1. Sets, Relations and Functions

a) Sets and their representation

a) Sets and their representation

a) Sets and their representation

a) Sets and their representation

a) Sets and their representation

b) Union, intersection

b) Union, intersection

b) Union, intersection

b) Union, intersection

b) Union, intersection

c) Complement of sets

c) Complement of sets

c) Complement of sets

c) Complement of sets

c) Complement of sets

d) Algebraic properties

e) Power set; Relation, Types of relations, equivalence relations

e) Power set; Relation, Types of relations, equivalence relations

e) Power set; Relation, Types of relations, equivalence relations

e) Power set; Relation, Types of relations, equivalence relations

e) Power set; Relation, Types of relations, equivalence relations

f) Functions; one-one, into and onto functions, composition of functions.

f) Functions; one-one, into and onto functions, composition of functions.

f) Functions; one-one, into and onto functions, composition of functions.

f) Functions; one-one, into and onto functions, composition of functions.

f) Functions; one-one, into and onto functions, composition of functions.

2. Complex Numbers and Quadratic Equations

a) Complex numbers as ordered pairs of reals

a) Complex numbers as ordered pairs of reals

b) Representation of complex numbers in the form a+ib and their representation in a plane

b) Representation of complex numbers in the form a+ib and their representation in a plane

c) Argand diagram

c) Argand diagram

d) Algebra of Complex Numbers

d) Algebra of Complex Numbers

e) Modulus and Argument (or amplitude) of a complex number

e) Modulus and Argument (or amplitude) of a complex number

f) Square root of a Complex Number

f) Square root of a Complex Number

g) Triangle Inequality

g) Triangle Inequality

h) Quadratic Equations in Real and Complex Number System and their Solutions.

h) Quadratic Equations in Real and Complex Number System and their Solutions.

i) Relation between roots and Coefficients

i) Relation between roots and Coefficients

j) Nature of Roots

j) Nature of Roots

j) Nature of Roots

j) Nature of Roots

k) Formation of Quadratic Equations with given Roots.

k) Formation of Quadratic Equations with given Roots.

k) Formation of Quadratic Equations with given Roots.

k) Formation of Quadratic Equations with given Roots.

3. Matrices and Determinants

a) Matrices

a) Matrices

a) Matrices

a) Matrices

b) Algebra of Matrices

b) Algebra of Matrices

c) Types of Matrices

c) Types of Matrices

d) Determinants and Matrices of Order Two

d) Determinants and Matrices of Order Two

e) Determinants and Matrices of Order Three

e) Determinants and Matrices of Order Three

f) Properties of Determinants

f) Properties of Determinants

g) Evaluation of Determinants

g) Evaluation of Determinants

h) Area of Triangles using Determinants

h) Area of Triangles using Determinants

h) Area of Triangles using Determinants

h) Area of Triangles using Determinants

i) Adjoint and Evaluation of Inverse of a Square Matrix using Determinants and Elementary Transformations

i) Adjoint and Evaluation of Inverse of a Square Matrix using Determinants and Elementary Transformations

i) Adjoint and Evaluation of Inverse of a Square Matrix using Determinants and Elementary Transformations

i) Adjoint and Evaluation of Inverse of a Square Matrix using Determinants and Elementary Transformations

j) Test of Consistency and Solution of Simultaneous Linear Equations in Two or Three Variables using Determinants and Matrices.

j) Test of Consistency and Solution of Simultaneous Linear Equations in Two or Three Variables using Determinants and Matrices.

4. Permutations and Combinations

a) Fundamental principle of counting

a) Fundamental principle of counting

b) Permutation as an Arrangement and Combination as selection

b) Permutation as an Arrangement and Combination as selection

c) Meaning of P (n,r) and C (n,r), simple applications.

c) Meaning of P (n,r) and C (n,r), simple applications.

d) Mathematical Induction – Principle of Mathematical Induction and its simple applications.

d) Mathematical Induction – Principle of Mathematical Induction and its simple applications.

e) Binomial theorem – Binomial theorem for a positive integral index

e) Binomial theorem – Binomial theorem for a positive integral index

f) General Term

f) General Term

g) Middle Term

g) Middle Term

h) Properties of Binomial Coefficients and Simple Applications.

h) Properties of Binomial Coefficients and Simple Applications.

i) Sequences and Series – Arithmetic and Geometric progressions

i) Sequences and Series – Arithmetic and Geometric progressions

j) Insertion of Arithmetic

j) Insertion of Arithmetic

k) geometric means between two given numbers

k) geometric means between two given numbers

l) Relation between A.M. and G.M.

l) Relation between A.M. and G.M.

m) Sum upto n terms of Special Series: Sn, Sn2, Sn3. Arithmetic - Geometric progression.

m) Sum upto n terms of Special Series: Sn, Sn2, Sn3. Arithmetic - Geometric progression.

5. Limit, Continuity and Differentiaility

a) Real - valued functions

a) Real - valued functions

b) Algebra of functions

b) Algebra of functions

c) Polynomials, Rational Functions

c-1) Trigonometric, Logarithmic Functions

c-2) Exponential functions

c-3) Inverse Functions

6. Graphs

a) Simple Functions Limits

a) Simple Functions Limits

b) Continuity and Differentiability

b) Continuity and Differentiability

c) Differentiation of the sum

c) Differentiation of the sum

d) Difference, product and quotient of two functions

d) Difference, product and quotient of two functions

e) Differentiation of Trigonometric Functions

e) Differentiation of Trigonometric Functions

e-1) Inverse Trigonometric Functions

e-2) Logarithmic Functions

e-2) Logarithmic Functions

e-3) Exponential

e-3) Exponential

e-4) Composite Functions

e-4) Composite Functions

e-5) Immplicit functions

e-5) Immplicit functions

e-6) Derivatives of Order up to Two.

e-6) Derivatives of Order up to Two.

7. Rolle’s and Lagrange’s Mean Value Theorems

7.0. Introduction

7.0. Introduction

a) Applications of derivatives: Rate of change of quantities

a) Applications of derivatives: Rate of change of quantities

b) Monotonic Functions

b) Monotonic Functions

c) Increasing and Decreasing Functions

c) Increasing and Decreasing Functions

d) Maxima and minima of functions of one variable

d) Maxima and minima of functions of one variable

e) Tangents and Normals.

e) Tangents and Normals.

8. Integral Calculus

a) Integral as an anti

a) Integral as an anti

b) Derivative

b) Derivative

c) Fundamental integrals involving algebraic

c) Fundamental integrals involving algebraic

d) Trigonometric

d) Trigonometric

e) Exponential and logarithmic functions

e) Exponential and logarithmic functions

f) Integration by Substitution

f) Integration by Substitution

g) Integration used by Parts

g) Integration used by Parts

h) Integration used by Partial Fractions

h) Integration used by Partial Fractions

i) Integration using Trigonometric Identities

i) Integration using Trigonometric Identities

j) Evaluation of simple integrals

j) Evaluation of simple integrals

k) Integral as limit of a sum

k) Integral as limit of a sum

l) Fundamental Theorem of Calculus

l) Fundamental Theorem of Calculus

m) Properties of Definite Integrals

m) Properties of Definite Integrals

n) Evaluation of Definite Integrals

n) Evaluation of Definite Integrals

o) Determining Areas of the Regions bounded by Simple Curves in Standard Form

o) Determining Areas of the Regions bounded by Simple Curves in Standard Form

9. Differential Equations – Ordinary differential equations, their order and degree.

9.0. Introduction

9.0. Introduction

9.0. Introduction

9.0. Introduction

a) Formation of differential equations

a) Formation of differential equations

b) Solution of differential equations by the method of separation of variables

b) Solution of differential equations by the method of separation of variables

b) Solution of differential equations by the method of separation of variables

b) Solution of differential equations by the method of separation of variables

c) Solution of Homogeneous and Linear Differential Equations

c) Solution of Homogeneous and Linear Differential Equations

c) Solution of Homogeneous and Linear Differential Equations

c) Solution of Homogeneous and Linear Differential Equations

10. Coordinate Geometry

a) Cartesian system of rectangular co-ordinates in a plane

a) Cartesian system of rectangular co-ordinates in a plane

b) Distance Formula

b) Distance Formula

c) Section Formula

c) Section Formula

d) Locus and its Equation

d) Locus and its Equation

e) Translation of Axes

e) Translation of Axes

f) Slope of a line

f) Slope of a line

g) Parallel and Perpendicular lines

g) Parallel and Perpendicular lines

h) Intercepts of a line on the coordinate axes.

h) Intercepts of a line on the coordinate axes.

11. Straight Lines

a) Various forms of equations of a Line

a) Various forms of equations of a Line

b) Intersection of Lines

b) Intersection of Lines

c) Angle between Two Lines

c) Angle between Two Lines

c) Angle between Two Lines

c) Angle between Two Lines

d) Conditions for Concurrence of Three Lines

d) Conditions for Concurrence of Three Lines

e) Distance of a Point from a Line

e) Distance of a Point from a Line

f) Equations of Internal and External bisectors of Angles between Two Lines

f) Equations of Internal and External bisectors of Angles between Two Lines

f) Equations of Internal and External bisectors of Angles between Two Lines

f) Equations of Internal and External bisectors of Angles between Two Lines

f) Equations of Internal and External bisectors of Angles between Two Lines

f) Equations of Internal and External bisectors of Angles between Two Lines

g) Coordinates of Centroid

g) Coordinates of Centroid

h) Orthocentre and Circumcentre of a Triangle

h) Orthocentre and Circumcentre of a Triangle

i) Equation of Family of Lines passing through the Point of intersection of Two Lines

i) Equation of Family of Lines passing through the Point of intersection of Two Lines

12. Circles, Conic Sections

a) Standard form of Equation of a Circle

a) Standard form of Equation of a Circle

b) General form of the Equation of a Circle, its Radius and Center Equation of a Circle when the end points of a Diameter are given

b) General form of the Equation of a Circle, its Radius and Center Equation of a Circle when the end points of a Diameter are given

c) Points of intersection of a Line and a Circle with the Center at the Origin and Condition for a Line to be Tangent to a Circle

c) Points of intersection of a Line and a Circle with the Center at the Origin and Condition for a Line to be Tangent to a Circle

d) Equation of the Tangent

d) Equation of the Tangent

e) Sections of Cones

e) Sections of Cones

f) Equations of Conic Sections of parabola

f) Equations of Conic Sections of parabola

f-1) Ellipse

f-1) Ellipse

f-2) hyperbola

f-2) hyperbola

f-3) Condition for y = mx + c to be a Tangent and Point (s) of Tang-ency

f-3) Condition for y = mx + c to be a Tangent and Point (s) of Tang-ency

13. Three Dimensional Geometry

a) Coordinates of a Point in Space

a) Coordinates of a Point in Space

a) Coordinates of a Point in Space

a) Coordinates of a Point in Space

b) Distance between Two Points

b) Distance between Two Points

c) Section Formula

c) Section Formula

d) Direction Ratios and Direction Cosines

d) Direction Ratios and Direction Cosines

e) Angle between Two Intersecting Lines

e) Angle between Two Intersecting Lines

f) Skew lines

f) Skew lines

g) The Shortest distance between Two Lines and its Equation.

g) The Shortest distance between Two Lines and its Equation.

h) Equations of a Line and a Plane in Different Forms

h) Equations of a Line and a Plane in Different Forms

i) Intersection of a Line and a Plane

i) Intersection of a Line and a Plane

j) Coplanar Lines

j) Coplanar Lines

14. Vector Algebra

a) Vectors and Scalars

a) Vectors and Scalars

b) Addition of Vectors

b) Addition of Vectors

b) Addition of Vectors

b) Addition of Vectors

c) Components of a Vector in Two Dimensions and Three Dimensional Space

c) Components of a Vector in Two Dimensions and Three Dimensional Space

d) Scalar and Vector Products

d) Scalar and Vector Products

d) Scalar and Vector Products

d) Scalar and Vector Products

e) Scalar and Vector Triple Product

e) Scalar and Vector Triple Product

e) Scalar and Vector Triple Product

e) Scalar and Vector Triple Product

15. Statistics and Probability

a) Measures of Dispersion - Calculation of mean, median, mode of Grouped and Ungrouped Data.

a) Measures of Dispersion - Calculation of mean, median, mode of Grouped and Ungrouped Data.

b) Calculation of Standard Deviation

b) Calculation of Standard Deviation

c) Variance and Mean Deviation for Grouped and Ungrouped Data

c) Variance and Mean Deviation for Grouped and Ungrouped Data

d) Probability - Probability of an event

d) Probability - Probability of an event

e) Addition and Multiplication Theorems of Probability

e) Addition and Multiplication Theorems of Probability

f) Baye’s theorem

f) Baye’s theorem

g) Probability Distribution of a Random Variate

g) Probability Distribution of a Random Variate

h) Bernoulli trials and Binomial distribution

h) Bernoulli trials and Binomial distribution

16. Trigonometry

a) Trigonometrical Identities and Equations

a) Trigonometrical Identities and Equations

b) Trigonometrical Functions

b) Trigonometrical Functions

c) Inverse Trigonometrical Functions and their Properties

c) Inverse Trigonometrical Functions and their Properties

d) Heights and Distances

d) Heights and Distances

d) Heights and Distances

d) Heights and Distances

17. Mathematical Reasoning

a) Statements

a) Statements

b) Logical Operations and, or, implies, implied by, if and only if

b) Logical Operations and, or, implies, implied by, if and only if

c) Understanding of Tautology, contradiction, converse and contrapositive

c) Understanding of Tautology, contradiction, converse and contrapositive

c) Understanding of Tautology, contradiction, converse and contrapositive

c) Understanding of Tautology, contradiction, converse and contrapositive