# Mathematics and Statistics 11th HSC Arts 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 2022-2023 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 2022-2023. 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 Angle and Its Measurement
1.2 Trigonometry - 1
1.3 Trigonometry - 2
1.4 Determinants and Matrices
• 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
• 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
• Scalar Multiplication of a Matrix
• Multiplication of Two Matrices
• Matrices
1.5 Straight Line
1.6 Circle
1.7 Conic Sections
• 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
1.8 Measures of Dispersion
1.9 Probability
2.1 Complex Numbers
2.2 Sequences and Series
2.3 Permutations and Combination
• Fundamental Principles of Counting
• Tree Diagram
• 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
• 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.
• 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.

2.4 Methods of Induction and Binomial Theorem
2.5 Sets and Relations
• 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:
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
• Intervals
1. Open Interval
2. Closed Interval
3. Semi-closed Interval
4. 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
2.6 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
• 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
2.7 Limits
• 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
2.8 Continuity
• 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
2.9 Differentiation