variable.
   5. Linear equation in one variable
4. Geometry
   1. Basic geometrical ideas
      1. Line, line segment, ray.
      2. Open and closed figures.
      3. Exterior and interior of a closed figure.
      4. Linear and Curvilinear boundaries.
      5. Angle – Arm, vertex, exterior and interior.
      6. Triangle – Sides, angles, vertices, interior and exterior, altitude and median
      7. Quadrilaterals – Vertices, sides, diagonals, angles, diagonals, adjacent sides and opposite sides, interior and exterior of a quadrilateral.
      8. Circle – Radius, Centre, diameter, sector, arc, segment, chord, circumference, semicircle, exterior and interior.
   2. Understanding Elementary Shapes (2-D and 3-D)
      1. Measure of Line Segment, angles.
      2. Pair of lines – Intersecting and perpendicular lines, Parallel lines.
      3. Angles – Acute, obtuse, right, straight, complete, reflex and zero angles.
      4. Classification of triangles on the basis of sides and angles.
      5. Types of quadrilaterals – Trapezium, parallelogram, rectangle, rhombus, square.
      6. Identification of 3-D shapes: Cuboids, Cubes, Cylinder, Sphere, Cone, Prism.
      7. Elements of #D figures.
   3. Symmetry: (reflection)
      1. Observation and identification of 2-D symmetrical objects for reflection symmetry.
      2. Operation of reflection.
   4. Constructions (using Straight edge Scale, protractor, compasses )
      1. Perpendicular bisector
      2. Drawing of a line segment.
      3. Construction of angles by using a protractor.
      4. An angle equal to the given angle.
      5. Construction of circle.
5. Mensuration
   1. Introduction to area and concept of perimeter.
   2. General understanding of perimeter using many shapes.
   3. Concept of area, Area of a rectangle and a square.
   4. Conversion of units : (Mass, time, money, and capacity) from a smaller to larger and vice versa.
   5. The perimeter of a rectangle – and its special case a square.
   6. Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation.
6. Data Handling
   1. Collection of data to examine a hypothesis
   2. Mean and median of data not having more than ten observations.
   3. Construction of bar graphs for given data interpreting bar graphs.

ICSE Class 6 English syllabus

ICSE Class 6 English Syllabus – Prose

1. Old Tirumala
2. Clever Jadhoji
3. The White House Circus
4. Across Three Millennia
5. In a Tunnel
6. Uncle Podger Hangs A Picture
7. Goodbye Party For Miss Pushpa T.S
8. The Black Beauty

ICSE Class 6 English Syllabus – Poems

1. Mother To Son
2. The Old Brown Horse
3. The Way Through The Woods
4. The Railway Junction
5. In The Bazaars Of Hyderabad

ICSE Class 6 English Syllabus – Grammar

1. Types of Sentences
2. Articles
3. Conjunctions
4. Idiomatic Phrases
5. Comprehension Questions
6. Nouns
7. Subjects and Predicates
8. Adjectives
9. Prepositions
10. Direct and Indirect Objects
11. Verbs and Objects

The syllabus of ICSE Class 5 Social Studies

The syllabus of ICSE Class 5 Social Studies 

1. Evolution of Mankind
2. The Constitution of India – Basic Features
3. The Earth – Its Geographical Features
4. India – A Diverse Country
5. The Environment – Major Concerns
6. Natural Resources
7. Major Occupations in India

The syllabus of ICSE Class 5 MATHEMATICS

The syllabus of ICSE Class 5 MATHEMATICS

Chapter 1: Numbers
Chapter 2: Number Operations
Chapter 3: Fractions and Decimals
Chapter 4: Playing with Numbers (Factors and Multiples)
Chapter 5: Introduction to Negative Numbers
Chapter 6: Geometry
Chapter 7: Measurement
Chapter 8: Introduction to Percentage
Chapter 9: Data Handling
Chapter 10: Patterns

The syllabus of ICSE Class 5 SCIENCE

The syllabus of ICSE Class 5 SCIENCE

1. Human Body: The Circulatory System
2. Human Body: The Skeletal System
3. Food and Health
4. Pollination
5. Plant Reproduction
6. Solids, Liquids and Gases
7. Interdependence in Living Beings-Plants and Animals
8. Sound and Noise
9. Work and Energy
10. Light and Shadows
11. Simple Machines
12. Cleanliness and Hygiene

TYPES OF RELATIONS

EMPTY RELATIONS - An empty relation is a type of relation, there is no relation between any object / element of sets. Empty relation is also called void relation.
Therefore, R =  ɸ 
EXAMPLE - A = Set of all student of boys school
R = {(a, b) ; a and b are sisters}.
UNIVERSAL - A relation R in a set A is called universal relation if each element of set A is related to every element of A. Universal Relation is also called full relation.
Therefore, R = A❌A.
EXAMPLE -  R = {(a, b) : a and b is greater than 2 feet}.
IDENTITY - A relation R in a set A is called identity relation if every element of set A is related to itself only.
Therefore, R = I {(a,a) belongs to A}.
INVERSE - Let R be a relation from set A to set B.
Therefore R belongs to A❌B.
The relation R-1 is called inverse relation, if relation from set B to A is denoted by R-1 = {(b, a) : a and b belongs to R}.
EXAMPLE - R = {(1, 2), (2,3)}
R-1 = {(2,1), (3,2)}.
REFLEXIVE - If every element of set A maps to itself.
for every a ∈ A, (a, a) ∈ R.
SYMMETRIC - A relation R in a set A is said to be symmetric if (a,b) ∈ R then (b,a) ∈ R.
TRANSITIVE - A relation in a set A is said to be transitive, if 
(a,b) ∈ R , (b, c) ∈ R , then (a, c) ∈ R.
EQUIVALENCE - A relation is said to be equivalence relation if it is reflexive, symmetric and transitive relation.
EXAMPLE - If we throw two dices A and B and note down all the possible outcome.
Define, a relation; R = {(a, b) : a ∈ R , b ∈ R}
we find that {(1,1), (2, 2), (3, 3), (4, 4),......} ∈ R (Reflexive)
If {(a,b) = (1,2) ∈ R} then {(B,A) = (2,1)} ( Symmetric)
IF {(a,b) = (1, 2) ∈ R }, {(b,c) = (2,3) ∈ R } 
then  {(a,c ) = (1,3)  ∈ R } (Transitive ).

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)}.

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 ).

CLASS 12 COURSE STRUCTURE

      SYLLABUS 2020 - 2021

           CLASS - 12

        COURSE STRUCTURE

     NUMBER                 UNITS                                                                                 Marks

1. Relation and function                                                                       08
2. Algebra                                                                                            10
3. Calculus                                                                                           35
4. Vector and Three - Dimensional Geometry                                     14
5.  Linear Programming                                                                       05
6.  Probability                                                                                       08

            Total                                                                                                80 

                                                                                                 

       Internal Assessment                                                                           20

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.

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.

NCERT MATHS SYLLABUS CLASS 2

Number System

NCERT MATHS SYLLABUS CLASS 12

NCERT MATHS SYLLABUS CLASS 11

NCERT MATHS SYLLABUS CLASS 10

NCERT MATHS SYLLABUS CLASS 9

NCERT MATHS SYLLABUS CLASS 8

NCERT MATHS SYLLABUS CLASS 7

NCERT MATHS SYLLABUS CLASS 6

NCERT MATHS SYLLABUS CLASS 5

NCERT MATHS SYLLABUS CLASS 4

SHAPES IN 3D

Multiplication, the product of any number and zero, is zero.

SOME MATHEMATICAL SYMBOLS........

FLOWERS