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Mathematics and Statistics 11th HSC Commerce (Marketing and Salesmanship) Maharashtra State Board Topics and Syllabus

Academic year:

Syllabus

1.1 Sets and Relations
  • Introduction of Set 
  • Representation of a Set 
    1. Roster method
    2. Set-Builder method
    3. Venn Diagram
  • Intervals 
    1. Open Interval
    2. Closed Interval
    3. Semi-closed Interval
    4. Semi-open Interval
  • Types of Sets 
    • Types of Sets:
    1.  Empty Set
    2. Singleton set 
    3. Finite set
    4. Infinite set 
    5. Subset 
    6. Superset 
    7. Proper Subset 
    8. Power Set
    9. Equal sets 
    10. Equivalent sets 
    11. Universal set
  • Operations on Sets 
    1. Complement of a set
    2. Union of Sets
    3. Intersection of sets
    4. Distributive Property
  • Relations of Sets 
    1. Ordered Pair
    2. Cartesian Product of two sets
    3. Number of elements in the Cartesian product of two finite sets
    4. Relation (Definition)
  • Types of Relations 
    1. One-One Relation(Injective)
    2. Many-one relation
    3. Into relation
    4. Onto relation (Surjective)

    Reflexive, symmetric, transitive, not reflexive, not symmetric and not transitive.

1.2 Functions
  • Concept of Functions 
    • Function, Domain, Co-domain, Range
    • Types of function
      1. One-one or One to one or Injective function
      2. Onto or Surjective function
    • Representation of Function
    • Graph of a function
    • Value of funcation
    • Some Basic Functions - Constant Function, Identity function, Power Functions, Polynomial Function, Radical Function, Rational Function, Exponential Function, Logarithmic Function, Trigonometric function
  • Types of Functions 
    • one-one (or injective)
    • many-one
    • onto (or surjective)
    • one-one and onto (or bijective)
  • Representation of Function 
    • Arrow form/Venn Diagram Form
    • Ordered Pair(x, y)
    • Rule / Formula
    • Tabular Form 
    • Graphical form
  • Graph of a Function 

    Evaluation of function

  • Fundamental Functions 

    Constant Function
    - Identity function
    - Linear Function
    - Quadratic Function
    - Function of the form - Square Function, Cube Function
    - Polynomial Function
    - Rational Function
    - Exponential Function 
    - Logarithmic Function

  • Algebra of Functions 
    • Composition of Functions
    • Inverse functions
    • Piecewise Defined Functions
      1) Signum function
      2) Absolute value function (Modulus function)
      3) Greatest Integer Function (Step Function)
      4) Fractional part function
  • Composite Function 
  • Inverse Functions 
  • Some Special Functions 
    • Signum function
    • Absolute value function (Modulus function)
    • Greatest Integer Function (Step Function)
1.3 Complex Numbers 33
1.4 Sequences and Series
1.5 Locus and Straight Line
  • Locus 
  • Equation of Locus 
  • Line 
    • Inclination of a line
    • Slope of a line
    • Perpendicular Lines
    • Angle between intersecting lines
  • Equations of Lines in Different Forms 
    • Slope-Point Form
    • Slope-Intercept  form
    • Two-points  Form
    • Double-Intercept  form
    • Normal  Form 
    • General  form 
  • General Form Of Equation Of Line 
    • Point  of  intersection  of  lines  
    • The  distance  of  the  Origin  from  a  Line
    • Distance  of  a  point  from  a  line
    • Distance  between  parallel  lines
1.6 Determinants
  • Determinants 
    • Definition of Determinants
    • Determinant of order 3
    • Expansion of Determinant
  • Properties of Determinants 
    • Property 1 - The value of the determinant remains unchanged if its rows are turned into columns and columns are turned into rows.
    • Property 2 -  If any two rows  (or columns)  of a determinant are interchanged then the value of the determinant changes only in sign.
    • Property 3 - If any two rows ( or columns) of a  determinant are identical then the value of the determinant is zero.
    • Property  4  -  If each element of a row (or column)  of a determinant is multiplied by a  constant k then the value of the new determinant is k times the value of the original determinant.
    • Property  5  -  If each element of a row (or column) is expressed as the sum of two numbers then the determinant can be expressed as the sum of two determinants
    • Property  6  -  If a constant multiple of all elements of any row  (or column)  is added to the corresponding elements of any other row  (or column  )  then the value of the new determinant so obtained is the same as that of the original determinant. 
    • Property 7 -  (Triangle property) - If all the elements of a  determinant above or below the diagonal are zero then the value of the determinant is equal to the product of its diagonal elements.
  • Application of Determinants 
1.7 Limits
1.8 Continuity
1.9 Differentiation
2.2 Measures of Dispersion
2.5 Correlation
2.6 Permutations and Combinations
2.7 Probability
2.8 Linear Inequations
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