This course is suitable for:

• CBSE Class 11 & 12 Mathematics students

• JEE Main Mathematics aspirants

• A & AS Level / Year 11 Mathematics learners

• BA (Hons.) Mathematics students

• Applied Mathematics (Class 12) students

• Students preparing for advanced mathematics tracks

• Learners who want conceptual depth beyond exam memorisation

The syllabus is taught in a progressive and logically connected manner, ensuring continuity across algebra, calculus, coordinate geometry, trigonometry, vectors, and advanced topics.

🔹 What Students Will Learn

1. Foundations & Algebra

• Basics of Mathematics

• Quadratic Equations

• Complex Numbers

• Sequences and Series

• Permutations and Combinations

• Binomial Theorem

• Sets and Relations

• Functions

• Matrices and Determinants

• Statistics and Probability

Focus is placed on proof-based understanding, logical derivations, and advanced problem-solving techniques.

2. Calculus (Core of Pure Mathematics)

• Limits

• Continuity and Differentiability

• Applications of Derivatives

• Indefinite Integration

• Definite Integration

• Area under Curves

• Differential Equations

Students gain strong conceptual clarity, graphical intuition, and analytical methods essential for higher mathematics.

3. Coordinate Geometry

• Straight Lines

• Circle

• Parabola

• Ellipse

• Hyperbola

Emphasis is given to equation-based reasoning, transformations, and geometric interpretation.

4. Trigonometry

• Trigonometric Ratios and Identities

• Trigonometric Equations

• Inverse Trigonometric Functions

The course focuses on identity manipulation, function behavior, and analytical problem-solving.

5. Vector Algebra & Three-Dimensional Geometry

• Vector Algebra fundamentals

• Dot and cross products

• Direction cosines and ratios

• Lines and planes in 3D space

6. Advanced & Higher-Level Mathematics (Selective Coverage)

• Applied Mathematics (CBSE Class 12)

• A & AS Level Mathematics topics

• BA (Hons.) Mathematics foundations

• DAE Mathematics (1st & 2nd Year)

• IAS Mathematics foundations (introductory)

• Introduction to abstract concepts such as Galois Theory (conceptual orientation)

🔹 Teaching Method (Online Mode)

Roshani Gupta follows a concept-first, logic-driven teaching methodology:

• Live online interactive classes

• Step-by-step derivations and proofs

• Focus on theory + application balance

• Problem-solving from basic to advanced level

• Regular assignments and practice sets

• Doubt-clearing and concept reinforcement sessions

• Exam-oriented guidance where applicable

The pace is adjusted based on student level and academic goals.

🔹 Why Learn from Roshani Gupta

Roshani Gupta specializes in pure and advanced mathematics teaching, with a focus on:

• Deep conceptual clarity

• Mathematical reasoning and proofs

• Connecting school-level math to higher studies

• Structured explanation of complex ideas

• Encouraging analytical and independent thinking

Her approach benefits students aiming for long-term mastery, not just short-term exam success.

🔹 Benefits / Learning Outcomes

By the end of this course, students will:

• Develop strong fundamentals in pure mathematics

• Understand advanced algebra and calculus concepts clearly

• Improve logical reasoning and analytical thinking

• Handle complex, multi-step mathematical problems confidently

• Perform better in CBSE, JEE, and A/AS Level exams

• Build a solid foundation for university-level mathematics

• Gain confidence for advanced academic and competitive paths