# Mathematics and Statistics 11th HSC Commerce (English Medium) Maharashtra State Board Topics and Syllabus

Maharashtra State Board Syllabus For 11th Mathematics and Statistics: Knowing the Syllabus is very important for the students of 11th. Shaalaa has also provided a list of topics that every student needs to understand.

The Maharashtra State Board 11th Mathematics and Statistics syllabus for the academic year 2023-2024 is based on the Board's guidelines. Students should read the 11th Mathematics and Statistics Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the Maharashtra State Board 11th Mathematics and Statistics Syllabus pdf 2023-2024. They will also receive a complete practical syllabus for 11th Mathematics and Statistics in addition to this.

## Maharashtra State Board 11th Mathematics and Statistics Revised Syllabus

Maharashtra State Board 11th Mathematics and Statistics and their Unit wise marks distribution

## Syllabus

1.1 Sets and Relations
• Introduction of Set
• Creating a Set
• Creating Set using List or Tuple
• Set Operations
• Programs using Sets
• 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
• Empty Relation
• Universal Relation
• Trivial Relations
• Equivalence Relation - Reflexive, symmetric, transitive, not reflexive, not symmetric and not transitive.
• One-One Relation (Injective)
• Many-one relation
• Into relation
• Onto relation (Surjective)
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 a 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

1.1.1 Recall

• Matrix
• Order of a matrix
• General form of a Matrix
• Types of matrices
1. Row matrix
2. Column matrix
3. Zero matrix (or) Null matrix
4. Square matrix
5. Triangular matrix
6. Diagonal matrix
7. Scalar matrix
8. Unit matrix (or) Identity matrix
9. Multiplication of a matrix by a scalar
10. Negative of a matrix
11. Equality of matrices
12. Addition and subtraction of matrices
13. Multiplication of matrices
14. Transpose of a matrix

1.1.2 Minors

1.1.3 Cofactors

1.1.4 Properties of determinants

• 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
2.1 Partition Values
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