📘 1-Year Foundation Program 

Syllabus Overview

Unit 1: Sets, Relations & Functions

• Sets and Venn diagrams
  
  

• Types of sets, power set
  
  

• Relations and their types
  
  

• Functions – domain, range, types of functions
  
  

Unit 2: Trigonometry

• Trigonometric functions
  
  

• Trigonometric identities
  
  

• Trigonometric equations
  
  

• Inverse trigonometric functions
  
  

Unit 3: Algebra

• Complex numbers
  
  

• Quadratic equations
  
  

• Sequences and series (AP, GP)
  
  

• Binomial theorem
  
  

• Mathematical induction
  
  

Unit 4: Coordinate Geometry

• Straight line
  
  

• Conic sections (parabola, ellipse, hyperbola)
  
  

• Three-dimensional geometry basics
  
  

Unit 5: Calculus (Introduction)

• Limits
  
  

• Continuity
  
  

• Differentiation and basic applications
  
  

Unit 6: Statistics & Probability

• Measures of dispersion
  
  

• Standard deviation
  
  

• Probability basics
  
  

Unit 7: Number Theory (Additional Foundation Module)

• Divisibility rules
  
  

• Prime numbers, composite numbers
  
  

• HCF & LCM (advanced methods)
  
  

• Modular arithmetic
  
  

• Congruences
  
  

• Fermat’s Little Theorem (basic level)
  
  

• Euler’s Totient Function (intro)
  
  

• Number theory problems for competitive exams
  
  

Year 2

Unit 1: Relations & Functions

• Types of relations
  
  

• Types of functions
  
  

• Inverse trigonometric functions (advanced)
  
  

Unit 2: Algebra

• Matrices
  
  

• Determinants
  
  

• Applications of determinants
  
  

Unit 3: Calculus

• Continuity & differentiability
  
  

• Applications of derivatives
  
  

• Integrals (definite & indefinite)
  
  

• Applications of integrals (areas)
  
  

• Differential equations
  
  

Unit 4: Vectors & 3D Geometry

• Vector algebra
  
  

• Scalar & vector products
  
  

• 3D geometry – direction cosines, lines, planes
  
  

Unit 5: Linear Programming

• Linear inequalities
  
  

• Graphical method of solving LPP
  
  

Unit 6: Probability

• Conditional probability
  
  

• Bayes’ theorem
  
  

• Random variables (intro)