1. Algebra & Graph Sketching | Finding stationary points, sketching polynomial and trigonometric functions, determining conditions for distinct real roots. 2. Quadratic Equations & Inequalities | Solving equations for non-real roots, analyzing quadratic discriminants. 3. Logarithms & Exponential Functions | Simplifying logarithmic expressions, solving logarithmic equations. 4. Polynomials & Factorization | Finding unknown coefficients in polynomials, applying factor and remainder theorems. 5. Graphs & Curve Fitting | Plotting logarithmic graphs, estimating constants, interpolating values. 6. Differentiation & Integration | Derivatives of logarithmic functions, definite integral evaluations. 7. Coordinate Geometry & Intersection Points | Finding intersection of curves and lines, perpendicular bisectors, geometric properties. 8. Vectors & Geometry | Vector calculations, finding intersection points, solving for parameters in geometric conditions. 9. Trigonometry & Equations | Solving trigonometric equations in degrees and radians, applying identities. 10. Sequences & Series | Summation of arithmetic and geometric progressions, conditions for infinite sums. 11. Probability & Combinatorics | Arranging elements with conditions, choosing groups with restrictions.