## Topics with syllabus and resources

- Measurement of Angles
- Revision of Directed Angle
+ve and –ve angles

- Theorem - Length of an Arc of a Circle
s = r. θ, θ is in radians (without proof)

- Theorem - Area of the Sector of a Circle
Area of the sector of a circle A = ½ r2 . θ, θ is in radians (without proof)

- Revision of Directed Angle

- Need & concept
- Revision of directed angle (+ve and –ve angles), zero angle, straight angle, angles in standard position, coterminal angles, angles in quadrant & quadrantal angles.
- Sexagesimal system, circular system, relation between degree measure and radian measure.
- Theorem: Radian is a constant angle. Length of an arc of a circle (s = r. θ, θ is in radians) (without proof). Area of the sector of a circle A = ½ r2 . θ, θ is in radians (without proof).

- Trigonometric Functions of Particular Angles
(0°, 30° , 45° , 60° , 90° , 180° , 270° , 360°)

- Introduction of Trigonometric Functions
- Trigonometric Functions with the Help of Unit Circle

- Signs of Trigonometric Functions
- Negative Function Or Trigonometric Functions of Negative Angles
- Domain and Range of Trigonometric Functions
- Domain and Range of Trignometric Functions and Their Graphs

- Periodicity of Functions
- Trigonometric Functions
- Graphs of Trigonometric Functions

- Need & concept
- Trigonometric functions with the help of standard unit circle, signs of trigonometric functions in different quadrants, trigonometric functions of particular angles (00 , 300 , 450 , 600 , 900 , 1800 , 2700 , 3600 )
- domain and range of trigonometric functions, periodicity of functions
- fundamental identities
- graphs of trigonometric functions, Graph of y = a sin bx, y = a cos bx, trigonometric functions of negative angles.

- Trigonometric Functions of Compound Angles
- Trigonometric Functions of Multiple Angles
upto double and triple angles only

- Trigonometric Functions of Multiple Angles

- Introduction
- trigonometric functions of sum and difference, trigonometric functions of multiple angles (upto double and triple angles only), trigonometric functions of half angles.

- Introduction
- Formulae for conversion of sum or difference into products, formulae for conversion of product into sum or difference
- trigonometric functions of angles of a triangle

- Locus
- Shift of the Origin
Locus

- Shift of the Origin

- Introduction
- Definition and equation of locus, points of locus, shift of the origin.

- Slope of a Line
- Slope of a Line Or Gradient of a Line.
- Parallelism of Line
- Perpendicularity of Line in Term of Slope
- Collinearity of Points
- Slope of a line when coordinates of any two points on the line are given
- Conditions for parallelism and perpendicularity of lines in terms of their slopes
- Angle between two lines
- Collinearity of three points

- Various Forms of the Equation of a Line
- Straight Lines
- Inclination of a Line
straight lines

- Theorems
- Theorem 1 : A general linear equation Ax + By+ C =0, provided A and B are not both zero, simultaneously, always represents straigh tline.
- Theorem 2 : Every straight line has an equation of the form Ax +By + C = 0, where A, B and C are constants (without proof)

- parallel lines
straight lines

- perpendicular lines
straight lines

- Identical Lines
identical lines

- Inclination of a Line
- Distance of a Point from a Line
- Introduction of Distance of a Point from a Line
- Distance between two parallel lines

- Other Forms of Equations of a Line

- Revision.
- Inclination of a line, slope of a line, equation of lines parallel to coordinate axes, intercepts of a line, revision of different forms of equations of a line, slope-point form, slope-intercept form, two point form, double intercept form, other forms of equations of a line, parametric form, normal form, general form,
- Theorem 1 : A general linear equation Ax + By+ C =0, provided A and B are not both zero, simultaneously, always represents straigh tline.
- Theorem 2 : Every straight line has an equation of the form Ax +By + C = 0, where A, B and C are constants (without proof),
- Reduction of general equation of a line into normal form, intersection of two lines, parallel lines, perpendicular lines, identical lines,
- condition for concurrency of three lines, angle between lines, distance of a point from a line,
- distance between two parallel lines,
- equations of bisectors of angle between two lines,
- family of lines,
- equation of a straight line parallel to a given line,
- equation of a straight line perpendicular to a given line,
- equation of family of lines through the intersection of two lines

- Circle and Conics Revision
- Circle
- Ellipse
- Hyperbola
- Conics
- Focus-directrix Property
focus-directrix property of parabola, ellipse, hyperbola, parabola

- Focus-directrix Property

- Revision
- standard equation, centre-radius form, diameter form, general equation, parametric equations of standard equation,
- Conics Napees – Intersection of Napees of a cone and Plane, introduction,
- focus-directrix property of parabola, ellipse, hyperbola, parabola,
- standard equation (different forms of parabola), parametric equations, ellipse, standard equation, hyperbola, standard equation, parametric equations.
- Application of conic section

- Vectors
- Moment of a Force
vector

- Moment of a Force
- Magnitude and Direction of a Vector
- Like and Unlike Vectors
- Scalar Multiple of a Vector
- Types of Vectors
Zero Vector, Unit Vector, Coinitial Vectors, Collinear Vectors, Equal Vectors, Negative of a Vector (Free Vector)

- Three - Dimensional Geometry
- Coordinate Axes and Coordinate planes
Coordinate Axes and Coordinate Planes in Three Dimensions

- Distance Between Two Points
- Distance Between Two Points in 3-D Space

- Coordinate Axes and Coordinate planes
- Addition of Vectors
- Coplaner Vector
- Basic Concepts of Vector Algebra
- Position Vector
- Direction Cosines and Direction Ratios of a Vector

- Definition
- magnitude of a vector, free and localized vectors, types of vectors, zero vector, unit vector, equality at vectors, negative of a vector, collinear vectors, coplanar vectors, coinitial vectors, like and unlike vectors, scalar multiple of a vector
- triangle law, parallelogram law, polygon law
- properties of addition of vectors
- three dimensional co-ordinate geometry, coordinate axes & coordinate planes in space, co-ordinates of a point in space, distance between two points in a space, unit vectors along axes, position vector of a point in a space
- product of vectors, scalar product, definition, properties, vector product, definition, properties
- simple applications, work done by force, resolved part of a force, moment of a force.

- Linear Inequations
- Transposition
Linear Inequations

- Transposition
- Graphical Solution of Linear Inequalities in Two Variables
Linear Inequalities - Graphical Representation of Linear Inequalities in Two Variables

- Solution of System of Linear Inequalities in Two Variables

Linear inequations in one variable

- solution of linear inequation in one variable & graphical solution
- solutions of system of linear inequations in one variable

Linear inequations in two variables

- solution of linear inequations in two variables & graphical solution,
- solutions of system of linear inequations in two variables,
- Replacement of a set or domain of a set, Transposition

- Determinants
- Properties of Determinants
properties of determinants

- Condition of Consistency
determinant

- Properties of Determinants
- Minors and Co-factors
- Area of a Triangle

- Revision
- determinant of order three, definition, expansion
- properties of determinants
- minors & co-factors
- applications of determinants
- condition of consistency
- area of a triangle
- Cramer’s rule for system of equations in three variables.

- Introduction of Matrices
- Matrices
- Matrices Notation
Matrices Notation

- Properties of Transpose of a Matrix
(A')' = A, (KA)' = KA', (AB)' = B'A'.

- Matrices Notation
- Types of Matrices
Column matrix, Row matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity matrix, Zero matrix

- Types of Matrices - Determinant of a Square Matrix
- Types of Matrices - Triangular Matrices
- Types of Matrices - Singular and Non-singular Matrices
- Types of Matrices - Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Order of a Matrix
- Operations on Matrices - Equality
- Operations on Matrices - Subtraction
- Operations on Matrices

- Introduction, concepts, notations, order
- types of matrices – zero matrix, row matrix, column matrix, square matrix, determinant of a square matrix, diagonal matrix, scalar matrix, identity matrix, triangular matrices, singular & non-singular matrices, transpose of a matrix, symmetric & skew symmetric matrices,
- operations on matrices – equality, addition, subtraction, multiplication of a matrix by a scalar,
- simple properties multiplication of matrices – definition
- properties of matrix multiplication
- properties of transpose of a matrix - (A')' = A, (KA)' = KA', (AB)' = B'A'.

- Sets and Their Representations
- The Empty Set
- Empty Set
- null set or the void set

- Finite and Infinite Sets
- Equal Sets
- Subsets
- Subsets of a Set of Real Numbers Especially Intervals - With Notation
- Singleton Set
- Super Set
- Subsets of set of real numbers
- Intervals as subsets of R

- Proper and Improper Subset
- Sets
- Power Set
- Universal Set
- Venn Diagrams
- Operations on Sets
- Union Set
- Some Properties of the Operation of Union

- Intersection of Sets
- Some Properties of Operation of Intersection

- Difference of Sets
- “ A minus B” Or "A – B"

- Union Set
- Operation on Set - Disjoint Sets
- Complement of a Set
- Properties of Complement Sets

- Cartesian Product of Sets
- Number of Elements in the Cartesian Product of Two Finite Sets
- Cartesian Product of set of the Reals with Itself

Revision, subset, proper improper subset and their properties, union, intersection, disjoint sets, empty set, finite & infinite sets, equal sets, equivalent sets, universal set, Venn diagrams, complement of a set, difference of two sets, power set, ordered pairs, equality of ordered pairs, Cartesian product of two sets, No. of elements in the Cartesian product of two finite sets, Cartesian product of the reals with itself

- Relation
- Definition of Relation
- Domain
- Co-domain and Range of a Relation

- Relations
- Binary Equivalence Relation
Type of Relation

- Binary Equivalence Relation
- One to One Relation
Type of Relation

- Many to One Relation
Type of Relation

definition of relation, pictorial diagrams, domain, codomain and range of a relation, types of relations, one-one, many-one, binary equivalence relation

- Functions
- Exponential Function
Domain and range of this function

- Logarithmic Functions
Concept of Logarithmic Functions

Domain and range of this function

- Exponential Function
- Relations
- Pictorial Representation of a Function
Domain, Co-domain and Range of a function

- Pictorial Representation of a Function
- Some Functions and Their Graphs
- Identity function - Domain and range of this function
- Constant function - Domain and range of this function
- Polynomial function -Domain and range of this function
- Rational functions - Domain and range of this function
- The Modulus function - Domain and range of this function
- Signum function - Domain and range of this function
- Greatest integer function

- Types of Functions
- one-one (or injective)
- many-one
- onto (or surjective)
- one-one and onto (or bijective)

- Composition of Functions and Invertible Function
- Concept of Binary Operations
Definition, Commutative Binary Operations, Associative Binary Operations , Identity Binary Operation, Invertible Binary Operation

- Scalar Multiplication

function as a special kind of relation, pictorial representation of a function, domain, codomain and range of a function, equal functions

types of functions - constant function, identity function, one-one function, onto function, into function, even & odd functions, polynomial function, rational function, modulus function signum & greatest integer, exponential function, logarithmic function, functions with their graphs, sum, difference, product, quotient of functions, scalar multiplication, composite function, inverse function, binary operations, real valued function of the real variable, domain and range of these functions

- Logarithms
- Concept of Logarithms
Introduction, Definition, Properties of Logarithms

- change of base
logarithms

- Characteristics and Mantissa
logarithms

- Method of Finding Mantissa
logarithms

- Concept of Logarithms
- Method of Finding Characteristics

- Introduction, definition, properties
- laws of logarithms, change of base,
- characteristics & mantissa – method of finding characteristics, method of finding mantissa, method of finding antilogarithm

- Complex Numbers
- Defination of Complex Number - Real part and imaginary part
- Need for Complex Numbers

- Definition of Argument
- Complex Numbers
- Need for Complex Numbers
Need for complex numbers, especially √−1, to be motivated by inability to solve some of the quardratic equations

- Algebra of Complex Numbers - Equality
Equality of Complex number

- Need for Complex Numbers
- Algebra of Complex Numbers
- Addition of two complex number
- Difference of two complex numbers - Difference Or Substraction
- Multiplication of two complex numbers - The closure law, The commutative law, The associative law, The existence of multiplicative identity, The existence of multiplicative inverse, The distributive law
- Division of two complex numbers
- Power of i
- The square roots of a negative real number
- Identities

- The Modulus and the Conjugate of a Complex Number
- Modulus of Complex Number
- Conjugate of Complex Number

- Argand Plane and Polar Representation
- Representation of Complex Number - Argand Plane Representation
- Representation of Complex Number - Polar Representation of Complex Numbers

- Quadratic Equations

- Introduction,
- need for complex numbers,
- definitions –(real parts, imaginary parts, complex conjugates, modulus, argument),
- algebra of complex numbers – equality, addition, subtraction, multiplication, division, powers and square root of a complex number, higher powers of i, DeMoivre’s formula – (without proof), square root of a complex number,
- properties of complex numbers – properties of addition of complex numbers, 1) Closure Property 2) Commulative Law 3) Associative law 4) Existence of additive identity 5) Existence of additive inverse.
- Properties of product of complex numbers – Existance of multiplicative identity –
- Existance of multiplicative inverse, properties of conjugate & modulus of complex numbers, Argand Diagram
- representation of a complex number as a point in plane, geometrical meaning of modulus and argument, polar representation of complex numbers, Fundamental theorem of algebra, cube roots of unity
- solution of quadratic equations in the complex number system, cube roots of unity

- Sequence and Series
- Containing Finitely Many Terms and Sum to Infinite Terms
(n terms from the end of G.P.)

- Containing Finitely Many Terms and Sum to Infinite Terms
- Arithmetic Progression (A.P.)
- Nth Term of Arithematic Progression
- Sum of Term in Arithematic Progression S_n =n/2 {2a+(n-1)d}`
- Arithmetic mean - Sequence and Series

- Geometric Progression (G. P.)
- Nth Term of Geometric Progression (G.P.) - T_n=ar^(n-1)
- General Term of a Geometric Progression (G.P.)
- Sum of First N Terms of a Geometric Progression (G.P.) - S_n=a(r^n-1)/(r-1)
- Infinite Geometric Progression (G.P.) and Its Sum - S∞=a1−r;|r|<1S∞=a1-r;|r|<1
- Geometric Mean (G.M.)

- Relationship Between A.M. and G.M.
- Relation Between Arithematic Mean (A.M.) and Geometric Mean (G.M.)

- Harmonic Mean (H.M.)
- Sum to N Terms of Special Series

- Revision - sequence, A.P.,
- Sum of first n terms of A.P.,
- properties of A.P.,
- geometric progression – introduction, general term, sum of the first ‘n’ terms, (n terms from the end of G.P.) containing finitely many terms & sum to infinite terms,
- properties of G.P., H.P. as a special type of A.P,
- Means – arithmetic mean, geometric mean, harmonic mean,
- relation between A.M., G.M., H.M.,
- Arithmetico-Geometric sequence, special series, sum of cube of first n natural numbers, sum of cube of first n odd natural nos., exponential & logarithmic series.

- Introduction of Permutations and Combinations
- Fundamental Principle of Counting
- Concept of Permutations
- Permutations and Combinations
- Permutations (Objects Are Distinct)
when all objects are distinct

- Permutations (Objects Are Not Distinct)
when all r objects are not distinct

- Permutations (Objects Are Distinct)
- Properties of Combination

- Introduction,
- fundamental principle of counting, factorial notation, permutations, when all r objects are distinct, when all r objects are not distinct, circular permutations, simple applications,
- combinations – definition, properties, relations between permutations and combinations, simple applications

- Principle of Mathematical Induction
- Principle of Mathematical Induction and Simple Applications.

- Binomial Theorem
- Binomial Theorem for Positive Integers

- Principle of mathematical induction,
- simple applications,
- binomial theorem – binomial theorem for positive integers, general term, particular term, properties of binomial coefficient with simple application, binomial theorem for any index (without proof), particular cases of binomial theorem,
- simple applications.

- Introduction of concept,
- meaning of x→a, 83 the limit of a function, fundamental theorem on limits,
- algebra of limits – standard limits, without proof,
- limits at infinity – concepts, simple problems.

- Introduction of Derivatives
- Derivative at a Point
- Derivative
- Physical Significance of Derivative
velocity as a rate of change of displacement

- Physical Significance of Derivative
- Derivative of Logarithmic Functions
- Derivative of Algebraic Functions
- Derivative of Exponential Function

- Definition : derivative,
- derivative at a point,
- geometrical significance of derivative, physical significance (velocity as a rate of change of displacement),
- derivatives from first principle - of trigonometric functions, logarithmic functions, algebraic functions, exponential functions,
- rules of differentiation –derivative of sum, difference, product and quotient

- Definition of integration as antiderivative,
- geometrical interpretation of indefinite integrals,
- algebra of integrals – integrals of some standard functions, rules of integration

- Concept of Range
- Measures of Dispersion - Range

- Statistics
- Mean Deviation
- Variance and Standard Deviation
- Introduction of Variance and Standard Deviation

- Measures of dispersion – range,
- quartile & quartile deviation (for grouped and ungrouped data),
- comparison of two frequency distributions with same mean,
- mean deviation about mean,
- mean deviation about median (for grouped & ungrouped data), variance, standard deviation,
- effect of change of origin and scale on variance and standard deviation,
- combined variance and standard deviation, co-efficient of variation.

- Event
- Exhaustive Events
- Types of Event - Exhaustive Events

- Mutually Exclusive Events
- Types of Event - Mutually Exclusive Events

- Exhaustive Events
- Probability
- Axiomatic Approach to Probability
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
- Baye'S Theorem
- Partition of a sample space
- Theorem of total probability

- Revision,
- types of events – events and algebra of events,
- axiomatic definition of probability,
- mutually exclusive and exhaustive events, mutually exclusive events,
- addition theorem – for any two events A and B, Result on complementary events.
- Conditional probability – definition, multiplication theorem, independent events, Baye’s theorem, odds in favour and against