# 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