1. Trigonometric Identities & Equations | Simplifying Expressions – Proving trigonometric identities and solving equations using fundamental identities. 2. Differentiation & Application | Derivatives of Trigonometric Functions – Finding derivatives, using differentiation rules, and evaluating second derivatives at specific values. 3. Logarithms & Exponential Equations | Solving for Unknowns – Manipulating logarithmic equations to determine variable values. 4. Vectors & Geometric Proofs | Position Vectors & Ratios – Expressing vectors in terms of parameters and proving relationships using vector algebra. 5. Coordinate Geometry & Curve Properties | Normal Equations & Areas – Finding the normal to a curve, intersection points, and enclosed areas. 6. Kinematics & Motion Analysis | Displacement, Velocity, and Acceleration – Analyzing motion equations to determine direction changes, velocity at specific times, and total distance traveled. 7. Quadratic Functions & Graph Analysis | Determining Minimum and Intersections – Finding values of constants ensuring intersections and non-negative function values. 8. Probability & Combinatorics | Selection & Arrangement Problems – Calculating ways to form groups and sequences under given constraints. 9. Sequences & Series | Arithmetic Progressions & Sum Properties – Finding terms and conditions where sequences satisfy given equations. 10. Functions & Transformations | Composition & Inverse Functions – Determining function compositions, inverses, and their graphical relationships.