# 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
• 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)
• 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