Intermediate 1 st Year Mathematics

SYLLABUS

MATHEMATICS – IA

Unit 1: Functions

Types of Functions – Inverse Functions and Theorems – Domain and Range – Inverse of Real Valued Functions.

Unit 2: Mathematical Induction

Principle of Mathematical Induction – Applications of Mathematical Induction – Problems on Divisibility.

Unit 3: Matrices

Types of Matrices – Scalar Multiplication – Matrix Multiplication – Transpose of a Matrix – Determinants – Adjoint and Inverse of a Matrix – Rank of a Matrix – Consistency and Inconsistency of Equations – Solution of Simultaneous Linear Equations.

Unit 4: Addition of Vectors

Vectors as Ordered Triples – Classification of Vectors – Addition of Vectors – Scalar Multiplication – Angle Between Vectors – Linear Combination of Vectors – Components of a Vector in Three Dimensions – Vector Equations of Line and Plane.

Unit 5: Product of Vectors

Scalar Product – Geometrical Interpretation – Orthogonal Projections – Properties of Dot Product – Dot Product in i, j, k Form – Angle Between Vectors – Vector Product – Vector Areas – Scalar Triple Product – Vector Triple Product – Vector Equations of Planes.

Unit 6: Trigonometric Ratios up to Transformations

Graphs and Periodicity of Trigonometric Functions – Compound Angles – Multiple and Sub-Multiple Angles – Transformations – Sum and Product Formulae.

Unit 7: Trigonometric Equations

General Solutions of Trigonometric Equations – Simple Trigonometric Equations and Their Solutions.

Unit 8: Inverse Trigonometric Functions

Reduction of Trigonometric Functions into Bijections – Graphs of Inverse Trigonometric Functions – Properties of Inverse Trigonometric Functions. 

Unit 9: Hyperbolic Functions

Definition and Graphs of Hyperbolic Functions – Inverse Hyperbolic Functions – Addition Formulae.

Unit 10: Properties of Triangles

Relation Between Sides and Angles – Sine Rule – Cosine Rule – Tangent Rule – Projection Rule – Half-Angle Formulae – Area of Triangle – In-circle and Ex-circle of a Triangle.

MATHEMATICS – IB

Unit 1: Locus

Definition of Locus – Equations of Locus – Applications and Problems on Locus.

Unit 2: Transformation

Transformation of Axes – Translation of Axes – Rotation of Axes – Derivations and Applications.

Unit 3: The Straight Line

Fundamental Results – Normal Form – Symmetric Form – Reduction into Various Forms – Intersection of Two Lines – Family of Straight Lines – Concurrent Lines – Conditions for Concurrency – Angle Between Lines – Length of Perpendicular – Distance Between Parallel Lines – Triangle Properties Based on Concurrent Lines.

Unit 4: Pair of Straight Lines

Equations of Pair of Lines Through Origin – Angle Between Pair of Lines – Conditions for Perpendicular and Coincident Lines – Bisectors of Angles – Pair of Lines from Second Degree Equations – Parallel Lines – Distance Between Parallel Lines – Point of Intersection – Homogenization of Equations.

Unit 5: Three Dimensional Coordinates

Coordinates in Space – Section Formula – Centroid of Triangle and Tetrahedron.

Unit 6: Direction Cosines and Direction Ratios

Direction Cosines – Direction Ratios – Relationship Between Direction Cosines and Direction Ratios.

Unit 7: Plane

Cartesian Equation of a Plane – Problems and Applications.

Unit 8: Limits and Continuity

Intervals and Neighbourhoods – Limits – Standard Limits – Continuity of Functions.

 Unit 9: Differentiation

Derivative of a Function – Elementary Properties of Derivatives – Derivatives of Trigonometric, Inverse Trigonometric and Hyperbolic Functions – Methods of Differentiation – Second Order Derivatives.

Unit 10: Applications of Derivatives

Errors and Approximations – Tangents and Normals – Geometrical Interpretation of Derivatives – Lengths of Tangent and Normal – Angle Between Curves – Orthogonality of Curves – Derivative as Rate of Change – Rolle’s Theorem – Lagrange’s Mean Value Theorem – Increasing and Decreasing Functions – Maxima and Minima.