AP Intermediate Mathematics Syllabus 2023-24 - AP Inter 2nd Year Mathematics Syllabus Download PDF

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1

Chapter-1: 

Complex Numbers Introduction

• 1.1 Complex number as and ordered pair of real numbers Fundamental operations 
• 1.2 Representation of 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 number 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