#### Topics

##### Sets and Relations

- Introduction of Set
- Representation of a Set
- Intervals
- Types of Sets
- Operations on Sets
- Relations of Sets
- Types of Relations

##### Functions

- Concept of Functions
- Types of Functions
- Representation of Function
- Graph of a Function
- Fundamental Functions
- Algebra of Functions
- Composite Function
- Inverse Functions
- Some Special Functions

##### Complex Numbers 33

- Introduction of Complex Number
- Imaginary Number
- Concept of Complex Numbers
- Conjugate of a Complex Number
- Algebraic Operations of Complex Numbers
- Square Root of a Complex Number
- Solution of a Quadratic Equation in Complex Number System
- Cube Root of Unity

##### Sequences and Series

- Concept of Sequences
- Geometric Progression (G.P.)
- General Term Or the nth Term of a G.P.
- Sum of the First n Terms of a G.P.
- Sum of Infinite Terms of a G. P.
- Recurring Decimals
- Harmonic Progression (H. P.)
- Types of Means
- Special Series (Sigma Notation)

##### Locus and Straight Line

- Locus
- Equation of Locus
- Line
- Equations of Lines in Different Forms
- General Form Of Equation Of Line

##### Determinants

- Determinants
- Properties of Determinants
- Application of Determinants
- Cramer’s Rule
- Consistency of Three Linear Equations in Two Variables
- Area of a Triangle Using Determinants
- Collinearity of Three Points

##### Limits

- Definition of Limit of a Function
- Algebra of Limits
- Evaluation of Limits
- Direct Method
- Factorization Method
- Rationalization Method
- Limits of Exponential and Logarithmic Functions

##### Continuity

- Continuous and Discontinuous Functions
- Continuity of a Function at a Point
- Definition of Continuity
- Continuity from the Right and from the Left
- Properties of Continuous Functions
- Continuity in the Domain of the Function
- Examples of Continuous Functions Whereever They Are Defined

##### Differentiation

- The Meaning of Rate of Change
- Definition of Derivative and Differentiability
- Derivative by the Method of First Principle
- Rules of Differentiation (Without Proof)
- Applications of Derivatives

##### Partition Values

- Concept of Median
- Partition Values
- Quartiles
- Deciles
- Percentiles
- Relations Among Quartiles, Deciles and Percentiles
- Graphical Location of Partition Values

##### Measures of Dispersion

- Measures of Dispersion
- Range of Data
- Quartile Deviation (Semi - Inter Quartile Range)
- Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation

##### Skewness

- Skewness
- Asymmetric Distribution (Positive Skewness)
- Asymmetric (Negative Skewness)
- Measures of Skewness
- Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
- Features of Pearsonian Coefficient
- Bowley’s Coefficient of Skewness

##### Bivariate Frequency Distribution and Chi Square Statistic

- Bivariate Frequency Distribution
- Classification and Tabulation of Bivariate Data
- Marginal Frequency Distributions
- Conditional Frequency Distributions
- Categorical Variables
- Contingency Table
- Chi-Square Statistic ( χ2 )

##### Correlation

- Correlation
- Concept of Covariance
- Properties of Covariance
- Concept of Correlation Coefficient
- Scatter Diagram
- Interpretation of Value of Correlation Coefficient

##### Permutations and Combinations

- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Combination
- Properties of Combinations

##### Probability

- Introduction of Probability
- Types of Events
- Algebra of Events
- Elementary Properties of Probability
- Addition Theorem of Probability
- Conditional Probability
- Multiplication Theorem on Probability
- Independent Events

##### Linear Inequations

- Linear Inequality
- Solution of Linear Inequality
- Graphical Representation of Solution of Linear Inequality in One Variable
- Graphical Solution of Linear Inequality of Two Variable
- Solution of System of Linear Inequalities in Two Variables

##### Commercial Mathematics

- Percentage
- Profit and Loss
- Simple and Compound Interest (Entrance Exam)
- Depreciation
- Partnership
- Goods and Service Tax (GST)
- Shares and Dividends

- Imaginary number
- Complex Number

## Notes

Complex Number is a combination of a real and an imaginary number in the form a + bi. a and b are real numbers, and. i is the "unit imaginary number" `sqrt(−1).`

For the complex number z = a + ib, a is called the real part, denoted by Re z and b is called the imaginary part denoted by Im z of the complex number z. For example, if z = 2 + i5, then Re z = 2 and Im z = 5.

Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.

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