Maharashtra State BoardHSC Science (General) 11th
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Mathematics and Statistics 11th HSC Science (General) Maharashtra State Board Topics and Syllabus

Academic year:

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 
  • 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 
1.5 Straight Line
1.6 Circle
1.7 Conic Sections
  • Double Cone 
  • Conic Sections 
    • 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


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
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