## Units and Topics

# | Unit/Topic | Marks |
---|---|---|

1 | Matrices and Determinants | - |

2 | Algebra | - |

3 | Analytical Geometry | - |

4 | Trigonometry | - |

5 | Differential Calculus | - |

6 | Applications of Differentiation | - |

7 | Financial Mathematics | - |

8 | Descriptive Statistics and Probability | - |

9 | Correlation and Regression Analysi | - |

10 | Operations Research | - |

Total | - |

## Syllabus

- Determinants
1.1.1 Recall

- Matrix
- Order of a matrix
- General form of a Matrix
- Types of matrices

- Row matrix
- Column matrix
- Zero matrix (or) Null matrix
- Square matrix
- Triangular matrix
- Diagonal matrix
- Scalar matrix
- Unit matrix (or) Identity matrix
- Multiplication of a matrix by a scalar
- Negative of a matrix
- Equality of matrices
- Addition and subtraction of matrices
- Multiplication of matrices
- Transpose of a matrix

1.1.2 Minors

1.1.3 Cofactors

1.1.4 Properties of determinants

- Inverse of a Matrix
1.2.1 Singular matrix

1.2.2 Non – singular matrix

1.2.3 Adjoint of a matrix

1.2.4 Inverse of a matrix

1.2.5 Solution of a system of linear equations

- Inputâ€“Output Analysis
1.3.1 The Hawkins – Simon conditions

- Partial Fractions
- Rational Expression
- Partial Fractions

2.1.1 Denominator contains non-repeated Linear factors

2.1.2 Denominator contains Linear factors, repeated n times

2.1.3 Denominator contains quadratic factor, which cannot be factorized into linear factors

- Permutations
2.2.1 Factorial

2.2.2 Fundamental principle of counting

- Multiplication principle of counting

2.2.3 Addition principle of counting

2.2.4 Permutation

- Permutation of repeated things
- Permutations when all the objects are not distinct

2.2.5 Circular permutation

- Combinations
- Mathematical Induction
- Binomial Theorem

- Locus
- Equation of a locus

- System of Straight Lines
3.2.1 Recall

- Various forms of Straight Lines

3.2.2 Angle between two straight lines

3.2.3 Distance of a point from a line

3.2.4 Concurrence of three lines

- Conditions for three given straight lines to be concurrent

- Pair of Straight Lines
3.3.1 Combined equation of the pair of straight lines

3.3.2 Pair of straight lines passing through the origin

3.3.3 Angle between pair of straight lines passing through the origin

3.3.4 The condition for general second degree equation to represent the pair of straight lines

- Circles
3.4.1 The equation of a circle when the centre and radius are given

3.4.2 Equation of a circle when the end points of a diameter are given

3.4.3 General equation of a circle

3.4.4 Parametric form of a circle

3.4.5 Tangents

- Length of the tangent to the circle

- Conics
3.5.1 Parabola

3.5.2 Definitions regarding a parabola: y

^{2}= 4ax3.5.3 Other standard parabolas

3.5.4 General form of the standard equation of a parabola, which is open rightward

- Trigonometric Ratios
4.1.1 Quadrants

4.1.2 Signs of the trigonometric ratios of an angle θ as it varies from 0º to 360º

4.1.3 Trigonometric ratios of allied angles

- Trigonometric Ratios of Compound Angles
4.2.1 Compound angles

4.2.2 Sum and difference formulae of sine, cosine and tangent

4.2.3 Trigonometric ratios of multiple angles

- Transformation Formulae
4.3.1 Transformation of the products into sum or difference

4.3.2 Transformation of sum or difference into product

- Inverse Trigonometric Functions
4.4.1 Inverse Trigonometric Functions

4.4.2 Properties of Inverse Trigonometric Functions

- Functions and Their Graphs
- Quantity
- Constant
- Variable
- Intervals

- Open interval
- Closed interval

- Neighbourhood of a point
- Function
- Classification of functions
- Even and odd functions
- Explicit and implicit functions
- Constant function
- Identity function
- Modulus function
- Signum function
- Step function
- Rational function
- Polynomial function
- Linear function
- Quadratic function
- Exponential function
- Logarithmic function
- Sum, difference, product and quotient of two functions
- Graph of a function

- Limits and Derivatives
- Existence of limit
- Algorithm of left hand limit
- Algorithm of right hand limit
- Some results of limits
- Indeterminate forms and evaluation of limits
- Methods of evaluation of algebraic limits
- Some standard limits
- Continuous function
- Some properties of continuous functions
- Differentiability at a point
- Left hand derivative and right hand derivative
- Differentiation from first principle
- Derivatives of some standard functions using first principle

- Differentiation Techniques
- Some standard results
- General rules for differentiation
- Derivative of implicit functions
- Logarithmic differentiation
- Differentiation of parametric functions
- Differentiation of a function with respect to another function
- Successive differentiation

- Applications of Differentiation in Business and Economics
- Demand, supply, cost, revenue and profit functions

- Demand function
- Supply function
- Cost function
- Revenue function

- Elasticity

- Price elasticity of demand
- Price elasticity of supply

- Maxima and Minima
- Increasing and decreasing functions
- Stationary Value of a function
- Local and Global (Absolute) Maxima and Minima

- Applications of Maxima and Minima
- Problems on profit maximization and minimization of cost function
- Inventory control
- Economic Order Quantity (EOQ)

- Partial Derivatives
- Successive partial derivatives
- Euler’s theorem and its applications

- Applications of Partial Derivatives
- Production function and marginal productivities of two variables
- Partial elasticity of demand

- Annuities
- Types of annuities

- Based on the number of periods
- Based on the mode of payment

- Stocks, Shares, Debentures and Brokerage
- Types of shares
- Definitions

- Measures of Central Tendency
- Average
- Related Positional Measures - Quartiles, Deciles and Percentiles
- Computations for Related positional measure
- Geometric mean
- Harmonic mean
- Relationship among the averages

- Measures of Dispersion
- Quartile Deviation
- Mean deviation

- Probability
- Basic concepts of Probability
- Independent and Dependent events
- Conditional Probability
- Baye’s Theorem

- Correlation
- Meaning of Correlation
- Types of correlation

- Positive Correlation
- Negative Correlation
- Simple correlation

- Scatter Diagram
- Karl Pearson’s Correlation Coefficient

- Rank Correlation
- Spearman’s Rank Correlation Coefficient

- Regression Analysis
- Dependent and independent variables
- Regression Equations

- Linear Programming Problem (L.P.P.)
- Mathematical formulation of a linear programming problem
- Solution of LPP by graphical method

- Network Analysis
- Construction of network
- Critical path analysis