Maths HSC Commerce (English Medium) 11th Standard Maharashtra State Board Syllabus 2025-26

• Creating a Set
• Creating Set using List or Tuple
• Set Operations
• Programs using Sets

1. Roster method
2. Set-Builder method
3. Venn Diagram

1. Open Interval
2. Closed Interval
3. Semi-closed Interval
4. Semi-open Interval

1. Ordered Pair
2. Cartesian Product of two sets
3. Number of elements in the Cartesian product of two finite sets
4. Relation (Definition)

• Empty Relation
• Universal Relation
• Trivial Relations
• Identity relation
• Symmetric relation
• Transitive relation
• Equivalence Relation
• Antisymmetric relation
• Inverse relation
• One-One Relation (Injective)
• Many-one relation
• Into relation
• Onto relation (Surjective)

• 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 Function based on Elements:
  1) One One Function (or injective)
  2) Many One Function
  3) Onto Function (or surjective)
  4) One One and Onto Function (or bijective)
  5) Into Function
  6) Constant Function
• Types of Function based on Equation:
  1) Identity Function
  2) Linear Function
  3) Quadratic Function
  4) Cubic Function
  5) Polynomial Functions
• Types of Function based on the Range:
  1) Modulus Function
  2) Rational Function
  3) Signum Function
  4) Even and Odd Functions
  5) Periodic Functions
  6) Greatest Integer Function
  7) Inverse Function
  8) Composite Functions
• Types of Function based on the Domain:
  1) Algebraic Functions
  2) Trigonometric Functions
  3) Logarithmic Functions
• Explicit and Implicit Functions
• Value of a Function
• Equal Functions

• Arrow form/Venn Diagram Form
• Ordered Pair(x, y)
• Rule / Formula
• Tabular Form 
• Graphical form

Evaluation of function

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

• 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

• Signum function
• Absolute value function (Modulus function)
• Greatest Integer Function (Step Function)

• Imaginary number
• Complex Number

• Equality of two Complex Numbers 
• Conjugate of a Complex Number 
• Properties of `barz`
• Addition of complex numbers - Properties of addition, Scalar Multiplication
• Subtraction of complex numbers - Properties of Subtraction
• Multiplication of complex numbers - Properties of Multiplication
• Powers of i in the complex number
• Division of complex number - Properties of Division
• The square roots of a negative real number
• Identities

• Properties of 1, w, w²

• Finite sequence 
• Infinite sequence
• Progression

Properties of Geometric Progression.

• Expressing recurring decimals as rational numbers

• Arithmetic mean (A. M.)
• Geometric mean (G. M.) 
• Harmonic mean (H. M.)

Properties of Sigma Notation

• Equation of a locus

• Inclination of a line
• Slope of a line
• Perpendicular Lines
• Angle between intersecting lines

• Slope-Point Form
• Slope-Intercept  form
• Two-points  Form
• Double-Intercept  form
• Normal  Form 
• General  form 

• Point  of  intersection  of  lines  
• The  distance  of  the  Origin  from  a  Line
• Distance  of  a  point  from  a  line
• Distance  between  parallel  lines

1.1.1 Recall

Matrix 
Order of a matrix
General form of a Matrix
Types of matrices
Row matrix
Column matrix
Zero matrix (or) Null matrix 
Square matrix
Triangular matrix
Diagonal matrix
Scalar matrix
Unit matrix (or) Identity matrix
Multiplication of a matrix by a scalar
Negative of a matrix
Equality of matrices
Addition and subtraction of matrices
Multiplication of matrices
Transpose of a matrix

1.1.2 Minors 

1.1.3 Cofactors

1.1.4 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.

• One-Sided Limit
• Right-hand Limit
• Left-hand Limit
• Existence of a limit of a function at a point x = a

• Evaluation of Limits when X → ∞
• Evaluation of Limits of the form 1^∞

1. `lim_(x → 0) ((e^x - 1)/x) = log e = 1`

2. `lim_(x → 0) ((a^x - 1)/x) = log a (a > 0, a ≠ 0)`

3. `lim_(x → 0) [ 1 + x]^(1/x) = e`

4. `lim_(x → 0) (log(1 + x)/x) = 1`

5. `lim_(x → 0) ((e^(px) - 1)/(px)) = 1`, (p constant)

6. `lim_(x → 0) ((a^(px) - 1)/(px)) = log a`, (p constant)

7. `lim_(x → 0) (log(1 + px)/(px)) = 1`, (p constant)

8. `lim_(x → 0) [ 1 + px]^(1/(px)) = e`, (p constant)

• Continuity of a function at a point
• Definition of Continuity
• Continuity from the right and from the left
• Examples of Continuous Functions
• Properties of continuous functions
• Types of Discontinuities
• Jump Discontinuity
• Removable Discontinuity
• Infinite Discontinuity
• Continuity over an interval
• The intermediate value theorem for continuous functions

Discontinuous Function

• Derivative by the method of the first Principle
• Derivatives of some standard functions
• Relationship between differentiability and continuity

• Theorem 1. Derivative of Sum of functions
• Theorem 2. Derivative of Difference of functions.
• Theorem 3. Derivative of Product of functions.
• Theorem 4. Derivative of Quotient of functions.

• Demand function
• Marginal Demand (MD)
• Supply function(S)
• Total cost function (C)
• Marginal Cost (MC)
• Revenue and Profit Functions
• Total Revenue (R)

• Computing Median for Ungrouped Data
• Computing Median for Grouped Data

• Individual Data
• Discrete Data
• Continuous data

• Individual Data
• Discrete Data
• Continuous data

• Individual Data
• Discrete Data
• Continuous data

• Quartile Deviation
• Mean deviation

• Meaning of Correlation
• Types of correlation

1. Positive Correlation
2. Negative Correlation
3. Simple correlation

• Scatter Diagram
• Karl Pearson’s Correlation Coefficient

Properties of correlation coefficient r(x, y)

• Tree Diagram 
• Addition Principle 
• Multiplication principle

Properties of the factorial function

• Permutation
• Permutation of repeated things
• Permutations when all the objects are not distinct
• Number of Permutations Under Certain Restricted Conditions
• Circular Permutations

• ⁿC_r , ⁿC_n =1, ⁿC₀ = 1, ⁿC_r = ⁿC_n–r, ⁿC_x = ⁿC_y, then x + y = n or x = y, ⁿ⁺¹C_r = ⁿC_r-1 + ⁿC_r
• When all things are different
• When all things are not different.
• Mixed problems on permutation and combinations.

• Properties of Combinations:
  1. Consider ⁿC_{n - r} = ⁿC_r for 0 ≤ r ≤ n.
  2. ⁿC₀ = `(n!)/(0!(n - 0)!) = (n!)/(n!) = 1, because 0! = 1` as has been stated earlier.
  3. If ⁿC_r = ⁿC_s, then either s = r or s = n - r.
  4. `"" ^nC_r = (""^nP_r)/(r!)`
  5. ⁿC_r + ⁿC_{r - 1} = ^{n + 1}C_r
  6. ⁿC₀ + ⁿC₁ + ......... ⁿC_n = 2ⁿ 
  7. ⁿC₀ + ⁿC₂ + ⁿC₄ + ...... = ⁿC₁ + ⁿC₃ + ⁿC₅ + ....... = 2^{(n - 1)}
  8. ⁿC_r = `"" (n/r) ^(n - 1)C_(r- 1) = (n/r)((n - 1)/(r - 1)) ^(n - 2)C_(r - 2) = ....`
  9. ⁿC_r has maximum value if (a) r = `n/2 "when n is even (b)" r = (n - 1)/2 or (n + 1)/2` when n is odd.

• Random experiment
• Outcome
• Equally likely outcomes
• Sample space
• Event

1. Union of two events
2. Exhaustive Events
3. Intersection of two events
4. Mutually Exclusive Events

• Independent Events

• Representation of solution of linear inequality in one variable on the number line

Consider linear inequalities in two variables x and y

• Meaning of Depreciation
• Features of Depreciation