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

## 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
- 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
2.4 Bivariate Frequency Distribution and Chi Square Statistic
2.5 Correlation
2.6 Permutations and Combinations
2.7 Probability
2.8 Linear Inequations
2.9 Commercial Mathematics