AP Intermediate Mathematics Syllabus 2025-26- AP Inter 2nd Year Mathematics Syllabus Download PDF

1

Chapter-1:

Complex Numbers Introduction

• 1.1 Complex number as an ordered pair of real numbers. Fundamental operations
• 1.2 Representation ofa  complex number in the form a+ib
• 1.3 Modules and Amplitude of a Complex Number- Illustrations
• 1.4 Geometrical and Polar representation of complex numbers in Argand plane-Argand diagram

2

Chapter-2:

De Moivre’s Theorem Introduction

• 2.1 De Moivre’s Theorem- Integral and Rational Indices
• 2.2 nth roots of unity- Geographical Interpretations- Illustrations

3

Chapter-3:

Quadratic Expressions Introduction

• 3.1 Quadratic Expressions, Equations in one Variable
• 3.2 Sign of quadratic expressions- Change in signs and Maximum and Minimum
• 3.3 Quadratic Inequations

4

Chapter-4:

Theory of Equations Introduction

• 4.1 Relation between the roots and the coefficients in an Equation
• 4.2 Solving an equation when two or more of its roots are connected by certain relations
• 4.3 Equations with real coefficients – occurrence of complex roots in conjugate pairs and its consequences
• 4.4 Transformation of equations – Reciprocal equations

5

Chapter-5:

Permutations and Combinations Introduction

• 5.1 Fundamental Principles of Counting – Linear and Circular permutations
• 5.2 Permutations of n dissimilar things taken r at a time
• 5.3 Permutations when repetitions are allowed
• 5.4 Circular Permutations
• 5.5 Permutations with Constant repetitions
• 5.6 Combinations- Definitions and Certain Theorems

6

Chapter – 6 :

Binomial Theorem Introduction

• 6.1 Binomial Theorem for positive integral index
• 6.2 Binomial Theorem for Rational Index
• 6.3 Approximations using Binomial Theorem

7

Chapter-7:

Partial Fractions Introduction

• 7.0 Rational Fractions
• 7.1 Partial Fractions of f(x)/g(x), when g(x) contains non-repeated linear factors
• 7.2 Partial Fractions of f(x)/g(x), when g(x) contains repeated and I or non-repeated linear factors
• 7.3 Partial Fractions of f(x)/g(x), when g(x) contains irreducible factors

8

Chapter-8:

Measure of Dispersion Introduction

• 8.1 Range
• 8.2 Mean Deviation
• 8.3 Variance and Standard Deviation of ungrouped /grouped data
• 8.4 Coefficient of Variation and analysis of frequency distributions with equal means but different variances

9

Chapter-9:

Probability Introduction

• 9.1 Random Experiments and Events
• 9.2 Classical definition of probability, Axiomatic approach and addition theorem of probability
• 9.3 Independent and Dependent events, Conditional Probability, Multiplication Theorem1 and Baye’s Theorem

10

Chapter -10:

Random Variables and Probability Distributions Introduction

• 10.1 Random Variables
• 10.2 Theoretical discrete distributions Binomial and Poisson distributions

1

Chapter-1:

Circle Introduction

• 1.1 Equation of a circle, standard form, centre and radius
• 1.2 Position of a point in the plane of a circle Definition of a tangent
• 1.3 Position of a straight line in the plane of a circle condition for a line to be tangent
• 1.4 Chord of contact and polar
• 1.5 Relative Positions of two circles

2

Chapter-2:

System of Circles Introduction

• 2.1 Angle between two intersecting circles
• 2.2 Radical axis of two circles

3

Chapter-3:

Parabola Introduction

• 3.1 Conic Sections
• 3.2 Equation of tangent and normal at a point on the Parabola

4

Chapter-4:

Ellipse Introduction

• 4.1 Equation of ellipse in standard form, Parametric equations
• 4.2 Equation of tangent and normal at a point on the ellipse

5

Chapter-5:

Hyperbola Introduction

• 5.1 Equation of hyperbola in standard form Parametric equations
• 5.2 Equation of Tangent and Normal at a point on the hyperbola

6

Chapter-6:

Integration Introduction

6.1 Integration as the inverse process of differentiation, standard forms and properties of integrals

6.2 Method of substitution-Integration of algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions-Integration by parts

• 6.2(A) Integration by the method of substitution-Integration of algebraic and trigonometric functions
• 6.2(B) Integration by parts-Integration of exponential, logarithmic and inverse trigonometric functions

6.3 Integration- Partial fractions method

6.4 Reduction formulae

7

Chapter-7:

Definite Integrals Introduction

• 7.1 Define Integral as the limit of sum
• 7.2 Interpretation of definite integral as an area
• 7.3 The Fundamental Theorem of Integral Calculus
• 7.4 Properties
• 7.5 Reduction Formulae
• 7.6 Applications of definite integral to areas

8

Chapter-8:

Differential Equation Introduction

8.1 Formation of differential equations-Degree and order of an ordinary differential Equation

8.2 Solving Differential Equations

• 8.2 (a) Variables separable method
• 8.2(b) Homogenous Differential Equation
• 8.2(c) Non-Homogeneous Different Equations
• 8.2(d) Linear Differential Equations