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 | Angle and Its Measurement | |
1.2 | Trigonometry - 1 | |
1.3 | Trigonometry - 2 | |
1.4 | Determinants and Matrices | |
1.5 | Straight Line | |
1.6 | Circle | |
1.7 | Conic Sections | |
1.8 | Measures of Dispersion | |
1.9 | Probability | |
2.1 | Complex Numbers | |
2.2 | Sequences and Series | |
2.3 | Permutations and Combination | |
2.4 | Methods of Induction and Binomial Theorem | |
2.5 | Sets and Relations | |
2.6 | Functions | |
2.7 | Limits | |
2.8 | Continuity | |
2.9 | Differentiation | |
Total | - |
Syllabus
- Directed Angle
- Angles of Different Measurements
- Zero angle
- One rotation angle
- Straight angle
- Right angle
- Angles in Standard Position
- Angle in a Quadrant
- Quadrantal Angles
- Co-terminal angles
- Measures of Angles
- Sexagesimal system (Degree measure)
- Circular system (Radian measure)
- Theorem:The radian so defined is independent of the radius of the circle used and πc = 1800.
- Area of a Sector of a Circle
- Length of an Arc of a Circle
- Introduction of Trigonometry
- Trigonometric Functions with the Help of a Circle
- Trigonometric ratios of any angle
- Signs of Trigonometric Functions in Different Quadrants
- Range of Cosθ and Sinθ
- Trigonometric Functions of Specific Angles
- Angle of measure 0°
- Angle of measure 90° or (π/2)c
- Angle of measure 360° or (2π)c
- Angle of measure 120° or (2π/3)c
- Angle of measure 225° or (5πc/4)c
- Angle of measure –60° or - π/3
- Trigonometric Functions of Negative Angles
- Fundamental Identities
- Periodicity of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Domain and Range of Trignometric Functions and Their Graphs
- Graphs of Trigonometric Functions
- The graph of sine function
- The graph of cosine function
- The graph of tangent function
- Polar Co-ordinate System
- Trigonometric Functions of Sum and Difference of Angles
1. For any two angles A and B, cos (A -B) = cos A cos B + sin A sin B
2. For any two angles A and B, cos (A + B) = cos A cos B − sin A sin B
3. For any two angles A and B, sin (A − B) = sin A cos B − cos A sin B
4. For any two angles A and B, sin (A + B) = sin A cos B + cos A sin B
5. For any two angles A and B, tan (A + B) =` (tan A + tan B)/(1 –tan A tan B)`
6. For any two angles A and B, tan (A -B) = `(tan A -tan B)/(1 + tan A tan B)`
- Trigonometric Functions of Allied Angels
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Double Angles
- Trigonometric Functions of Triple Angle
- Factorization Formulae
- Formulae for Conversion of Sum Or Difference into Product
For any angles C and D
1. sin C + sin D = 2 sin`((C + D)/2) cos ((C-D)/2)`
2. sin C - sin D = 2 cos`((C + D)/2) sin ((C -D)/2)`
3. cos C + cos D = 2 cos`((C + D)/2) cos ((C -D)/2)`
4. cos C -cos D = -2 sin`((C + D)/2) sin ((C -D)/2)`
= `2 sin((C + D)/2) sin((D -C)/2)`
- Formulae for Conversion of Product in to Sum Or Difference
For any angles A and B
1. 2sin A cos B = sin (A + B) + sin (A -B)
2. 2cos A sin B = sin (A + B) -sin (A -B)
3. 2cos A cos B = cos (A + B) + cos (A -B)
4. 2sin A sin B = cos (A -B) -cos (A + B)
- Formulae for Conversion of Sum Or Difference into Product
- Definition and Expansion of Determinants
- Value of a Determinant
- Determinant of order 3
- Expansion of Determinant
- Minors and Cofactors of Elements 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
- Introduction to Matrices
- Matrices
- Determinants
- Cramer’s Rule
- Application in Economics
- Types of Matrices
- Row Matrix
- Column Matrix
- Zero or Null matrix
- Square Matrix
- Diagonal Matrix
- Scalar Matrix
- Unit or Identity Matrix
- Upper Triangular Matrix
- Lower Triangular Matrix
- Triangular Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Determinant of a Matrix
- Singular Matrix
- Transpose of a Matrix
- Algebra of Matrices
- Transpose of a Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Equality of Two matrices
- Addition of Two Matrices
- Scalar Multiplication of a Matrix
- Multiplication of Two Matrices
- Matrices
- Properties of Transpose of a Matrix
(A')' = A, (KA)' = KA', (AB)' = B'A'.
- Properties of Transpose of a Matrix
- Locus of a Points in a Co-ordinate Plane
- Locus
- Equation of Locus
- Shift of Origin
- Straight Lines
- Inclination of a line
- Slope of a line
- Perpendicular Lines
- Angle between intersecting lines
- Different Forms of an equation of a straight line
- General form to other forms
- Equations of Line in Different Forms
- Point-slope Form
- Slope-Intercept form
- Two-points Form
- Double-Intercept form
- Normal Form
- General Form of Equation of a Line
- The distance of the Origin from a Line
- The distance of the point (x1,y1) from a line
- The distance between two parallel lines
- Different Forms of Equation of a Circle
- Standard form
- Centre-radius form
- Diameter Form
- General Equation of a Circle
The general equation of a circle is of the form x2 + y2 + 2gx + 2fy + c = 0, if g2 + f2 − e > 0.
- Parametric Form of a Circle
- Tangent
- The equation of tangent to a standard circle x2 + y2 = r2 at point P(x1, y1) on it.
- Circle
- Condition of tangency
only for line y = mx + c to the circle x2 + y2 = a2
- Condition of tangency
- Tangents from a Point to the Circle
- Double Cone
- Conic Sections
- Geometric description of conic section
- Degenerate Forms
- Identifying the conics from the general equation of the conic
- Parabola
- Standard equation of the parabola
- Tracing of the parabola y2 = 4 ax (a>0)
- Parametric expressions of standard parabola y2 = 4ax
- General forms of the equation of a parabola
- Tangent
- Condition of tangency
- Tangents from a point to a parabola
- Ellipse
- Standard equation of the ellipse
- Special cases of an ellipse
- Tangent to an ellipse
- Equation of tangent to the ellipse
- Condition for tangency
- Tangents from a point to the ellipse
- Locus of point of intersection of perpendicular tangents
- Auxilary circle and director circle of the ellipse
- Hyperbola
- Standard equation of the hyperbola
- Tangent to a hyperbola
- Tangent at a point on a hyperbola
- Equation of tangent to the hyperbola
- Condition for tangency
- Tangents from a point to the hyperbola
- Locus of point of intersection of perpendicular tangents
- Auxiliary Circle, Director Circle
- Asymptote
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Measures of Dispersion
- Variance
- 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
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
- Basic Terminologies
- Random Experiment
- Outcome
- Sample space
- Favourable Outcome
- Event and Its Types
- Elementary Event
- Certain Event
- Impossible Event
- Algebra of Events
- Union of Two Events
- Exhaustive Events
- Intersection of Two Events
- Mutually Exclusive Events
- Concept of Probability
- Equally likely outcomes
- Probability of an Event
- Elementary Properties of Probability
- Addition Theorem for Two Events
- Using the definition of probability
- Using Venn diagram
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
- Bayes’ Theorem
- Partition of a sample space
- Theorem of total probability
- Odds (Ratio of Two Complementary Probabilities)
- Introduction of Complex Number
- Concept of Complex Numbers
- Imaginary number
- 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
- Fundamental Theorem of Algebra
- Solution of a Quadratic Equation in complex number system
- Argand Diagram Or Complex Plane
- Modulus of z
- Argument of z
- Argument of z in different quadrants/axes - Properties of modulus of complex numbers, Properties of arguments
- Polar & Exponential form of C.N.
- De Moivres Theorem
- Cube Root of Unity
- Properties of 1, w, w2
- Set of Points in Complex Plane
- Concept of Sequences
- Finite sequence
- Infinite sequence
- Progression
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Nth Term of Geometric Progression (G.P.)
- General Term of a Geometric Progression (G.P.)
- Sum of First N Terms of a Geometric Progression (G.P.)
- Sum of infinite terms of a G.P.
- Geometric Mean (G.M.)
- Harmonic Progression (H. P.)
- Arithmetico Geometric Series
- nth term of A.G.P.
- Sum of n terms of A.G.P.
- Properties of Summation
- Power Series
- Fundamental Principles of Counting
- Tree Diagram
- Addition Principle
- Multiplication principle
- Invariance Principle
- Factorial Notation
- Properties of the factorial notation:
For any positive integers m, n.,
1) n! = n × (n - 1)!
2) n > 1, n! = n × (n - 1) × (n - 2)!
3) n > 2, n! = n × (n - 1) × (n - 2) × (n - 3)!
4) (m + n)! is always divisible by m! as well as by n!
5) (m × n)! ≠ m! × n!
6) (m + n)! ≠ m! + n!
7) m > n, (m - n)! ≠ m! - n! but m! is divisible by n!
8) (m ÷ n)! ≠ m! ÷ n
- Properties of the factorial notation:
- 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:
- 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:
- Sets and Their Representations
1) Roster or Tabular method or List method
2) Set-Builder or Rule Method
3) Venn Diagram - 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
- Intervals
- Open Interval
- Closed Interval
- Semi-closed Interval
- Semi-open Interval
- Concept of Relations
- Ordered Pair
- Cartesian Product of two sets
- Cartesian product of a set with itself
- Definitions of relation, Domain, Co-domain, and Range of a Relation
- Binary relation on a set
- Identity Relation
- Types of relations
- Equivalence relation
- Congruence Modulo
- 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
- 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
- Concept of Limits
- Definition of Limit
- One-Sided Limit
- Left-hand Limit
- Right-hand Limit
- Existence of a limit of a function at a point x = a
- Algebra of limits:
Let f(x) and g(x) be two functions such that
`lim_(x→a) f(x) = l and lim_(x → a) g(x) = m, then`
1. `lim_(x → a) [f(x) ± g(x)] = lim_(x → a) f(x) ± lim_(x → a) g(x) = l ± m`
2. `lim_(x → a) [f(x) xx g(x)] = lim_(x→ a) f(x) xx lim_(x→ a) g(x) = l xx m`
3. `lim_(x → a) [kf(x)] = k xx lim_(x→ a) f(x) = kl, "where" ‘k’ "is a constant"`
4. `lim_(x → a) f(x)/g(x) = (lim_(x → a) f(x))/(lim_(x → a) g(x)) = l/m "where" m≠ 0`.
- Factorization Method
- Rationalization Method
- Limits of Trigonometric Functions
- Substitution 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)
- Limit at Infinity
- Limit at infinity
- Infinite Limits
- 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 Derivative and Differentiability
- Derivative by the method of the first Principle
- Derivatives of some standard functions
- Relationship between differentiability and continuity
- 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.
- Derivative of Algebraic Functions
- Derivatives of Trigonometric Functions
- Derivative of Logarithmic Functions
- Derivatives of Exponential Functions
- L' Hospital'S Theorem