**Contents
GROUP – A: ALGEBRA
Chapter-1 1 – **
Complex Numbers **

Definition

Geometric representation

Modulus, amplitude

Polar form of a complex number

Rationalisation, addition, multiplication, conjugate

Square root of a complex number

Cube root of unity

De Moivre’s Theorem (statement only)

Simple problems

**Chapter-2 **-**
Partial Fractions **

Definition

Proper and improper fractions

To resolve proper fraction into partial fraction with non- repeated linear factors

Repeated linear factors and irreducible non-repeated quadratic factors

Simple problems

**Chapter-3 **-**
Permutation and Combination **

Factorial notation and basic principle of counting

Deduction of formulae for permutation and combination

**Chapter-4 **-**
Binomial Theorem **

Binomial Theorem for positive integral index (statement only)

General term, middle term, specific terms

Co-efficient of , Terms independent of

Problems with engineering applications

**Chapter-5 **-**
Logarithm **

Introduction

Definition

Laws of logarithm

Problems related to Laws of Logarithm and application

**Chapter-6 **-**
Series **

Arithmetic Progression Series, arithmetic mean, sum to n-terms

Geometric Progression Series, geometric mean, sum to n-terms

Sum to infinity of a G.P.Series

Exponential Series

Logarithmic Series

**Chapter-7 **-**
Matrix **

Definition

Types of matrix – row matrix, column matrix, square matrix, diagonal matrix, unit matrix, symmetric matrix, skew-symmetric matrix

Algebra of matrices: equality, addition, subtraction, scalar multiplication, multiplication

Simple application problems

**Chapter-8 **-**
Determinants **

Definition and expansion of determinants of third order, minors , co-factors

Properties of determinants and problems using properties

Solution of simultaneous equations using Crammer’s rule

**GROUP – B: TRIGONOMETRY**

**Chapter-9 **-**
Trigonometric Ratios**

Introduction

Compound Angles and Associated Angles

Transformation of sum or differences into products and products into sum or differences

Multiple and sub-multiple Angles

Solution of Trigonometric Equations (angle between 0 and 2π)

Trigonometric Identities

**Chapter-10 **-**
Inverse Trigonometric Functions **

Introduction

Definition and basic concepts

Properties of Inverse Trigonometric Functions.

**Chapter-11 **-**
Properties of Triangles**

Introduction

Relation between the sides and angles of a triangle

Sine – Cosine formulae

**GROUP – C: MENSURATION**

**Chapter-12 **-**
Area of Curvilinear Figures**

Area of Curvilinear Figures using Simpson’ rule

**Chapter-13 **-****

Volume and Surface Area

Volume and Surface Area

Volume and Surface area of prism

Pyramid, Zone and sector of a sphere, Frustum of pyramid and cone.

**GROUP – D
CO-ORDINATE GEOMETRY OF TWO-DIMENSIONS**

**Chapter-14 **-**
Cartesian and Polar Coordinate System**

Introduction

Cartesian coordinate system

Polar coordinate system

Relation between Cartesian and Polar coordinate system

Distance between two points in Cartesian coordinate system

Distance between Two points in Polar coordinate system

**Chapter-15 **-****

Straight Line

Straight Line

Introduction

Slope or gradient

Different forms of straight lines, Point-slope from, Point-point form, Intercept form, Perpendicular form

Angle between two straight lines

Equation of parallel and perpendicular straight lines

Distance of a point from a straight line, Distance between two straight lines

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