#### Topics

##### Angle and Its Measurement

- Directed Angle
- Angles of Different Measurements
- Angles in Standard Position
- Measures of Angles
- Area of a Sector of a Circle
- Length of an Arc of a Circle

##### Trigonometry - 1

- Introduction of Trigonometry
- Trigonometric Functions with the Help of a Circle
- Signs of Trigonometric Functions in Different Quadrants
- Range of Cosθ and Sinθ
- Trigonometric Functions of Specific Angles
- Trigonometric Functions of Negative Angles
- Fundamental Identities
- Periodicity of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Graphs of Trigonometric Functions
- Polar Co-ordinate System

##### Trigonometry - 2

- Trigonometric Functions of Sum and Difference of Angles
- Trigonometric Functions of Allied Angels
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Double Angles
- Trigonometric Functions of Triple Angle
- Factorization Formulae
- Formulae for Conversion of Sum Or Difference into Product
- Formulae for Conversion of Product in to Sum Or Difference
- Trigonometric Functions of Angles of a Triangle

##### Determinants and Matrices

- Definition and Expansion of Determinants
- Minors and Cofactors of Elements of Determinants
- Properties of Determinants
- Application of Determinants
- Cramer’s Rule
- Consistency of Three Equations in Two Variables
- Area of Triangle and Collinearity of Three Points
- Introduction of Matrices
- Types of Matrices
- Algebra of Matrices
- Properties of Matrix Multiplication
- Properties of Transpose of a Matrix

##### Straight Line

- Locus of a Points in a Co-ordinate Plane
- Straight Lines
- Equations of Line in Different Forms
- General Form of Equation of a Line
- Family of Lines

##### Circle

- Different Forms of Equation of a Circle
- General Equation of a Circle
- Parametric Form of a Circle
- Tangent
- Condition of tangency
- Tangents from a Point to the Circle
- Director circle

##### Conic Sections

- Double Cone
- Conic Sections
- Parabola
- Ellipse
- Hyperbola

##### Measures of Dispersion

- Meaning and Definition of Dispersion
- Measures of Dispersion
- Range of Data
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation

##### Probability

- Basic Terminologies
- Event and Its Types
- Concept of Probability
- Addition Theorem for Two Events
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events
- Bayes’ Theorem
- Odds (Ratio of Two Complementary Probabilities)

##### Complex Numbers

- Introduction of Complex Number
- Concept of Complex Numbers
- Algebraic Operations of Complex Numbers
- Square Root of a Complex Number
- Fundamental Theorem of Algebra
- Argand Diagram Or Complex Plane
- De Moivres Theorem
- Cube Root of Unity
- Set of Points in Complex Plane

##### Sequences and Series

- Concept of Sequences
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Harmonic Progression (H. P.)
- Arithmetico Geometric Series
- Power Series

##### Permutations and Combination

- Fundamental Principles of Counting
- Invariance Principle
- Factorial Notation
- Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When Some Objects Are Identical
- Circular Permutations
- Properties of Permutations
- Combination
- Properties of Combinations

##### Methods of Induction and Binomial Theorem

- Principle of Mathematical Induction
- Binomial Theorem for Positive Integral Index
- General Term in Expansion of (a + b)n
- Middle term(s) in the expansion of (a + b)n
- Binomial Theorem for Negative Index Or Fraction
- Binomial Coefficients

##### Sets and Relations

- Sets and Their Representations
- Types of Sets
- Operations on Sets
- Intervals
- Concept of Relation

##### Functions

- Concept of Functions
- Algebra of Functions

##### Limits

- Concept of Limits
- Factorization Method
- Rationalization Method
- Limits of Trigonometric Functions
- Substitution Method
- Limits of Exponential and Logarithmic Functions
- Limit at Infinity

##### Continuity

- Continuous and Discontinuous Functions

##### Differentiation

- Definition of Derivative and Differentiability
- Rules of Differentiation (Without Proof)
- Derivative of Algebraic Functions
- Derivatives of Trigonometric Functions
- Derivative of Logarithmic Functions
- Derivatives of Exponential Functions
- L' Hospital'S Theorem

- Roster or Tabular method or List method
- Set-Builder or Rule Method

## Notes

Set is a collection of well defined objects. By well defined objects, we mean the definition should not vary it should be definite.

Example 1- Collection of vowels of English alphabet. The collection will be a, e, i, o, u. This is a well defined collection.

Example 2- Collection of good maths books available in market. Here, the collection will vary form person to person because of different personal choices and preferences.

There are two methods of representing a set :

(i) Roster or tabular form

(ii) Set-builder form.

Example- Collection of vowels of English alphabet.

A= {a, e, i, o, u} this is the roster form of a set.

Here, A is represented as a set, and the elements of set are enclosed in { }.

Set builder form, A= {x: x is a vowel in English alphabet}

x represents the elements in the enclosed brackets { }.**Note:**

1) Order is immaterial. That the sequence in which the elements appear is not important, even if the sequence is changed the meaning remains same.

Take the same example- Collection of vowels of English alphabet.

A= {e, i, o, u, a}

2) Same elements are not repeated.

Example- B= set of all letters of the word SCHOOL

Roster form: B= {S, C, H, O, L}

Set-builder form: B= {x:x is letter used in word SCHOOL}

3) C= Set of all natural numbers.

Set-builder form C = {x :x ∈ N}

Roster form C= {1, 2, 3, 4, ...}

As natural numbers are infinite so we will represent them with three dots.

∈ means belongs to and ∉ means does not belongs to.

Example- A= {1, 2, 3, 4, 5, 6}

Here, 2 ∈ A, 9 ∉ A, 8 ∉ A, 5 ∈ A

We give below a few more examples of sets used particularly in mathematics, viz.

`"N"` : the set of all natural numbers

`"Z"` : the set of all integers

`"Q"` : the set of all rational numbers

`"R"` : the set of real numbers

`"Z"^+` : the set of positive integers

`"Q"^+` : the set of positive rational numbers, and

`"R"^+` : the set of positive real numbers.