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
Maharashtra State Board 11th Mathematics and Statistics Course Structure 2023-2024 With Marking Scheme
# | Unit/Topic | Weightage |
---|---|---|
1.1 | Sets and Relations | |
1.2 | Functions | |
1.3 | Complex Numbers 33 | |
1.4 | Sequences and Series | |
1.5 | Locus and Straight Line | |
1.6 | Determinants | |
1.7 | Limits | |
1.8 | Continuity | |
1.9 | Differentiation | |
2.1 | Partition Values | |
2.2 | Measures of Dispersion | |
2.3 | Skewness | |
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 | |
Total | - |
Syllabus
- Introduction of Set
- Creating a Set
- Creating Set using List or Tuple
- Set Operations
- Programs using Sets
- Representation of a Set
- Roster method
- Set-Builder method
- Venn Diagram
- Intervals
- Open Interval
- Closed Interval
- Semi-closed Interval
- Semi-open Interval
- Types of Sets
- Types of Sets:
- Empty Set
- Singleton set
- Finite set
- Infinite set
- Subset
- Superset
- Proper Subset
- Power Set
- Equal sets
- Equivalent sets
- Universal set
- Operations on Sets
- Complement of a set
- Union of Sets
- Intersection of sets
- Distributive Property
- Relations of Sets
- Ordered Pair
- Cartesian Product of two sets
- Number of elements in the Cartesian product of two finite sets
- 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)
- 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)
- Introduction of Complex Number
- Imaginary Number
- Concept of Complex Numbers
- Imaginary number
- Complex Number
- Conjugate of a Complex Number
- Algebra of Complex Numbers
- 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
- Square Root of a Complex Number
- Solution of a Quadratic Equation in Complex Number System
- Cube Root of Unity
- Properties of 1, w, w2
- Concept of Sequences
- Finite sequence
- Infinite sequence
- Progression
- Sequence and Series
- General Term Or the nth Term of a G.P.
Properties of Geometric Progression.
- Sum of the First n Terms of a G.P.
- Sum of Infinite Terms of a G. P.
- Expressing recurring decimals as rational numbers
- Recurring Decimals
- Harmonic Progression (H. P.)
- Types of Means
- Arithmetic mean (A. M.)
- Geometric mean (G. M.)
- Harmonic mean (H. M.)
- Special Series (Sigma Notation)
Properties of Sigma Notation
- 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
- Determinants
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
- 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
- Cramer’s Rule
- Non Homogeneous linear equations upto three variables
- Cramer’s Rule
- Definition of Limit of a Function
- One-Sided Limit
- Right-hand Limit
- Left-hand Limit
- Existence of a limit of a function at a point x = a
- Concept of Limits
- Evaluation of Limits
- Factorization Method
- Rationalization Method
- Limits of Exponential and Logarithmic Functions
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)
- Continuous and Discontinuous Functions
- 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
- Definition of Continuity
Discontinuous Function
- Continuity from the Right and from the Left
- Properties of Continuous Functions
- Continuity in the Domain of the Function
- Examples of Continuous Functions Whereever They Are Defined
- The Meaning of Rate of Change
- Definition of Derivative and Differentiability
- Derivative by the method of the first Principle
- Derivatives of some standard functions
- Relationship between differentiability and continuity
- Derivative by the Method of First Principle
- Rules of Differentiation (Without Proof)
- 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.
- Applications of Derivatives
- Demand function
- Marginal Demand (MD)
- Supply function(S)
- Total cost function (C)
- Marginal Cost (MC)
- Revenue and Profit Functions
- Total Revenue (R)
- Concept of Median
- Computing Median for Ungrouped Data
- Computing Median for Grouped Data
- Partition Values
- Quartiles
- Individual Data
- Discrete Data
- Continuous data
- Deciles
- Individual Data
- Discrete Data
- Continuous data
- Percentiles
- Individual Data
- Discrete Data
- Continuous data
- Relations Among Quartiles, Deciles and Percentiles
- Graphical Location of Partition Values
- Measures of Dispersion
- Quartile Deviation
- Mean deviation
- Variance and Standard Deviation
- Variance and Standard Deviation for raw data:
- Variance and Standard Deviation for ungrouped frequency distribution:
- Variance and Standard Deviation for grouped frequency distribution :
- Standard Deviation for Combined Data
- Coefficient of Variation
- Correlation
- Meaning of Correlation
- Types of correlation
- Positive Correlation
- Negative Correlation
- Simple correlation
- Scatter Diagram
- Karl Pearson’s Correlation Coefficient
- Concept of Covariance
- Properties of Covariance
- Concept of Correlation Coefficient
Properties of correlation coefficient r(x, y)
- Statistics (Entrance Exam)
- Scatter Diagram
(I) a) Perfect positive correlation, b) Positive correlation with high degree, c) Positive correlation with low degree
(II) a) Perfect negative correlation, b) Negative correlation with high degree, c) Negative correlation with low degree
(III) No correlation (Zero correlation)
- Scatter Diagram
- Interpretation of Value of Correlation Coefficient
- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Tree Diagram
- Addition Principle
- Multiplication principle
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
Properties of the factorial function
- Permutations
- Permutation
- Permutation of repeated things
- Permutations when all the objects are not distinct
- Circular Permutations
- Permutations of distinct objects
- Properties of Permutations
- Objects always together (String method)
- No two things are together (Gap method)
- Properties of Permutations
- Properties of Permutations:
(i) nPn = n!
(ii) nP0 = 1
(iii) nP1 = n
(iv) nPr = n × (n - 1)P(r - 1)
= n(n -1) × (n - 2)P(r - 2)
= n(n - 1)(n - 2) × (n - 3)P(r - 3) and so on.
(v) `(np_r)/(np_(r - 1))= n - r + 1`.
- Properties of Permutations:
- Permutations When All Objects Are Not Distinct
- Combination
- nCr , nCn =1, nC0 = 1, nCr = nCn–r, nCx = nCy, then x + y = n or x = y, n+1Cr = nCr-1 + nCr
- When all things are different
- When all things are not different.
- Mixed problems on permutation and combinations.
- Properties of Combinations
- Properties of Combinations:
1. Consider nCn - r = nCr for 0 ≤ r ≤ n.
2. nC0 = `(n!)/(0!(n - 0)!) = (n!)/(n!) = 1, because 0! = 1` as has been stated earlier.
3. If nCr = nCs, then either s = r or s = n - r.
4. `"" ^nC_r = (""^nP_r)/(r!)`
5. nCr + nCr - 1 = n + 1Cr
6. nC0 + nC1 + ......... nCn = 2n
7. nC0 + nC2 + nC4 + ...... = nC1 + nC3 + nC5 + ....... = 2(n - 1)
8. nCr = `"" (n/r) ^(n - 1)C_(r- 1) = (n/r)((n - 1)/(r - 1)) ^(n - 2)C_(r - 2) = ....`
9. nCr 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.
- Properties of Combinations:
- Introduction of Probability
- Random experiment
- Outcome
- Equally likely outcomes
- Sample space
- Event
- Event
- Types of Events
- Simple or elementary event
- Occurrence and non-occurrence of event
- Sure Event
- Impossible Event
- Complimentary Event
- Types of Events
- Algebra of Events
- Union of two events
- Exhaustive Events
- Intersection of two events
- Mutually Exclusive Events
- Elementary Properties of Probability
- Addition Theorem of Probability
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
- Linear Inequality
- Solution of Linear Inequality
Representation of solution of linear inequality in one variable on the number line
- Graphical Representation of Solution of Linear Inequality in One Variable
- Graphical Solution of Linear Inequality of Two Variable
Consider linear inequalities in two variables x and y
- Solution of System of Linear Inequalities in Two Variables
- Percentage
- Profit and Loss
- Simple and Compound Interest (Entrance Exam)
- Depreciation
- Meaning of Depreciation
- Features of Depreciation
- Partnership
- Goods and Service Tax (GST)
- Shares and Dividends