1. Algebra and Functions | Factor theorem application, polynomial factorization, solving equations with function transformations, and expression simplification using algebraic identities. 2. Coordinate Geometry and Circles | Determining circle center and radius from general form, finding shortest distance from a point or line to a circle, and sketching curves with roots and tangents. 3. Calculus – Differentiation and Integration | Differentiation for tangents and normals, area under curves using definite integrals, logarithmic differentiation, and exponential decay modeling. 4. Vectors and Geometry | Finding vector magnitudes and directions, ratio division in line segments, and position vectors for internal points. 5. Logarithms, Exponentials, and Binomial Expansion | Solving exponential equations using logs, interpreting growth models in log-linear form, and expanding expressions with the binomial theorem. 6. Proof, Trigonometry, and Optimization | Proving identities, solving trigonometric equations, calculus-based optimization problems with constraints, and algebraic and divisibility proofs.