AP Inter 1st Year Syllabus 2023 Maths IA

SYLLABUS
MATHEMATICS – I(A) FIRST YEAR
S. No. TOPIC
1. Functions
1.0 Ordered Pairs
1.1 Types of Function-Definitions
1.2 Inverse Functions and Theorems
1.3 Real valued functions (Demain, Range and Inverse)
2. Mathematical Induction
2.1 Principles of Mathematical Induction and Theorems
2.2 Applications of Mathematical Induction
2.3 Problems on divisibility
3. Matrices
3.1 Types of Matrices
3.2 Scalar multiple of a matrix and multiplication of matrices
3.3 Transpose of a matrix
3.4 Determinants
3.5 Adjoint and Inverse of a Matrix
3.6 Consistency and Inconsistency of system of Simultaneous Equations-
Rank of a Matrix
3.7 Solution of Simultaneous Linear Equations
4. Addition of Vectors
4.1 Vectors as a triad of real numbers, some basic concepts
4.2 Classification (Types) of Vectors
4.3 Sum (Addition) of Vectors
4.4 Scalar Multiplication of a vector
4.5 Angle between two non- zero vectors
4.6 Linear Combination of Vectors
4.7 Components of a vectors in Three Dimensions
4.8 Vector Equations of Line and Plane
5. Product of Vectors

5.1 Scalar or dot product of two vectors-Geometrical interpretation
Orthogonal Projections
5.2 Properties of dot product
5.3 Expression for Scalar(dot) product, Angle between two vectors
5.4 Geometrical Vector methods
5.5 Vector equation of a plane –normal form
5.6 Angle between two planes
5.7 Vector product (cross product) of two vectors and properties
5.8 Vector product in (i,j,k) system
5.9 Vector Areas
5.10 Scalar triple product
5.11 Vector equation of a plane-different forms, skew lines, shortest distance-
plane, condition for coplanarity etc.
5.12 Vector triple product-results
5.13 Solved Problems
6. Trigonometric Ratios upto Transformations
6.1 Trigonometric ratios –variation –Graphs and periodicity
6.2 Trigonometric ratios of compound angles
6.3 Trigonometric ratios of multiple and sub- multiple angles
6.4 Sum and product transformation
7. Trigonometric Equations
7.1 General solutions of trigonometric equations
7.2 Simple trigonometric equations-solutions
8. Inverse Trigonometric Functions
8.1 To reduce a trigonometric function into a bijective function
8.2 Graphs of Inverse trigonometric functions
8.3 Properties of inverse trigonometric functions
9. Hyperbolic Functions
9.1 Definitions of Hyperbolic Functions, graphs
9.2 Definitions of inverse Hyperbolic Functions and graphs
9.3 Additions formula of Hyperbolic Functions

10. Properties of Triangles
10.1 Relation between the sides and angles of a triangle
10.2 Sine, cosine and Tangent Rules- Projection Rules
10.3 Half angle formulae and area of a triangle
10.4 Incircle and excircles of a triangle
Appendix
(No Question is to be set in IPE,Mathematics-IA from the topics mentioned below)
1. Sets
1.1 Set
1.2 Examples
1.3 Representation of a Set
1.4 Classification (Types) of sets

SYLLABUS
MATHEMATICS – I(A) FIRST YEAR
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