Mathematics - XI Syllabus

UNIT 1: SETS, REAL NUMBER SYSTEM AND LOGIC (10 TEACHING HOURS)

Sets:

  • Sets and set operations
  • Theorems based on set operations

Real Number System:

  • Real numbers
  • Field axioms
  • Order axioms
  • Interval
  • Absolute value
  • Geometrical representation of the real numbers

Logic:

  • Introduction
  • Statements
  • Logical connectives
  • Truth tables
  • Basic laws of logic

UNIT 2: RELATIONS, FUNCTIONS AND GRAPHS (12 TEACHING HOURS)

Relations:

  • Ordered pair
  • Cartesian product
  • Geometrical representation of Cartesian product relation
  • Domain and range of a relation
  • Inverse of a relation

Functions:

  • Definition
  • Domain and range of a function
  • Functions defined as mappings
  • Inverse function
  • Composite function
  • Functions of special type (Identity, Constant, Absolute value, Greatest integer)
  • Algebraic (Linear, quadratic and cubic)
  • Trigonometric
  • Exponential logarithmic function and their graphs.

UNIT 3: CURVE SKETCHING (10 TEACHING HOURS)

  • Off and even functions
  • Periodicity of a function
  • Symmetry (about x – axis, y – axis and origin) of elementary functions
  • Monotonocity of a function
  • Sketching graphs of polynomial functions (\frac{1}{x},\frac{x^2-a^2}{x-a},\frac{1}{x+a},x^2,x^3)
  • Trigonometric, exponential, logarithmic functions (simple cases only)

UNIT 4: TRIGONOMETRY (10 TEACHING HOURS)

  • Inverse circular functions
  • Trigonometric equations and general values
  • Properties of a triangle (sine law, cosine law, tangent law, Projection laws, Half angle laws)
  • The areas of a triangle
  • Solution of a triangle (simple cases)

UNIT 5: SEQUENCE AND SERIES AND MATHEMATICAL INDUCTION (12 TEACHING HOURS)

Sequence and Series:

  • Sequence and series
  • Types of sequences and series (Arithmetic, Geometric, Harmonic)
  • Properties of Arithmetic, Geometric, and Harmonic sequences, A.M., G.M. and H.M.
  • Relation among A.M., G.M. and H.M.
  • Sum of infinite geometric series

Mathematical induction:

  • Sum of finite numbers
  • Sum of the squares of first n – natural numbers
  • Sum of cubes of first n – natural numbers
  • Intuition and induction
  • Principle of mathematical induction

UNIT 6: MATRICES AND DETERMINANTS (8 TEACHING HOURS)

  • Matrices and operation on matrices (Review)
  • Transpose of a matrix and its properties
  • Minors and Cofactors
  • Adjoint
  • Inverse matrix
  • Determinant of a square matrix
  • Properties of determinants (Without proof) upto 3 x 3

UNIT 7: SYSTEM OF LINEAR EQUATIONS (8 TEACHING HOURS)

  • Consistency of system of linear equations
  • Solution of a system of linear equations by Cramer’s rule
  • Matrix method (row – equivalent and inverse) upto three variables

UNIT 8: COMPLEX NUMBER (12 TEACHING HOURS)

  • Definition of a complex number
  • Imaginary unit
  • Algebra of complex numbers
  • Geometric representation of a complex number
  • Conjugate and absolute value (Modulus) of a complex number
  • Conjugate and absolute value (Modulus) of a complex numbers and their properties
  • Square root of a complex number
  • Polar form of a complex number
  • Product and Quotient of complex numbers
  • De Moivre’s theorem and its application in finding the roots of a complex number
  • Properties of cube roots of unity

UNIT 9: POLYNOMIAL EQUATIONS (8 TEACHING HOURS)

  • Polynomial function and polynomial equations
  • Fundamental theorem of algebra (without proof)
  • Quadratic equation
  • Nature and roots of a quadratic equation
  • Relation between roots and coefficients
  • Formation of a quadratic equation
  • Symmetric roots
  • One or both roots common

UNIT 10: CO – ORDINATE GEOMETRY (12 TEACHING HOURS)

Straight line:

  • Review of various forms of equation of straight lines
  • Angle between two straight lines
  • Condition for parallelogram and perpendicularity
  • Length of perpendicular from a given point to a given line
  • Bisectors of the angles between two straight lines

Pair of lines:

  • General equation of second degree in x and y
  • Condition for representing a pair of lines
  • Homogeneous second degree equation in x and y
  • Angle between pair of lines
  • Bisectors of the angles between pair of lines

UNIT 11: CIRCLE (10 TEACHING HOURS)

  • Equation of a circle in various forms (Centre at origin, centre at any point, general equation of a circle, circle with a given diameter)
  • Condition of Tangency of a line at a point to the circle
  • Tangent and normal to a circle

UNIT 12: THE DERIVATIVES (8 TEACHING HOURS)

  • Limits of a function
  • Indeterminate forms
  • Algebraic properties of limits (without proof)
  • Theorem on limits of algebraic, Trigonometric, Exponential and logarithmic functions (\lim_{x \to a} \frac{x^n-a^n}{x-a},\lim_{x \to 0} \frac{sinx}{x},\lim_{x \to 0}\frac{e^x-1}{x},\lim_{x \to 0}\frac{log(1+x)}{x})
  • Continuity of a function
  • Types of discontinuity
  • Graph of discontinuous function

UNIT 13: APPLICATIONS OF DERIVATIVES (12 TEACHING HOURS)

  • Derivative of a function
  • Derivatives of algebraic, trigonometric, exponential and logarithmic function by definition (simple forms)
  • Rules of differentiation
  • Derivatives of parametric and implicit functions
  • Higher order derivatives

UNIT 14: ANTIDERIVATIVES AND ITS APPLICATIONS (10 TEACHING HOURS)

  • Antiderivative
  • Integration using basic integrals
  • Integration by substitution and by parts method
  • The definite integral
  • The definite integral as an area under the given curve
  • Area between two curves