- Sets and their representation
- Types of sets: empty sets, finite and infinite sets, power set, universal set
- Cardinality of sets
- Subset and superset
- Venn diagram
- Operation on sets: union of sets
- Operation on sets: intersection and difference of sets
- Complement of sets
- Practical problems on union and intersection of two sets

- Cartesian product of sets
- Relations
- Function: domain and range
- identity function, constant function and modulus function
- Graphs of polynomial function
- Algebra of real functionsn

- Positive and negative angles
- Measuring angles in radians and in degrees and conversion of one into other
- Definition of trigonometric functions with the help of unit circle
- Truth of the sin
^{2}x+cos^{2}x=1, for all x - Signs of trigonometric functions
- Domain and range of trignometric functions and their graphs
- Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application
- Deducing identities like the following:
- Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x
- General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

- Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers
- The principle of mathematical induction
- Simple Application of principle of mathematical induction

- Need for complex numbers, especially √1, to be motivated by inability to solve some of the quardratic equations
- Algebraic properties of complex numbers
- Modulus and conjugate of complex numbers
- Argand plane and polar representation of complex numbers
- Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system
- Euler's formula and De Moivre's theorem
- Square root of a complex number.

- Linear inequalities
- Algebraic solutions of linear inequalities in one variable and their representation on the number line
- Graphical solution of linear inequalities in two variables
- Graphical solution of system of linear inequalities in two variables.

- Fundamental principle of counting
- Permutations
- Combinations

- History, statement and proof of the binomial theorem for positive integral indices.
- Pascal's triangle, General and middle term in binomial expansion, simple applications.

- Sequence and Series
- Arithmetic Progression (A.P.).
- Geometric progression
- Relationship between Aithmetic mean and geometric mean
- Formula for the following special sum:

- Brief recall of two dimensional geometry from earlier classes
- Shifting of origin
- Slope of a line and angle between two lines.
- Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line
- AEquation of family of lines passing through the point of intersection of two lines
- Distance of a point from a line.

- Sections of cone
- Circle
- Parabola
- Ellipse
- Hyperbola
- a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section
- Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

- Coordinates of point in space
- Distance between two points
- Section formula

- Derivative introduced as rate of change both as that of distance function and geometrically.
- Intutive idea of limit
- Limits of polynomials and rational functions, trignometric, exponential and logarithmic functions
- Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions
- The derivative of polynomial and trignometric functions

- Introduction
- Statements
- New statements from old
- Special word/phrase
- Implications
- validating statements

- Measures of dispersion and range
- Mean deviation
- mean deviation for ungrouped data
- mean deviation for discrete frequency distribution
- mean deviation for continuous frequency distribution
- Variance and standard deviation
- Shortcut method for finding variance and standard deviation
- Analysis of frequency distribution

- Random experiments; outcomes, sample spaces
- Event and types of event
- Algebra of event
- Axiomatic approach to probability